Constrained Motion Planning of Nonholonomic Systems Mariusz Janiak and Krzysztof Tcho ´ n 1 Institute of Computer Engineering, Control and Robotics Wroclaw University of Technology ul. Janiszewskiego 11/17, 50–372 Wroclaw, Poland email: mariusz.janiak|krzysztof.tchon@pwr.wroc.pl Abstract This paper addresses the constrained motion planning problem for nonholonomic sys- tems represented by driftless control systems with output. The problem consists in defining a control function driving the system output to a desirable point at a given time instant, whereas state and control variables remain over the control horizon within prescribed bounds. The state and control constraints are handled by extending the con- trol system with a pair of state equations driven by the violation of constraints, and adding regularizing perturbations. For the regularized system a Jacobian motion plan- ning algorithm is designed, called imbalanced. Solution of example constrained motion planning problem for the rolling ball illustrates theoretical concepts. Key words: Nonholonomic system, motion planning, constraints, Jacobian algorithm 1. Introduction A mechanical system whose motion is subject to non-integrable position and ve- locity constraints is called nonholonomic. When the constraints assume the Pfaffian form, the nonholonomic system gets represented by a smooth driftless control system. A dependence of external variables of the system on state variables is described by an output function. Examples of nonholonomic systems are robotic systems, like wheeled mobile platforms or certain systems of dexterous manipulation. 1 The corresponding author, tel. 48 (071) 3203271, fax: 48 (071) 3212677 1