ABSTRACT

Title of Dissertation: DESIGN OF COMPLIANT NONLINEAR
ARTICULATED SUSPENSION FOR
EXTRATERRESTRIAL ROVING VEHICLES

Charles Hanner
Doctor of Philosophy, 2025

Dissertation Directed by: Professor David Akin
Department of Aerospace Engineering

Designing extreme-access planetary rovers requires advanced articulation mechanisms to

traverse rugged terrain, conquer steep slopes, and reduce mission risk. These qualities involve

balancing geometric constraints, load distribution, and passive compliance for astronauts on EVA.

This dissertation develops a generalizable framework for creating compliant, articulated suspen-

sion systems with high degrees of articulation. By closely examining the relationships among

kinematics, applied forces, and component-level constraints, the proposed methods address sig-

nificant gaps in rover mobility research in the areas of systems design, dynamic formulation,

and commonly overlooked real-world considerations. In particular, this work demonstrates a

holistic approach that integrates quasi-static sum-of-moments tools with Lagrangian-based dy-

namic modeling and machine learning-driven parameter identification, ensuring robust perfor-

mance throughout a wide range of operating conditions. The resulting methodology offers a

scalable, adaptable framework for future rovers tasked with extreme-access missions.



DESIGN OF COMPLIANT NONLINEAR ARTICULATED SUSPENSION
FOR EXTRATERRESTRIAL ROVING VEHICLES

by

Charles Hanner

Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment

of the requirements for the degree of
Doctor of Philosophy

2025

Advisory Committee:
Professor David L. Akin, Chair/Advisor
Professor Craig Carignan
Professor Raymond Sedwick
Professor Michael Otte
Professor William Goldman



© Copyright by
Charles Hanner

2025



Preface

”He’s got about two wheels on the ground. There’s a big rooster tail out of all four wheels. And

as he turns, he skids. The back end breaks loose just like on snow.... Man, I’ll tell you, Indy’s

never seen a driver like this... Hey, that was a good stop. Those wheels just locked.”

- Charlie Duke, Apollo 16

ii



Dedication

To Chris Coche and Walter Hanner, whose passions for engineering ignited my own.

iii



Acknowledgments

First and foremost, I must thank Dave for his continual ability to ensure I could stay in grad

school, support my degrees, and dream up the multitude of hair-brained schemes I have been able

to leap between in my years at the SSL. Your laboratory and your own way of encouragement

has enabled me to push my passions into my career spanning from some of the best SCUBA

diving there ever may be to spacesuits, habitats, rovers, robots, and just about anything else a

space-obsessed young kid could look to the stars and imagine. Thank you.

Mom and Dad, thank you for the unending support and push behind me that kept me going

and through the finish line. From Devo to Rusty, you always made sure I had everything I needed

to let me do what I needed to do, and do it right. I just kept swimming and somehow we made it.

But you saw the path, especially when I couldn’t and it’s taken a lot from each of us to get here.

I sincerely appreciate it and I cannot thank you enough. Sono Affamato.

Sean, thank you for introducing me to the world of photography, for which many of my

last-minute presentations and conference papers have greatly benefited, even though my hard

drive space may not have. Oh, and for being a great brother and supporter.

Chris, thank you for being the person in my life who continually motivates me to work as

hard as I possibly can towards the things I want in life. Your endless positivity, encouragement,

and understanding self have helped me through each of my struggles in accomplishing this and

I hope you know how much I appreciate all you’ve done for me. I look forward to the coming

iv



years of us finding ways to teach ourselves the things we never knew how to do, and struggling

through it together on Facetime.

Romeo and Rahul, I truly have you two to thank for making a large portion of this research

possible. Without your software and willingness to support the data collection I needed, and stay

up late or show up on weekends to help me get data and run the robots this absolutely would

not have happened. But also thank you for being encouraging every time my model spat out

nonsense, for leaving many a random thing on my desk, and for acting like the silly unserious

friends I sometimes needed to keep the mood light and the project rolling forward. Hours away

and my software can support that are now words I live by.

I must also thank all of the wonderful people (in no particular order) I have had the pleasure

of working with over my years at the SSL. Lem, thank you for being the voice that took a chance

on me and brought my into the lab. No, I won’t stop, thank you very much. Thank you to Kate,

Chris, and Nick for being the guiding voices and teaching me how the lab worked and how to

write update slides very quickly on a Friday. I have had the great fortune of working with so

many fellow graduate students over the years - thank you to all of you.

Some of you fellow grad students I have had the pleasure of seeing at 3:30am just a few too

many times, so I fear I must now speak to you directly. Daniil and Nicolas, BioBot (and nearly

every single other project I’ve worked on at the SSL) would not have been possible without you

and I sincerely thank you.

There are so many other people that BioBot would not be what it is today without. Thank

you to Meredith for being the best suit lead the team could have asked for and a ray of positivity

within the project. Thank you Ryan for offering to help every single time you could have, and

supporting the absolute best you possibly could.

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To the array of undergraduate students who have dedicated their time and considerable

efforts to the bettering of BioBot including but certainly not limited to Chandler, Spencer, Rowan,

Ian, Robbie, and Wyatt and every other person who touched our project. Each one of you made

BioBot better, and have made a lasting impact.

Lastly, thank you to all my friends, fellow graduate students in other labs, and everybody

else who I had the opportunity to work, learn, and travel with. To everyone who supported me

and encouraged me all these years, I am incredibly thankful.

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Table of Contents

Preface ii

Dedication iii

Acknowledgements iv

Table of Contents vii

List of Tables ix

List of Figures x

List of Abbreviations xv

Chapter 1: Introduction 1
1.1 Suspension Architectures Review . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Heritage Suspension Architectures . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Prototype, Earth-Analogue, and Unflown Active Wheel-Articulation Fo-

cused Rover Suspension Systems . . . . . . . . . . . . . . . . . . . . . . 7
1.1.3 Suspension Architectures Summary . . . . . . . . . . . . . . . . . . . . 13

1.2 Design Tools and Methodologies For Articulated Suspension Systems . . . . . . 14
1.2.1 Kinematic Simulation and Optimization . . . . . . . . . . . . . . . . . . 15
1.2.2 Spring Damper Inclusive Rover Suspension Analysis . . . . . . . . . . . 16
1.2.3 Quasi-Static Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.3 Earth-Analogue Vehicle Design Approaches for Mobility Systems Testing . . . . 18
1.3.1 Similarity Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.3.2 Equivalent Size, Equivalent Weight . . . . . . . . . . . . . . . . . . . . 20
1.3.3 Matched Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.4 Suspension Approaches Summary . . . . . . . . . . . . . . . . . . . . . . . . . 21

Chapter 2: System Design and Validation of Independently Articulated Suspension Us-
ing a Sum-of-Moments Framework for the BioBot System 24

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.1 Articulating Extraterrestrial Roving Vehicle Concepts . . . . . . . . . . . 27
2.1.2 Applications Beyond Spaceflight . . . . . . . . . . . . . . . . . . . . . . 28
2.1.3 Motivation and Contribution . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.1 VERTEX Suspension Development Issues . . . . . . . . . . . . . . . . . 31
2.2.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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2.3.1 Series Elastic Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.2 Parallel Spring (PS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.3 Wheel Force Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3.4 Total System Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.3.5 System Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.3.6 As-Built System Upgrades . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.4 Force Sensing and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.4.1 Load Cell Integration and Calibration . . . . . . . . . . . . . . . . . . . 62
2.4.2 Data Collection and Analysis . . . . . . . . . . . . . . . . . . . . . . . . 63
2.4.3 Operational Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.4.4 Validation of Kinematics and Regime Transitions . . . . . . . . . . . . . 70

2.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.5.1 System Failure Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . 71

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Chapter 3: Lagrangian Formulation 76
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.2.1 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.2.2 Non-Conservative Forces . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.2.3 Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.2.4 Compliance Mechanism Considerations . . . . . . . . . . . . . . . . . . 100
3.2.5 Lagrangian Approach Summary . . . . . . . . . . . . . . . . . . . . . . 104

3.3 Applied Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.3.1 Potential Energy - Gravity Offset Springs . . . . . . . . . . . . . . . . . 106
3.3.2 Sprung, Unsprung, and Swingarm - K.E. & P.E. . . . . . . . . . . . . . . 107
3.3.3 Potential Energy - Series Elastic Element . . . . . . . . . . . . . . . . . 112
3.3.4 Non-Conservative Forces - Reaction Moments . . . . . . . . . . . . . . . 115
3.3.5 Non-Conservative Forces - Damping . . . . . . . . . . . . . . . . . . . . 116
3.3.6 Bushing Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Chapter 4: Validation and System Improvement 122
4.1 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.1.1 Quasi-Static Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.1.2 ML-Based Parameter Identification . . . . . . . . . . . . . . . . . . . . 127
4.1.3 Dynamic Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.1.4 ML-Based Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Chapter 5: Conclusions and Future Work 152
5.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.2 Lessons Learned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
A.1 Suspension Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Bibliography 161

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List of Tables

2.1 Condensed table of slope statistics from the Lunar Surface Data Book’s Example
EVA Traverses. A = 7.3.1 Large Logistics Transfer, B = 7.3.2 Long Uncrewed
Science Traverse, C = 7.3.3 Traverse into crater/PSR Table 0-3, D = 7.3.12 Tra-
verse Table 0-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2 Roll and pitch statistics from dataset in Figure 2.29 . . . . . . . . . . . . . . . . 65
2.3 Variability between each swingarm range of motion. FR = Front Right, FL =

Front Left, RR = Rear Right, and RL = Rear Left . . . . . . . . . . . . . . . . . 65

3.1 Variables in Figure 3.4 from left to right . . . . . . . . . . . . . . . . . . . . . . 83
3.2 Regimes for the Lagrangian formulation based on pivot motion, crossover, and

tension conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.3 Frame assignment logic for the reference frames as shown in Figure 3.15 . . . . . 112

1 Parameters used for the Rover class. . . . . . . . . . . . . . . . . . . . . . . . 158
2 Parameters used for the Prismatic SEA class. . . . . . . . . . . . . . . . . . 159
3 Parameters used for the Gravity Offset Spring class. . . . . . . . . . . . 160

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List of Figures

1.1 SSL’s Raven rover, built as an astronaut transport rover for analogue field testing. 4
1.2 BioBot during initial field testing on the UMD campus . . . . . . . . . . . . . . 4
1.3 US Patent No. 4,840,394 ”ARTICULATED SUSPENSION SYSTEM” - held by

