# Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference

arXiv: https://arxiv.org/abs/1707.07383 · HTML: https://mlsanity.com/paper/1707.07383/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2017.

## Built on by (most cited first, 30 of 49)

- [Habitat 2.0: Training Home Assistants to Rearrange their Habitat](https://mlsanity.com/paper/2106.14405/) (2021)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [iSDF: Real-Time Neural Signed Distance Fields for Robot Perception](https://mlsanity.com/paper/2204.02296/) (2022)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Motion Policy Networks](https://mlsanity.com/paper/2210.12209/) (2022)
- [PoCo: Policy Composition from and for Heterogeneous Robot Learning](https://mlsanity.com/paper/2402.02511/) (2024)
- [Potential Based Diffusion Motion Planning](https://mlsanity.com/paper/2407.06169/) (2024)
- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [Composable Energy Policies for Reactive Motion Generation and Reinforcement Learning](https://mlsanity.com/paper/2105.04962/) (2021)
- [Regularized Deep Signed Distance Fields for Reactive Motion Generation](https://mlsanity.com/paper/2203.04739/) (2022)
- [FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching](https://mlsanity.com/paper/2503.06135/) (2025)
- [Real-Time Trajectory Planning for Autonomous Driving with Gaussian Process and Incremental Refinement](https://mlsanity.com/paper/2205.11853/) (2022)
- [A visual introduction to Gaussian Belief Propagation](https://mlsanity.com/paper/2107.02308/) (2021)
- [Motion Planning by Learning the Solution Manifold in Trajectory Optimization](https://mlsanity.com/paper/2107.05842/) (2021)
- [Variational Inference MPC using Normalizing Flows and Out-of-Distribution Projection](https://mlsanity.com/paper/2205.04667/) (2022)
- [Inferring Smooth Control: Monte Carlo Posterior Policy Iteration with Gaussian Processes](https://mlsanity.com/paper/2210.03512/) (2022)
- [Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Models](https://mlsanity.com/paper/2309.05803/) (2023)
- [Fast Kinodynamic Planning on the Constraint Manifold with Deep Neural Networks](https://mlsanity.com/paper/2301.04330/) (2023)
- [Hierarchical Policy Blending as Inference for Reactive Robot Control](https://mlsanity.com/paper/2210.07890/) (2022)
- [Reaching Through Latent Space: From Joint Statistics to Path Planning in Manipulation](https://mlsanity.com/paper/2210.11779/) (2022)
- [Constrained Stein Variational Trajectory Optimization](https://mlsanity.com/paper/2308.12110/) (2023)
- [A Survey on the Integration of Machine Learning with Sampling-based Motion Planning](https://mlsanity.com/paper/2211.08368/) (2022)
- [Distributing Collaborative Multi-Robot Planning with Gaussian Belief Propagation](https://mlsanity.com/paper/2203.11618/) (2022)
- [Hierarchical Policy Blending As Optimal Transport](https://mlsanity.com/paper/2212.01938/) (2022)
- [Efficient Stochastic Optimal Control through Approximate Bayesian Input Inference](https://mlsanity.com/paper/2105.07693/) (2021)
- [Path Signatures for Diversity in Probabilistic Trajectory Optimisation](https://mlsanity.com/paper/2308.04071/) (2023)
- [Integrating DeepRL with Robust Low-Level Control in Robotic Manipulators for Non-Repetitive Reaching Tasks](https://mlsanity.com/paper/2402.02551/) (2024)
- [Mixed Strategy Nash Equilibrium for Crowd Navigation](https://mlsanity.com/paper/2403.01537/) (2024)
- [SwarmDiff: Swarm Robotic Trajectory Planning in Cluttered Environments via Diffusion Transformer](https://mlsanity.com/paper/2505.15679/) (2025)

## Abstract (arXiv)

We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian process (GP) models. We next develop an efficient gradient-based optimization algorithm that exploits this sparsity and GP interpolation. We call this algorithm the Gaussian Process Motion Planner (GPMP). We then detail how motion planning problems can be formulated as probabilistic inference on a factor graph. This forms the basis for GPMP2, a very efficient algorithm that combines GP representations of trajectories with fast, structure-exploiting inference via numerical optimization. Finally, we extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan when conditions change. We benchmark our algorithms against several sampling-based and trajectory optimization-based motion planning algorithms on planning problems in multiple environments. Our evaluation reveals that GPMP2 is several times faster than previous algorithms while retaining robustness. We also benchmark iGPMP2 on replanning problems, and show that it can find successful solutions in a fraction of the time required by GPMP2 to replan from scratch.