DiffCo: Auto-Differentiable Proxy Collision Detection with Multi-Class Labels for Safety-Aware Trajectory Optimization

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 com- putationally efficient and, ideally, analytically differentiable to facilitate stable and rapid gradient descent during optimization. However, methods today lack an elegant approach to detect colli- sion 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.