Asymptotic Stabilization of Nonholonomic Robots Leveraging Singularity

Due to the nonholonomic constraints as well as the constraints on torque and power resources, it is challenging to design a controller to asymptotically stabilize a nonholonomic robot at a predefined pose. In this paper, a switched controller is introduced for the asymptotic stabilization of nonholonomic robots using singularity, which is deemed undesirable due to loss of controllability. The proposed controller is inspired by a new insight on the singularity set of the nonholonomic robot, i.e., the singularity set includes a subset that can be asymptotically stabilized. The proposed controller is applicable to chained form systems that make an important class of drift-less nonholonomic systems, especially for those robots with a differential-drive mechanism. Considering its simplicity and efficiency, our method has the potential to be used in practice.