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Dynamics Simulation of Rovers On Soft Terrain: Modeling and Experimental Validation

Ali Azimi1,2, Daniel Holz2,

, József Kövecses1, Jorge Angeles1, Marek Teichmann2

1 Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, Montreal, Canada

2 CM-Labs Simulations Inc., Montreal, Canada

ISTVS 7th Americas Regional Conference,

Tampa, Florida, USA, November , 2013

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2 Dynamics Simulation of Rovers On Soft Terrain 2 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Purpose of our work:

Developing efficient model(s) for wheel-soil interaction compatible with multibody dynamics simulation environments (e.g. CMLabs’ Vortex)

In this presentation:

Novel framework for implementation of semi-empirical terramechanics models in multibody environments

Experimental verifications

Introduction

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3 Dynamics Simulation of Rovers On Soft Terrain 3 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Semi-empirical Models

Scope: Steady-state operation

Shortcomings: No energy dissipation in vertical motion

Not suitable for transient operations

Undefined slip-ratio for a stationary wheel

At slow speed, abrupt changes to reaction forces stiff system

Common approach in the literature for dynamic simulation: Soil reaction as external forces/moments (explicit force)

Causes problems with undefined slip-ratio for a wheel stationary or at low speed

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4 Dynamics Simulation of Rovers On Soft Terrain 4 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Developed Framework

A semi-empirical model provides normal and shear stress distributions (Bekker, 1956), (Wong and Reece, 1967), (Ishigami et al., 2007).

Summation of stresses gives soil reaction forces/moments

Normal force Fz

A viscoelastic system with variable stiffness and damping coefficients:

Other reactions ( Ft , Rc , and Trr )

By means of kinematic constraints with set-valued force laws, which can form a LCP (linear complementarity problem)

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5 Dynamics Simulation of Rovers On Soft Terrain 5 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Developed Framework (continued…)

Traction force:

Resistance force:

Residual resistance torque:

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6 Dynamics Simulation of Rovers On Soft Terrain 6 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Lateral Force

(shear) (Bulldozing)

Revised lateral force model:

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7 Dynamics Simulation of Rovers On Soft Terrain 7 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

LCP Formulation

Soil reaction as:

Mathematical model of an n-DOF system

can be represented as a Mixed LCP, defined by (details in Azimi 2013):

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8 Dynamics Simulation of Rovers On Soft Terrain 8 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Mobility Prediction of Rovers on Soft Terrain

Analyze wheel—ground overlap: Examine “wheel footprint”

8 D. Holz, A. Azimi, M. Teichmann, J. Kövecses

Contact region is approximated by a (least-squares) plane

Cylinder/plane intersection

Sinkage estimation

Stable simulation

Active vertices are used to determine soil hardening and compaction

Irregular Terrains

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9 Dynamics Simulation of Rovers On Soft Terrain 9 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Mobility Prediction of Rovers on Soft Terrain

Place contact constraints according to cylinder/plane inters.

Constraint are added for Rc, Ft,

Trr, and Fl

9 D. Holz, A. Azimi, M. Teichmann, J. Kövecses

zF

tFlF

cR

Irregular Terrains (continued…)

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10 Dynamics Simulation of Rovers On Soft Terrain 10 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Soil Hardening and Compaction

Active vertices are used in determining soil hardening and compaction

Wheel sinkage

Pre

ssu

re

reloading

unloading

loading

Multi-pass model of Wong is adapted here

Normal stress ( ), as shown:

Shear stress( ): same relation as uncompacted soil:

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11 Dynamics Simulation of Rovers On Soft Terrain 11 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Experimental Verification: Juno Rover

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12 Dynamics Simulation of Rovers On Soft Terrain 12 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Measurements

Juno rover measurements: Load cell: drawbar pull

Total station: rover position

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13 Dynamics Simulation of Rovers On Soft Terrain 13 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Experimental Verification: Juno Rover

Drawbar pull experiments:

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14 Dynamics Simulation of Rovers On Soft Terrain 14 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Experimental Verification: Juno Rover

Drawbar pull experiments with added mass:

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15 Dynamics Simulation of Rovers On Soft Terrain 15 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Juno Experiments: Irregular Terrain

LIDAR Scan

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16 Dynamics Simulation of Rovers On Soft Terrain 16 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Juno Rover Simulation in Vortex

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17 Dynamics Simulation of Rovers On Soft Terrain 17 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Juno Experiments: Irregular Terrain

Motor speed from experiment used as input in simulation

Results from the Wong-Reece-Ishigami model with our framework:

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18 Dynamics Simulation of Rovers On Soft Terrain 18 A. Azimi, D. Holz, J. Kövecses, J. Angeles, M. Teichmann

Conclusions

Developing a framework for implementation of semi-empirical terramechanics models in a multi-body dynamics environment

Computationally efficient: The interaction is modelled via using kinematic constraints with set-valued force laws. With that, the problem was formulated as LCP.

Various forms of semi-empirical Bekker models can be incorporated

Operation on irregular terrain with soil compaction and hardening in a stable way

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Multipass Soil Compaction Model