# Stochastic Motion Planning as Gaussian Variational Inference: Theory and Algorithms

arXiv: https://arxiv.org/abs/2308.14985 · HTML: https://mlsanity.com/paper/2308.14985/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2023.

## Built on by (most cited first, 2 of 2)

- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification](https://mlsanity.com/paper/2506.00589/) (2025)

## Abstract (arXiv)

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.