RMPD - A Recursive Mid-Point Displacement Algorithm for Path Planning

Motivated by what is required for real-time path planning, the paper starts out by presenting RMPD, a new recursive “local” planner founded on the key notion that, unless made necessary by an obstacle, there must be no deviation from the shortest path between any two points, which would normally be a straight line path in the configuration space. Subsequently, we increase the power of RMPD by introducing the notion of cost-awareness into the algorithm to improve the path quality – this is done by associating obstacle and smoothness costs with the currently selected path points and factoring those costs in choosing the best points for the next iteration. In this manner, the overall strategy in the cost-aware form of RMPD, cRMPD, combines the computational efficiency made possible by the recursive RMPD planner with the cost efficacy of a stochastic trajectory optimizer to rapidly produce high-quality local collision-free paths. Based on the test cases we have run, our experiments show that cRMPD can reduce planning time by up to two orders of magnitude as compared to RRT-Connect, while still maintaining a path length optimality equivalent to that of RRT*.