Time Generalization of Trajectories Learned on Articulated Soft Robots

To avoid feedback-related stiffening of articulated soft robots, a substantive feedforward contribution is crucial. However, obtaining reliable feedforward actions requires very accurate models, which are not always available for soft robots. Learning-based approaches are a promising solution to the problem. They proved to be an effective strategy achieving good tracking performance, while preserving the system intrinsic compliance. Nevertheless, learning methods require rich data sets, and issues of scalability and generalization still remain to be solved. This letter proposes a method to generalize learned control actions to execute a desired trajectory with different velocities - with the ultimate goal of making these learning-based architectures sample efficient. More specifically we prove that the knowledge of how to execute a same trajectory at five different speeds is necessary and sufficient to execute the same trajectory at any velocity - without any knowledge of the model. We also give a simple constructive way to calculate this new feedforward action. The effectiveness of the proposed technique is validated in extensive simulation on a Baxter robot with soft springs playing a drum, and experimentally on a VSA double pendulum performing swinging motions.