Research Papers

A Multibody Dynamics Framework for Simulation of Rovers on Soft Terrain

[+] Author and Article Information
Ali Azimi

CM Labs Simulations, Inc.,
645 Wellington Street, Suite 301,
Montreal, QC H3C1T2, Canada
e-mail: ali.azimi@cm-labs.com

Daniel Holz

CM Labs Simulations, Inc.,
645 Wellington Street, Suite 301,
Montreal, QC H3C1T2, Canada
e-mail: daniel.holz@cm-labs.com

Jozsef Kövecses

Department of Mechanical Engineering,
McGill University,
Montreal, QC H3A0C3, Canada
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A2A7, Canada
e-mail: jozsef.kovecses@mcgill.ca

Jorge Angeles

Fellow ASME
Department of Mechanical Engineering,
McGill University,
Montreal, QC H3A0C3, Canada
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A2A7, Canada
e-mail: angeles@cim.mcgill.ca

Marek Teichmann

CM Labs Simulations, Inc.,
645 Wellington Street, Suite 301,
Montreal, QC H3C1T2, Canada
e-mail: marek@cm-labs.com

Vortex allows for changes of the stiffness and damping coefficients of any contact point at every simulation step.

Equation (24) needs special treatment: if βs → 90 deg, jy, which in turn means that the shear stress becomes equal to the shear strength, as the exponentially decaying term in Eq. (23) becomes zero. In our implementation in Vortex, βs is limited to a value slightly smaller than 90 deg to avoid any singularities.

The other cases, summation of angles equal to zero or 360 deg, do not have a physical meaning.

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 30, 2014; final manuscript received December 16, 2014; published online February 11, 2015. Assoc. Editor: Rudranarayan Mukherjee.

J. Comput. Nonlinear Dynam 10(3), 031004 (May 01, 2015) (12 pages) Paper No: CND-14-1084; doi: 10.1115/1.4029406 History: Received March 30, 2014; Revised December 16, 2014; Online February 11, 2015

A new framework is developed for efficient implementation of semi-empirical terramechanics models in multibody dynamics environments. In this approach, for every wheel in contact with soft soil, unilateral contact constraints are added for both the normal direction and the tangent plane. The forces associated with the latter, like traction and rolling resistance, are formulated in this approach as set-valued force laws, their properties being determined by deregularization of the terramechanics relations. As shown in the paper, this leads to the dynamics representation in the form of a linear complementarity problem (LCP). With this formulation, stable simulation of rovers is achieved even at relatively large time steps. In addition, a high-resolution height-field (HF) is employed to model terrain-surface deformation and changes in hardening of soil under the wheel. As a result, the multipass effect is captured in the presented approach. In addition, an extensive set of experiments was conducted using a version of the Juno rover (Juno II). The experimental results are analyzed and compared with the model developed in the paper.

Copyright © 2015 by ASME
Topics: Simulation , Soil , Wheels
Your Session has timed out. Please sign back in to continue.


