  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.