NASA. Precursor suspension system to traditional rocker-bogie [2] . . . . . . . . 5
1.4 JPL’s Mars Exploration Rover in testing, featuring Rocker-Bogie suspension [3] . 5
1.5 Lunokhod-1 annotated mockup vehicle [13] . . . . . . . . . . . . . . . . . . . . 6
1.6 Lunar Roving Vehicle mobility subsystem drawing [14] . . . . . . . . . . . . . . 6
1.7 NASA’s VIPER rover demonstrating suspension articulation, leveling chassis on

a rock in a testbed [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.8 NASA’s Resource Prospector active suspension with passive spring damping [20] 8
1.9 Annotated drawing of NASA’s Chariot suspension system [21] . . . . . . . . . . 8
1.10 Articulating chassis design of the CMU Nomad rover [24] . . . . . . . . . . . . 9
1.11 CMU’s SCARAB rover conforming to terrain during field trials [25] . . . . . . . 9
1.12 Annotated diagram of the active SherpaTT suspension system [26] . . . . . . . . 10
1.13 Large articulation range of motion, hydraulically-driven, wheel concept for off-

road logger/loader [29] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.14 AWLFC concept showing a separated, active articulated rocker-bogie style log-

ging suspenison concept [30] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.15 Marsokhod rover in testing with NASA AMES [31] . . . . . . . . . . . . . . . . 11
1.16 Annotated drawing of the EX1 suspension design, featuring passive spring damp-

ing combined with a rocker suspension system. . . . . . . . . . . . . . . . . . . 12
1.17 Side profile of the VERTEX rover carrying the umbilical-tending arm (ARM-

LiSS), featuring it’s high range of motion articulated suspension system with
passive spring damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.18 ExoMars-style rover within the DRL ROT[41] . . . . . . . . . . . . . . . . . . . 15
1.19 Lumped-parameters spring/damper model for LRV analysis [17] . . . . . . . . . 16
1.20 Articulating suspension design, based on a 4-bar linkage - utilizes a linear as-

sumption in the suspension analysis presented [51] . . . . . . . . . . . . . . . . 16
1.21 Nonlinear spring integration example with a swingarm-based suspension system

[56] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.22 Spring-damper drawing of the VERTEX suspension system . . . . . . . . . . . . 17
1.23 1/3 scale model of a rocker-style suspension rover [64] . . . . . . . . . . . . . . 19
1.24 Linear suspension model use in a scaled-rover context [65] . . . . . . . . . . . . 19
1.25 NASA’s Chariot, a full-size analogue vehicle, in testing with two test subjects [21] 21
1.26 BioBot during testing with a test subject connected to the umbilical, ready to

begin a surface traverse simulation . . . . . . . . . . . . . . . . . . . . . . . . . 21

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2.1 BioBot driving in a field with the umbilical-tending manipulator deployed to a
nominal walking state. VERTEX drives alongside the test subject as they walk
along a preplanned route. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2 VERTEX roving vehicle side profile showcasing suspension system. The fully
independent suspension features a series-elastic actuator with a parallel dual-rate
spring damper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3 VERTEX first suspension system diagram. Note the suspension rotates a swingarm
that which the linear actuator and gas strut are mounted on to achieve the range
of motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4 Initial suspension system during preliminary VERTEX build stages with the first
suspension system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.5 Example scenarios moving from negative to positive swingarm angle showing
variability in sine losses between the gas strut and linear actuator. The swingarm
is shown from left to right in this plot, moving from a ’low’ position (as seen in
Figure 2.3) to a ’high’ position (as shown in Figure 2.4). The gas spring force
and lever arm used to calculate its moment contribution are depicted in the image. 33

2.6 Sine loss effect on the moment the gas strut produces about the swingarm’s pivot. 34
2.7 Spring-damper diagram of final BioBot suspension configuration. Labeled com-

ponents: A) Series-elastic element, B) Linear actuator, C) Dual-rate spring sys-
tem, D) Swingarm. Swingarm is at 0°, level with the chassis. Positive direction
indicated by arrow around swingarm pivot. . . . . . . . . . . . . . . . . . . . . . 36

2.8 Series elastic actuator side profile, with force path from elastic element to swingarm
illustrated including sine loss angles and fulcrum lever arms at an example swingarm
angle. Retention mechanisms to resist tension loading additionally present. . . . . 38

2.9 Maximum series-elastic actuator moment contribution across all swingarm angles 40
2.10 Maximum moment contribution as a function of preload and spring rate in the

series-elastic element. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.11 Deflection of the integrated dual-rate spring damper with finalized settings. . . . 43
2.12 Spring force and moment sum of the as-integrated dual-rate spring damper across

swingarm angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.13 Sensitivity of the moment curve across a variety of preload (in) settings. . . . . . 44
2.14 Effect of changing crossover (in) on the dual-rate spring damper moment sum . . 45
2.15 Bottom spring rate (lbf/in) adjustment effect on dual-rate moment contribution . . 45
2.16 Top spring rate (lbf/in) adjustment effect on dual-rate moment contribution . . . . 46
2.17 CAD drawing depicting the wheel position at maximum extension of the caster

angle adjustment system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.18 VERTEX rover during its first field excursion, showing the caster angle adjust-

ment system is in its minimum angle state. . . . . . . . . . . . . . . . . . . . . 49
2.19 VERTEX at steady state on flat ground demonstrating a single wheel lift config-

uration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.20 Total moment sum of the suspension model with the 200/400 lb-in rate dual-rate

parallel spring damper integrated. . . . . . . . . . . . . . . . . . . . . . . . . . . 51

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2.21 Generalized coordinates used to define component placements in the optimization
scheme. The A, B, C labels correspond to the diagram in Figure 2.7, with the ”U”
subscript corresponding to upper mounting points, and ”L” subscript to lower
mounting points. (x, y) coordinates are measured from the swingarm pivot, and l
coordinates are lengths measured down the swingarm from the same point. . . . . 53

2.22 Close perspective of the arrangement of the series-elastic elements on the VER-
TEX suspension system. For system compactness, these elements were placed
offset of the main suspension plane and require careful consideration to ensure
the nominal ranges of motion are not compromised. . . . . . . . . . . . . . . . . 54

2.23 Comparison between the best single-rate spring replacement and the best dual-
rate spring replacement results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.24 Dual rate spring modification exhibiting lack of rebound and controllability at
steady state conditions due to higher than expected sprung mass during electron-
ics integration phase. Top rate 150 lb/in, bottom rate 200 lb/in. Increasing the
dual-rate damper’s preload returned the system to positive static stability. . . . . . 57

2.25 Heavy chassis modifications required for upgraded suspension including removal
of old structure and welding of new supports to support dual-rate spring dampers. 59

2.26 Chassis after modification to remove old mounts and create new structure . . . . 60
2.27 Compression/tension load cell sensor replacing the series-elastic element in the

VERTEX suspension system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.28 Calibration curve for transforming recorded voltages from the load cell and am-

plifier to forces exerted on the cell. The red Galil curve recorded voltages from
the onboard Galil motion control system, and the blue Fluke curve used manually
measured and recorded values from a Fluke 117 multimeter. . . . . . . . . . . . 62

2.29 Subset of data collected on an experiment run, cycling the chassis between max-
imum and minimum height while maintaining as low pitch and roll values as
possible. Note that startup and shutdown transients have been removed from
the beginning and ending of the approximately 300 second run. In the labeling,
”FR” designates the ”Front Right” suspension corner, and ”SW” abbreviated for
”Swingarm”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.30 Overlaid angles and angular rates for all four swingarms plotted across time from
the dataset shown in Figure 2.29. FR = Front Right, FL = Front Left, RR = Rear
Right, and RL = Rear Left . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.31 2D plot depicting relationship between swingarm angle and swingarm velocity,
colorized by force experienced by load cell. Positive force is tension, and negative
force is compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

2.32 Strut length for the original gas struts plotted across swingarm angle showing
varied rate in length change as swingarm travels upwards . . . . . . . . . . . . . 68

2.33 Wheel moment and parallel spring-damper moment plotted together. Wheel mo-
ment is inverted to more clearly see the point of transition where the series-elastic
actuator does not provide counteractive force to the wheel-moment and instead is
placed under tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

2.34 VERTEX suspension system at steady state with both series elastic elements re-
moved from the vehicle’s right side. This indicates the point of no-load in the
series elastic element, and the point of transition between tension/compression. . 72

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2.35 VERTEX during a crane lift to remove vehicle from trailer. . . . . . . . . . . . . 73
2.36 Failure of the linear actuator structural housing after crane lift. The two pieces of

the linear actuator are highlighted within the ellipses. . . . . . . . . . . . . . . . 74

3.1 BioBot concept during first field trial . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2 VERTEX suspension system high-level diagram . . . . . . . . . . . . . . . . . . 81
3.3 BioBot alternate vide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.4 Variable-Labeled BioBot Suspension Illustration . . . . . . . . . . . . . . . . . . 83
3.5 CG allocation diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.6 Ground force vector decomposition to moments about the generalized coordinate 87
3.7 Stribeck’s curve ”Coefficient of friction (Reibungskoeffizienten) versus revolu-

tions per minute (Umlaufe in 1 min) at different loads (T = 25° C, dia shaft = 70
mm, PGeom = 0.1–2.0 MPa, oil for gas powered engines η ≈ 180 mPa s).” [79] . . 88

3.8 Illustration showing a set of example example linear, progressive, and digressive
profiles [80] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.9 Labeled photo of the gravity offset damper from Radflo Suspension Technology,
Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.10 Gravity offset system near crossover point . . . . . . . . . . . . . . . . . . . . . 94
3.11 Bushing elements shown in a perspective image of the suspension system. The

bushings are seen at the top and bottom connectors for the series elastic element
and at the central pivot point between the linear actuator and the SEE. . . . . . . 97

3.12 Flowchart for selecting which Lagrangian equation to use . . . . . . . . . . . . 105
3.13 Diagram of pertinent frames for the gravity offset spring system. . . . . . . . . . 108
3.14 Frame assignments for the sprung and unsprung mass . . . . . . . . . . . . . . . 109
3.15 Frame assignments for the series elastic actuator system . . . . . . . . . . . . . . 121

