Locally active globally stable dynamical systems: Theory, learning, and experiments

State-dependent dynamical systems (DSs) offer adaptivity, reactivity, and robustness to perturbations in motion planning and physical human-robot interaction tasks. Learning DS-based motion plans from non-linear reference trajectories is an active research area in robotics. Most approaches focus on learning DSs that can (i) accurately mimic the demonstrated motion, while (ii) ensuring convergence to the target, i.e., they are globally asymptotically (or exponentially) stable. When subject to perturbations, a compliant robot guided with a DS will continue following the next integral curves of the DS towards the target. If the task requires the robot to track a specific reference trajectory, this approach will fail. To alleviate this shortcoming, we propose the locally active globally stable DS (LAGS-DS), a novel DS formulation that provides both global convergence and stiffness-like symmetric attraction behaviors around a reference trajectory in regions of the state space where trajectory tracking is important. This allows for a unified approach towards motion and impedance encoding in a single DS-based motion model, i.e., stiffness is embedded in the DS. To learn LAGS-DS from demonstrations we propose a learning strategy based on Bayesian non-parametric Gaussian mixture models, Gaussian processes, and a sequence of constrained optimization problems that ensure estimation of stable DS parameters via Lyapunov theory. We experimentally validated LAGS-DS on writing tasks with a KUKA LWR 4+ arm and on navigation and co-manipulation tasks with iCub humanoid robots.

Adaptive sensorimotor peripersonal space representation and motor learning for a humanoid robot

Micha Hersch

This thesis presents possible computational mechanisms by which a humanoid robot can develop a coherent representation of the space within its reach (its peripersonal space), and use it to control its movements. Those mechanisms are inspired by current theories of peripersonal space representation and motor control in humans, targeting a cross-fertilization between robotics on one side, and cognitive science on the other side. This research addresses the issue of adaptivity the sensorimotor level, at the control level and at the level of simple task learning. First, this work considers the concept of body schema and suggests a computational translation of this concept, appropriate for controlling a humanoid robot. This model of the body schema is adaptive and evolves as a result of the robot sensory experience. It suggests new avenues for understanding various psychophysical and neuropsychological phenomenons of human peripersonal space representation such as adaptation to distorted vision and tool use, fake limbs experiments, body-part centered receptive fields, and multimodal neurons. Second, it is shown how the motor modality can be added to the body schema. The suggested controller is inspired by the dynamical system theory of motor control and allows the robot to simultaneously and robustly control its limbs in joint angles space and in end-effector location space. This amounts to controlling the robot in both proprioceptive and visual modalities. This multimodal control can benefit from the advantages offered by each modality and is better than traditional robotic controllers in several respects. It offers a simple and elegant solution to the singularity and joint limit avoidance problems and can be seen as a generalization of the Damped Least Square approach to robot control. The controller exhibits several properties of human reaching movements, such as quasi-straight hand paths and bell-shaped velocity profiles and non-equifinality. In a third step, the motor modalities is endowed with a statistical learning mechanism, based on Gaussian Mixture Models, that enables the humanoid to learn motor primitives from demonstrations. The robot is thus able to learn simple manipulation tasks and generalize them to various context, in a way that is robust to perturbations occurring during task execution. In addition to simulation results, the whole model has been implemented and validated on two humanoid robots, the Hoap3 and the iCub, enabling them to learn their arm and head geometries, perform reaching movements, adapt to unknown tools, and visual distortions, and learn simple manipulation tasks in a smooth, robust and adaptive way. Finally, this work hints at possible computational interpretations of the concepts of body schema, motor perception and motor primitives.

EPFL2009

Handling of multiple constraints and motion alternatives in a robot programming by demonstration framework

Aude Billard, Sylvain Calinon

We consider the problem of learning robust models of robot motion through demonstration. An approach based on Hidden Markov Model (HMM) and Gaussian Mixture Regression (GMR) is proposed to extract redundancies across multiple demonstrations, and build a time- independent model of a set of movements demonstrated by a human user. Two experiments are presented to validate the method, that consist of learning to hit a ball with a robotic arm, and of teaching a humanoid robot to manipulate a spoon to feed another humanoid. The experiments demonstrate that the proposed model can efficiently handle several aspects of learning by imitation. We first show that it can be utilized in an unsupervised learning manner, where the robot is autonomously organizing and encoding variants of motion from the multiple demonstrations. We then show that the approach allows to robustly generalize the observed skill by taking into account multiple constraints in task space during reproduction.

2009

Bimanual Skill Learning with Pose and Joint Space Constraints

Sylvain Calinon

As humanoid robots become commonplace, learning and control algorithms must take into account the new challenges imposed by this morphology, if we aim to fully exploit their potential. One of the most prominent characteristics of such robots is their bimanual structure. Most research on learning bimanual skills has focused on the coordination between end-effectors, exploiting operational space formulations. However, motion patterns in bimanual scenarios are not exclusive to operational space, also occurring at joint level. Moreover, in addition to position, the end-effector orientation is also essential for bimanual operation. Here, we propose a framework for simultaneously learning constraints in configuration and operational spaces, while considering end-effector orientations, overlooked in previous works. In particular, we extend the Task-Parameterized Gaussian Mixture Model (TP-GMM) with novel, Jacobian-based operators that address the foregoing problem. The proposed framework is evaluated in a bimanual task with the COMAN humanoid that requires the consideration of operational and configuration space movements.

2018

Adaptive sensorimotor peripersonal space representation and motor learning for a humanoid robot

Micha Hersch

EPFL2009