Sampling-Based Motion Planning Algorithms for Replanning and Spatial Load Balancing

Abstract

The common theme of this dissertation is sampling-based motion planning with the two key contributions being in the area of replanning and spatial load balancing for robotic systems. Here, we begin by recalling two sampling-based motion planners: the asymptotically optimal rapidly-exploring random tree (RRT*), and the asymptotically optimal probabilistic roadmap (PRM*). We also provide a brief background on collision cones and the Distributed Reactive Collision Avoidance (DRCA) algorithm. The next four chapters detail novel contributions for motion replanning in environments with unexpected static obstacles, for multi-agent collision avoidance, and spatial load balancing. First, we show improved performance of the RRT* when using the proposed Grandparent-Connection (GP) or Focused-Refinement (FR) algorithms. Next, the Goal Tree algorithm for replanning with unexpected static obstacles is detailed and proven to be asymptotically optimal. A multi-agent collision avoidance problem in obstacle environments is approached via the RRT*, leading to the novel Sampling-Based Collision Avoidance (SBCA) algorithm. The SBCA algorithm is proven to guarantee collision free trajectories for all of the agents, even when subject to uncertainties in the knowledge of the other agents’ positions and velocities. Given that a solution exists, we prove that livelocks and deadlock will lead to the cost to the goal being decreased. We introduce a new deconfliction maneuver that decreases the cost-to-come at each step. This new maneuver removes the possibility of livelocks and allows a result to be formed that proves convergence to the goal configurations. Finally, we present a limited range Graph-based Spatial Load Balancing (GSLB) algorithm which fairly divides a non-convex space among multiple agents that are subject to differential constraints and have a limited travel distance. The GSLB is proven to converge to a solution when maximizing the area covered by the agents. The analysis for each of the above mentioned algorithms is confirmed in simulations.