Bekker, M. G., 1956, Theory of Land Locomotion, The University of Michigan Press, Ann Arbor, MI.
Bekker, M. G., 1969, Introduction to Terrain-Vehicle Systems, The University of Michigan Press, Ann Arbor, MI.
Wong, J. Y., and Reece, A. R., 1967, “Prediction of Rigid Wheel Performance Based on the Analysis of Soil-Wheel Stresses Part I: Performance of Driven Rigid Wheels,” J. Terramechanics, 4(1), pp. 81–98. [CrossRef]
Azimi, A., Hirschkorn, M., Ghotbi, B., Kövecses, J., Angeles, J., Radziszewski, P., Teichmann, M., Courchesne, M., and Gonthier, Y., 2011, “Terrain Modelling in Simulation-Based Performance Evaluation of Rovers,” Can. Aeronaut. Space J., 57(1), pp. 24–33. [CrossRef]
Azimi, A., Holz, D., Kövecses, J., Angeles, J., and Teichmann, M., 2012, “Efficient Dynamics Modeling for Rover Simulation on Soft Terrain,” AIAA Paper No. 2012-804. [CrossRef]
Schmid, I. C., 1995, “Interaction of Vehicle and Terrain Results From 10 Years Research at IKK,” J. Terramechanics, 32(1), pp. 3–26. [CrossRef]
Janosi, Z., and Hanamoto, B., 1961, “Analytical Determination of Drawbar Pull as a Function of Slip for Tracked Vehicles in Deformable Soils,” First International Conference on Terrain-Vehicle Systems, Turin, Italy.
AESCO, 2005, Matlab/Simulink Module AS2TM User's Guide, Version 1.12, AESCO GbR, Hamburg, Germany.
Bauer, R., Leung, W., and Barfoot, T., 2005, “Development of a Dynamic Simulation Tool for the Exomars Rover,” 8th International Symposium on Artificial Intelligence, Robotics and Automation in Space, iSAIRAS, Munich, Germany.
Ishigami, G., Miwa, A., Nagatani, K., and Yoshida, K., 2007, “Terramechanics-Based Model for Steering Maneuver of Planetary Exploration Rovers on Loose Soil,” J. Field Rob., 24(3), pp. 233–250. [CrossRef]
Ding, L., Nagatani, K., Sato, K., Mora, A., Yoshida, K., Gao, H., and Deng, Z., 2010, “Terramechanics-Based High-Fidelity Dynamics Simulation for Wheeled Mobile Robot on Deformable Rough Terrain,” IEEE International Conference on Robotics and Automation, Anchorage, AK, May 3–7, pp. 4922–4927. [CrossRef]
Ding, L., Gao, H., Deng, Z., and Tao, J., 2010, “Wheel Slip-Sinkage and Its Prediction Model of Lunar Rover,” J. Cent. South Univ. Technol., 17(1), pp. 129–135. [CrossRef]
Schafer, B., Gibbesch, A., Krenn, R., and Rebele, B., 2010, “Planetary Rover Mobility Simulation on Soft and Uneven Terrain,” Veh. Syst. Dyn.: Int. J. Veh. Mech. Mobility, 48(1), pp. 149–169. [CrossRef]
Trease, B., Arvidson, R., Lindemann, R., Bennett, K., Zhou, F., Iagnemma, K., Senatore, C., and Dyke, L. V., 2011, “Dynamic Modeling and Soil Mechanics for Path Planning of the Mars Exploration Rovers,” ASME Paper No. DETC2011-47896. [CrossRef]
Petersen, W., 2012, “A Volumetric Contact Model for Planetary Rover Wheel/Soil Interaction,” Ph.D. thesis, University of Waterloo, Waterloo, ON, Canada.
Azimi, A., Kövecses, J., and Angeles, J., 2013, “Wheel-Soil Interaction Model for Rover Simulation and Analysis Using Elastoplasticity Theory,” IEEE Trans. Rob., 29(5), pp. 1271–1288. [CrossRef]
Azimi, A., Kövecses, J., and Angeles, J., 2011, “Wheel-Soil Interaction Model for Rover Simulation Based on Plasticity Theory,” IEEE/RSJ International Conference Intelligent Robots and Systems (IROS), San Francisco, CA, Sept. 25–30, pp. 280–285. [CrossRef]
Azimi, A., 2013, “Wheel-Soil Interaction Modelling for Rover Simulation and Analysis,” Ph.D. thesis, McGill University, Montréal, QC, Canada.
Pfeiffer, F., 2007, “Deregularization of a Smooth System—Example Hydraulics,” Nonlinear Dyn., 47(1–3), pp. 219–233. [CrossRef]
Wong, J. Y., 2010, Terramechanics and Off-Road Vehicle Engineering: Terrain Behaviour, Off-Road Vehicle Performance and Design, 2nd ed., Elsevier, Oxford.
Anitescu, M., and Potra, F. A., 1997, “Formulating Dynamic Multi-Rigid-Body Contact Problems With Friction as Solvable Linear Complementarity Problems,” Nonlinear Dyn., 14(3), pp. 231–247. [CrossRef]
Schwanghart, H., 1968, “Lateral Forces on Steered Tyres in Loose Soil,” J. Terramechanics, 5(1), pp. 9–29. [CrossRef]
Yoshida, K., and Ishigami, G., 2004, “Steering Characteristics of a Rigid Wheel for Exploration on Loose Soil,” IEEE/RSJ International Conference Intelligent Robots and Systems (IROS), Sendai, Japan, Sept. 28–Oct. 2, pp. 3995–4000. [CrossRef]
Reece, A. R., 1964, “The Fundamental Equation of Earth-Moving Mechanics,” Proc. Inst. Mech. Eng., 179(6), pp. 16–22. [CrossRef]
McKyes, E., 1985, Soil Cutting and Tillage, Elsevier, Oxford.
Wong, J. Y., 2008, Theory of Ground Vehicles, 4th ed., Wiley, Hoboken, NJ.
Ding, Y., Gravish, N., and Goldman, D. I., 2011, “Drag Induced Lift in Granular Media,” Phys. Rev. Lett., 106(2), p. 028001. [CrossRef] [PubMed]
Stewart, D. E., 2000, “Rigid-Body Dynamics With Friction and Impact,” SIAM Rev., 42(1), pp. 3–39. [CrossRef]
Acary, V., and Brogliato, B., 2008, Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics (Lecture Notes in Applied and Computational Mechanics, Vol. 35), Springer, Berlin.
Visscher, P., and Reid, E., 2012, “Continued Development of Juno Rover,” AIAA Paper No. 2012-632. [CrossRef]


Grahic Jump Location
Fig. 1

Normal stress distribution under a rigid wheel moving on an uncompacted soil as proposed by the WRI model

Grahic Jump Location
Fig. 2

Schematic of wheel and soil contact in the planar case. (a) Original soil reaction representation and (b) equivalent soil reaction representation.

Grahic Jump Location
Fig. 3

Forces acting on the soil wedge

Grahic Jump Location
Fig. 4

Schematic illustration of determination of bulldozing force via integration over the submerged portion of the wheel sidewall

Grahic Jump Location
Fig. 5

Illustration of contact points between a rolling cylindrical wheel and a planar terrain

Grahic Jump Location
Fig. 6

Schematic of HF/wheel interaction and the approximating least-squares plane

Grahic Jump Location
Fig. 7

Schematic of unloading/reloading model of Wong used to find normal stress distribution with multipass

Grahic Jump Location
Fig. 9

An image from the simulation of Juno in Vortex

Grahic Jump Location
Fig. 10

Comparing the drawbar pull obtained from experiments with the values obtained from simulation

Grahic Jump Location
Fig. 11

Comparing the driving torque of the right side motor obtained from experiments with the values obtained from simulation

Grahic Jump Location
Fig. 12

The HF terrain produced using the LIDAR scan data, with the initial rover location

Grahic Jump Location
Fig. 13

The global position of the reflector, attached to the rover

Grahic Jump Location
Fig. 14

The energy expenditure of the right side motor

Grahic Jump Location
Fig. 15

The driving torque of the right side motor

Grahic Jump Location
Fig. 16

The computation time involved in every simulation time step. The total computation time is divided into the time required for the collision detection algorithm and integration of the mathematical model.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In