4.1 Load cell integration into the front-right suspension system on VERTEX, replac-
ing the series elastic element. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.2 Initial diagram comparing load cell sensed force (colored points) with predicted
force in the series elastic element (black curve). Colorization of the points shows
a force hysteresis is present and is dependent on swingarm velocity direction. . . 125

4.3 VERTEX’s right side with no series elastic elements installed on the front and
rear suspension while investigating the no-load condition. . . . . . . . . . . . . . 126

4.4 Initial NN model attempt relying on forming multipliers for each numerical sus-
pension parameter and bounding within a set multiplier boundary, shown as 0.1
in this example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

4.5 Final curve-matching result from using the ML approach to identify vehicle pa-
rameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

4.6 Magnified section of Figure 4.5 focusing on the transition region as the system
nears crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.7 Position of new equivalent swingarm tip position as indicted by the minimum loss
result, overlaid to approximate scale onto as-built swingarm photo . . . . . . . . 136

4.8 Experimental setup for generating an approximate impulse-response scenario un-
der driving conditions. VERTEX as pictured is in an abnormally high driving
position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

xiii



4.9 Encoder mounting on swingarm pivot . . . . . . . . . . . . . . . . . . . . . . . 138
4.10 FR swingarm angle data pre-filtering, used for tuning model damping values. . . 139
4.11 Dataset from Figure 4.10 after outlier filtering . . . . . . . . . . . . . . . . . . . 139
4.12 Best fit for the training set of data found using the Ray-based optimization scheme

in Python. The blue line shows filtered encoder data recorded onboard the BioBot
rover, whereas the red line showcases the optimizer’s best attempt at fitting the
nonlinear dynamics to the real data by varying damping characteristics and the
initially-applied step input. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

4.13 An early, not well fit optimization run with the old θ̇ impulse strategy - note
the highly linear displacement trend in the first ∼0.15 seconds compared to the
accelerative rise shown in the true data. In this case, the light blue data showcases
the same training dataset as shown in Figure 4.12 and the magenta color shows
the early simulated response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.14 Test data run using same settings as identified in Figure 4.12, with parameter-
based optimization for the step impulse magnitude and duration. . . . . . . . . . 145

4.15 Curve match to a set of partial dataset recovered from a run . . . . . . . . . . . . 146
4.16 A third test dataset showing limitations of the model’s ability to match to recorded

curves, indicating further investigation into the nonlinear damping characteristics
is needed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

4.17 Spring rates over epochs during setting optimization run . . . . . . . . . . . . . . 150
4.18 Improved force profile from ML-output settings plotted with the maxima and

minima of the old settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.1 BioBot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

xiv



List of Abbreviations

ARMLiSS Active Rover Mounted Life Support System
ATHLETE All-Terrain Hex-Legged Extra-Terrestrial Explorer
CG Center of Gravity
CMU Carnegie Mellon University
EVA Extravehicular Activity
JPL Jet Propulsion Laboratory
KE Kinetic Energy
LTV Lunar Terrain Vehicle
NASA National Aeronautics and Space Administration
PE Potential Energy
PLSS Portable Life Support System
SSL Space Systems Laboratory
UMD University of Maryland
VIPER Volatiles Investigating Polar Exploration Rover
VERTEX Vehicle for Extraterrestrial, Research, Transportation and Exploration
xEMU Exploration Extravehicular Mobility Unit

xv



Chapter 1: Introduction

Exploring planetary surfaces often involves traversing highly uneven terrain, supporting

large or shifting payloads, and mitigating the risks associated with steep slopes. Rover suspen-

sion systems must not only provide adequate terrain adaptability, but also meet mission con-

straints in power, mass, and reliability. This dissertation focuses on suspension architectures that

combine active articulation with passive spring damping, an approach that can significantly in-

crease mobility and operator comfort while preserving slope compensation and load distribution

advantages.

This dissertation specifically addresses the creation of a new design path and optimization

of such suspension systems in high nonlinearity regimes, using developed methodologies that

range from quasi-static sum-of-moments-based design to Lagrangian dynamics approach focused

in tackling real-world considerations, and machine-learning-enabled parameter identification and

optimization. The result is a cohesive framework that can be extended to many roving vehicles,

including both Earth-analogue prototypes and future off-world platforms.

Rovers with actively articulated suspensions, especially those that incorporate passive spring

damping, demonstrate advantages in slope compensation, high-speed traversal, and occupant/payload

comfort. However, including damping introduces mechanical and analytical complexity to tradi-

tional rover design paths, specifically in the realm of nonlinear geometry. Conventional linearized

1



or kinematics-based methods are most often used in rover suspension design, but struggle to co-

hesively handle complex suspension systems like the experimental rover presented in this disser-

tation, VERTEX (Vehicle for Extraterrestrial Research, Transportation, and EXploration).

In this dissertation, a comprehensive analysis of suspension architectures is followed by

a discussion of existing computational tools for rover design, highlighting where a quasi-static

sum-of-moments method can fill gaps in early-stage system design. The dissertation then ex-

plores dynamic modeling using a Lagrangian-based formulation focusing on tackling real-world

assumptions often made, using a machine learning (ML) approach for parameter identification

and settings optimization of in-house-fabricated hardware. The VERTEX rover serves as a work-

ing platform to validate these concepts.

VERTEX is the roving vehicle component of the BioBot system. BioBot is an astronaut-

assistance concept comprised of: (1) a highly-capable roving vehicle (VERTEX), (2) an umbilical-

tending manipulator (named ARMLiSS - Active Rover Mounted Life Support System), and (3) a

spacesuit with a variable-duration portable life support system (PLSS). The main goal of BioBot

is to offload portions of the PLSS onto the roving vehicle and provide water, power, air, data, and

communications to the astronaut through an umbilical in response to the growing expected mass

of the xEMU (Exploration Extravehicular Mobility Unit). For more detail on the specific details

behind the BioBot application case, please see the previous publication Hanner et al. [1].

This dissertation advances the design, modeling, and optimization of compliant articulated

rover suspensions through three major contributions. First, a computationally efficient design ap-

proach was established, relying on quasistatic equilibrium and moment-based analyses to capture

the large articulation angles often demanded by extreme-access rovers, applied to the BioBot ve-

hicle. This framework focused on vehicle design for early stage space systems by systematically

2



assessing the suspension geometry and force profiles while retaining sufficient fidelity to ensure

reliable performance in a wide range of operating regimes.

Second, a universal Lagrangian-based modeling approach was formulated to integrate both

static and dynamic behaviors in rover suspensions. This approach explicitly incorporates real-

world complexities such as damper force limitations, non-linear spring-damper relationships, and

the inclusion of system bushings. Experimental validation on the VERTEX rover highlighted the

model’s ability to fully capture system responses, providing a versatile baseline to refine and

predict highly nonlinear and compliant suspension performance.

Finally, a data-driven framework was introduced to reconcile the differences between the

designed and as-built hardware. By incorporating machine learning algorithms into the iden-

tification efforts of the system, the presented method refines the parameter estimates to reflect

the manufacturing variants and the true operational characteristics. The resulting approach was

then applied to optimize BioBot’s suspension system, producing a more linear force profile at the

component level with reduced peak loads.

1.1 Suspension Architectures Review

Suspension systems play a critical role in planetary surface rovers as they directly influence

a vehicle’s stability, payload capacity, energy efficiency, and adaptability across varied terrains. In

general, rover suspension systems can be classified by two Boolean characteristics: (1) presence

of active articulation and (2) presence of passive spring damping. For example, a vehicle where

both of these propositions are false would directly mount wheels or tracks to the vehicle chassis.

The Raven vehicle built at the University of Maryland (UMD) Space Systems Laboratory (SSL)

3



as seen in Figure 1.1 is an example of this class of rover and has advantages in simplifying

design, but limiting speed of travel and adaptability to terrain. In contrast, actively articulated

suspensions with spring damping can enhance slope compensation and occupant comfort for a

trade-off in system complexity, as shown with BioBot in Figure 1.2.

Figure 1.1: SSL’s Raven rover, built as an astro-
naut transport rover for analogue field testing.

Figure 1.2: BioBot during initial field testing
on the UMD campus

This dissertation aims to provide an analytical framework for designing and optimizing

actively articulated suspension systems inclusive of passive spring damping, largely regardless of

the selected articulation mechanism.

1.1.1 Heritage Suspension Architectures

Within the articulated and spring-damping categories, specific design decisions such as

rocker vs. rocker-bogie or fully independent vs. multibogie must be aligned to mission require-

ments for mobility, load capacity, and reliability. The historic population of suspension design

architectures from both flight missions and ground test rovers shows a notable evolution in sus-

pension designs and objectives over time.

4



1.1.1.1 Rocker-Bogie Suspension

Figure 1.3: US Patent No. 4,840,394 ”ARTIC-
ULATED SUSPENSION SYSTEM” - held by
NASA. Precursor suspension system to tradi-
tional rocker-bogie [2]

Figure 1.4: JPL’s Mars Exploration Rover in
testing, featuring Rocker-Bogie suspension [3]

Rocker-bogie suspension systems are the most prevalent type on vehicles deployed in ex-

traterrestrial environments. NASA’s Sojourner (1996) [4], Mars Exploration Rovers Spirit and

Opportunity (2003) [5], Mars Science Laboratory: Curiosity (2011) [6], and Mars 2020: Perse-

verance (2020) [7] each feature a 6-wheeled rocker-bogie design. China’s Yutu series of lunar

rovers also adopt rocker-bogie [8–10]. A passive differential mechanism helps maintain continu-

ous wheel contact and balanced loading at low speeds [11].

China’s Zhurong Mars rover, launched in 2021, features a combination ”active / pas-

sive” rocker-bogie suspension system. The design incorporates a clutch-operated angle adjust-

ment mechanism, enabling operational freedom to modify the vehicle’s kinematic configuration.

Specifically, this allows for raising and lowering the rover chassis, adjust the distance of the front

wheels with respect to the bogie, and altering the front wheel height all using the traction motors.

This adjustability diversifies locomotive strategies and improves obstacle climbing performance

5



in varied terrain [12].

