Active Inverse Model Learning with Error and Reachable Set Estimates In this work, we propose a framework to learn an inverse model of redundant systems. We address three problems. By formalizing what it actually means to learn an inverse model, we derive a method where the inverse model, represented as a neural network, is learned by minimizing an upper bound on the real performance error, which is provided by a forward model (kernel regression or Gaussian process) learned on the currently available data. Most machine learning methods focus on learning the mapping of the function. For inverse models, it is, however, crucial to know the reachable set of the true forward model, since this becomes the domain of the inverse. Therefore, we secondly propose a method to estimate the reachable set of the system. Finally, we develop an active exploration strategy that is based on maximizing a lower bound on the true filldistance to efficiently generate the data in the high dimensional input space. A key feature of our method is that the resulting learned inverse model provides error bounds on its performance.From an application point of view, this work is motivated by learning to control musculoskeletal systems. In the experiments, we show for both a simulated model of a human arm with six muscles and a real muscledriven robot that the proposed method is able to learn the reachable set of these systems as well as a policy that enables to accurately control the position.

Cascaded Gaussian Processes for Dataefficient Robot Dynamics Learning Motivated by the recursive NewtonEuler formulation, we propose a novel cascaded Gaussian process learning framework for the inverse dynamics of robot manipulators. This approach leads to a significant dimensionality reduction which in turn results in better learning and data efficiency. We explore two formulations for the cascading: the inward and outward, both along the manipulator chain topology. The learned modeling is tested in conjunction with the classical inverse dynamics model (semiparametric) and on its own (nonparametric) in the context of feedforward control of the arm. Experimental results are obtained with Jaco 2 sixDOF and SARCOS sevenDOF manipulators for randomly defined sinusoidal motions of the joints in order to evaluate the performance of cascading against the standard GP learning. In addition, experiments are conducted using Jaco 2 on a task emulating a pouring maneuver. Results indicate a consistent improvement in learning speed with the inward cascaded GP model and an overall improvement in data efficiency and generalization.