Path Signatures for Diversity in Probabilistic Trajectory Optimisation
Lucas Barcelos Tin Lai Rafael Oliveira Paulo Borges Fabio Ramos
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.