Abstract-Sampling-based algorithms such as the Rapidlyexploring Random Tree (RRT) have been recently proposed as an effective approach to computationally hard motion planning problem. However, while the RRT algorithm is known to be able to find a feasible solution quickly, there are no guarantees on the quality of such solution, e.g., with respect to a given cost functional. To address this limitation, the authors recently proposed a new algorithm, called RRT * , which ensures asymptotic optimality, i.e., almost sure convergence of the solution returned by the algorithm to an optimal solution, while maintaining the same properties of the standard RRT algorithm, both in terms of computation of feasible solutions, and of computational complexity. In this paper, the RRT * algorithm is extended to deal with differential constraints. A sufficient condition for asymptotic optimality is provided. It is shown that the RRT * algorithm equipped with any local steering procedure that satisfies this condition converges to an optimal solution almost surely. In particular, simple local steering procedures are provided for a Dubins' vehicle as well as a double integrator. Simulation examples are also provided for these systems comparing the RRT and the RRT * algorithms.
In REF , sufficient conditions were established to ensure asymptotic optimality of the RRT* algorithm for systems with differential constraints, and it was shown how to apply RRT* to two specific instances of kinodynamic systems: the Dubin's car and the double integrator.
Optimal kinodynamic motion planning using incremental sampling-based methods
49th IEEE Conference on Decision and Control (CDC)
49th IEEE Conference on Decision and Control (CDC)
Computer Science