Pose Control With an Input-to-state Safe Control Barrier Function for Rigid Body Motion

Abstract

In this paper, we present a pose control method for rigid body motion via an input-to-state safe control barrier function (ISSf-CBF). The control objective is that a mobile robot converges to the desired pose with avoiding any obstacles under input disturbances. First, we derive a control error system to discuss stability via the Lyapunov method. Through the kinematic model for a rigid body, we design an ISSf-CBF for obstacle avoidance under input disturbances. Next, we present a control Lyapunov function (CLF) for the control error system. By using the ISSf-CBF and the CLF, we discuss a unified quadratic program formulation that ensures both safety and stability for pose control of rigid body motion under input disturbances. Our proposed approach, which deals with both the position and the orientation of rigid body motion, connects the safety and the stability via the ISSf-CBF and the CLF. Finally, simulation and experimental results confirm the validity of the proposed ISSf-CBF control method compared to the stabilizing one.