  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) collision-avoidance 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.
