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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.

Parallel manipulators are prone to have force-unconstrained configurations. If the resultant. forces together do not span the system of forces to be applied or sustained, the manipulator is degenerate and is force unconstrained. Physically. the mobile platform can have motion even if all the actuated ,joints are locked, i.e., the manipu¬lator can instantaneously gain one or more degrees of freedom that are unconstrained by the actuators. Since force-unconstrained configurations are uncontrollable, the identification and elimination of such configurations become critical. Two methodologies for identifying the force-unconstrained poses are analyzed. The first method involves the differentiation of the nonlinear kinematic constraints of the input and output variables with respect to time. The second method makes use of the reciprocal screws associated with the actuated joints. Force-unconstrained poses of planar manipulators are analyzed depending on their actuation: Non Redundant Planar Parallel Manipulators.- Force-unconstrained poses of non-redundantly actuated planar parallel manipulators can be mathematically expressed as a function of the three variables that define the dimensional space of the ma¬nipulator. i.e., the location and orientation of the mobile platform. As a conse- Quence, these poses can be plotted as surfaces in the mentioned three dimensional space. i.e., there are two orders of infinity of force-unconstrained poses. Examples of force-unconstrained poses of parallel manipulators are presented: 3-RPR, 3-PRR, and 3-RRR, where the underscore indicates the actuated joint. For the 3-RPR ma¬nipulator, a comparison and discussion between both methodologies is carried out. For the 3-PRR and 3-RRR manipulators, an efficient technique for identifying their force-unconstrained poses, based upon having joint displacements as known values, is presented. Planar Parallel Manipulators with In-Branch Redundancy.- Force-unconstrained poses of planar parallel manipulators with actuated joints replacing passive joints lead to conditions of the joint displacements that have to be satisfied. In particular, the RRR - 2RRR. PRR - 2PRR. and RRR - 2RRR layouts are analyzed. In addi¬tion, equivalent mechanisms, whose motions describe the path of continuous force-unconstrained poses. are presented. The force-unconstrained poses of the analyzed layouts with in-branch redundancy represent curves in the three dimensional space, i.e., there is one order of infinity of force-unconstrained poses. Planar Parallel Manipulators with, Additional Actuated Branches.- Force-uncon-strained poses of planar parallel manipulators with the inclusion of actuated branches, beyond three. lead to a system of multivariable polynomials. Elimination methods are used to reduce the multivariable polynomials to a single polynomial in terms of one variable. In particular, Gröbner Bases and dialytic elimination methods are employed. The actuation layouts 4-RPR. 4-PRR. and 4-RRR are analyzed. The force-unconstrained poses of the analyzed planar parallel manipulators with additional actuated branches also represent curves in the mentioned three dimensional space, i.e.. there is one order of infinity of force-unconstrained poses.