Abstract
Feedback control schemes for manipulators for high-speed/high-accuracy trajectory execution are studied. Also separately from this issue, kinematic singularity problems and a model based feedback control method for parallel manipulators are studied.
For the first part, a near-minimum time feedback controller is developed using the non-uniform time scaling technique. Using this controller, the speed of a manipulator is automatically adjusted reacting to the experienced parameter errors and external disturbances. The controller moves the manipulator to follow a given path within a near-minimum time using the available actuator torque capacities in the most efficient manner and maintaining the stability of the controller. A scheme to maintain the stability of feedback controllers for saturated input torque conditions is introduced by locally applying the non-uniform time scaling technique. A variable gain control scheme is combined with the non-uniform time scaling technique to develop a near-minimum time class controller to provide satisfactory accurate trajectory control under extremely uncertain dynamic environment. The uniform time scaling technique is used to strengthen the stability effect of feedback controllers.
For the second part, a general theory is developed for obtaining global properties, such as unstable configurations, of parallel manipulators using direct kinematic polynomial discriminants and Jacobians. The unstable configurations of the platform of a parallel manipulator occur when two branches of the direct kinematics coalesce into one, and the discriminant of the direct kinematic polynomial vanishes. The Jacobian of the direct kinematics, which relates the passive joint velocities and the active joint velocities, is also singular at the unstable configurations. The workspace and accessibility regions of the platform of parallel manipulators are obtained by analyses of the direct and inverse kinematic polynomials and the topological maps between the joint space and task space. The dynamic equations of parallel manipulators are derived using two different approaches, the Newton-Euler formulation and the Lagrangian formulation with the Lagrange multipliers. Then a model based feedback controller is developed using these dynamic equations.