Sampling-Based Methods for Factored Task and Motion Planning

TL;DR

This paper introduces a theoretical framework and sampling-based algorithms for efficiently solving factored transition systems in complex robotic planning tasks involving multiple objects and constraints.

Contribution

It develops a general probabilistically complete planning framework for factored transition systems with a focus on robotic manipulation problems.

Findings

Algorithms demonstrate empirical efficiency on challenging manipulation tasks.

Framework characterizes conditions for robust feasibility in factored systems.

Conditional samplers effectively produce solutions on complex submanifolds.

Abstract

This paper presents a general-purpose formulation of a large class of discrete-time planning problems, with hybrid state and control-spaces, as factored transition systems. Factoring allows state transitions to be described as the intersection of several constraints each affecting a subset of the state and control variables. Robotic manipulation problems with many movable objects involve constraints that only affect several variables at a time and therefore exhibit large amounts of factoring. We develop a theoretical framework for solving factored transition systems with sampling-based algorithms. The framework characterizes conditions on the submanifold in which solutions lie, leading to a characterization of robust feasibility that incorporates dimensionality-reducing constraints. It then connects those conditions to corresponding conditional samplers that can be composed to produce values on this submanifold. We present two domain-independent, probabilistically complete planning algorithms that take, as input, a set of conditional samplers. We demonstrate the empirical efficiency of these algorithms on a set of challenging task and motion planning problems involving picking, placing, and pushing.