We propose a learning framework, named Multi-Coordinate Cost Balancing (MCCB), to address the problem of acquiring point-to-point movement skills from demonstrations. MCCB encodes demonstrations simultaneously in multiple differential coordinates that specify local geometric properties. MCCB generates reproductions by solving a convex optimization problem with a multi-coordinate cost function and linear constraints on the reproductions, such as initial, target, and via points. Further, since the relative importance of each coordinate system in the cost function might be unknown for a given skill, MCCB learns optimal weighting factors that balance the cost function. We demonstrate the effectiveness of MCCB via detailed experiments conducted on one handwriting dataset and three complex skill datasets.
Dynamical systems-based trajectory learning methods, such as @cite_17 @cite_0 @cite_19 , encode demonstrations using statistical dynamical systems and generate reproductions by forward propagating the dynamics. While such deterministic methods exhibit several advantages, such as convergence guarantees and robustness to perturbations, they are restricted to learning in a single coordinate system and ignore inherent uncertainties in the demonstrations. They incentivize conformance to the norm even when demonstrations exhibit high variance.
@cite_0 @cite_19 @cite_17
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This paper presents a unified framework of model-learning algorithms, called contracting dynamical system primitives (CDSP), that can be used to learn pose (i.e., position and orientation) dynamics of point-to-point motions from demonstrations. The position and the orientation (represented using quaternions) trajectories are modeled as two separate autonomous nonlinear dynamical systems. The special constraints of the ( S ^ 3 ) manifold are enforced in the formulation of the system that models the orientation dynamics. To capture the variability in the demonstrations, the dynamical systems are estimated using Gaussian mixture models (GMMs). The parameters of the GMMs are learned subject to the constraints derived using partial contraction analysis. The learned models’ reproductions are shown to accurately reproduce the demonstrations and are guaranteed to converge to the desired goal location. Experimental results illustrate the CDSP algorithm’s ability to accurately learn position and orientation dynamics and the utility of the learned models in path generation for a Baxter robot arm. The CDSP algorithm is evaluated on a publicly available dataset and a synthetic dataset, and is shown to have the lowest and comparable average reproduction errors when compared to state-of-the-art imitation learning algorithms. Nonlinear dynamical systems are a promising representation to learn complex robot movements. Besides their undoubted modeling power, it is of major importance that such systems work in a stable manner. We therefore present a neural learning scheme that estimates stable dynamical systems from demonstrations based on a two-stage process: first, a data-driven Lyapunov function candidate is estimated. Second, stability is incorporated by means of a novel method to respect local constraints in the neural learning. We show in two experiments that this method is capable of learning stable dynamics while simultaneously sustaining the accuracy of the estimate and robustly generates complex movements. This paper presents a method to learn discrete robot motions from a set of demonstrations. We model a motion as a nonlinear autonomous (i.e., time-invariant) dynamical system (DS) and define sufficient conditions to ensure global asymptotic stability at the target. We propose a learning method, which is called Stable Estimator of Dynamical Systems (SEDS), to learn the parameters of the DS to ensure that all motions closely follow the demonstrations while ultimately reaching and stopping at the target. Time-invariance and global asymptotic stability at the target ensures that the system can respond immediately and appropriately to perturbations that are encountered during the motion. The method is evaluated through a set of robot experiments and on a library of human handwriting motions.