Control of uncertain nonholonomic mechanical systems with chained form kinematics: case study

We employ two adaptive strategies for motion control of uncertain nonholonomic mechanical systems with chained form kinematics. Chained form systems possess sufficient structure to permit very effective control strategies to be developed for them. For example, these systems are differentially flat, which can be shown to be quite useful for motion control, and they are also easier to stabilize than some other classes of nonholonomic systems; both of these properties are exploited in the paper. As a consequence of the adaptive nature of the control laws and the properties of chained form systems, the employed schemes are simple and modular, are easily implemented with a wide range of mechanical systems, and provide a reasonable starting point for addressing such practical problems as collision avoidance and sensor-based planning and control. The first controller combines an efficient trajectory generation algorithm with an adaptive tracking strategy to obtain the desired motion control, while the second scheme achieves this control objective through the use of a stabilizing control law developed utilizing adaptation and homogeneous system theory. Each of the control strategies is computationally efficient, ensures accurate motion control, and is implementable in the presence of considerable uncertainty concerning the mechanical system model. The efficacy of the approach is illustrated through computer simulations with a single chain nonholonomic system.