A Convex Obstacle Avoidance Formulation

2025-12-15

AI Summary

Real-time obstacle avoidance for autonomous driving in dynamic environments remains challenging, particularly due to the high computational complexity of nonlinear model predictive control (NMPC), which hinders its deployment under stringent high-frequency control requirements. Method: This paper proposes the first general-purpose convex obstacle-avoidance modeling framework. Leveraging a novel logic-integrated convexification strategy, it rigorously transforms nonconvex collision-avoidance constraints into convex ones, enabling tractable and analytically guaranteed obstacle avoidance within a convex MPC formulation—including robust handling of obstacles beyond the prediction horizon. The approach integrates linear time-varying system modeling, convex approximation of nonlinear vehicle dynamics, and convex encoding of logical constraints. Results: Experiments demonstrate maintained obstacle-avoidance efficacy even with short prediction horizons, significantly accelerated solving speed, and enhanced real-time performance. On highly nonlinear vehicle models, the method matches or surpasses state-of-the-art nonconvex NMPC in control performance and has been validated on real-world autonomous driving obstacle-avoidance tasks.

Technology Category

• Search and Optimization: Non-convex Optimization
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Multiagent Systems: Adversarial Agents

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Develops a convex obstacle avoidance method for autonomous driving
• Improves computational efficiency in nonlinear model predictive control
• Enables real-time collision avoidance with shorter prediction horizons

Innovation

• Convex obstacle avoidance formulation for autonomous driving
• Integrates logic for convex MPC with improved efficiency
• Effective even when obstacles are beyond prediction horizon