Title: HyRRT-Connect: A Bidirectional Rapidly-Exploring Random Trees Motion Planning Algorithm for Hybrid Systems

Abstract: This paper proposes a bidirectional rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. The proposed algorithm, called HyRRT-Connect, propagates in both forward and backward directions in hybrid time until an overlap between the forward and backward propagation results is detected. Then, HyRRT-Connect constructs a motion plan through the reversal and concatenation of functions defined on hybrid time domains, ensuring the motion plan thoroughly satisfies the given hybrid dynamics. To address the potential discontinuity along the flow caused by tolerating some distance between the forward and backward partial motion plans, we reconstruct the backward partial motion plan by a forward-in-hybrid-time simulation from the final state of the forward partial motion plan. By applying the reversed input of the backward partial motion plan, the reconstruction process effectively eliminates the discontinuity and ensures that as the tolerance distance decreases to zero, the distance between the endpoint of the reconstructed motion plan and the final state set approaches zero. The proposed algorithm is applied to an actuated bouncing ball example and a walking robot example so as to highlight its generality and computational improvement.