1.1.1.2 Independent Wheel Suspension

Figure 1.5: Lunokhod-1 annotated mockup ve-
hicle [13]

Figure 1.6: Lunar Roving Vehicle mobility sub-
system drawing [14]

Russia’s Lunokhod-1, as seen in Figure 1.5, launched in 1970 and featured a non-adjustable,

elastic eight-wheel independent suspension employing torsion bars with an auxiliary ninth wheel

for slip measurement [13, 15]. Lunokhod-2 followed in 1973, improving traction drives and

achieving an extraterrestrial traverse record of 39 km in 4 months, only surpassed by Opportu-

nity after a decade of driving [16]. Meanwhile, the Apollo-era Lunar Roving Vehicle (LRV), as

seen in Figure 1.6, used a double-Ackermann steering layout combined with double wishbone

suspension with torsion bars [14]. The four-bar linkage of the double wishbone system allows

the wheel to respond when disturbed from steady state in a way that can be trivially linearized,

simplifying the optimization problem to a series of linear springs and dampers translated into

appropriate characteristic values [17].

6



1.1.2 Prototype, Earth-Analogue, and Unflown Active Wheel-Articulation Fo-

cused Rover Suspension Systems

The development of active and articulated rover suspension systems has seen steady growth

in recent years. Research in this area has come from national space agencies across the world,

university researchers, and corporations such as Venturi Astrolab, one of three providers currently

developing LTV (Lunar Terrain Vehicle) concepts for Artemis. The development of prototype,

Earth-analogue, and unflown rover systems provides a vital platform for testing and advanc-

ing suspension designs that address unique challenges posed by planetary surfaces learned from

the experiences of planetary surface vehicles in history. These new vehicles broach innovative

solutions to mobility, stability, and terrain challenges leveraging active and/or articulation mech-

anisms to overcome limitations found in traditional suspension platforms. Some systems balance

articulation with passive spring damping; others focus on pure articulation to satisfy mission

requirements.

Figure 1.7: NASA’s VIPER rover demonstrat-
ing suspension articulation, leveling chassis on a
rock in a testbed [18]

NASA’s Volatiles Investigating Polar

Exploration Rover (VIPER), a ground-testing

model of which can be seen in Figure 1.7, is a

four-wheeled vehicle designed with indepen-

dently articulated suspension alongside inde-

pendent steering and traction drives. Origi-

nally slated to explore the lunar south pole

ahead of the Artemis surface missions [19].

As of the time of writing, the future of

7



VIPER’s launch is still unclear, but no matter the outcome, the rover presents a huge step forward

for flight-qualified articulated suspension. VIPER does not possess a dedicated passive spring

damping system alongside the articulation, as the roll and pitch control of the chassis is largely

focused on ice sample drilling operations. The VIPER team draws an interesting distinction, clas-

sifying the 10 Hz bandwidth of the suspension as actuated rather than active, a distinction that

BioBot similarly makes. NASA intends to use the articulated suspension as an alternative mode

of locomotion, as a mechanism to improve stability margins on slopes by leveling the chassis,

and for finer intentional positioning of each wheel [18].

Figure 1.8: NASA’s Resource Prospector active
suspension with passive spring damping [20]

Figure 1.9: Annotated drawing of NASA’s
Chariot suspension system [21]

NASA’s Resource Prospector and Chariot vehicles both have actively articulated indepen-

dent suspension including passive spring damping. Resource Prospector utilizes a revolute actu-

ator for control of its 4-bar linkage to actively control wheel position, hinged on a spring system

as seen in Figure 1.8 [20]. The latter cleverly uses a ball screw instead to articulate the entire

suspension mechanism, preserving the spring-damper characteristics in a very consistent way as

shown in Figure 1.9. The ball screw mechanism is able to actuate across a range of 25” in vertical

travel in just 9 seconds and features 11” of wheel deflection [21].

8



The Jet Propulsion Lab’s (JPL) All-Terrain Hex-Legged Extra-Terrestrial Explorer (ATH-

LETE) rover uses 6 wheel-on-limb actuators to integrate rolling and walking gaits for greater

efficiency during traversal operations on the lunar surface. The system uses a series of revolute

actuators to create 6-DOF manipulators to strategically position the wheels and conquer more

challenging terrain, setting records in rover suspension articulation range without passive impact

attenuation [22].

Carnegie Mellon University (CMU) has developed innovative suspension systems on rov-

ing vehicles including the Nomad and Scarab vehicles. Nomad utilizes an expanding wheelbase,

as shown in Figure 1.10, to influence the stability margins by creating a wider stability platform

for the vehicle, and additionally increases tractive effort when climbing slopes [23]. Nomad also

features a body-averaging suspension mechanism. Pivoting alongside the centerline of the chas-

sis, the left and right halves of the vehicle are allowed to articulate, restricted by a differential

averaging bar between the sides [24]. This combines active manipulation of stability margins

with relatively simple yet effective suspension articulation.

Figure 1.10: Articulating chassis design of the CMU
Nomad rover [24]

Figure 1.11: CMU’s SCARAB rover
conforming to terrain during field trials
[25]

9



CMU’s Scarab rover, seen in Figure 1.11, somewhat similar to the ultimate design of

VIPER uses an articulated suspension system without traditional spring damping to support sta-

bility control and drilling operations, but in a different mechanism. Scarab uses a body-averaging

suspension linkage system, similar to Nomad in that the left- and right-hand systems are inde-

pendent, but with linked front and rear main members on each side. This provides a mechanism

for control of chassis roll and body height, and uses skid steer [25].

Figure 1.12: Annotated diagram of the active
SherpaTT suspension system [26]

DFKI’s (Deutsches Forschungszentrum

für Künstliche Intelligenz) SherpaTT (the evo-

lution from the original Sherpa rover - Fig-

ure 1.12) features a wheel-on-limb articulating

suspension system, without traditional pas-

sive spring damping, that combines hybrid

rolling/walking gaits to create a highly effi-

cient and capable exploration chassis. Each of

its four limbs use a revolute pan actuator, two

linear actuators for effectively hip and knee extension and flexion, and finally a pair of revolute

actuators for over-wheel steering and traction drive [26, 27]. A force-torque sensor is placed at

each wheel along the wheel drive axis and allows for intentional distribution of force between

each wheel [28].

In terrestrial applications, forestry equipment uses both articulated body and independently

articulated wheels via hydraulics to achieve large ranges of motion and a high degree of terrain

compensation [29]. Guaranteed stability from these advantages guarantees stability in the highly

variable terrain required to be engaged in forestry, but have little need for passive spring damping

10



Figure 1.13: Large articulation range
of motion, hydraulically-driven, wheel
concept for off-road logger/loader [29]

Figure 1.14: AWLFC concept showing a separated, ac-
tive articulated rocker-bogie style logging suspenison
concept [30]

at the slow speeds required from these style vehicles. The availability of hydraulic actuators has

allowed for innovative mechanisms to be created such as the Articulated Wheel-Legged Forestry

Chassis (AWLFC), combining active four-bar linkage articulation with a separated rocker-bogie

[30].

1.1.2.1 Alternate Suspension Articulation Configurations

Figure 1.15: Marsokhod rover in testing with
NASA AMES [31]

Beyond the many creative ways in

which rovers and terrestrial vehicles have fo-

cused on articulation of wheels with respect

to the chassis, alternative creative configura-

tions have been developed. One category of

this would be articulated body vehicles. The

ability to simplify attachment mechanisms be-

tween traction (and sometimes steering) actu-

ators to rigid sections of a segmented chassis

11



may provide an avenue for simplified and stiffer actuation mechanisms. One type of articulated

body vehicle is the Marsokhod-style design, which uses roll and pitch mechanisms between the

front and rear wheel pairs relative to a central set of wheels to control both the level of the

chassis and the steering conditions [uropean˙space˙agency˙esa˙2012, 32–35]. This design also

allows wheel walking as an alternative locomotive strategy in challenging terrain or anomaly.

The vast majority of articulated body platforms built in history are not in roving vehicles, but in

the terrestrial mining, forestry, and construction industries, highlighting their adaptability [36].

Specifically, the design is common in dump trucks and in front loaders and rely on hydraulic

systems for actuation [37, 38].

Figure 1.16: Annotated drawing of the EX1 suspension design, featuring passive spring damping
combined with a rocker suspension system.

Other unconventional rover suspension design configurations include the EX1 vehicle from

Tohoku University’s Space Robotics Lab (SRL) in combining a traditional rocker articulation sys-

tem with independent passive spring-damping suspension per each wheel (Figure 1.16), allowing

for a higher traverse speed with lower vibration and harshness [39]. Another vehicle, the FWRA

12



(Four Wheel Rhombus Arranged) rover both places the wheels in more of diamond shape and uti-

lizes a series of motors, an electromagnetic clutch, and optimized swingarm lengths to perform

terrain compensation, allowing new approaches to slope climbing to be developed [40].

1.1.3 Suspension Architectures Summary

These examples highlight broad innovation in suspension systems, from purely kinematic

linkages to fully active, compliance-rich articulations. However, no unified approach or previ-

ously built rover exists in building a suspension system capable of articulating a chassis to ac-

commodate steep slopes (≥ 30°) while including passive spring damping in all configurations. In

the coming age of return to human exploration, developing tools and rovers in this trade space is

likely to augment more advanced planetary surface research through astronaut support, especially

when looking towards metabolic impact of EVAs (Extravehicular Activities) on Mars.

In particular, the SSL’s VERTEX rover stands out for its swingarm travel range of 58.8°,

combined with passive spring damping for impact attenuation across the full range of motion.

The large range of motion allows the vehicle to level its chassis on 40° cross-slopes, 30° up-

slopes and can raise and lower the chassis by over one meter. The suspension features both a

custom series-elastic actuator system and a secondary spring system to offload force requirements

from the prismatic joint under Earth gravity conditions. Due to the articulation method and

wide range of motion, the system is highly nonlinear, mandating careful considerations of the

vehicle’s kinematics, sine loss effects, and real-world considerations for components such as

tension-limited dampers. This dissertation focuses on the largely on a new 2-part design path

taken to design VERTEX’s final suspension system, comprised of a systems-level design tool

13



Figure 1.17: Side profile of the VERTEX rover carrying the umbilical-tending arm (ARMLiSS),
featuring it’s high range of motion articulated suspension system with passive spring damping

and a fine-detail Lagrangian dynamics scheme. The next sections examine the analytical and

computational tools that have been deployed historically, clarifying why new techniques and

approaches are necessary for vehicles like VERTEX.

