# Stochastic Optimization for Trajectory Planning with Heteroscedastic Gaussian Processes

arXiv: https://arxiv.org/abs/1907.07521 · HTML: https://mlsanity.com/paper/1907.07521/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Optimal Motion Planning using Finite Fourier Series in a Learning-based Collision Field](https://mlsanity.com/paper/2312.09073/) (2023)
- [Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions](https://mlsanity.com/paper/2409.12622/) (2024)

## Abstract (arXiv)

Trajectory optimization methods for motion planning attempt to generate trajectories that minimize a suitable objective function. Such methods efficiently find solutions even for high degree-of-freedom robots. However, a globally optimal solution is often intractable in practice and state-of-the-art trajectory optimization methods are thus prone to local minima, especially in cluttered environments. In this paper, we propose a novel motion planning algorithm that employs stochastic optimization based on the cross-entropy method in order to tackle the local minima problem. We represent trajectories as samples from a continuous-time Gaussian process and introduce heteroscedasticity to generate powerful trajectory priors better suited for collision avoidance in motion planning problems. Our experimental evaluation shows that the proposed approach yields a more thorough exploration of the solution space and a higher success rate in complex environments than a current Gaussian process based state-of-the-art trajectory optimization method, namely GPMP2, while having comparable execution time.