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A path-following collision-avoidance model predictive control (MPC) method is proposed which approximates obstacle shapes as convex polygons. Collision-avoidance is ensured by means of the signed distance function which is calculated efficiently as part of the MPC problem by making use of a dual formulation. The overall MPC problem can be solved by standard nonlinear programming (NLP) solvers. The dual signed distance formulation yields, besides the (dual) collisionavoidance constraints, norm, and consistency constraints. A novel approach is presented that combines the arising norm equality with the dual collision-avoidance inequality constraints to yield an alternative formulation reduced in complexity. Moving obstacles are considered using separate convex sets of linearly predicted obstacle positions in the dual problem. The theoretical findings and simplifications are compared with the often-used ellipsoidal obstacle formulation and are analyzed with regard to efficiency by the example of a simulated path-following autonomous surface vessel during a realistic maneuver and AIS obstacle data from the Kiel bay area.

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We present the case of a patient who developed a bronchopleural fistula, which was treated with the use of a chest drain with application of suction. The patient significantly deteriorated clinically and developed a tension pneumothorax. After some delay, the wall suction unit was found to be blocked, thereby creating a closed system and causing a pneumothorax under tension. We discuss the safe application of suction to chest drains with particular reference to the use of the three-bottle system.

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