Cooperative Multi-Agent Control for Autonomous Ship Towing Under Environmental Disturbances Zhe Du, Rudy R. Negenborn, and Vasso Reppa, Member, IEEE Abstract—Among the promising application of autonomous surface vessels (ASVs) is the utilization of multiple autonomous tugs for manipulating a floating object such as an oil platform, a broken ship, or a ship in port areas. Considering the real conditions and operations of maritime practice, this paper proposes a multi-agent control algorithm to manipulate a ship to a desired position with a desired heading and velocity under the environmental disturbances. The control architecture consists of a supervisory controller in the higher layer and tug controllers in the lower layer. The supervisory controller allocates the towing forces and angles between the tugs and the ship by minimizing the error in the position and velocity of the ship. The weight coefficients in the cost function are designed to be adaptive to guarantee that the towing system functions well under environmental disturbances, and to enhance the efficiency of the towing system. The tug controller provides the forces to tow the ship and tracks the reference trajectory that is computed online based on the towing angles calculated by the supervisory controller. Simulation results show that the proposed algorithm can make the two autonomous tugs cooperatively tow a ship to a desired position with a desired heading and velocity under the (even harsh) environmental disturbances. Index Terms—Cooperative control, environmental disturbances, multiple autonomous vessels, robust control, ship towing.    I. Introduction I N recent years, the advancements in information and communication technologies, sensor technology, as well as automatic control and computational intelligence have increased the intelligence level of transportation systems [1], [2]. For waterborne transportation, we have seen significant development of autonomous surface vessels (ASVs), whose application areas are gradually transformed from military deployment [3] and scientific research [4] to civil uses [5]. In the meanwhile, the number of controlled ASVs is increased from one to multiple to carry out more complex missions and scenarios [6]–[8], which makes the original problem become more challenging from the viewpoint of coordination [9]. Ship manipulation in or near port areas is considered one of the most sophisticated operations in waterborne transportation [10], while the environmental disturbances make it more challenging, even for the experienced captain [11]. To make the operation of ship manipulation safer and more effective, two solutions are put forward according to the concept of “smart shipping” [12]: The first is to focus on the automation of the ship itself to increase the efficiency in the shipping process [13]; The second is to involve auxiliary operations through the cooperation of autonomous marine agents to ensure the ship safety [14]. Thus, the first approach to solve the sophisticated ship manipulation problem is called self-berthing by autonomous ship, while the second approach is called assisted-berthing by multiple autonomous tugs.    A. Related Works The classification of autonomous ship berthing, correspon- ding control methods, and disturbance considerations are shown in Table I; The upper half [15]–[22] is dedicated to self-berthing and lower half [23]–[31] are the assisted- berthing. Self-berthing is a single-agent under-actuated control problem, aiming to control the ship motion in 3 degrees of freedom (DoF) with usually, less number of control inputs (rudder angle and propeller revolution). For the control method, artificial neural networks (ANN) is most used [32]. Research works combine ANN with other control algorithms to get a better performance and adapt to the environment disturbances (mainly the wind influence). Combining with model predictive control (MPC) [15], a short computing time and good tracking performance method in real sea conditions is achieved. Combining with nonlinear adaptive control [16], the unknown ship dynamics, environmental disturbances and measurement noise can be estimated. Combining with PD control [17], the proposed method can deal with abrupt disturbance like gust wind. Combining with genetic algorithm [18], the ANN structure and training cost are optimized and reduced, respectively, guaranteeing that the ship reach the dock smoothly. Apart from ANN, other methods, like adaptive backstepping control [19], PID-based nonlinear- feedback control [20], genetic algorithm-based optimal control [21], and PID-based active disturbance rejection control [22], provide solutions for self berthing aiming at handling wind loads. Overall, self-berthing puts a high demand on the controller, requiring high control performance to force the ship stop at the exact place with a desired heading in the end. However, the real berthing situation at the end phase is a dynamic Manuscript received February 3, 2021; accepted March 28, 2021. This work was supported by the China Scholarship Council (201806950080), the Researchlab Autonomous Shipping (RAS) of Delft University of Technology, and the INTERREG North Sea Region Grant “AVATAR” funded by the European Regional Development Fund. Recommended by Associate Editor Qing-Long Han. (Corresponding author: Zhe Du.) Citation: Z. Du, R. R. Negenborn, and V. Reppa, “Cooperative multi-agent control for autonomous ship towing under environmental disturbances,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 8, pp. 1365–1379, Aug. 2021. The authors are with the Department of Maritime and Transport Technology, Delft University of Technology, 2628 CD, Delft, The Netherlands (e-mail: Z.Du@tudelft.nl; R.R.Negenborn@tudelft.nl; V.Reppa@ tudelft.nl). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2021.1004078 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 8, AUGUST 2021 1365