Efficient Formulation of Collision Avoidance Constraints in Optimization Based Trajectory Planning and Control

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