On the Dual Implementation of Collision-Avoidance Constraints in Path-Following MPC for Underactuated Surface Vessels

TL;DR

This paper introduces a dual formulation for collision-avoidance constraints in path-following MPC for underactuated surface vessels, improving computational efficiency and handling moving obstacles with convex shape approximations.

Contribution

It presents a novel dual signed distance formulation that reduces complexity and integrates obstacle motion prediction into the MPC framework.

Findings

The dual formulation simplifies collision-avoidance constraints.

The method efficiently handles moving obstacles with predicted positions.

Simulation demonstrates improved efficiency over traditional ellipsoidal models.

Abstract

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.