# A Unifying Variational Framework for Gaussian Process Motion Planning

arXiv: https://arxiv.org/abs/2309.00854 · HTML: https://mlsanity.com/paper/2309.00854/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 2 Sep 2023.

## Builds on (most cited first, 13 of 13)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Pathwise Conditioning of Gaussian Processes](https://mlsanity.com/paper/2011.04026/) (2020)
- [On Sparse variational methods and the Kullback-Leibler divergence between stochastic processes](https://mlsanity.com/paper/1504.07027/) (2015)
- [Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Models](https://mlsanity.com/paper/1803.09151/) (2018)
- [Fast yet Simple Natural-Gradient Descent for Variational Inference in Complex Models](https://mlsanity.com/paper/1807.04489/) (2018)
- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [Manipulation Trajectory Optimization with Online Grasp Synthesis and Selection](https://mlsanity.com/paper/1911.10280/) (2019)
- [ILoSA: Interactive Learning of Stiffness and Attractors](https://mlsanity.com/paper/2103.03099/) (2021)
- [A Gaussian variational inference approach to motion planning](https://mlsanity.com/paper/2209.05655/) (2022)
- [Assisted Teleoperation in Changing Environments with a Mixture of Virtual Guides](https://mlsanity.com/paper/2008.05251/) (2020)

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

- [Mixed Likelihood Variational Gaussian Processes](https://mlsanity.com/paper/2503.04138/) (2025)
- [Shadow Program Inversion with Differentiable Planning: A Framework for Unified Robot Program Parameter and Trajectory Optimization](https://mlsanity.com/paper/2409.08678/) (2024)

## Abstract (arXiv)

To control how a robot moves, motion planning algorithms must compute paths in high-dimensional state spaces while accounting for physical constraints related to motors and joints, generating smooth and stable motions, avoiding obstacles, and preventing collisions. A motion planning algorithm must therefore balance competing demands, and should ideally incorporate uncertainty to handle noise, model errors, and facilitate deployment in complex environments. To address these issues, we introduce a framework for robot motion planning based on variational Gaussian processes, which unifies and generalizes various probabilistic-inference-based motion planning algorithms, and connects them with optimization-based planners. Our framework provides a principled and flexible way to incorporate equality-based, inequality-based, and soft motion-planning constraints during end-to-end training, is straightforward to implement, and provides both interval-based and Monte-Carlo-based uncertainty estimates. We conduct experiments using different environments and robots, comparing against baseline approaches based on the feasibility of the planned paths, and obstacle avoidance quality. Results show that our proposed approach yields a good balance between success rates and path quality.