A Convex Obstacle Avoidance Formulation

TL;DR

This paper introduces a novel convex obstacle avoidance formulation for autonomous driving, enabling efficient, reliable collision avoidance in dynamic environments with improved computational performance and effectiveness even with limited prediction horizons.

Contribution

It presents the first general convex formulation for obstacle avoidance integrated into convex MPC, enhancing real-time applicability in nonlinear autonomous vehicle systems.

Findings

Convex formulation improves computational efficiency over nonconvex methods.

Effective obstacle avoidance even when obstacles are outside the prediction horizon.

Performance matches or exceeds nonconvex approaches in autonomous vehicle scenarios.

Abstract

Autonomous driving requires reliable collision avoidance in dynamic environments. Nonlinear Model Predictive Controllers (NMPCs) are suitable for this task, but struggle in time-critical scenarios requiring high frequency. To meet this demand, optimization problems are often simplified via linearization, narrowing the horizon window, or reduced temporal nodes, each compromising accuracy or reliability. This work presents the first general convex obstacle avoidance formulation, enabled by a novel approach to integrating logic. This facilitates the incorporation of an obstacle avoidance formulation into convex MPC schemes, enabling a convex optimization framework with substantially improved computational efficiency relative to conventional nonconvex methods. A key property of the formulation is that obstacle avoidance remains effective even when obstacles lie outside the prediction horizon, allowing shorter horizons for real-time deployment. In scenarios where nonconvex formulations are unavoidable, the proposed method meets or exceeds the performance of representative nonconvex alternatives. The method is evaluated in autonomous vehicle applications, where system dynamics are highly nonlinear.