Path Signatures for Diversity in Probabilistic Trajectory Optimisation

TL;DR

This paper introduces a novel trajectory optimisation method using path signatures and Hilbert space representations to promote diversity among solutions, reducing mode collapse and improving global optimality in complex environments.

Contribution

It presents a new algorithm leveraging rough path theory and diversity kernels to enhance parallel trajectory optimisation, addressing mode collapse issues.

Findings

Achieves lower average costs compared to existing methods.

Effective in 2D navigation and robotic manipulation tasks.

Promotes solution diversity to improve global optimality.

Abstract

Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem is usually difficult to solve and prone to local minima. However, recent advancements in computing hardware allow for parallel trajectory optimisation where multiple solutions are obtained simultaneously, each initialised from a different starting point. Unfortunately, without a strategy preventing two solutions to collapse on each other, naive parallel optimisation can suffer from mode collapse diminishing the efficiency of the approach and the likelihood of finding a global solution. In this paper we leverage on recent advances in the theory of rough paths to devise an algorithm for parallel trajectory optimisation that promotes diversity over the range of solutions, therefore avoiding mode collapses and achieving better global properties. Our approach builds on path signatures and Hilbert space representations of trajectories, and connects parallel variational inference for trajectory estimation with diversity promoting kernels. We empirically demonstrate that this strategy achieves lower average costs than competing alternatives on a range of problems, from 2D navigation to robotic manipulators operating in cluttered environments.