Optimal control with state and command limits for a simulated ball batting task

We introduce a task oriented optimal controller based on the finite horizon quadratic regulator (LQR). The task of being at a specified position with a specified velocity in specified time is formalized by cost functions. Moreover, we include soft constraints which are part of the cost function, such that the optimal control can be computed in fixed time. We show how soft constraints help to use redundancy and point out the limitations of our soft constraint approach in simulations.