1.2 Design Tools and Methodologies For Articulated Suspension Systems

Substantial prior work emphasizes kinematic optimization for rocker-bogie or other linked

suspensions, while certain specialized studies address compliance or soil contact models. Yet for

more complicated suspension design paths, these baseline models must be enhanced to manage

nonlinear geometry and multi-spring constraints.

14



1.2.1 Kinematic Simulation and Optimization

Figure 1.18: ExoMars-style rover within the
DRL ROT[41]

Kinematic simulations are the founda-

tion for modern rover suspension analysis.

These simulations tend to use a simulated set

of varying terrain topologies and often simu-

late and evaluate varying rover characteristics

such as drawbar pull, stability, or load distribu-

tion while optimizing a set of vehicle param-

eters, usually in some form of a distributed-

mass model [42–46]. As these types of sim-

ulations provide insight into the efficiency of kinematic designs in compensating for these un-

even terrains, they focus on systems without dedicated spring-damper mechanisms therefore are

largely applied to rocker and rocker-bogie configuration vehicles.

The DLR-developed Planetary Rover Optimization Tool (ROT - shown in Figure 1.18)

optimizes Rocker Bogie and ExoMars type rovers through geometric variability and includes a

distributed mass approach to increase realism [47]. Other DLR-developed analysis tools utilize

simulated performance of a vehicle’s design to optimize mechanical structure and suspension

design parameters [48]. Similarly, advanced simulation schemes that include surface contact

dynamics modeling can be used to modify the rocker-bogie parameters of a vehicle with sim-

ulated drawbar pull [49]. These models have been validated using deterministic and stochas-

tic parameter estimation methods, establishing correlations between predicted and experimental

soil interaction parameters and increasing the reliability of performance simulations used in ve-

15



hicle design optimization [50]. Combining optimization schemes that are terrain-considerate,

terramechanics-informed, contact dynamic tracking, and systems-focused allow rover suspen-

sions to be optimized as a subsystem of a complete rover vehicle, usually looking to decrease

system mass or required power [41].

1.2.2 Spring Damper Inclusive Rover Suspension Analysis

Figure 1.19: Lumped-parameters
spring/damper model for LRV analy-
sis [17]

Figure 1.20: Articulating suspension design, based on
a 4-bar linkage - utilizes a linear assumption in the sus-
pension analysis presented [51]

Traditional analyses with passive damping often assume linear stiffness and damping [17,

51, 52], valid for short-travel double-wishbone setups. Figure 1.19 shows the traditional lumped

parameter linear model that a large majority of sprung rovers use. Some advanced concepts

(differential four-bar, parallel linkages, suspended bogies) incorporate partial compliance while

targeting continuous wheel-ground contact [53–55].

In contrast, VERTEX’s swingarm spans nearly 60°, linking multiple springs and an ac-

tuator with potentially large sine losses and tension restrictions. Simple linear approximations

are insufficient. Some dynamic models exist for single swingarm-based suspension systems on

16



rovers [56], and efforts in non-linear components such as inerters or geometry-based compliance

[55, 57] show promise but remain application-specific. The design approach presented in this pa-

per accommodates arbitrary suspension mechanism configurations and component placements,

provided that the kinematic relationships between the primary suspension axis, wheel position,

and the states of individual components—including springs, dampers, and auxiliary joints (with

friction)—can be clearly defined and traced.

Figure 1.21: Nonlinear spring integration ex-
ample with a swingarm-based suspension sys-
tem [56]

Figure 1.22: Spring-damper drawing of the
VERTEX suspension system

1.2.3 Quasi-Static Assumption

Quasi-static analysis assumes that a system moves at a sufficiently slow rate such that in-

ertia and damping effects can be neglected, reducing the problem to one of kinematics and static

force equilibrium. This assumption is particularly relevant to planetary rovers, which typically

operate at low velocities (leq10 cm/s), making dynamic effects negligible [58]. By treating mo-

tion as a sequence of static equilibria, quasi-static models simplify the design and analysis of

17



articulated suspensions, especially applicable early in the design process.

While quasi-static models effectively characterize slow rover motion, their assumptions

become invalid at higher speeds or when transient effects such as impact forces or oscillations

arise. The classical rocker-bogie suspension was explicitly designed to function under quasi-

static conditions, but emerging high-speed rover concepts require a more detailed treatment of

inertia and compliance [59]. When a rover begins to encounter rapid wheel-terrain interactions,

dynamic effects dominate, requiring a transition to advanced system modeling [60, 61].

This dissertation adopts a hybrid approach: beginning with a quasi-static methodology for

initial system design and transitioning to a Lagrangian framework for detailed dynamics model-

ing and parameter optimization. The integration of machine learning further refines parameter

selection, bridging the gap between theoretical modeling and real-world system identification and

optimization.

1.3 Earth-Analogue Vehicle Design Approaches for Mobility Systems Testing

Specifically, looking at the design of flight rovers with suspension systems designed to

perform under the gravitational conditions of the moon or Mars, teams must consider how to

best test on Earth. Looking beyond gravity-offload mechanisms such as pulleys and suspended

masses, which can significantly limit testing, Earth-analogue rovers can be built to preserve spe-

cific aspects of a design and allow qualification and characterization efforts to occur in different

areas [62]. Most often these vehicles sacrifice selected specific aspect pertinent to the flight ve-

hicle in pursuit of accurate testing of various qualities of mobility; an acceptable trade-off as the

focus of the experimentation is in evaluating the mobility system in one way or another. The dif-

18



ferent approaches to building an Earth-analogue vehicle are dependent on the testing goals and

requirements, and the goal of this dissertation is to apply to all three categories.

1.3.1 Similarity Law

The first approach is to use what is known as the ”Similarity Law” to scale rover mobility

systems to evaluate items such as power consumption and peak torque requirements reflective

of the deployed extraterrestrial counterpart vehicle [63]. This scaling factor is effectively the

fractionalized ratio of gravity levels between the planetary or satellitic body and the testing grav-

ity condition on Earth [64]. Testing with alternative gravity-level approaches such as half-G

parabolic flights (rover for which is shown in Figure 1.23) allow the scaling factors to be dou-

bled and thus reduce the scale proportions between the flight kinematics and the testing vehicle

kinematics.

Figure 1.23: 1/3 scale model of a
rocker-style suspension rover [64]

Figure 1.24: Linear suspension model use in a scaled-
rover context [65]

This approach has been shown to provide very similar dynamic responses across different

vehicle scales as long as the scaling factors are correctly translated into the scaled design pa-

rameters, allowing linear models to be easily maintained (example scaled linear model shown in

Figure 1.24) [65]. Extending this generalized approach to more complex nonlinear approaches

19



will augment pathways to a wider variance in testing of extraterrestrial vehicles.

1.3.2 Equivalent Size, Equivalent Weight

The second approach is to maintain the testing vehicle at the same size as the flight version,

with the same effective weight as would be experienced on the body of the study’s surface. Often,

this approach allows the test vehicle to be engineered with a center of mass and wheel force very

similar to those of the flying rover, allowing the principles of terramechanics to be validated [66].

An example of this is the VIPER Moon Gravity Representative Unit (shown in Figure 1.7) as it

has a ground-pressure equivalent variant that requires a weight offloading tether from the power

system and a variant that preserves the center of gravity of the vehicle at the expense of greater

wheel loading ≈ 30% [18]. Some approaches within this category prioritize the use of the flight

chassis and actuators to analyze mechatronic performance, adaptive control systems, or vehicle

stability in flight-like conditions [67, 68].

1.3.3 Matched Capability

The third approach largely focuses on operational testing through the creation of a test-

ing vehicle of equivalent size and equivalent mobility capabilities, thus requiring a higher mass

compared to the lunar design. Systems involving the testing of human-related CONOPS in Earth

conditions, such as Desert RATS and other analogue field trials, often follow this design approach

to allow realistic payloads, slope climbing abilities, and system operations to be tested.

NASA’s Chariot rover (Figure 1.25) was designed from the ground up to support Earth-

gravity testing of that vehicle design. Tuning the springs, dampers, articulation actuator torques,

20



gearboxes, structures, etc. all for Earth gravity generates a heavier vehicle than would be needed

for the lunar surface, but allows the concepts of operations surrounding that vehicle to be tested

in high-fidelity analogue field events [69, 70].

Figure 1.25: NASA’s Chariot, a full-size ana-
logue vehicle, in testing with two test subjects
[21]

Figure 1.26: BioBot during testing with a test
subject connected to the umbilical, ready to
begin a surface traverse simulation

BioBot strictly adheres to this design methodology. Maintaining scale is critical for refining

the operational concepts that make these roving vehicles unique in paralleling fidelity to the final

surface. It is especially important with BioBot to preserve scale as well as slope climbing/leveling

abilities to understand how useful an extreme-access roving vehicle can be to supporting EVAs,

a difficult task under scaled gravity from the Moon or Mars. Figure 1.26 shows the full scale of

BioBot in preparation for an EVA simulation task, allowing the astronaut to walk when they want

and drive when they do not.

1.4 Suspension Approaches Summary

Rover suspension architectures have evolved from simple passively articulated configura-

tions to highly active spring-damped solutions designed to handle extreme slopes, loads, and ter-

rain variability. Although historically prevalent systems such as the rocker-bogie favor low-speed

21



exploration and quasi-static design, emerging concepts for both terrestrial off-road applications

and next-generation surface missions push toward higher speeds, greater slope compensation, and

more extensive articulation. Such capabilities introduce significant design complexity, especially

in nonlinear systems.

This dissertation focuses on bridging gaps in design methodology for these advanced sus-

pensions. It begins by leveraging a quasi-static, sum-of-moments approach to handle early-stage

system sizing and trade-offs, then integrates a Lagrangian-based modeling framework to capture

higher-speed, real-world dynamics while tackling real-world considerations often overlooked. Fi-

nally, it uses machine learning-enabled parameter identification created for parameter identifica-

tion, model refinement, and system optimization. VERTEX serves as the principal demonstration

platform.

The ensuing chapters detail each step in this multi-layered approach, culminating in a flex-

ible design framework that can be applied to a wide array of roving vehicles, ranging from Earth-

analogue prototypes like BioBot to future off-world exploration platforms. By unifying quasi-

static design, rigorous dynamic modeling, and data-driven refinement, this work aims to ease the

path toward rovers that are simultaneously robust, high-performing, and adaptable to the rigorous

demands of extraterrestrial terrain.

