db-A*: Discontinuity-bounded Search for Kinodynamic Mobile Robot Motion Planning

TL;DR

This paper introduces db-A* and kMP-db-A*, innovative kinodynamic motion planning algorithms that combine graph search with optimization, enabling efficient near-optimal solutions for various mobile robots.

Contribution

It presents a novel discontinuity-bounded A* algorithm and a kinodynamic planner that integrate sampling-based trajectories with optimization, improving solution quality and speed.

Findings

kMP-db-A* solves more problems than baselines.

It finds lower-cost initial solutions.

It converges faster to near-optimal solutions.

Abstract

We consider time-optimal motion planning for dynamical systems that are translation-invariant, a property that holds for many mobile robots, such as differential-drives, cars, airplanes, and multirotors. Our key insight is that we can extend graph-search algorithms to the continuous case when used symbiotically with optimization. For the graph search, we introduce discontinuity-bounded A* (db-A*), a generalization of the A* algorithm that uses concepts and data structures from sampling-based planners. Db-A* reuses short trajectories, so-called motion primitives, as edges and allows a maximum user-specified discontinuity at the vertices. These trajectories are locally repaired with trajectory optimization, which also provides new improved motion primitives. Our novel kinodynamic motion planner, kMP-db-A*, has almost surely asymptotic optimal behavior and computes near-optimal solutions quickly. For our empirical validation, we provide the first benchmark that compares search-, sampling-, and optimization-based time-optimal motion planning on multiple dynamical systems in different settings. Compared to the baselines, kMP-db-A* consistently solves more problem instances, finds lower-cost initial solutions, and converges more quickly.