# Sampling-Based Methods for Factored Task and Motion Planning

arXiv: https://arxiv.org/abs/1801.00680 · HTML: https://mlsanity.com/paper/1801.00680/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2018.

## Built on by (most cited first, 8 of 8)

- [Sequence-Based Plan Feasibility Prediction for Efficient Task and Motion Planning](https://mlsanity.com/paper/2211.01576/) (2022)
- [Open-World Task and Motion Planning via Vision-Language Model Generated Constraints](https://mlsanity.com/paper/2411.08253/) (2024)
- [Motion Reasoning for Goal-Based Imitation Learning](https://mlsanity.com/paper/1911.05864/) (2019)
- [STAMP: Differentiable Task and Motion Planning via Stein Variational Gradient Descent](https://mlsanity.com/paper/2310.01775/) (2023)
- [KiloBot: A Programming Language for Deploying Perception-Guided Industrial Manipulators at Scale](https://mlsanity.com/paper/2409.03439/) (2024)
- [Leveraging Pre-trained Large Language Models with Refined Prompting for Online Task and Motion Planning](https://mlsanity.com/paper/2504.21596/) (2025)
- [A Framework for Task and Motion Planning based on Expanding AND/OR Graphs](https://mlsanity.com/paper/2509.00317/) (2025)
- [Optimistic Reinforcement Learning-Based Skill Insertions for Task and Motion Planning](https://mlsanity.com/paper/2510.14065/) (2025)

## Abstract (arXiv)

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.