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This paper proposes a stable sparse rapidly-exploring random trees (SST)algorithm to solve the optimal motion planning problem for hybrid systems. Ateach iteration, the proposed algorithm, called HySST, selects a vertex with thelowest cost among all the vertices within the neighborhood of a randomlyselected sample and then extends the search tree by flow or jump, which is alsochosen randomly when both regimes are possible. In addition, HySST maintains astatic set of witness points such that all the vertices within the neighborhoodof each witness are pruned except the vertex with the lowest cost. Through adefinition of concatenation of functions defined on hybrid time domains, weshow that HySST is asymptotically near optimal, namely, the probability offailing to find a motion plan such that its cost is close to the optimal costapproaches zero as the number of iterations of the algorithm increases toinfinity. This property is guaranteed under mild conditions on the datadefining the motion plan, which include a relaxation of the usual positiveclearance assumption imposed in the literature of classical systems. Theproposed algorithm is applied to an actuated bouncing ball system and acollision-resilient tensegrity multicopter system so as to highlight itsgenerality and computational features.

HySST: A Stable Sparse Rapidly-Exploring Random Trees Optimal Motion Planning Algorithm for Hybrid Dynamical Systems