Optimal control for viscoelastic robots and its generalization in real-time

Inspired by the elasticity contained in human muscles and tendons, viscoelastic joints are designed with the aim of imitating human motions by exploiting their ability to mechanically store and release potential energy. This distinct feature makes elastic robots especially interesting to the application of optimal control principles, as generating such motions is not possible by data-driven paradigms. In particular, reaching peak velocities by using the stored energy in the springs is of great interest, as such capabilities might open up entirely new application domains. In this paper, we review our results on solving various optimal control problems for elastic joints and full scale robot arms, as well as the experimental validation. Clearly, solving optimal control problems for highly nonlinear full robot dynamics is feasible nowadays only numerically, i.e. offline. In turn, optimal solutions would only contribute a clear benefit for real tasks, if they would be accessible/generalizable in real-time. For this, we developed a framework for executing near-optimal motions of elastic robot arms in real-time. In contrast to existing approaches, we use dynamically optimal motions (i.e. offline solutions of optimal control problems) as given learning input and then apply generalization via Dynamic Movement Primitives (DMPs). With this approach, we intend to overcome the well-known problems of optimal control and data-driven learning with associated generalization: being offline and being suboptimal (In fact, data-driven approaches can only be applied if the solution is already quite obvious for the human teacher. In case of highly nonlinear problems these “intuitive” initial solutions are typically not available.), respectively.