• Chapter 2: Presents the sum-of-moments design methodology in depth, including the

original quasi-static models, design decisions, and validation results.

• Chapter 3: Introduces the Lagrangian-based dynamic model for articulated suspensions

with passive compliance and application within the VERTEX kinematics.

• Chapter 4: Describes the ML-based parameter identification framework and shows how

22



as-built can deviate from as-designed in manufactured hardware, as well as the use of the

framework for focused optimization. The dynamic validation method and results for the

Lagrangian model are also presented.

• Chapter 5: Summarizes results and discusses future work.

23



Chapter 2: System Design and Validation of Independently Articulated Sus-

pension Using a Sum-of-Moments Framework for the BioBot Sys-

tem

This chapter has been written as a stand-alone paper and is under second review in Acta

Astronautica as of thesis submission. Please check for the final version to find any supplementary

media or prose adjustments.

Contributions In This Chapter This chapter focuses in the development of a quasi-static

computationally-efficient approach for articulated suspension design with passive spring damp-

ing. A key assumption is presented in this chapter as the ”full-contribution assumption”, allowing

system stability and stiffness to be evaluated very quickly between suspension configurations.

The goal in this chapter is to provide a workflow to design these articulated systems in a reliable

way that guarantees stability even with nonlinear systems.

24



2.1 Introduction

BioBot is a versatile Earth-analogue roving vehicle and umbilical-tending manipulator

pairing designed, manufactured, and assembled in-house at the University of Maryland’s Space

Systems Laboratory. The rover component, named VERTEX (Vehicle for Extraterrestrial Re-

search, Transportation, and EXploration), is built to simulate full-duration Extravehicular Activ-

ities (EVAs) in Earth conditions, specifically targeting a reduction in astronaut metabolic strain

by transferring a majority of the mass of the astronaut’s portable life support system (PLSS) onto

the vehicle. Figure 2.1 depicts BioBot operating during field trials with a test subject attached via

the actively-tended umbilical.

Figure 2.1: BioBot driving in a field with the umbilical-tending manipulator deployed to a nom-
inal walking state. VERTEX drives alongside the test subject as they walk along a preplanned
route.

VERTEX is capable of climbing slopes up to 30°, and leveling the chassis on such slopes

using a combination of parallel and series-elastic actuator systems. The rover can steer each

25



wheel independently with a range of±180° and supports a 5-meter-long umbilical-tending robotic

manipulator. More detailed information regarding BioBot’s design path, methodology, and initial

field trials is available in recent work Hanner et al. [1]. Known as the Vehicle for Extraterrestrial

Research, Transportation, and Exploration (VERTEX), the rover component is designed for flex-

ibility in field trials, supporting a multitude of payloads and mission configurations across a wide

variety of analogue environments.

Figure 2.2: VERTEX roving vehicle side profile showcasing suspension system. The fully inde-
pendent suspension features a series-elastic actuator with a parallel dual-rate spring damper.

VERTEX has a uniquely broad range of motion among independently articulated planetary

surface rovers, featuring a kinematically-limited 58.8° of movement and passive spring damping

compliance at all articulation angles. The chassis can compensate 30° in pitch, 40° in roll, and

over 1 meter of chassis height variation. This articulating flexibility allows payloads whether

26



it be an umbilical-tending manipulator, scientific sampling devices, or astronauts to navigate

geologically diverse and steep terrains without compromising vehicle stability. Additionally, for

particularly challenging payloads such as BioBot’s 5-meter long umbilical tending manipulator,

requirements for control of its free-spinning yaw joint can be reduced or eliminated through

the active pitch and roll control. If unwieldy payloads remain unaffected by slopes, especially

important with BioBot as the astronaut is attached to the manipulator arm via the umbilical, safety

of the operator and the rover can be better guaranteed and requirements for mounting and control

of these payloads can be reduced.

2.1.1 Articulating Extraterrestrial Roving Vehicle Concepts

Articulated suspension systems enable rovers to adapt to and better explore rugged and

uneven terrains. NASA’s Chariot [21], ATHLETE [22], Resource Prospector [20], and VIPER

[18] rovers incorporate independently articulated suspension systems, allowing each wheel to

adjust position relative to the chassis for improved stability and mobility. Similarly, academic

prototypes, including CMU’s Scarab [25], Nomad [23], and DFKI’s Sherpa/SherpaTT [26], em-

ploy unique articulation systems tailored for specific mission goals such as terrain compensation,

stability enhancement, and sampling.

Common to these designs is a focus on articulating wheels relative to the chassis. This

approach enables precise adjustments to wheel height and in some configurations steering angle,

effecting measurable and intentional positioning of the CG relative to stability margins. In con-

trast, articulated body rovers move entire sections of the vehicle chassis to accommodate terrain.

Examples include the Marsokhod series: Lama by Alcatel Space Industries [32], Eve and IARES

27



by CNES [33], and a Marsokhod rover from NASA Ames [34]. These articulated body rovers

utilize roll and pitch control across wheel pairs, relative to central wheels, to achieve effective

terrain compensation and steering capabilities. Most of the articulated-body vehicles in existence

are focused in mining, forestry, or construction [36]. Often this architecture is commonly present

in front loaders and dump trucks, and relies on hydraulic actuators [37, 38].

The EX1 rover from Tohoku University’s Space Robotics Lab incorporates passive sus-

pension at each wheel to overcome speed limitations in traditional rocker/rocker-bogie systems.

Dubbed the ”Mechanically Hybrid Suspension” (MHS), EX1’s passive spring damping lowers

suspension forces, minimizes harsh impacts, and improves dynamic stability when traversing

obstacles [39].

Highlighting the necessity of these terrain-adaptive designs, NASA’s Lunar Surface Data

Book emphasizes the operational challenges of the extreme-access EVA conditions expected to

be seen in the Artemis missions including steep slope navigation, payload management, and

crew safety [71]. Table 2.1 shows a condensed overview of slope conditions seen across the

four example EVA routes outlined in the document. Working to best prepare roving vehicles

to compensate for the large slopes present will likely have positive downstream effects on the

success of surface EVA goals, motivating the large articulation range in VERTEX.

2.1.2 Applications Beyond Spaceflight

Articulated suspension systems are equally valuable in terrestrial fields like forestry and

construction, where equipment often combines body articulation with independent wheel adjust-

ments facilitated by hydraulic systems. Forestry harvesters and forwarders use such systems to

28



Table 2.1: Condensed table of slope statistics from the Lunar Surface Data Book’s Example EVA
Traverses. A = 7.3.1 Large Logistics Transfer, B = 7.3.2 Long Uncrewed Science Traverse, C =
7.3.3 Traverse into crater/PSR Table 0-3, D = 7.3.12 Traverse Table 0-4

EVA Max. Mean Std. Dev.

A.1 9.76° 3.26° 1.88°

B.1 20.51° 5.17° 4.01°

B.2 28.26° 5.24° 4.69°

C.1 28.71° 8.4° 7.15°

C.2 11.66° 3.3° 2.03°

C.3 41.55° 7.8° 6.02°

D.1 23.64° 5.28° 4.03°

D.2 17.5° 5° 3.74°

D.3 36.12° 11.65° 6.91°

prevent tipping on uneven ground under heavy loads [29]. In construction, vehicles like articu-

lated dump trucks [37] and loaders [72] often leverage single-axis body articulation to gain ad-

vantages in steering and turning radii. Other construction equipment leverages wheel-articulation

for stability advantages, including multi-DOF articulation for walking excavators including hy-

draulic force sensing [73]. The use of quasi-statics in the design of articulated suspension vehicles

is a common approach, and has extensions into both wheeled and tracked sprung suspension sys-

tems [74]. A plethora of terrestrial experience with articulating vehicle systems allows for an

evolutionary rather than a foundational step in the development of extraterrestrial vehicles.

2.1.3 Motivation and Contribution

Of the articulating extraterrestrial roving vehicle concepts, Resource Prospector and Char-

iot are the roving vehicles who include both active articulation and passive spring damping in

29



their design. The decision to include both of these items in the VERTEX rover was focused in

the comfort of the operator, and the inclusion of passive spring damping was included as a level

1 requirement. Existing system examples of articulated suspension systems that include passive

spring damping do not

The focused contribution of this work is in creating a computationally-efficient, high-level

systems analysis framework for the design of nonlinear articulated suspension systems with pas-

sive compliance.

This work uses a quasi-static assumption for estimating the stability of the system and is

intended to be a first step in the full suspension design process where a more in-depth dynamics-

focused approach is undertaken to fine-tune system details and responses. This follow-on work

on the creation of a Lagrangian-based dynamic system is shown later in Chapters 3 and 4.

2.2 Modeling

Modeling rover suspension as a quasi-static articulation system allows for the use of a

sum-of-moments-based approach [75]. Traditionally, vehicle suspension modeling relies on spe-

cialized simulation packages that are not adaptable to the extensive variability in actuators and

structural configurations required in early-stage space systems design. Although these packages

typically emphasize dynamic responses, the approach used in this generated approach focuses

specifically on quasi-static stability, accurate force estimation, and payload support. This quasi-

static assumption is justified by the linear actuators selected for the VERTEX project, which

exhibit relatively low bandwidth and slow response compared to traditional active suspension

actuators. Specifically, VERTEX requires approximately 60 seconds to complete a complete

30



articulation cycle spanning the ≈ 58.8° range of motion.

2.2.1 VERTEX Suspension Development Issues

Initial design requirements highlighted the need for passive spring damping to enhance

operator comfort. Prior SSL-built rovers featured rigid suspensions, resulting in uncomfortable

operator experiences and motivating the adoption of passive damping for VERTEX. In particular,

all three Lunar Terrain Vehicle (LTV) prototype providers contracted in 2024 incorporate passive

spring-damped suspensions, with Astrolab FLEX explicitly featuring independently articulated

suspension [76]. The inclusion of independently articulated suspension with passive compliance

enhances BioBot’s applicability to the extreme-access activity foci of the Artemis missions and

beyond.

Figure 2.3: VERTEX first suspension system diagram. Note the suspension rotates a swingarm
that which the linear actuator and gas strut are mounted on to achieve the range of motion.

