Control Barrier Function based Energy optimal Obstacles Avoidance for Point-to-Point Maneuvers

This paper focuses on developing a motion planning algorithm for static obstacle avoidance for a kinematic unicycle robot undergoing an energy-optimal point-to-point maneuver. The standard kinematic model is redefined in the geometric center space, motivated by the feedback linearization technique, resulting in a reduced order kinematic model. The proposed optimal motion planning approach is decomposed into two sequential stages: pre-planning and re-planning. In the pre-planning stage, an obstacle-free point-to-point optimal control problem is formulated and solved. Utilizing the solution from the optimal control problem, a perturbation controller is introduced which incorporates the nominal optimal control as a feedforward controller and a feedback tracking controller. In the second stage, the control barrier function method is employed to account for safety requirements, resulting in a minimum intervention control and solved in a point-wise optimization framework that accounts for the obstacles. The safety constraints are used as a quantitative metric to trigger trajectory re-planning, ultimately resulting in a nearly optimal control and trajectory.