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

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