Admissible Abstractions for Near-optimal Task and Motion Planning

TL;DR

This paper introduces a new admissibility condition for abstractions in motion planning that accelerates search for near-optimal plans in complex continuous domains while maintaining optimality guarantees.

Contribution

It defines angelic semantics-based admissible abstractions, derives bounds for motion planning, and demonstrates significant complexity reduction enabling near-optimal planning in extremely large state spaces.

Findings

Abstractions can dramatically reduce search complexity.

Near-optimal plans found in $10^{13}$ states without separate task planner.

Admissibility conditions preserve optimality guarantees.

Abstract

We define an admissibility condition for abstractions expressed using angelic semantics and show that these conditions allow us to accelerate planning while preserving the ability to find the optimal motion plan. We then derive admissible abstractions for two motion planning domains with continuous state. We extract upper and lower bounds on the cost of concrete motion plans using local metric and topological properties of the problem domain. These bounds guide the search for a plan while maintaining performance guarantees. We show that abstraction can dramatically reduce the complexity of search relative to a direct motion planner. Using our abstractions, we find near-optimal motion plans in planning problems involving $10^{13}$ states without using a separate task planner.