Optimal Throwing Motion of Three-Link Underactuated Robot: A Study of Virtual Holonomic Constraints
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Control design for weakly or underactuated systems, i.e. more degrees of freedom than number of control inputs available, has proven to be much more complex than fully actuated due to the new constraints it impose. This thesis will use a three degree of freedom model with passive spring articulated wrist joint for maximizing a ball pitch. A suitable dynamic model is found by the forward kinematic approach, using joint two, three and five of KUKA lightweight robot 4+ as foundation, resulting in planar motions. Then, by using virtual holonomic constraints, the dynamics is reduced in such a way that the wrist is controlled through shoulder and elbow joint. With these new dynamics, the optimization toolbox in MATLAB is used, searching for a motion that will optimize the pitch distance. This report contains both numerical research of optimal trajectory and results of these trajectories implemented on the robot for experiments. A variety of different motions are found, however, the Matlab-function fmincon finds local minimum, which means the results perhaps are only close to the optimal motion for longest pitch.