Optimal Encirclement Control Along Arbitrary Orbits for Vehicles Considering Safety Constraints: A Safe Learning Approach

This paper studies the optimal encirclement problem for autonomous vehicles along arbitrary patterns subject to safety constraints (i.e., avoidance region). A learning-based safe optimal encircling control scheme is proposed to steer vehicles to pursue the target within arbitrary shapes while minimizing the cost and avoiding obstacles. Specifically, an encirclement orbit generator is explored to produce user-specified reference paths centered on targets, rendering the optimal circling problem converted to an optimal tracking issue with additional safety constraints. Furthermore, by mathematically describing the obstacles as control barrier functions (CBFs), a new Hamilton-Jacobi-Bellman (HJB) equation with CBF constraints is constructed, and then a crucial safety declaration is incorporated into the reinforcement learning (RL) strategy to assure safety. Afterward, an improved critic-only approximator is tailored to synthesize the control policy, in which a novel finite-time learning rule formulated by parametric adaptation with guaranteed convergence is developed via setting the auxiliary variables. Compared with the prevailing enclosing alternatives forming an ordinary circular or elliptical path, the proposed approach can not only deliver an arbitrarily user-defined encirclement pattern but also endow an optimum encircling performance without violating safety constraints via online safe learning. Finally, simulations verify the feasibility and superiority of the suggested algorithm.