Multi-Objective Path-Based D* Lite

Incrementalgraph search algorithms such as D* Lite reuse previous, and perhaps partial, searches to expedite subsequent path planning tasks. In this article, we are interested in developing incremental graph search algorithms for path finding problems to simultaneously optimize multiple objectives such as travel risk, arrival time, etc. This is challenging because in a multi-objective setting, the number of “Pareto-optimal” solutions can grow exponentially with respect to the size of the graph. This article presents a new multi-objective incremental search algorithm called Multi-Objective Path-Based D* Lite (MOPBD*) which leverages a path-based expansion strategy to prune dominated solutions. Additionally, we introduce a sub-optimal variant of MOPBD* to improve search efficiency while approximating the Pareto-optimal front. We numerically evaluate the performance of MOPBD* and its variants in various maps with two and three objectives. Results show that our approach is more efficient than search from scratch, and runs up to an order of magnitude faster than the existing incremental method for multi-objective path planning.

I. Introduction

The Shortest Path Problem (SPP), which aims of finding a minimum-cost path between two nodes in a graph, is a problem of fundamental importance with numerous applications in robotics and logistics [23], [24]. There are several algorithms [3], [7] that can solve SPP to optimality. Incremental search algorithms, such as LPA* [9], D* Lite [8] etc., generalize these planners to a dynamic setting that allows for cost changes in the edges of the graph. When edge costs change, incremental search algorithms aim to reuse previous searches to speed up subsequent planning tasks. Incremental search is very useful in robotic applications which include navigation in an unknown terrain [23].