Fig. 3.

Two-layer controller for the hybrid task. A: discrete dynamics between impacts: the discrete-time controller (light gray box) computes the racket state to reach at the next impact that drives the ball to the desired height. The impact symbol (ellipse) reflects that only the racket state at impact influences the discrete-time dynamics. B: the implementation of the racket trajectory is continuous in time and is achieved by the optimal feedback control policy (dark gray box). It uses the measured state evolution of the racket to generate the control variable u(t), which drives the racket to the desired impact state. The corresponding equations of the model are referenced in the figure boxes.