  We propose NH-TTC, a general method for fast, anticipatory collision
avoidance for autonomous robots having arbitrary equations of motions. Our
proposed approach exploits implicit differentiation and subgradient descent to
locally optimize the non-convex and non-smooth cost functions that arise from
planning over the anticipated future positions of nearby obstacles. The result
is a flexible framework capable of supporting high-quality, collision-free
navigation with a wide variety of robot motion models in various challenging
scenarios. We show results for different navigating tasks, with our method
controlling various numbers of agents (with and without reciprocity), on both
physical differential drive robots, and simulated robots with different motion
models and kinematic and dynamic constraints, including acceleration-controlled
agents, differential-drive agents, and smooth car-like agents. The resulting
paths are high quality and collision-free, while needing only a few
milliseconds of computation as part of an integrated sense-plan-act navigation
loop.
