Dynamic optimality in real-time: A learning framework for near-optimal robot motions

Elastic robots have a distinct feature that makes them especially interesting to optimal control: their ability to mechanically store and release potential energy. However, solving any kind of optimal control problem for such highly nonlinear dynamics is feasible only numerically, i.e. offline. In turn, optimal solutions would only contribute a clear benefit for dynamic environments/tasks (apart from rather general insights), if they would be accessible/generalizable in real-time. In this paper, we propose a framework for executing near-optimal motions for elastic arms in real-time. We approach the problem as follows. First, we define a set of prototypical optimal control problems. These represent a reasonable set of motions that an intrinsically elastic robot arm is sought to execute. Exemplary, we solve the optimal control problem for some of these prototypes in a roughly covered task space. Then, we encode the resulting optimal trajectories in a dynamical system via Dynamic Movement Primitives (DMPs). Finally, a distance and cost function based metric forms the basis to generalize from the learned parameterizations to a new unsolved optimal control problem in real-time. In short, we intend to overcome the well known problems of optimal control and learning with associated generalization: being offline and being suboptimal, respectively.