# NH-TTC: A gradient-based framework for generalized anticipatory collision avoidance

## TL;DR

NH-TTC is a versatile, gradient-based framework enabling fast, anticipatory collision avoidance for diverse autonomous robots by optimizing over future obstacle positions using implicit differentiation.

## Contribution

It introduces NH-TTC, a novel method that applies implicit differentiation and subgradient descent to efficiently plan collision-free paths for various robot models.

## Key findings

- Supports multiple robot types and motion models.
- Achieves collision-free navigation with high-quality paths.
- Operates within a few milliseconds per planning cycle.

## Abstract

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.