Towards a Real-Time Optimal Motion Framework

Abstract

Variable stiffness robots have a distinct feature that makes them especially interesting to application of energetic optimality: their ability to mechanically store and release energy. However, solving any kind of optimization problem for such highly nonlinear dynamics is only possible numerically, i.e. offline. In turn, numerical 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 thesis, a general framework for executing near-optimal motions for Rigid Robots and Variable Stiffness Arms in real-time is proposed. The approach for the problem is formulated as follows. First, a set of prototypical optimization problems, which represent a reasonable set of motions are sought to execute is defined. For some of these distinct tasks, the optimization problem for an ensemble roughly covering the respective task space is solved. Then, the associated cost function is used as a clustering metric for learning manifolds of the optimal solution space and encode them in a dynamical system via Dynamic Movement Primitives (DMPs). Then, a distance and cost function based metric is proposed to generalize from the learned parameterizations to a new optimization problem in real-time. In short, this thesis intense to overcome some of the well known problems of optimal control and nonlinear optimization, which are offline schemes, and the one of learning with associated generalization, which is suboptimality. The developed verified on two robotic systems, namely the DLR Light Weight Robot and the DLR Hand-Arm System. Several dynamic tasks as ball throwing or energy optimal point-to-point motions are considered and experimental validated.