ON THE REDUCTION AND CONTROL FOR A CLASS OF NONHOLONOMIC UNDERACTUATED SYSTEMS

Faïçal Mnif

   This paper addresses the reduction and control of underactuated mechanical systems with first order nonholonomic constraints and kinetic symmetry. It is shown that this class of system can be reduced to a well-defined reduced order Lagrangian system in Cascade with the constraint equation. Depending on whether the number of control inputs and constraint equations is less or equal to the number of configuration variables, the reduced Lagrangian system is fully actuated or underactuated, respectively. The problem of quasi-exponential stabilization for this class of nonholonomic underactuated mechanical systems is also addressed is this paper using discontinuous control of the chained-form systems. The enclosed simulation made for a car-like vehicle model shows the effectiveness of the method.

Keywords: Underactuated, Nonholonomic, Stabilization, Mobile Robots

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