The first iteration of VERTEX’s articulated suspension system employed force-based mod-

eling, aiming to optimize linear actuator mounting locations to minimize actuator force demands

while maximizing suspension range of motion. Initial modeling relied upon preliminary vehicle

31



mass estimates and assumed a fixed upper actuator mounting point, as the series-elastic part of

the system was still under development. The optimization scheme incorporated a pair of 250 lb

constant force gas springs (often referred to as ”gas struts”) to offload physical requirements from

the linear actuator, allowing faster articulation, lower forces, and reduced cost and is shown in

Figures 2.3 and 2.4.

Figure 2.4: Initial suspension system during preliminary VERTEX build stages with the first
suspension system.

Testing revealed that while linear actuators could achieve full articulation throughout the

specified range, payload capacity varied significantly. At low swingarm angles, with the chassis

in a raised position (Figure 2.4), the suspension could support both a test subject and additional

payload with stability. However, at higher swingarm angles and lower chassis heights (Figure

2.3), the suspension could support less than 20 lbs of additional payload before sagging.

32



Suspension sagging occurs when payload exceeds suspension capability, causing compres-

sion of series-elastic element in line with the linear actuator in a quasi-static scenario. Under

these conditions, the chassis sinks toward the compressed elements without rebound capability

unless payload is removed. Adjustments of the linear actuator length proportionally compress

the elastic elements without significantly altering the angle of the swing arm, thereby reducing

the controllability and stiffness of the suspension.

Figure 2.5: Example scenarios moving from negative to positive swingarm angle showing vari-
ability in sine losses between the gas strut and linear actuator. The swingarm is shown from left
to right in this plot, moving from a ’low’ position (as seen in Figure 2.3) to a ’high’ position (as
shown in Figure 2.4). The gas spring force and lever arm used to calculate its moment contribu-
tion are depicted in the image.

This issue primarily arises due to ”sine loss,” defined here as the reduction in effective

torque resulting from the angle at which the actuator or gas strut applies force relative to the

swingarm. Specifically, if these components apply force at angles other than perpendicular to

the swingarm, part of the applied force is redirected along the swingarm itself (compression or

tension) rather than producing rotational torque. In this application, torque is generated by the

suspension components applying force at their respective mounting points along the swingarm.

The linear distance from the pivot to the mounting point acts as the lever arm, converting applied

33



linear forces into moments about the swingarm pivot.

Figure 2.6: Sine loss effect on the moment the gas strut produces about the swingarm’s pivot.

Figure 2.5 illustrates the position of the linear actuator and the gas strut at three angle

angles of the swingarm, showing the force profile transitioning through the perpendicular state

of maximum moment. Consequently, the torque contributions of these components decrease

significantly at high angles, limiting suspension performance.

Figure 2.6 depicts the moment quantity that the gas strut generates as a function of swingarm

angle. It should be noted the gas strut’s force is independent of the swingarm angle and acts with

a constant value. At the upper 45° limit the moment has decreased to less than 50% of the peak

value due to the sine loss. This lack of moment to counteract the vehicle’s weight is what led to

the rover’s lack of static stability.

2.2.2 Motivation

The key issues and limitations identified in the initial suspension configuration are summa-

rized below.

34



• Limited payload capacity at high swingarm angles: Reduced effective torque due to

sine loss leads to insufficient payload support and sagging.

• Loss of suspension rebound: Excessive compression of the series elastic element without

adequate torque recovery capability.

• Reduced controllability and stiffness: Lower torque generation significantly compro-

mises suspension performance, failing articulation requirements.

Addressing these limitations required a redesign focused on optimizing the suspension sys-

tem to generate a more stable and performative system, evaluating the significant nonlinearities

within the system and the sine loss effects. This combination of effects results in unstable com-

pression of the elastic element as the reactive moment from the gas struts continues to decline and

places a greater compressive force on the SEE. This formed the primary motivation and starting

point for subsequent modeling and suspension design iterations detailed in this manuscript.

2.3 Method

A statics-based approach was employed to quantify and relate the moment contributions

from the suspension components, enabling optimization of an upgraded system that ensures sta-

bility over all swingarm angles and a broad range of payloads. A stable configuration in this

application is defined as a suspension system that does not sag, i.e. does not compress the series-

elastic element in quasi-static scenarios.

By modeling the suspension as a sum of moments in static steady-state scenarios, the col-

lective contributions of each subsystem are examined to evaluate overall system stiffness and

35



Figure 2.7: Spring-damper diagram of final BioBot suspension configuration. Labeled compo-
nents: A) Series-elastic element, B) Linear actuator, C) Dual-rate spring system, D) Swingarm.
Swingarm is at 0°, level with the chassis. Positive direction indicated by arrow around swingarm
pivot.

rebound capability. The modeling process began by defining the three primary suspension sub-

systems:

• Series Elastic Actuator - comprised of A and B in Figure 2.7

• Parallel Spring - component C’s configuration in Figure 2.7

• Wheel Forces - applied at the swingarm endpoint

The moment of each subsystem is calculated about the main pivot axis of the suspension,

the rotational pin joint at the swingarm base as indicated in Figure 2.7.

36



Figure 2.7 shows a spring-damper model diagram of the VERTEX suspension system in

its final configuration. Initially, as mentioned before, the suspension employed two 250 lb gas

struts instead of the dual-rate spring damper (component C) as shown in Figure 2.4. The system

modeling, analysis, and optimization presented in this publication identified this replacement as

the best configuration to resolve the issues presented in section 2.2.2. The specific details behind

the model, configuration considerations, and optimization criteria are discussed in the following

sections.

2.3.1 Series Elastic Actuator

The Series Elastic Actuator (SEA) consists of a Progressive Automation PA-17 8-inch lin-

ear actuator, which can provide up to 2000 lbf, and a spring-damper that compresses above 550

lbf. Since the series-elastic element is not rated for tension loads, two retention systems were

implemented to minimize tension in the suspension. Figure 2.8 illustrates these: a yellow circum-

ferential retention strap serves as the primary restraint, and a secondary mechanism of rubberized

hard stops plus plate steel housing serves as a backup.

These elements are joined by a fulcrum with unequal moment arms on each side, allow-

ing the actuator force to be partially reduced before reaching the series-elastic element. Some

sine loss occurs at each interface with the fulcrum axes, enabling a compact layout. In the as-

built mechanism, the series-elastic spring dampers extend between the front and rear halves of

the vehicle. To reduce the system’s footprint, they are offset slightly outside the plane of main

suspension travel, as can be seen in Figure 2.8 with the series-elastic elements forming an ’X’.

The moment contribution of the SEA is modeled at its maximum value for any given angle

37



Figure 2.8: Series elastic actuator side profile, with force path from elastic element to swingarm
illustrated including sine loss angles and fulcrum lever arms at an example swingarm angle.
Retention mechanisms to resist tension loading additionally present.

38



of the swingarm. This key assumption creates an effective method for predicting if a suspension

configuration will remain stable (i.e. the series elastic element remains uncompressed) and con-

trollable in any given quasi-static scenario. The maximum contribution from the SEA subsystem

can be defined as follows:

MSEA =
FSEE cos(α1) ∗ lSEE

lLA cos(α2)
cos(α3) ∗ lBL

(2.1)

where FSEE depends on the specific spring-damper selected for the elastic element within

SEA. lBL
is defined as the length down the swingarm the linear actuator is mounted as shown in

Figure 2.21.

The quantity FSEE depends on the characteristics of the selected elastic element. For this

component single-rate (SR) spring dampers are used as a wide variety of commercial components

are available to select from and can be made to fit within the suspension system. The force of SR

dampers is relatively simple to calculate, accounting for a set preload distance the force model is

as shown in equation 2.2. Preload controls the initial deflection of the springs before the damper

experiences deflection, increasing the amount of force required to be applied before it begins to

compress.

FSEE = k1(dpreload + ddeflection) (2.2)

Here dpreload is the amount of preload applied and ddeflection is any compression of the

damper from external forces. ddeflection is 0 for stable quasi-static scenarios.

Figure 2.9 depicts the maximum SEA moment across all swingarm angles for the elastic

element shown in Figure 2.8 with FSEE = 550 lbf under the full contribution assumption.

39



Figure 2.9: Maximum series-elastic actuator moment contribution across all swingarm angles

2.3.1.1 Spring Rate and Preload Impact on Moment

To illustrate how the single-rate spring parameters affect the full-moment contribution of

the series elastic actuator system, Figures 2.10 depict the sensitivity of the torque generated over

the swingarm range across a variety of spring rates and preload values. It should be noted in

Figure 2.10 that all curves presented have a very similar shape to that of the moment presented

in Figure 2.9 but due to the difference in magnitude the lower rate and preload curves appear to

have a more linear shape.

2.3.2 Parallel Spring (PS)

The parallel spring system, whether originally implemented with gas struts or ultimately

replaced by another spring system, reduces the load borne by the SEA. Its moment is defined as:

MPS = FPS ∗ cos(αPS) ∗ lPS (2.3)

40



Figure 2.10: Maximum moment contribution as a function of preload and spring rate in the series-
elastic element.

where αPS is the angle between the force direction of the spring and the lever arm of the

swingarm, analogous to α3 in Figure 2.8. In the first suspension design, the gas struts contributed

a constant FPS of 500 lbf (two 250 lb struts), producing the moment curve as shown in Figure

2.6.

Due to the extended stroke length required for a component placed in a location similar to

gas springs, only one category of consumer-available replacement component was found to be

viable: a dual-rate spring damper. The order of magnitude for the required deflection length is

approximately 14 inches or greater, depending on the final component placement. Stroke lengths

of this magnitude are only found in commercial dampers that include more than one spring, and a

wide variety of dampers were found specifically in the two-spring configuration referred to here

as ”dual-rate” (DR) dampers.

Dual-rate shock absorbers use two different spring rates, commonly referred to as “top” and

“bottom” rates, and feature a customizable crossover point to transition between the combined

41



spring rate and the lower rate. This transition point occurs when the carrier between the two

springs contacts a set of adjustable arresting rings on the damper body, not allowing the top

spring to deflect any further.

2.3.2.1 Dual-Rate Spring Mechanics

The force of the dual rate springs can be modeled as a piecewise function as shown in

Equation 2.4, depending on the crossover settings and the deflection of the damper at the current

swingarm state. The damper deflection, ddeflection, can be derived from the kinematic distance

between the damper’s chassis and swingarm mounting points. The variable labels for the preload,

deflection, and crossover distances are shortened to the first letter for brevity (dp - preload dis-

tance, dd - damper displacement, dc - crossover distance, kc - combined spring rate, k2 - lower

spring rate).

