State constrained optimal control of a ball pitching robot

Article history: Received 30 January 2012 Received in revised form 13 June 2013 Accepted 21 June 2013 Available online 18 July 2013 Wepresent amethod for offline optimal control of a two-link ball pitching robot with the aim of throwing a ball as far as possible. The pitching robot is connected to a motor via a non-linear torsional spring at the shoulder joint. The elbow joint is passive and loaded with a linear torsional spring. Wemodel the system based on an Euler–Lagrange formulation. Constraints on the motor torque and power as well as the angular velocity of the motor shaft are included in the model. By using an interior point method with gradients supplied by a discrete adjoint method, we numerically solve the resulting constrained control problem of finding the optimal piecewise constant motor torque profile and release position. Numerical experiments illustrate the effectiveness of our strategy as well as the effect of the constraints on the objective. In our experiments, the optimal motor torque gives rise to motions comprising an initial backswing; a transition, where the elbow spring accumulates potential energy; and finally a fast acceleration phase leading up the ball release. © 2013 Elsevier Ltd. All rights reserved.