To be applicable to real world scenarios trajectory planning schemes for mobile autonomous systems must be able to efficiently deal with obstacles in the area of operation. In the context of optimization based trajectory planning and control a number of different approaches to formulate collision avoidance constraints can be found in the literature. Here the contribution of the present work is twofold. First, the most popular methods to represent obstacles are summarized, namely the simple ellipsoidal representation, the constructive solid geometry (CSG) method as well as a direct and an indirect implementation of a signed distance based approach. The formulations are characterized with respect to the impact on the complexity of the optimization problem, as well as the ability to meet different problem requirements. Second, this work presents a novel variant of the CSG method to describe collision avoidance constraints. It is highly efficient due to a very low number of nonlinear inequality constraints required for a given number of obstacles and sample points and in contrast to the original CSG formulation allows to consider the controlled system's shape. The good performance of the proposed formulation is demonstrated by a comparison to the previously mentioned alternatives. To this end optimal trajectory planning for marine surface vessels formulated as a nonlinear programming problem is used as a benchmark example where the scenario is designed based on the maritime test field in Kiel, Germany.

翻译：在优化轨迹规划和控制方面,在文献中可以找到一些不同的方法来提出避免碰撞的限制因素。目前工作的贡献是两方面的。首先,对代表障碍的最受欢迎的方法进行了总结,即简单的单向代号、建设性的固态几何方法以及直接和间接地采用签字的远距法。这些配方的特点是对优化问题的复杂性的影响,以及满足不同问题要求的能力。第二,这项工作是CSG方法中描述避免碰撞限制因素的新变式。由于对特定数量的障碍和抽样点所要求的非线性不平等限制数量很少,而且与最初的CSG提法不同,可以考虑受控系统的形状,因此效率很高。提议的配方的好性能通过与前面提到的替代方法的比较得到证明。对于作为非线性规划问题而拟订的海洋表面船只的这一最终最佳轨迹规划,以海上试验基为基准,以德国为基准,以海上试验为基准。