Nonlinear control of co-operating hydraulic manipulators
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This thesis presents the design, analysis, and numerical and experimental evaluation of nonlinear controllers for co-operation among several hydraulic robots operating in the presence of significant system uncertainties, non-linearities and friction. The designed controllers allow hydraulically driven manipulators to (i) co-operatively handle a rigid object (payload) following a given trajectory, (ii) share the payload and (iii) maintain an acceptable internal force on the object. A general description of the kinematic and dynamic relations for a hydraulically actuated multi-manipulator system is presented first. The entire mathematical model incorporates object dynamics, robot dynamics, hydraulic actuator functions and friction dynamics. For the purpose of simulations, a detailed numerical simulation program of such a system is also developed, in which two three-link planar robot manipulators resembling the Magnum hydraulic manipulators manufactured by ISE, interact with each other through manipulating a common object. The regulating control problem is studied next, in which the desired position of the object and the corresponding desired link displacement change step-wise. Initially, a controller is designed based on a backstepping technique, assuming that full knowledge of the dynamics and kinematics of the system is available. The assumption is then relaxed and the control system is analyzed. Based on the analysis, the controller is then modified to account for the uncertainty of the payload, robot dynamic parameters and hydraulic functions. Next, the regulating controller is extended to a tracking controller, which allows the object to follow a given trajectory and is robust against parameter uncertainties. Additionally, an observer is added to the controller to avoid the need of acceleration feedback. To investigate the effect of friction force, the above controllers are examined by introducing the most recent and complete LuGre friction model into the system dynamics. The tracking controller is then redesigned to compensate the effect of friction. Observers are designed to observe the immeasurable friction states. Based on the observed friction states and estimated friction parameters, an appropriate friction compensation scheme is designed which does not directly use velocity in order to avoid the need of acceleration feedback by the controller. Finally, the problem of “explosion of terms” coming from the backstepping method is solved by using the concept of dynamic surface control in which a low pass filter is integrated to avoid model differentiation. Simulations are carried out for analysis of the control system and verification of the developed controllers. Experimental examinations are performed on an available hydraulic system consisting of two single-axis hydraulic actuators.