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Adaptive Tracking Control of Underwater Vehicle-Manipulator Systems Based on the Virtual Decomposition Approach Gianluca Antonelli, Fabrizio Caccavale, and Stefano Chiaverini Abstract—A novel adaptive control law for the end-effector tracking problemofunderwatervehicle-manipulatorsystems(UVMSs)ispresented in this paper. By exploiting the serial-chain kinematic structure of the UVMS, the overall control problem is decomposed in a set of elementary control problems, each of them formulated with respect to a single rigid body in the system. The proposed approach results in a modular control scheme which simplifies application to UVMSs with a large number of links, reduces the required computational burden, and allows efficient implementation on distributed computing architectures. Furthermore, the occurrence of kinematic and representation singularities is overcome, respectively, by expressing the control law in body-fixed coordinates and representing the attitude via the unit quaternion. To show the effectiveness of the proposed control strategy, a simulation case study is developed for a vehicle in spatial motion carrying a six-degree-of-freedom manipulator. Index Terms—Adaptive control, control of redundant manipulators, un- derwater robotics, virtual decomposition control. I. INTRODUCTION The use of autonomous underwater vehicles (AUVs) equipped with an underwater vehicle-manipulator system (UVMS) to perform com- plex underwater tasks gives rise to challenging control problems in- volving nonlinear, coupled, and high-dimensional systems. Currently, the state of the art is represented by teleoperated master/slave archi- tectures; few research centers are equipped with autonomous systems [26]. Several control strategies based on perfect compensation of the UVMS’s dynamics have been proposed [6], [18]. However, it must Manuscript received January 14, 2003; revised April 23, 2003. This paper was recommended for publication by Associate Editor J. Leonard and Editor I. Walker upon evaluation of the reviewers’ comments. G. Antonelli and S. Chiaverini are with the Dipartimento di Automazione, Elettromagnetismo, Ingegneria dell’Informazione e Matematica Industriale, Università degli Studi di Cassino, 03043 Cassino, Italy (e-mail: an- tonelli@unicas.it; chiaverini@unicas.it). F. Caccavale is with the Dipartimento di Ingegneria e Fisica dell’Ambiente, Universià degli Studi della Basilicata, 85100 Potenza, Italy (e-mail: cac- cavale@unibas.it). Digital Object Identifier 10.1109/TRA.2004.825521 be pointed out that exact knowledge of the system dynamics rarely can be assumed, especially for underwater applications, where some dynamic terms strongly depend on the environmental conditions (e.g., hydrodynamic forces). To overcome this problem, adaptive control laws have been pro- posed, e.g., [13] and [14]. These approaches regard the UVMS model as a whole, thus giving rise to high-dimensional problems. In fact, differently from the case of earth-fixed manipulators, in the case of UVMS, it is not possible to reduce the number of dynamic parameters to be adapted, since the base of the manipulator (i.e., the vehicle) has full mobility. In detail, it can be stated that the computational load of such control algorithms grows as much as the fourth-order power of the number of the system’s degrees of freedom (DOFs). For this reason, practical application of adaptive control to UVMS has been usually limited, even in simulation, to vehicles carrying arms with very few joints (i.e., two or three) and usually performing planar tasks. An interesting approach is proposed in [10], where an adaptive con- trol law, based on the micro–macro manipulator concept, is designed for UVMSs carrying a nonredundant manipulator (e.g., with 6 DOFs). The approach needs the computation of the inverse kinematics (IK) of the system; this is achieved by using the inverse of the Jacobian matrix. Hence, the approach can be applied only to nonredundant manipulators (i.e., characterized by a square Jacobian matrix) in nonsingular config- urations (i.e., full-rank Jacobian matrix). As for nonadaptive approaches, in [9] the dynamic coupling between vehicle and manipulator is investigated. From the analysis of a specific UVMS structure, a sliding-mode approach, based on the approach in [24], with a feedforward compensation term is proposed. Numerical simulation results show that the knowledge of the dynamics allows im- provement of the tracking performance. This approach, however, re- quires knowledge of the symbolic expression for the interaction be- tween the first link and the vehicle. Reference [15] reports a control algorithm in which the importance of the compensation of the vehicle/manipulator interaction is high- lighted by the use of a force/torque sensor on the manipulator base or, in alternative, by the use of a disturbance observer. An adaptive, non- regressor-based control law for UVMSs is also presented in [27]. In sum, adaptive model-based control approaches for UVMSs are often based on the Lagrange formulation of the dynamic model of the whole system. This leads to computationally intensive control algo- rithms. On the other hand, nonadaptive approaches typically require accurate knowledge of the dynamic model of the system or have to be designed for specific UVMSs. This drawback strongly limits the appli- cation of model-based control for underwater applications. Hence, in practice, control engineers adopt simple control laws (e.g., of the pro- portional-integral-derivative (PID) type), which usually provide signif- icantly limited tracking performance of the control system in the face of a light computational effort. This paper is aimed at developing a new adaptive control scheme for the tracking problem of UVMS, which keeps the advantages of model- based adaptive control, in terms of tracking accuracy, while limiting the computational load. Also, the control algorithm is designed so as to have a modular structure. This brings several advantages in terms of control software design and maintenance. The control scheme is based on the virtual decomposition approach in [28]. Different from previous approaches, the serial-chain structure of the UVMS is exploited to decompose the overall motion-control problem in a set of elementary control problems regarding the motion of each rigid body in the system, namely, the manipulator’s links and the vehicle. For each body, a control action is designed to assign the desired motion, to adaptively compensate for the body dynamics, and 1042-296X/04$20.00 © 2004 IEEE