This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with standard nonlinear optimization solvers. The method represents convex shapes using a support function representation and is therefore quite general. For collision avoidance involving polyhedral or ellipsoidal shapes, the proposed method introduces fewer variables and constraints than existing approaches. Additionally the proposed method can be used to rigorously ensure continuous collision avoidance as the vehicle transitions between the discrete poses determined by the motion planning algorithm. Numerical examples demonstrate how this can be used to prevent problems of corner cutting and passing through obstacles which can occur when collision avoidance is only enforced at discrete time steps.

翻译：本文提出了一套新的条件,以在基于优化的机动规划算法中准确地代表避免碰撞的制约因素。这些条件始终可以区分,因此适合标准的非线性优化求解器使用。该方法代表了使用支持功能表示的二次曲线形状,因此相当笼统。对于涉及多面形或双向形状的避免碰撞,拟议方法提出的变量和制约因素比现有方法少。此外,拟议的方法可用于严格确保车辆在由运动规划算法决定的离散体之间转换时避免持续碰撞。数字实例表明,如何利用这一方法防止在离散时间步骤下才强制避免碰撞时可能出现的角切开和通过障碍的问题。