# Differentiable Gaussian Process Motion Planning

arXiv: https://arxiv.org/abs/1907.09591 · HTML: https://mlsanity.com/paper/1907.09591/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2019.

## Built on by (most cited first, 28 of 28)

- [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)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Differentiable Integrated Motion Prediction and Planning with Learnable Cost Function for Autonomous Driving](https://mlsanity.com/paper/2207.10422/) (2022)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Differentiable SLAM-net: Learning Particle SLAM for Visual Navigation](https://mlsanity.com/paper/2105.07593/) (2021)
- [Learning Model Predictive Controllers with Real-Time Attention for Real-World Navigation](https://mlsanity.com/paper/2209.10780/) (2022)
- [Differentiable Spatial Planning using Transformers](https://mlsanity.com/paper/2112.01010/) (2021)
- [Exploring Imitation Learning for Autonomous Driving with Feedback Synthesizer and Differentiable Rasterization](https://mlsanity.com/paper/2103.01882/) (2021)
- [APPLD: Adaptive Planner Parameter Learning from Demonstration](https://mlsanity.com/paper/2004.00116/) (2020)
- [Hybrid-Prediction Integrated Planning for Autonomous Driving](https://mlsanity.com/paper/2402.02426/) (2024)
- [Co-MTP: A Cooperative Trajectory Prediction Framework with Multi-Temporal Fusion for Autonomous Driving](https://mlsanity.com/paper/2502.16589/) (2025)
- [Coarse-to-Fine Q-attention with Learned Path Ranking](https://mlsanity.com/paper/2204.01571/) (2022)
- [Learning to Optimize in Model Predictive Control](https://mlsanity.com/paper/2212.02603/) (2022)
- [TaskMet: Task-Driven Metric Learning for Model Learning](https://mlsanity.com/paper/2312.05250/) (2023)
- [Learning Sampling Distributions for Model Predictive Control](https://mlsanity.com/paper/2212.02587/) (2022)
- [Occupancy Prediction-Guided Neural Planner for Autonomous Driving](https://mlsanity.com/paper/2305.03303/) (2023)
- [Revisiting Implicit Differentiation for Learning Problems in Optimal Control](https://mlsanity.com/paper/2310.14468/) (2023)
- [Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2510.06179/) (2025)
- [DiffTORI: Differentiable Trajectory Optimization for Deep Reinforcement and Imitation Learning](https://mlsanity.com/paper/2402.05421/) (2024)
- [Robot Program Parameter Inference via Differentiable Shadow Program Inversion](https://mlsanity.com/paper/2103.14452/) (2021)
- [CaRE: Finding Root Causes of Configuration Issues in Highly-Configurable Robots](https://mlsanity.com/paper/2301.07690/) (2023)
- [Decision-Oriented Learning with Differentiable Submodular Maximization for Vehicle Routing Problem](https://mlsanity.com/paper/2303.01543/) (2023)
- [From Variance to Veracity: Unbundling and Mitigating Gradient Variance in Differentiable Bundle Adjustment Layers](https://mlsanity.com/paper/2406.07785/) (2024)
- [Shadow Program Inversion with Differentiable Planning: A Framework for Unified Robot Program Parameter and Trajectory Optimization](https://mlsanity.com/paper/2409.08678/) (2024)
- [Reinforcement Learning for Adaptive Planner Parameter Tuning: A Perspective on Hierarchical Architecture](https://mlsanity.com/paper/2503.18366/) (2025)
- [Reinforcement Learning in a Safety-Embedded MDP with Trajectory Optimization](https://mlsanity.com/paper/2310.06903/) (2023)
- [Optimal Motion Planning using Finite Fourier Series in a Learning-based Collision Field](https://mlsanity.com/paper/2312.09073/) (2023)

## Abstract (arXiv)

Modern trajectory optimization based approaches to motion planning are fast, easy to implement, and effective on a wide range of robotics tasks. However, trajectory optimization algorithms have parameters that are typically set in advance (and rarely discussed in detail). Setting these parameters properly can have a significant impact on the practical performance of the algorithm, sometimes making the difference between finding a feasible plan or failing at the task entirely. We propose a method for leveraging past experience to learn how to automatically adapt the parameters of Gaussian Process Motion Planning (GPMP) algorithms. Specifically, we propose a differentiable extension to the GPMP2 algorithm, so that it can be trained end-to-end from data. We perform several experiments that validate our algorithm and illustrate the benefits of our proposed learning-based approach to motion planning.