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：我们为运动规划问题提出了一个高斯变式推断框架。在这个框架内,制定运动规划是为了优化轨道分布,以通过可移动高斯分布来接近理想的轨迹分布。同样,拟议框架可以被视为一种带有螺旋式正规化的标准运动规划。因此,获得的解决方案是从一个最佳确定性解决方案过渡到一个随机化解决方案,而拟议框架可以通过控制随机度来恢复确定性解决方案。为了解决这一优化,我们采用了自然梯度下沉方案。由因素化目标功能引发的拟议配方的宽度结构被进一步利用来提高算法的可缩缩缩缩性。我们评估了模拟环境中若干机器人系统的方法,并表明它与光滑轨轨轨相避免碰撞,同时使确定性基线的结果变得稳健,特别是在具有挑战性的环境和任务中。