Sampling-Based Constrained Motion Planning with Products of Experts

TL;DR

This paper introduces a novel sampling-based constrained motion planning method using products of experts, which improves efficiency and diversity in sampling by combining optimality and feasibility distributions, validated through various robotics tasks.

Contribution

The paper proposes a new project-then-sample strategy using products of experts with tensor train models for constrained motion planning, enhancing sampling efficiency and exploration.

Findings

Outperforms baseline methods in obstacle avoidance tasks.

Reduces sample boundary accumulation, improving exploration.

Effective in manipulation and restricted volume tasks.

Abstract

We present a novel approach to enhance the performance of sampling-based Model Predictive Control (MPC) in constrained optimization by leveraging products of experts. Our methodology divides the main problem into two components: one focused on optimality and the other on feasibility. By combining the solutions from each component, represented as distributions, we apply products of experts to implement a project-then-sample strategy. In this strategy, the optimality distribution is projected into the feasible area, allowing for more efficient sampling. This approach contrasts with the traditional sample-then-project and naive sample-then-reject method, leading to more diverse exploration and reducing the accumulation of samples on the boundaries. We demonstrate an effective implementation of this principle using a tensor train-based distribution model, which is characterized by its non-parametric nature, ease of combination with other distributions at the task level, and straightforward sampling technique. We adapt existing tensor train models to suit this purpose and validate the efficacy of our approach through experiments in various tasks, including obstacle avoidance, non-prehensile manipulation, and tasks involving staying in a restricted volume. Our experimental results demonstrate that the proposed method consistently outperforms known baselines, providing strong empirical support for its effectiveness. Sample codes for this project are available at https://github.com/idiap/smpc_poe.