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.

近期计算硬件的进展使得并行轨迹优化成为可能，为解决模式坍塌和寻找全局解提供了一种策略，该研究基于路径标记和 Hilbert 空间表示的轨迹，连接并行变分推断与多样性促进核技术。通过实验证明该策略在多个问题中均可获得比竞争方法更低的平均成本。