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Non-linear dynamical systems represent a compact, flexible, and robust toolfor reactive motion generation. The effectiveness of dynamical systems relieson their ability to accurately represent stable motions. Several approacheshave been proposed to learn stable and accurate motions from demonstration.Some approaches work by separating accuracy and stability into two learningproblems, which increases the number of open parameters and the overalltraining time. Alternative solutions exploit single-step learning but restrictthe applicability to one regression technique. This paper presents asingle-step approach to learn stable and accurate motions that work with anyregression technique. The approach makes energy considerations on the learneddynamics to stabilize the system at run-time while introducing small deviationsfrom the demonstrated motion. Since the initial value of the energy injectedinto the system affects the reproduction accuracy, it is estimated fromtraining data using an efficient procedure. Experiments on a real robot and acomparison on a public benchmark shows the effectiveness of the proposedapproach.

An Energy-based Approach to Ensure the Stability of Learned Dynamical Systems