Direct state-to-action mapping for high DOF robots using ELM

Methods of optimizing a single trajectory are mature enough for planning in many applications. Yet such optimization methods applied to high Degree-Of-Freedom robots either consume too much time to be real-time or approximate the dynamics such that they lack physical consistency. In this paper, we present a method of precomputing optimized trajectories and compressing the information to get a compact representation of the optimal policy function. By varying the initial configuration of a robot and optimizing multiple trajectories, the controller gains knowledge about the optimal policy function. Such computation can be performed on a powerful workstation or even supercomputers instead of an onboard computer of the robot. The precomputed optimal trajectories are stored in a Single-hidden Layer Feedforward neural Network (SLFN) using Optimally Pruned Extreme Learning Machine (OP-ELM). This ensures minimal representation of the model and fast evaluation of the SLFN. We first explain our method using a simple time-optimal control problem with an analytical solution. We then demonstrate how this method can work even for high dimensional state by optimizing a foothold strategy of a full quadruped robot in simulation.