Exponential stabilization problem of nonholonomic chained systems with specified transient response

In this paper, we propose a control method for nonholonomic systems expressed by the chained form, where the exponential convergence to the desired final state is guaranteed and the desired transient response is achieved simultaneously. Next, we propose a trajectory generation method for the chained system, which gives a systematic procedure to find a reference trajectory that passes several given points at each specified time and exponentially converges to the origin. Finally, our method is applied to control of a 4-wheeled car. In this case, to express all the state of the 4-wheeled car by the chained form, the above method is extended to the case where several coordinate frames are needed