In this research, time optimal control is considered for the hit motion of a badminton robot during a serve operation. For this task the racket always starts at rest in a given position and has to move to a target state, defined by a target position and a non-zero target velocity. The goal is to complete this motion in as little time as possible, yet without violating bounds on the actuator. To find controllers satisfying these requirements, a reinforcement learning approach is implemented, using a Natural Actor-Critic (NAC) reinforcement learning algorithm. This approach is experimentally shown to yield the desired robot motions after about 200 trials. Next to this model-free learning approach, the control signals obtained with a model-based optimization are also applied to the robot. The results achieved with both approaches are compared, and a thorough analysis is presented, highlighting the properties of each approach, as well as their advantages and drawbacks.@en