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Distributed MPC for autonomous ships on inland waterways with collaborative collision avoidance

Hoang Anh Tran, Tor Arne Johansen, Rudy R. Negenborn

TL;DR

This paper tackles collaborative collision avoidance for autonomous ships on inland waterways by introducing a two-layer C-CAS framework that decouples traffic-regulation compliance from collision-avoidance optimization. The lower layer performs distributed DMPC via NADMM to minimize a risk-based collision objective while enforcing conspicuous maneuvers, and the upper TAPD layer determines priority and rule-based give-way/stand-on behavior without a centralized coordinator. Key contributions include a risk-driven collision avoidance cost, a serial iterative ADMM scheme for distributed control, explicit handling of deadlock, and extensive simulations in head-on and intersection scenarios demonstrating rule-compliant and safe behavior. The framework supports regional variations in inland traffic rules by restructuring the upper layer, offering a practical approach to safe, scalable autonomous navigation on complex waterways.

Abstract

This paper presents a distributed solution for the problem of collaborative collision avoidance for autonomous inland waterway ships. A two-layer collision avoidance framework that considers inland waterway traffic regulations is proposed to increase navigational safety for autonomous ships. Our approach allows for modifying traffic rules without changing the collision avoidance algorithm, and is based on a novel formulation of model predictive control (MPC) for collision avoidance of ships. This MPC formulation is designed for inland waterway traffic and can handle complex scenarios. The alternating direction method of multipliers is used as a scheme for exchanging and negotiating intentions among ships. Simulation results show that the proposed algorithm can comply with traffic rules. Furthermore, the proposed algorithm can safely deviate from traffic rules when necessary to increase efficiency in complex scenarios.

Distributed MPC for autonomous ships on inland waterways with collaborative collision avoidance

TL;DR

This paper tackles collaborative collision avoidance for autonomous ships on inland waterways by introducing a two-layer C-CAS framework that decouples traffic-regulation compliance from collision-avoidance optimization. The lower layer performs distributed DMPC via NADMM to minimize a risk-based collision objective while enforcing conspicuous maneuvers, and the upper TAPD layer determines priority and rule-based give-way/stand-on behavior without a centralized coordinator. Key contributions include a risk-driven collision avoidance cost, a serial iterative ADMM scheme for distributed control, explicit handling of deadlock, and extensive simulations in head-on and intersection scenarios demonstrating rule-compliant and safe behavior. The framework supports regional variations in inland traffic rules by restructuring the upper layer, offering a practical approach to safe, scalable autonomous navigation on complex waterways.

Abstract

This paper presents a distributed solution for the problem of collaborative collision avoidance for autonomous inland waterway ships. A two-layer collision avoidance framework that considers inland waterway traffic regulations is proposed to increase navigational safety for autonomous ships. Our approach allows for modifying traffic rules without changing the collision avoidance algorithm, and is based on a novel formulation of model predictive control (MPC) for collision avoidance of ships. This MPC formulation is designed for inland waterway traffic and can handle complex scenarios. The alternating direction method of multipliers is used as a scheme for exchanging and negotiating intentions among ships. Simulation results show that the proposed algorithm can comply with traffic rules. Furthermore, the proposed algorithm can safely deviate from traffic rules when necessary to increase efficiency in complex scenarios.
Paper Structure (27 sections, 1 theorem, 22 equations, 13 figures, 2 algorithms)

This paper contains 27 sections, 1 theorem, 22 equations, 13 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and motivation
  3. Proposed two-layer framework for collision avoidance
  4. Contributions
  5. Outline
  6. Preliminaries
  7. Notation
  8. Assumptions
  9. Nonlinear Alternating Direction Method of Multipliers
  10. Traffic assessment & priority determination protocol
  11. Protocol development
  12. Resolving deadlock situations
  13. Collaborative collision avoidance algorithm
  14. Kinematic model of ship $i$
  15. Risk evaluation
  16. ...and 12 more sections

Key Result

Theorem 1

Assume Problem prob2 has feasible solutions for all $i \in {\mathcal{M}}$. Then the solution provided by Algorithm alg1 with $\lambda \in (0,2)$, $\beta > 2L$, and $L>0$ converges asymptotically to a (locally) optimal solution.

Figures (13)

  • Figure 1: Control scheme with the proposed C-CAS framework: $U_i^d$ and $\chi_{i,n}^d$ are nominal surge speed and course angle command (in the inertial frame $\{n\}$), respectively, used as input to an autopilot that contains course and speed control loops. The control signals from CAS are cross-track offset, $u^y_i$, and speed modification, $u^s_i$.
  • Figure 2: Path coordinate and inertial coordinate.
  • Figure 3: Example of deadlock situation: Each ship wait for the ship comes from their starboard side.
  • Figure 4: Behavior functions ${\mathcal{B}}_1(x,r)$ and ${\mathcal{B}}_2(x,r_1,r_2)$.
  • Figure 5: Head on situation in inland waterway between two ships. Ship 1 and 2 are illustrated in blue and green dots, respectively. The rectangle around each ship is the safety area. The waterway is illustrated in white, and the grey area is where a ship cannot sail. The dash line at $Y=0m$ is the central line divide port and starboard side of a waterway.
  • ...and 8 more figures

Theorems & Definitions (6)

  • Remark 1
  • Theorem 1
  • proof
  • Definition 1: lower semicontinuous function
  • Definition 2: image function
  • Definition 3: Lipchitz continuous gradient