This paper presents an optimal trajectory planner for a robotic batting task . The specific case of a table tennis game performed by a robot is considered. Given an estimation of the trajectory of the ball during the free flight, the method addresses the determination of the paddle configuration (pose and velocity) to return the ball at a desired position with a desired spin. The implemented algorithm takes into account the hybrid dynamic model of the ball in free flight as well as the state transition at the impact (the reset map). An optimal trajectory that minimizes the acceleration functional is generated for the paddle to reach the desired impact position, velocity and orientation. Simulations of different case studies further bolster the approach along with a comparison with state-of-the-art methods
