Stochastic Motion Planning as Gaussian Variational Inference: Theory and Algorithms

TL;DR

This paper introduces a new Gaussian variational inference framework for motion planning under uncertainty, providing algorithms that improve robustness and decision-making in robotic trajectory planning.

Contribution

It formulates motion planning as a Gaussian variational inference problem and develops two novel algorithms, GVI-MP and PCS-MP, for efficient solution.

Findings

Algorithms demonstrate improved robustness in experiments

Effective approximation of posterior distributions over trajectories

Framework bridges stochastic control and variational inference

Abstract

We present a novel formulation for motion planning under uncertainties based on variational inference where the optimal motion plan is modeled as a posterior distribution. We propose a Gaussian variational inference-based framework, termed Gaussian Variational Inference Motion Planning (GVI-MP), to approximate this posterior by a Gaussian distribution over the trajectories. We show that the GVI-MP framework is dual to a special class of stochastic control problems and brings robustness into the decision-making in motion planning. We develop two algorithms to numerically solve this variational inference and the equivalent control formulations for motion planning. The first algorithm uses a natural gradient paradigm to iteratively update a Gaussian proposal distribution on the sparse motion planning factor graph. We propose a second algorithm, the Proximal Covariance Steering Motion Planner (PCS-MP), to solve the same inference problem in its stochastic control form with an additional terminal constraint. We leverage a proximal gradient paradigm where, at each iteration, we quadratically approximate nonlinear state costs and solve a linear covariance steering problem in closed form. The efficacy of the proposed algorithms is demonstrated through extensive experiments on various robot models. An implementation is provided in https://github.com/hzyu17/VIMP.