Combination of optimal control methods and machine learning approaches allows to profit from complementary benefits of each field in control of robotic systems. Data from optimal trajectories provides valuable information that can be used to learn a near-optimal state-dependent feedback control policy. To obtain high-quality learning data, careful selection of optimal trajectories, determined by a set of start states, is essential to achieve a good learning performance. In this paper, we extend previous work with new comple-menting strategies to generate start points. These methods complement the existing approach, as they introduce new criteria to identify relevant regions in joint state space that need coverage by new trajectories. It is demonstrated that the extensions significantly improve the overall performance of the previous method in simulation on full nonlinear dynamics model of the industrial Manutec r3 robot arm. Further, it is demonstrated that it suffices to learn a policy that reaches the proximity of the goal state, from where a PI controller can be used for stable control reaching the final system state.

The ability to optimally control robotic systems offers significant advantages for their performance. While time-dependent optimal trajectories can numerically be computed for high dimensional nonlinear system dynamic models, constraints and objectives, finding optimal feedback control policies for such systems is hard. This is unfortunate, as without a policy, the control of real-world systems requires frequent correction or replanning to compensate for disturbances and model errors.In this paper, a feedback control policy is learned from a set of optimal reference trajectories using Gaussian processes. Information from existing trajectories and the current policy is used to find promising start points for the computation of further optimal trajectories. This aspect is important as it avoids exhaustive sampling of the complete state space, which is impractical due to the high dimensional state space, and to focus on the relevant region.The presented method has been applied in simulation to a swing-up problem of an underactuated pendulum and an energy-minimal point-to-point movement of a 3-DOF industrial robot.