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：本文提出了一组新的条件，用于在基于优化的运动规划算法中精确表示碰撞避免约束。这些条件具有连续可微性，因此适用于标准的非线性优化求解器。该方法采用支撑函数表示凸形状，因而具有普遍适用性。对于涉及多面体或椭圆体形状的碰撞避免，所提出的方法相比现有方法引入了更少的变量和约束。此外，该方法能够严格确保当车辆在运动规划算法确定的离散位姿之间过渡时实现连续碰撞避免。数值示例表明，该方法可有效避免仅在离散时间步长施加碰撞避免时可能出现的切角穿障问题。