Behavior-Aware Online Prediction of Obstacle Occupancy using Zonotopes

TL;DR

This work tackles online prediction of obstacle occupancy in urban environments without relying on prior data or road-geometry. It introduces a two-stage approach: (1) online estimation of the surrounding vehicle’s control actions using an Extended Kalman Filter on an augmented model, followed by a Linear Programming step that defines a compact zonotopic Control-Input set $\mathcal{U}$; (2) a zonotopic forward reachability analysis that propagates $\mathcal{U}$ to produce occupancy sets $\mathcal{X}_{k},\ldots,\mathcal{X}_{k+N_p}$. The method handles nonlinearity via a single-track model, uses interval matrices for robust propagation, and projects high-dimensional zonotopes to 2D occupancy regions with targeted simplifications. Simulation results in urban-like scenarios show about $89$–$90\%$ accuracy in occupancy prediction and $\sim$90% success in confirming observed actions within the estimated input set, with significantly less conservatism than worst-case baselines. The approach offers an online, adaptable, and computation-efficient alternative to training-based or geometry-dependent predictors, with direct applicability to safe motion planning in unstructured traffic.

Abstract

Predicting the motion of surrounding vehicles is key to safe autonomous driving, especially in unstructured environments without prior information. This paper proposes a novel online method to accurately predict the occupancy sets of surrounding vehicles based solely on motion observations. The approach is divided into two stages: first, an Extended Kalman Filter and a Linear Programming (LP) problem are used to estimate a compact zonotopic set of control actions; then, a reachability analysis propagates this set to predict future occupancy. The effectiveness of the method has been validated through simulations in an urban environment, showing accurate and compact predictions without relying on prior assumptions or prior training data.

Figures (6)

• Figure 1: Methodology stages: (1) estimate the Control-Input set $\mathcal{\hat{U}}_k$ of the SV from observed inputs $\hat{u}_k$ via EKF+LP; (2) predict the occupancies $\mathcal{\hat{X}}_k, \ldots, \mathcal{\hat{X}}_{k+N_p}$ by zonotopic reachability.
• Figure 2: Left: SV trajectory during $30 {\, s}$. Right: Observed control actions; black: samples used to fit the last Control-Input set; dashed red: optimized zonotope; solid red: dilated Control-Input set.
• Figure 3: Observed control actions during the simulation(colored by path segments as in Figure \ref{['fig:path_followed']}) and estimated Control-Input set bounds (gray dashed) at each time $k$.
• Figure 4: Classification of observed control actions over $150$ iterations: green = inside the estimated Control-Input set; red = outside.
• Figure 5: Proposed method. Dark red: current SV location; purple: subsequent locations used as ground truth; blue: successfully predicted occupancy sets; orange: missed.