Error Function Based Kinematic Control Design for Nonholonomic Mechanical Systems
Tracking or following a trajectory at a kinematic level is the most common approach to control nonholonomic systems. The classical feedback approaches may be either local or global. The local approach to feedback control is achieved through the standard linear control design. Convergence is obtained provided that a system, e.g. a vehicle, starts its motion sufficiently close to a desired trajectory. In the global approach, feedback linearization is pursued and it provides asymptotic stability of tracking errors for arbitrary initial states. Both static and dynamic nonlinear feedback linearization may be used in this approach. In this classical kinematic control design using feedback linearization, some additional properties of kinematic models are used. The first property is the chained-form representation. Transformation of the kinematic control model to the chained form simplifies the control design and provides a framework for the direct extension of the controller to vehicles with more complex kinematics [1, 2]. However, this transformation is not strictly necessary. The second property is that the kinematic control model of a system is Chaplygin. Most theoretic control results at the kinematic level are developed for Chaplygin systems; most of them fail for non-Chaplygin systems, which are recognized as systems hard to control .
Feedback linearization enables obtaining full-state or input-output linearization. In the latter method an internal dynamics may be left and stability of the internal dynamics must be analyzed separately. Using either linearization, a controller has to be selected in such a way that it provides some kind of the tracking error convergence.
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