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TECHNICAL PAPERS

Velocity and Acceleration Cones for Kinematic and Dynamic Constraints on Omni-Directional Mobile Robots

[+] Author and Article Information
Jianhua Wu

 Ohio University, Department of Mechanical Engineering, 257 Stocker Center, Athens, OH 45701-2979

Robert L. Williams

 Ohio University, Department of Mechanical Engineering, 257 Stocker Center, Athens, OH 45701-2979williar4@ohio.edu

Jae Lew

 Eaton Corporation, Eden Prairie, MN

J. Dyn. Sys., Meas., Control 128(4), 788-799 (Apr 05, 2006) (12 pages) doi:10.1115/1.2361318 History: Received September 24, 2004; Revised April 05, 2006

We consider the problems of kinematic and dynamic constraints, with actuator saturation and wheel slippage avoidance, for motion planning of a holonomic three-wheeled omni-directional robot. That is, the motion planner must not demand more velocity and acceleration at each time instant than the robot can provide. A new coupled non-linear dynamics model is derived. The novel concepts of Velocity and Acceleration Cones are proposed for determining the kinematic and dynamic constraints. The Velocity Cone is based on kinematics; we propose two Acceleration Cones, one for avoiding actuator saturation and the other for avoiding wheel slippage. The wheel slippage Acceleration Cone was found to dominate. In practical motion, all commanded velocities and accelerations from the motion planner must lie within these cones for successful motion. Case studies, simulations, and experimental validations are presented for our dynamic model and controller, plus the Velocity and Acceleration Cones.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Phase VI RoboCup robot (bottom)

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Figure 2

Omni-directional robot geometry

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Figure 3

Simulink diagram for closed-loop trajectory following

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Figure 4

Wheel velocity inner control loop

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Figure 5

Simulated circular motion

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Figure 6

Experimental circular motion

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Figure 7

Linear transformation to determine the space of Ẋm

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Figure 8

Velocity cone top and side views

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Figure 9

(a) Wheel angular velocity space and (b) robot velocity space

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Figure 10

(a) Top view and (b) side view, robot velocity space

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Figure 11

Determining the space of Ẍm by linear transformation

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Figure 12

(a) Input voltage space and (b) dynamics acceleration space

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Figure 13

(a) Top view and (b) side view, dynamics acceleration space

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Figure 14

(a) Traction force space and (b) no slippage acceleration space

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Figure 15

(a) Top view and (b) side view, no slippage acceleration space

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Figure 16

Path planning with initial/final positions/velocities

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Figure 17

(a) Simulated speed and (b) simulated acceleration norm

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Figure 18

(a) Experiment Case 1 and (b) experiment Case 2 and (c) experiment Case 3

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