# Stochastic Optimization for Trajectory Planning with Heteroscedastic Gaussian Processes

## TL;DR

This paper introduces a stochastic motion planning algorithm using heteroscedastic Gaussian processes and the cross-entropy method, improving exploration and success rates in complex environments while maintaining similar execution times.

## Contribution

It presents a novel trajectory optimization approach that employs heteroscedastic Gaussian processes and stochastic optimization to better avoid local minima in cluttered environments.

## Key findings

- Higher success rate in complex environments
- More thorough exploration of solution space
- Comparable execution time to state-of-the-art methods

## Abstract

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.