The objective of trajectory optimization algorithms is to achieve an optimal collision-free path between a start and goal state. In real-world scenarios where environments can be complex and non-homogeneous, a robot needs to be able to gauge whether a state will be in collision with various objects in order to meet some safety metrics. The collision detector should be computationally efficient and, ideally, analytically differentiable to facilitate stable and rapid gradient descent during optimization. However, methods today lack an elegant approach to detect collision differentiably, relying rather on numerical gradients that can be unstable. We present DiffCo, the first, fully auto-differentiable, non-parametric model for collision detection. Its non-parametric behavior allows one to compute collision boundaries on-the-fly and update them, requiring no pre-training and allowing it to update continuously in dynamic environments. It provides robust gradients for trajectory optimization via backpropagation and is often 10-100x faster to compute than its geometric counterparts. DiffCo also extends trivially to modeling different object collision classes for semantically informed trajectory optimization.

翻译：轨迹优化算法的目标是在起始状态和目标状态之间实现最佳无碰撞路径。 在现实世界中,环境可能复杂且不相容,机器人需要能够测量一个状态是否与各种物体碰撞,以便达到某些安全度。 碰撞探测器应具有计算效率,而且理想地在分析上可区分,以便于优化期间稳定和快速的梯度下降。 然而,今天的方法缺乏一种优雅的方法,可以不同地探测碰撞,而不是依赖不稳定的数字梯度。 我们展示了DiffCo, 即第一个完全可以自动区分的、非参数性碰撞探测模型。 它的非参数行为允许一个人在飞行上计算碰撞边界并加以更新,不需要预先训练,并允许其在动态环境中不断更新。 它提供了强大的梯度,通过回向调整来进行轨道优化,而且往往比对几何对应方更快10100x。 Diffco还微不足道地扩展到为测距轨道优化而模拟不同的物体碰撞等级。