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.

翻译：自动驾驶需要在动态环境中实现可靠的碰撞避免。非线性模型预测控制器（NMPC）适用于此任务，但在需要高频处理的实时关键场景中面临困难。为满足这一需求，优化问题常通过线性化、缩短预测时域窗口或减少时间节点等方式简化，这些方法均会牺牲精度或可靠性。本研究首次提出了一种通用的凸障碍物避让公式化方法，该方法通过一种新颖的逻辑集成途径实现。这使得障碍物避让公式能够融入凸模型预测控制框架，从而构建计算效率显著优于传统非凸方法的凸优化体系。该公式的关键特性在于：即使障碍物位于预测时域之外，避障功能依然有效，这为实时部署提供了采用更短预测时域的可能性。在必须使用非凸公式的场景中，本方法达到或超越了代表性非凸替代方案的性能。该方法在系统动力学高度非线性的自动驾驶应用中进行了验证。