Asymptotically Near-Optimal Motion Planning using Lower Bounds on Cost

Asymptotically-optimal sampling-based motion-planning algorithms often, from a certain stage of their execution, invest huge computational resources at only slightly improving the cost of of the current best existing solution. We aim to overcome this problem by (i) carefully using lower bounds on the cost between configurations and by (ii) relaxing asymptotic optimality to asymptotic near-optimality. We present Motion Planning using Lower Bounds (MPLB), an anytime asymptotic near-optimal algorithm, based on the Fast Marching Trees (FMT*) algorithm. An advantageous by-product of our approach is that we can reach situations where the weight of collision detection is almost negligible with respect to nearest-neighbor calls; this is in the spirit of recent suggestion by Bialkowski et al. We prove that MPLB performs no more collision-detection calls than an anytime version of FMT* (called aFMT*) and bound the additional number of nearest-neighbor calls for a family of configuration spaces. We show experimentally that for certain scenarios, MPLB produces paths of lower cost faster than aFMT*, while spending less than 20% of its time on collision detection.