MORRF*: Sampling-Based Multi-Objective Motion Planning

Many robotic tasks require solutions that maximize multiple performance objectives. For example, in path-planning, these objectives often include finding short paths that avoid risk and maximize the information obtained by the robot. Although there exist many algorithms for multi-objective optimization, few of these algorithms apply directly to robotic path-planning and fewer still are capable of finding the set of Pareto optimal solutions. We present the MORRF∗ (Multi-Objective Rapidly exploring Random Forest∗) algorithm, which blends concepts from two different types of algorithms from the literature: Optimal rapidly exploring random tree (RRT∗) for efficient path finding [Karaman and Frazzoli, 2010] and a decomposition-based approach to multi-objective optimization [Zhang and Li, 2007]. The random forest uses two types of tree structures: a set of reference trees and a set of subproblem trees. We present a theoretical analysis that demonstrates that the algorithm asymptotically produces the set of Pareto optimal solutions, and use simulations to demonstrate the effectiveness and efficiency of MORRF∗ in approximating the Pareto set.