Switched Modeling and Task–Priority Motion Planning of Wheeled Mobile Robots Subject to Slipping

This study is devoted to the modelling and control of Wheeled Mobile Robots moving with longitudinal and lateral slips of all wheels. Due to wheel slippage we have to deal with systems with changing dynamics. Wheeled Mobile Robots can be thus modeled as switched systems with both autonomous switches (due to wheel slippage) and smooth controls (due to control algorithm). It is assumed that the slipping is counteracted by the slip reaction forces acting at contact points of the wheels with the ground. A model of these reaction forces, borrowed from the theory of automotive systems, has been adopted and included into the Lagrangian dynamic equations of the robot. A framework for designing motion planning schemes devoid of chattering effects for systems with changing dynamics is presented. A task–priority motion planning problem for wheeled mobile robots subject to slipping is addressed and solved by means of Jacobian motion planning algorithm based on the Endogenous Configuration Space Approach. Performance of the algorithm is presented in simulations of the Pioneer 2DX mobile platform. The robot dynamics equations are derived and 4 variants of motion are distinguished. The motion planning problem is composed of two sub-tasks: robot has to reach a desired point in the task space (proper motion planning) and the motion should minimize either the control energy expendinture or the wheel slippage. Performance of the motion planning algorithm is illustrated by a sort of the parking maneuver problem.

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