Real-time optimal control allocation for underwater vehicle with non-convex dead-zone constraints

This paper proposes a computationally efficient control allocation method for Open-Frame Autonomous Underwater Vehicles (AUVs) that explicitly considers the non-convex dead-zone constraints of thrusters. Dead-zone constraints complicate accurate thrust allocation, and conventional approaches capable of handling non-convexity, such as Mixed-Integer Quadratic Programming (MIQP), suffer from prohibitive computational costs for AUVs with limited onboard resources. The proposed method decomposes the non-convex control allocation problem into multiple convex Quadratic Programming (QP) sub-problems and reduces computational load by pre-identifying their feasibility. The primary contribution is a rapid feasibility check technique that determines whether a feasible region realizing the desired thrust exists, significantly reducing the number of sub-problems solved in real-time. This study provides a geometric analysis of the relationship between the attainable thrust region of each thruster — represented as a convex hull of vertices — and the resulting total thrust region. Additionally, selecting the solution with the globally minimum objective function value among multiple candidate solutions causes frequent switching of thrust direction, increasing mechanical load on the thrusters. This issue is resolved through a strategic solution selection method. Numerical simulations and experimental validation using an actual vehicle demonstrate that the proposed method achieves high-precision thrust allocation while significantly reducing computational costs compared to conventional techniques.