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Motion planning can be cast as a trajectory optimisation problem where a costis minimised as a function of the trajectory being generated. In complexenvironments with several obstacles and complicated geometry, this optimisationproblem is usually difficult to solve and prone to local minima. However,recent advancements in computing hardware allow for parallel trajectoryoptimisation where multiple solutions are obtained simultaneously, eachinitialised from a different starting point. Unfortunately, without a strategypreventing two solutions to collapse on each other, naive parallel optimisationcan suffer from mode collapse diminishing the efficiency of the approach andthe likelihood of finding a global solution. In this paper we leverage onrecent advances in the theory of rough paths to devise an algorithm forparallel trajectory optimisation that promotes diversity over the range ofsolutions, therefore avoiding mode collapses and achieving better globalproperties. Our approach builds on path signatures and Hilbert spacerepresentations of trajectories, and connects parallel variational inferencefor trajectory estimation with diversity promoting kernels. We empiricallydemonstrate that this strategy achieves lower average costs than competingalternatives on a range of problems, from 2D navigation to robotic manipulatorsoperating in cluttered environments.

Path Signatures for Diversity in Probabilistic Trajectory Optimisation