Extended Chained Forms and Their Application to Nonholonomic Kinematic Systems with Affine Constraints: Control of a Coin on a Rotating Table

This paper proposes a transformation method from a class of asymmetric affine control systems into extended chained forms and considers their application to control of non-holonomic kinematic systems with affine constraints (NKSAC). Firstly, we give problem setting and an assumption for a class of asymmetric affine control systems. Then, a transformation into extended chained forms is derived. We next consider control of a coin on a rotating which is a physical example of the NKSAC and introduce a control algorithm for the system by using the extended chained form. Finally, some simulation results of the system are shown to confirm the effectiveness of our research