We propose a Gaussian variational inference framework for the motion planning problem. In this framework, motion planning is formulated as an optimization over the distribution of the trajectories to approximate the desired trajectory distribution by a tractable Gaussian distribution. Equivalently, the proposed framework can be viewed as a standard motion planning with an entropy regularization. Thus, the solution obtained is a transition from an optimal deterministic solution to a stochastic one, and the proposed framework can recover the deterministic solution by controlling the level of stochasticity. To solve this optimization, we adopt the natural gradient descent scheme. The sparsity structure of the proposed formulation induced by factorized objective functions is further leveraged to improve the scalability of the algorithm. We evaluate our method on several robot systems in simulated environments, and show that it achieves collision avoidance with smooth trajectories, and meanwhile brings robustness to the deterministic baseline results, especially in challenging environments and tasks.

翻译：我们提出了一种用于运动规划问题的高斯变分推断框架。在该框架中，运动规划被表述为对轨迹分布的优化，通过一个易于处理的高斯分布来逼近期望的轨迹分布。等价地，该框架可被视为带有熵正则化的标准运动规划。因此，所得解是从最优确定性解向随机解的过渡，且该框架可通过控制随机性程度恢复确定性解。为求解此优化问题，我们采用了自然梯度下降方案。进一步利用因子化目标函数所诱导的稀疏结构来提升算法的可扩展性。我们在模拟环境中对多个机器人系统进行了评估，结果表明该方法能实现平滑轨迹的避碰，同时增强确定性基线结果的鲁棒性，尤其在具有挑战性的环境和任务中表现显著。