Improving the Performance of Mobile Robots on Uneven Terrain

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Improving the Performance of Mobile Robots on
Uneven Terrain

• Joseph Auchter
• Dr. Carl Moore
• FAMU/FSU College of Engineering
• 9 October 2007

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Wheeled Mobile Robots

• Increasing interest in autonomous robots
  operating outdoors on difficult terrains

GDRS XUV
NASA Spirit Rover
CMU McArthur
GDRS TAC-C
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Wheel Slip for Outdoor Robots

• All wheeled vehicles will slip on uneven terrain
• Two kinds of wheel slip
• Dynamic due to insufficient friction, terrain
  deformation, etc
• Kinematic due to lack of an instantaneous center
  of rotation compatible with all wheels

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Why Slip Occurs on Uneven Terrain

• Example Ideal Ackermann Steering

Wheel / Ground Contact Points
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Why Slip Occurs on Uneven Terrain

• Ackermann Steering on Uneven Terrain

Wheel / Ground contact point locations vary
because of uneven ground
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Problems Caused by Wheel Slip

• Decreased localization ability due to odometric
  (wheel encoder) error accumulating without bound
• Power wastage
• Reduced traction, terrain traversibility

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Wheel Slip Example
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Effects of Wheel Slip Example

• Huntsberger, et al (2002) long-range rover
  autonomy
• Application to NASAs Spirit and Opportunity Mars
  rovers
• Found 15 error in odometry over test run
• Reported wheel slip resulting in increased power
  consumption

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The Proposed Solution

• Concept by N. Chakraborty and Dr. A. Ghosal at
  the Indian Institute of Science (2003)
• Passive Variable Camber (PVC) Lateral tilting of
  wheels allows the robot to move on uneven terrain
  without kinematic slip

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Research Hypotheses

• PVC will significantly reduce kinematic slipping
  on uneven terrain
• PVC will allow the wheel or tire to maintain
  better contact with the ground, improving
  traction and reducing dynamic slip
• PVC will reduce power consumption

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Kinematic Simulation of a WMR

• Uneven terrain
• Robot equipped with Passive Variable Camber (PVC)
  joints
• Traditional robot modeling is inadequate
• Need a new, precise way to simulate wheels
  rolling over uneven ground

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Analogy Between WMRs and Robot Hands
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Simulation Concept

• Apply dextrous manipulator modeling techniques to
  a wheeled mobile robot system
• Allows us to precisely simulate the motion of the
  wheels on an uneven terrain

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3-Wheeled Mobile Robot Model

• Front wheel is steered
• Rear two wheels have Passive Variable Camber
  (PVC) joints
• Robot moves on uneven terrain

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System Model

• The following ODEs describe the system

Rolling contact non-holonomic
constraints
Differentiated closure constraints
Input velocities consistent with constraints
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Robot Joint Velocities
Robot Joint Velocities
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Surface Parameterizations
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Contact Variables

• Contact variables for one wheel
• Grouped for all wheels
• Velocities of the wheel relative to the ground

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Rolling Contact Equations

• and Vc are related by Montanas1 equations of
  contact

• We abbreviate this by

1 Montana, D. 1988. The Kinematics of Contact
and Grasp. The International Journal of Robotics
Research, Vol.7, No. 3, 17-32.
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Rolling Contact Equations
Contact point on wheel
Contact point on ground

• CK relates the wheel velocity to the motion of
  the contact point on the wheel and ground
  surfaces.

1 Montana, D. 1988. The Kinematics of Contact
and Grasp. The International Journal of Robotics
Research, Vol.7, No. 3, 17-32.
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Closure Constraints

• Robot / ground system is a hybrid series /
  parallel mechanism.
• There are three serial kinematic chains in
  parallel
• Closure constraints each chain of coordinate
  transformations must end in the same frame (P
  in this case)

Chain 1
Chain 2
Chain 3
Purple intermediate frame
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Closure Constraints

• The closure constraints can be written in the
  form

• Group the configuration variables together as

• Differentiate the constraints to make ODEs

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Velocity Relationships

• Following Han2

Platform velocities
Wheel velocities

• Constraint equation originally developed for
  modeling dextrous robotic manipulators

2 Han, L., Trinkle, J.C., and Li, Z.X. 1997.
The Instantaneous Kinematics and Planning of
Dextrous Manipulation. Proc. 1997 IEEE Intl.
Symp. on Assembly and Task Planning, pp. 60-65.
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Velocity Relationships
Platform and wheel velocities
Joint velocities

• Want to choose input velocities which are
  consistent with these constraints.

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Velocity Relationships

• We want

• Start with the velocity constraints

• After some manipulation, we can write

Desired input velocities
Input velocities consistent with the constraints
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System Model

• The following ODEs describe the system

Rolling contact non-holonomic
constraints
Differentiated closure constraints
Input velocities consistent with constraints
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Kinematic Simulation Results
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Kinematic Simulation Results
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Simulation Results (Hill Climbing)
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Simulation Results (Hill Climbing)
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Simulation Results (Random Terrain)
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Simulation Results (Random Terrain)
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Simulation Results (Random Terrain)
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Next Steps

• Path planning for the robotic system using the
  kinematic model
• Design and construct experimental test-bed
• Show that a wheel with Passive Variable Camber
  can roll over an uneven terrain without kinematic
  slip
• Investigate effects of PVC on power consumption
  and dynamic slip