NULL-SPACE-BASED BEHAVIOR GUIDANCE OF PLANAR DUAL-ARM UVMS Signe Moe 1 , Gianluca Antonelli 2 and Kristin Y. Pettersen 1 Abstract— Dual-arm Underwater Vehicle-Manipulator Sys- tems are able perform a variety of interventions tasks, and there are still many challenges related to making such vehicles autonomous. This paper presents a guidance method for gen- erating reference trajectories for such a system by considering the main manipulator and the vehicle base as a leader unit and the secondary manipulator as a follower unit. The desired behavior of the system is expressed as different tasks, and the reference trajectories are calculated using pseudo-inverse Jacobian task matrices and the null-space-based method. The proposed method has been implemented for a particular planar UVMS and simulated for a defined set of tasks. Simulation results confirm the correctness of the proposed method. I. INTRODUCTION Unmanned Underwater Vehicles (UUVs) play an increas- ingly important role within subsea exploration, including marine archeology, biology and the oil and gas sector. There exists two main types of UUVs: Remotely Operated Vehi- cles (ROVs) and Autonomous Underwater Vehicles (AUVs). ROVs are linked to a surface ship through a physical tether and are often fully/partly operated by a human operator, whereas AUVs are operated independently and are not tethered [1]. Although research is aiming to increase the degree of autonomy of UUVs, there are still many challenges related to this. AUV survey operations has a high degree of autonomy, while inspection and in particular intervention operations still require a human in the loop, at the very least as an observer that can intervene if necessary [2]. A typical UUV has a camera mounted on the body so the operator/human supervisor can observe what is happening. However, a fixed camera can never give the same viewing freedom and flexibility as that of a movable camera. In case the mission requires interaction between the UUV and the environment, one or more manipulator arms can be attached to the vehicle body. This entire system is referred to as an Underwater Vehicle-Manipulator System (UVMS) [3]. Such vehicles have a much wider spectrum of possible missions since they are not limited to survey missions only, but can perform tasks such as sampling, retrieval of instruments, assembling and/or maintenance of underwater structures etc. At a kinematic level, a UVMS can be considered as a 1 S.Moe and K.Y.Pettersen are with the Center for Autonomous Marine Operations and Systems (AMOS), at The Department of Engineering Cybernetics, Norwegian University of Science and Technology (NTNU), Trondheim, Norway { signe.moe, kristin.y.pettersen }@itk.ntnu.no 2 G.Antonelli is with the Department of Electrical and Information Engineering, University of Cassino and Southern Lazio, Cassino, Italy antonelli@unicas.it manipulator arm mounted on a floating base. Thus, the theory also applies to other such systems, for instance a quadcopter or an UAV (Unmanned Aerial Vehicle) with one or more manipulator arms. A general floating base system without a manipulator arm has 6 Degrees of Freedom (DOFs): 3 for position and 3 for orientation. Adding a n-link manipulator arm results in a 6 + n DOF system, which is said to be kinematically redundant if it possesses more DOFs than those required to perform a certain task [4]. A general manipulation task is specified in terms of end effector position and orientation, and as such an UVMS is always kinematically redundant because the necessary DOFs are provided by the vehicle itself. In this case, it will be the guidance system’s task to calculate the desired vehicle position/velocity and manipulator angles/angular velocities based on the current system state and the desired position/orientation of the ma- nipulator end effector. To do so, one must solve the inverse kinematics problem. The most common approach to this is to use a Jacobian-based method [5]-[8]. The ”excess” DOFs can be utilized as a way to per- form several tasks using Null-Space-Based (NSB) behavioral control [9]. Several different tasks and their corresponding forward kinematics and Jacobian matrices are defined in [3]. Examples of such secondary tasks are manipulability maxi- mization, obstacle avoidance, joint limit avoidance, actuator power consumption, etc [10]-[13]. A task-priority framework has been successfully implemented within the TRIDENT EU FP7 project [14]. A two-manipulator system can use the two arms to cooperate and thereby perform more complex tasks and pick up larger/heavier objects. A lot of research has been done on fixed dual-arm systems regarding coordinated and cooperative control, leader/follower control, force control, collision detection and avoidance etc. A Jacobian based method is used to calculate the desired manipulator motion in [15]. This paper considers relative motion between the two end effectors rather than the motion relative to a world- fixed coordinate system as this is more intuitive. In [16] a leader-follower set-up between the two manipulators is proposed, where the reference of the leader manipulator is feed-forwarded to calculate the appropriate reference of the follower. A centralized impedance control strategy using force and moment measurements is considered in [17]. Here, the dynamics rather than the kinematics is regarded. How- ever, the dynamics of a dual-arm UVMS is highly complex, non-linear and nearly impossible to model correctly without making simplifications and approximations. The kinematics, however, is straight forward and exactly defined, and thus a