Design of Admissible Heuristics for Kinodynamic Motion Planning via Sum-of-Squares Programming

TL;DR

This paper introduces a method to systematically design admissible heuristics for kinodynamic motion planning problems using sum-of-squares programming, enabling efficient heuristic optimization directly from problem data.

Contribution

It provides a new analytical framework and polynomial-time optimization approach for constructing admissible heuristics based on problem data.

Findings

The proposed condition ensures heuristic admissibility directly from problem data.

Sum-of-squares programming effectively approximates and solves the heuristic optimization problem.

Examples demonstrate the practical applicability of the method.

Abstract

How does one obtain an admissible heuristic for a kinodynamic motion planning problem? This paper develops the analytical tools and techniques to answer this question. A sufficient condition for the admissibility of a heuristic is presented which can be checked directly from the problem data. This condition is also used to formulate a concave program to optimize an admissible heuristic. This optimization is then approximated and solved in polynomial time using sum-of-squares programming techniques. A number of examples are provided to demonstrate these concepts.