Control of Cooperative Underactuated Manipulators: A Robustness Comparison Study

In this article we present a comparison study of the robustness properties of three model-based nonlinear controllers for cooperative underactuated manipulators. Two of the controllers are based on feedback linearization of the nonlinear dynamic coupling between the torques applied at the actuated joints and the Cartesian acceleration of the load. The third is based on a gravity compensation scheme. Their robustness is checked against uncertainties in each of the links’ masses and inertias. Simulation results provide the basis for the comparison of the controllers’ robustness. 1 Underactuated cooperative manipulators In the past ten years two important robotics research areas have develop and matured, namely, control of a team of cooperative manipulators, and control of underactuated manipulators. Cooperative manipulators are utilized when a manipulation task involves bulky, large, or heavy loads. Progress attained in this area includes solutions to the problems of internal force control [19], load distribution among the manipulators [22], hybrid position / force control [20], teleoperation of multiple manipulators [21], joint flexibility [10], and distributed control [12]. Underactuated manipulators are those mechanisms equipped with unactuated joints, which arise in practice either because of actuator failures or because of design considerations. In this area, progress includes control of manipulators whose unactuated joints may or may not be equipped with brakes [1], [2], [6], [8], [13], [14], [16], optimal control of manipulators with any number of passive joints [7], and a pathplanning method for obstacle avoidance [5]. It is only recently that researchers have focussed on the combined control problem, i.e., controlling a team of cooperative underactuated manipulators, where one or more manipulators are equipped with unactuated joints [11], [17], [18]. Solutions to such problem are of significance because they will enhance tremendously the faulttolerance capabilities of regular manipulators working cooperatively on desolate or hard-toreach environments, such as space stations or nuclear plants. Recently, three control methods have been proposed for the positioning of a load jointly grasped by a team of underactuated manipulators. Two of them are based on the classical computed torque method, adapted to reflect the fact that the internal force on the load dictates the interaction between the manipulators in the team, and the fact that some of them are equipped with unactuated joints [3], [4]. The third is based on a gravity compensation scheme plus a proportionalderivative (PD) component [11]. All three controllers have been experimentally validated on a team of two 2-link underactuated manipulators. 1st Workshop on Robotics and Mechatronics, Shatin, Hong Kong, Sep. 1998, vol. 1, pp. 279-286. The contribution of this paper is the presentation of an extensive robustness comparison study of the three aforementioned controllers. The control methods are tested against parametric uncertainties in the dynamic model, a type of disturbance that is present in almost all commercial and academic manipulators. Simulation results provide the basis for the comparison of the controllers’ robustness. The paper is organized as follows: in Section 2 we review the kinematic and dynamic modeling of cooperative underactuated manipulators, already presented by the authors in [3], [11] and the basis for all three controllers’ derivation. In Section 3 we present each of the controllers’ formulation. In Section 4 we present the methodology adopted for the comparison study. In Section 5 we present the simulation results and the analysis of each controller ́s robustness properties. In section 6 we present our conclusions and directions for future work. 2 Modeling of cooperative underactuated manipulators 2.1 Kinematic modeling Without loss of generality, we consider in this paper two identical n-link nonredundant manipulators grasping a shared load (Figure 1). The vector q1 is the joint vector of the first manipulator, and q2 is the joint vector of the second one. The combined joint vector q is defined as