ZAPP! Zonotope Agreement of Prediction and Planning for Continuous-Time Collision Avoidance with Discrete-Time Dynamics

TL;DR

ZAPP introduces a unified approach combining coarse prediction models with fine planning representations using zonotopes, enabling safer, gradient-based collision avoidance in continuous-time robot navigation.

Contribution

It proposes ZAPP, a novel method that aligns prediction and planning representations through zonotopes and differentiable collision checks for improved safety.

Findings

ZAPP produces safer trajectories than baseline methods.

The method enables gradient-based optimization for collision avoidance.

Numerical examples demonstrate improved safety in interactive scenes.

Abstract

The past few years have seen immense progress on two fronts that are critical to safe, widespread mobile robot deployment: predicting uncertain motion of multiple agents, and planning robot motion under uncertainty. However, the numerical methods required on each front have resulted in a mismatch of representation for prediction and planning. In prediction, numerical tractability is usually achieved by coarsely discretizing time, and by representing multimodal multi-agent interactions as distributions with infinite support. On the other hand, safe planning typically requires very fine time discretization, paired with distributions with compact support, to reduce conservativeness and ensure numerical tractability. The result is, when existing predictors are coupled with planning and control, one may often find unsafe motion plans. This paper proposes ZAPP (Zonotope Agreement of Prediction and Planning) to resolve the representation mismatch. ZAPP unites a prediction-friendly coarse time discretization and a planning-friendly zonotope uncertainty representation; the method also enables differentiating through a zonotope collision check, allowing one to integrate prediction and planning within a gradient-based optimization framework. Numerical examples show how ZAPP can produce safer trajectories compared to baselines in interactive scenes.