Optimal control of a ball pitching robot

Summary form only given. We study a two-link pitching robot, with an active gripping mechanism and aim to make it throw a ball as far as possible. The two links are connected at the elbow joint by a linear torsional spring. The gripping mechanism is able to hold a ball and release it at any specified time. The two-link pitching robot is connected to a motor shaft at the shoulder joint by a non-linear torsional spring. The shoulder joint is held fixed at the origin of the coordinate system. The configuration of the arm and the motor shaft is illustrated in Figure 1 and described by the angels q₁ and q_m, measured with respect to the horizontal axis, respectively, whereas q₂ denote the angle change between the arm and forearm at the elbow joint.