一种凸避障公式
A Convex Obstacle Avoidance Formulation
AI总结：
提出首个通用凸避障公式，通过逻辑集成方法将避障融入凸MPC，相比非凸方法大幅提升计算效率，且障碍物在预测时域外仍有效，支持短时域实时部署。
摘要：
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，但在需要高频率的时间关键场景中表现不佳。为满足这一需求，优化问题通常通过线性化、缩小预测时域或减少时间节点来简化，这些方法均会牺牲准确性或可靠性。本文提出了首个通用的凸避障公式，通过一种新颖的逻辑集成方法实现。这有助于将避障公式纳入凸MPC方案中，从而构建一个凸优化框架，相比传统非凸方法大幅提高计算效率。该公式的一个关键特性是，即使障碍物位于预测时域之外，避障仍然有效，从而允许更短的时域以实现实时部署。在非凸公式不可避免的场景中，所提方法达到或超过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车辆应用中进行了评估。
英文摘要：
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.
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