FDR =


kc(dp + dd) if dd < dc,

kc(dp + dc) + k2(dd − dc) if dd ≥ dc.

(2.4)

The combined spring rate is defined from the conventional series spring equation kc =

1/( 1
k1

1
k2
). The crossover deflection value needs careful consideration of the arresting mechanism

and shifts by:

∆dcrossover =
dpreload ∗ kc

k2
(2.5)

Due to the preload compression of both springs, the floating spring carrier is repositioned

downwards away from the crossover rings. This distance must be added to any crossover setting

42



initially set to create dc. These equations are ultimately converted into functions of the swingarm

angle θ using the DH parameters. Figure 2.11 highlights the behavior of the dual-rate shock

model, showing deflection as a function of the swingarm angle for each spring and the system

total.

Figure 2.11: Deflection of the integrated dual-rate spring damper with finalized settings.

The force and moment contributions of the dual-rate damper model are shown in Figure

2.12. Note that while the spring force is increasing, the generated moment is decreasing at high

swingarm angles despite the aggressive force slope transition due to the sine loss, highlighting

the nonlinearity challenge.

2.3.2.2 Rates, Preload, and Crossover Moment Impact

To fully characterize the performance envelope of the dual-rate spring damper, one can

examine how variations in preload, crossover distance, and individual spring rates influence the

overall moment contribution. During the optimization process (see Section 2.3.5), these parame-

ters are systematically adjusted to identify configurations that improve stability and load carrying

43



Figure 2.12: Spring force and moment sum of the as-integrated dual-rate spring damper across
swingarm angle

capacity.

Figure 2.13: Sensitivity of the moment curve across a variety of preload (in) settings.

Figure 2.13 illustrates how changes in preload shift the moment curve. Increasing the

preload increases the initial spring force, thus elevating the overall moment profile. Mechani-

cally, higher preload translates the spring carrier downward and away from the crossover point,

delaying the onset of the stiffer spring regime. Consequently, the transition point is shifted to

higher swingarm angles.

44



Figure 2.14: Effect of changing crossover (in) on the dual-rate spring damper moment sum

Figure 2.14 demonstrates the impact of adjusting the crossover distance while keeping the

preload and spring rates constant. The crossover distance determines where the upper spring is

effectively locked out, causing the damper to deflect only the lower spring. As a result, a shorter

crossover distance initiates the higher rate regime sooner, whereas a larger distance extends the

combined spring rate region to higher angles.

Figure 2.15: Bottom spring rate (lbf/in) adjustment effect on dual-rate moment contribution

Figure 2.15 shows how altering the bottom spring rate modifies the final higher-rate portion

45



of the moment curve. In particular, changing the bottom rate also affects ∆dcrossover, influenc-

ing when the crossover event occurs. In many automotive and off-road applications, it is typical

for the lower (bottom) spring rate to exceed the upper (top) rate to provide additional resistance

against bottoming out. However, in the optimization routine of this study, no restriction is im-

posed that would mandate a larger lower rate.

Figure 2.16: Top spring rate (lbf/in) adjustment effect on dual-rate moment contribution

Finally, Figure 2.16 illustrates the effect of varying the top spring rate. Altering this pa-

rameter modifies the combined rate in the region before crossover occurs, thus shifting the pre-

crossover portion of the moment curve. Once the damper transitions beyond the crossover point,

the system behavior converges to the lower spring rate and remains unaffected by changes to the

top rate.

By examining these parameter sweeps, one can identify how preload, crossover distance,

and the individual spring rates interact to produce a range of stiffness behaviors under quasi-static

loading. This insight is helpful in tuning the dual-rate system to manage a variety of payloads or

terrain conditions.

46



2.3.3 Wheel Force Moment

During the initial upgrade analysis phase, the rover was still being designed and constructed

(see Figure 2.4), which required several assumptions about its final swingarm geometry, sprung

mass, and unsprung mass. To accommodate these unknowns, a constant-moment approxima-

tion for ground reaction forces was employed, providing a conservative estimate of the torque

imparted by the wheel-ground interface on the swingarm.

Figure 2.17: CAD drawing depicting the wheel position at maximum extension of the caster
angle adjustment system

Figure 2.17 illustrates the adjustable caster system at its maximum extension, which in-

creases the moment arm for the ground reaction forces acting against the suspension. In this

extended configuration, the reaction force is assumed to act at a distance equal to the nominal

47



length of the swing arm plus a 30% margin. This additional 30% accounts for sloped terrains

and various caster angle settings, providing a conservative buffer to ensure the suspension retains

sufficient capacity under worst-case loading conditions.

Several factors justify this constant-moment approach:

1. The independently articulated suspension described herein can actively level the chassis on

inclines, redistributing loads and aiding in equalizing the forces at each wheel.

2. The focus of this study is primarily on quasi-static scenarios, where transient dynamics

play a lesser role.

3. The 30% margin on swingarm length effectively provides a payload reserve in less extreme

caster settings. If the actual contact patch lies closer than 1.3lswingarm, the system can

tolerate a correspondingly higher ground-reaction force without exceeding design limits.

Subsequent subsystem testing and field tests revealed the caster angle adjustment is often

maintained at its minimum extension (Figure 2.18), where the chassis is at its lowest ride height

with a caster angle (defined as the angle between the steering axis and the ground normal) of

approximately 0°. Consequently, the system rarely approaches the worst-case lever arm for wheel

force, further reinforcing the conservatism of the constant-moment assumption.

To ensure that the final design can accommodate the ultimate vehicle weight and diverse

payload scenarios, the total (sprung + unsprung) mass was varied between 1,800 lbf and 3,600

lbf. This range captures potential payloads and the uncertain mass of late-stage subsystems (e.g.,

electronics, umbilical arm). Although the final rover mass is approximately 2,600 lbf (≈1,180 kg-

Earth), well within this range, the 30% margin at the minimum extension of the caster provides

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Figure 2.18: VERTEX rover during its first field excursion, showing the caster angle adjustment
system is in its minimum angle state.

the capacity for an additional 1,000 lbf payload before approaching the conservative limit of the

model.

Mmass = (1.3lswingarm)(mtotal − n ∗munsprung)/n (2.6)

Equation 2.6 represents the wheel-force moment, where mtotal is the gross vehicle mass,

munsprung is the mass of each wheel assembly, n is the the number of wheels in contact with the

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ground, and lswingarm is the baseline lever arm from the pivot to the tip of the swingarm. The

unsprung mass was estimated early on to be ≈ 250 lbf from the CAD as the unsprung systems

were some of the first to be developed, and this aligns very closely with the final weight of 250±2

lbf measured.

Although operating on fewer than four wheels (n < 4) is not expected for extended inter-

vals, incorporating n into the model provides useful information on load distribution if and when

wheel lift occurs.

Figure 2.19: VERTEX at steady state on flat ground demonstrating a single wheel lift configura-
tion

Figure 2.19 shows the rover without its umbilical-tending manipulator, balanced at rest

on three wheels. Despite the reduced support points, the suspension remains stable, indicating

that the constant-moment assumption of the model - augmented by the 30% margin - provides a

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robust design basis for quasi-static loading scenarios.

2.3.4 Total System Moment

After computing the moment contribution of each subsystem, the overall suspension mo-

ment is obtained by summing these contributions, as shown in Equation 2.7:

MTotal = MSEA +MPS −Mmass (2.7)

The plot of MTotal on the entire travel of the swing arm, as in Figure 2.20, provides key

insights into the quasi-static behavior of the suspension and the design margins.

Figure 2.20: Total moment sum of the suspension model with the 200/400 lb-in rate dual-rate
parallel spring damper integrated.

A primary metric of interest is system stability. Because the series-elastic actuator (SEA)

is modeled as providing its full rated force (Section 2.3.1), any negative value in MTotal indicates

that the SEA would compress under static loading and fail to rebound in equilibrium. Hence,

verifying that MTotal(θ) ≥ 0 for all swingarm angles θ ensures the suspension does not sag and

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remains stable.

Moreover, this approach also quantifies the suspension’s stiffness margin. The amount by

which MTotal exceeds zero at a given angle represents the additional external moment required

to compress the SEA. For example, if the rover traverses an obstacle at speed, the dynamic

load must surpass the quasi-static MTotal to deflect the spring-damper system. A larger positive

margin implies a stiffer response (greater resistance to deflection), while a smaller margin allows

increased compliance under transient loads.

2.3.5 System Optimization

The sum-of-moments model served as the evaluation metric within an optimization scheme

aimed at re-engineering the suspension for enhanced quasi-static stability. The primary objective

of the optimization was to achieve stability across a wide range of rover masses and payload

scenarios while simultaneously minimizing implementation costs and development time. Due to

budget constraints, only one component between the series-elastic element and parallel spring

system was allowed to be modified or replaced at a time. Initially, the linear actuator was also

considered for replacement; however, altering the actuator alone would not address the funda-

mental issue of inadequate spring response tuning and its existing specifications already satisfied

the vehicle’s kinematic requirements across the suspension’s range of motion. Consequently, it

was excluded from further consideration in this analysis. Instead, it was included as a constraint

requiring the suspension configurations to keep the force in the linear actuator beneath its operat-

ing range of ± 2000 lbf. It should be noted that the model and methodology presented are fully

capable of evaluating multiple simultaneous component adjustments and is capable of supporting

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broader and more complex system-level optimization in future work. The available budget was

the driving constraint to limit the number of adjustments.

Figure 2.21: Generalized coordinates used to define component placements in the optimization
scheme. The A, B, C labels correspond to the diagram in Figure 2.7, with the ”U” subscript
corresponding to upper mounting points, and ”L” subscript to lower mounting points. (x, y)
coordinates are measured from the swingarm pivot, and l coordinates are lengths measured down
the swingarm from the same point.

Optimization was performed using a structured grid search method, systematically explor-

ing combinations of component placement and suspension parameters. The initial placements

of the components began from the original suspension configuration, after which the upper and

lower mount positions were incrementally adjusted in a grid-wise pattern. Figure 2.21 illus-

trates the coordinate systems used to define these positional adjustments, with all coordinates

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referenced from the swingarm pivot centerpoint. This point is also the common reference point

for calculating moments within the sus