Optimal Ball Pitching with an Underactuated Model of a Human Arm

A new approach for solving an optimal control problem of ball pitching with an underactuated human-like robot arm is proposed. The system dynamics is simplified to a planar two-link robot with actuation only at the shoulder joint and a passive spring at the elbow joint representing the stiffness of the arm. The objective is to accelerate the ball from an initial configuration at rest in such a way that the projection of its velocity along a certain elevation angle is maximal at a predefined release line. The suggested procedure makes use of a parameterization of the robot motion in terms of geometric relations among the generalized coordinates. We systematically formulate a necessary condition for an optimal motion resulting in a nonlinear differential equation that describes a synchronization of the joint angles. A suitable solution is found by numerically searching over a finite number of free initial conditions.