Dual Collision Detection in Model Predictive Control Including Culling Techniques

An optimization-based approach for collision avoidance of fully dimensional autonomous vehicles in confined environments is considered. We discuss the dual re-formulations of indicator, distance, and signed distance functions which yield an exact re-formulation of the usually nonlinear, noncontinuously differentiable respective original formulations. Embedding the resulting dual collision avoidance constraints to a model predictive control (MPC) problem induces additional decision variables, which greatly increases problem complexity. Therefore, a culling procedure is combined with the dual approach to reduce the problem size by identifying and eliminating decision variables associated with faces of the polyhedral obstacles and the controlled vehicle, respectively. Three culling conditions are proposed, namely, frustum, occlusion, and backface culling. The proposed method is illustrated using a simulative study where a path-following task is performed for a ship autopilot model, and near-field obstacle information is extracted based on a set of automatic identification system (AIS) data from the Kiel canal.