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.

Intelligent Robotics Incorporating Machine Learning Algorithms for Improving Functional Capacity Evaluation and Occupational Rehabilitation

Introduction Occupational rehabilitation often involves functional capacity evaluations (FCE) that use simulated work tasks to assess work ability. Currently, there exists no single, streamlined solution to simulate all or a large number of standard work tasks. Such a system would improve FCE and functional rehabilitation through simulating reaching maneuvers and more dexterous functional tasks that are typical of workplace activities. This paper reviews efforts to develop robotic FCE solutions that incorporate machine learning algorithms. Methods We reviewed the literature regarding rehabilitation robotics, with an emphasis on novel techniques incorporating robotics and machine learning into FCE. Results Rehabilitation robotics aims to improve the assessment and rehabilitation of injured workers by providing methods for easily simulating workplace tasks using intelligent robotic systems. Machine learning-based approaches combine the benefits of robotic systems with the expertise and experience of human therapists. These innovations have the potential to improve the quantification of function as well as learn the haptic interactions provided by therapists to assist patients during assessment and rehabilitation. This is done by allowing a robot to learn based on a therapist's motions ("demonstrations") what the desired workplace activity ("task") is and how to recreate it for a worker with an injury ("patient"). Through Telerehabilitation and internet connectivity, these robotic assessment techniques can be used over a distance to reach rural and remote locations. Conclusions While the research is in the early stages, robotics with integrated machine learning algorithms have great potential for improving traditional FCE practice.

Action Generation Adapted to Low-Level and High-Level Robot-Object Interaction States

Our daily environments are complex, composed of objects with different features. These features can be categorized into low-level features, e.g., an object position or temperature, and high-level features resulting from a pre-processing of low-level features for decision purposes, e.g., a binary value saying if it is too hot to be grasped. Besides, our environments are dynamic, i.e., object states can change at any moment. Therefore, robots performing tasks in these environments must have the capacity to (i) identify the next action to execute based on the available low-level and high-level object states, and (ii) dynamically adapt their actions to state changes. We introduce a method named Interaction State-based Skill Learning (IS²L), which builds skills to solve tasks in realistic environments. A skill is a Bayesian Network that infers actions composed of a sequence of movements of the robot's end-effector, which locally adapt to spatio-temporal perturbations using a dynamical system. In the current paper, an external agent performs one or more kinesthetic demonstrations of an action generating a dataset of high-level and low-level states of the robot and the environment objects. First, the method transforms each interaction to represent (i) the relationship between the robot and the object and (ii) the next robot end-effector movement to perform at consecutive instants of time. Then, the skill is built, i.e., the Bayesian network is learned. While generating an action this skill relies on the robot and object states to infer the next movement to execute. This movement selection gets inspired by a type of predictive models for action selection usually called affordances. The main contribution of this paper is combining the main features of dynamical systems and affordances in a unique method to build skills that solve tasks in realistic scenarios. More precisely, combining the low-level movement generation of the dynamical systems, to adapt to local perturbations, with the next movement selection simultaneously based on high-level and low-level states. This contribution was assessed in three experiments in realistic environments using both high-level and low-level states. The built skills solved the respective tasks relying on both types of states, and adapting to external perturbations.

The Effect of Terrain Inclination on Performance and the Stability Region of Two-Wheeled Mobile Robots

Two-wheeled mobile robots (TWMRs) have a capability of avoiding the tip-over problem on inclined terrain by adjusting the centre of mass position of the robot body. The effects of terrain inclination on the robot performance are studied to exploit this capability. Prior to the real-time implementation of position control, an estimation of the stability region of the TWMR is essential for safe operation. A numerical method to estimate the stability region is applied and the effects of inclined surfaces on the performance and stability region of the robot are investigated. The dynamics of a TWMR is modelled on a general uneven terrain and reduced for cases of inclined and horizontal flat terrain. A full state feedback (FSFB) controller is designed based on optimal gains with speed tracking on a horizontal flat terrain. The performance and stability regions are simulated for the robot on a horizontal flat and inclined terrain with the same controller. The results endorse a variation in equilibrium points and a reduction in stability region for robot motion on inclined terrain.

Adaptation of Robot Skills Models to New Task Contraints

Humanoid robots are required to perform a wide repertoire of tasks working beside humans in complex dynamic environments. Learning mechanisms are important for building up these types of repertoires of robot skills. However, despite the clear advantages of these approaches, it would be impractical to teach the robot skills for every needed task and for every foreseen situation. Robot skills learning approaches to develop humanoid robotic systems would have greater impact if the models of the skills can be operated upon to generate new behaviors of increasing levels of complexity. A framework that allows the adaptation of previously learned motion skills to new unseen contexts is necessary. In this work, we present different modalities for the adaptation and generation of new skill models based on the already learned models of the skills. Experimental results are presented to validate this approach.

Motion planning and reactive control on learnt skill manifolds

We address the problem of encoding and executing skills, i.e. motion tasks involving a combination of specifications regarding constraints and variability. We take an approach that is model-free in the sense that we do not assume an explicit and complete analytical specification of the task – which can be hard to obtain for many realistic robot systems. Instead, we learn an encoding of the skill from observations of an initial set of sample trajectories. This is achieved by encoding trajectories in a skill manifold which is learnt from data and generalizes in the sense that all trajectories on the manifold satisfy the constraints and allowable variability in the demonstrated samples. In new instances of the trajectory-generation problem, we restrict attention to geodesic trajectories on the learnt skill manifold, making computation more tractable. This procedure is also extended to accommodate dynamic obstacles and constraints, and to dynamically react against unexpected perturbations, enabling a form of model-free feedback control with respect to an incompletely modelled skill. We present experiments to validate this framework using various robotic systems – ranging from a three-link arm to a small humanoid robot – demonstrating significant computational improvements without loss of accuracy. Finally, we present a comparative evaluation of our framework against a state-of-the-art imitation-learning method.

Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors

Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.