A dynamical system approach to realtime obstacle avoidance

This paper presents a novel approach to real-time obstacle avoidance based on Dynamical Systems (DS) that ensures impenetrability of multiple convex shaped objects. The proposed method can be applied to perform obstacle avoidance in Cartesian and Joint spaces and using both autonomous and non-autonomous DS-based controllers. Obstacle avoidance proceeds by modulating the original dynamics of the controller. The modulation is parameterizable and allows to determine a safety margin and to increase the robot's reactiveness in the face of uncertainty in the localization of the obstacle. The method is validated in simulation on different types of DS including locally and globally asymptotically stable DS, autonomous and non-autonomous DS, limit cycles, and unstable DS. Further, we verify it in several robot experiments on the 7 degrees of freedom Barrett WAM ar

A Dynamical System-based Approach to Modeling Stable Robot Control Policies via Imitation Learning

Despite tremendous advances in robotics, we are still amazed by the proficiency with which humans perform movements. Even new waves of robotic systems still rely heavily on hardcoded motions with a limited ability to react autonomously and robustly to a dynamically changing environment. This thesis focuses on providing possible mechanisms to push the level of adaptivity, reactivity, and robustness of robotic systems closer to human movements. Specifically, it aims at developing these mechanisms for a subclass of robot motions called “reaching movements”, i.e. movements in space stopping at a given target (also referred to as episodic motions, discrete motions, or point-to-point motions). These reaching movements can then be used as building blocks to form more advanced robot tasks. To achieve a high level of proficiency as described above, this thesis particularly seeks to derive control policies that: 1) resemble human motions, 2) guarantee the accomplishment of the task (if the target is reachable), and 3) can instantly adapt to changes in dynamic environments. To avoid manually hardcoding robot motions, this thesis exploits the power of machine learning techniques and takes an Imitation Learning (IL) approach to build a generic model of robot movements from a few examples provided by an expert. To achieve the required level of robustness and reactivity, the perspective adopted in this thesis is that a reaching movement can be described with a nonlinear Dynamical System (DS). When building an estimate of DS from demonstrations, there are two key problems that need to be addressed: the problem of generating motions that resemble at best the demonstrations (the “how-to-imitate” problem), and most importantly, the problem of ensuring the accomplishment of the task, i.e. reaching the target (the “stability” problem). Although there are numerous well-established approaches in robotics that could answer each of these problems separately, tackling both problems simultaneously is challenging and has not been extensively studied yet. This thesis first tackles the problem mentioned above by introducing an iterative method to build an estimate of autonomous nonlinear DS that are formulated as a mixture of Gaussian functions. This method minimizes the number of Gaussian functions required for achieving both local asymptotic stability at the target and accuracy in following demonstrations. We then extend this formulation and provide sufficient conditions to ensure global asymptotic stability of autonomous DS at the target. In this approach, an estimation of the underlying DS is built by solving a constraint optimization problem, where the metric of accuracy and the stability conditions are formulated as the optimization objective and constraints, respectively. In addition to ensuring convergence of all motions to the target within the local or global stability regions, these approaches offer an inherent adaptability and robustness to changes in dynamic environments. This thesis further extends the previous approaches and ensures global asymptotic stability of DS-based motions at the target independently of the choice of the regression technique. Therefore, it offers the possibility to choose the most appropriate regression technique based on the requirements of the task at hand without compromising DS stability. This approach also provides the possibility of online learning and using a combination of two or more regression methods to model more advanced robot tasks, and can be applied to estimate motions that are represented with both autonomous and non-autonomous DS. Additionally, this thesis suggests a reformulation to modeling robot motions that allows encoding of a considerably wider set of tasks ranging from reaching movements to agile robot movements that require hitting a given target with a specific speed and direction. This approach is validated in the context of playing the challenging task of minigolf. Finally, the last part of this thesis proposes a DS-based approach to realtime obstacle avoidance. The presented approach provides a modulation that instantly modifies the robot’s motion to avoid collision with multiple static and moving convex obstacles. This approach can be applied on all the techniques described above without affecting their adaptability, swiftness, or robustness. The techniques that are developed in this thesis have been validated in simulation and on different robotic platforms including the humanoid robots HOAP-3 and iCub, and the robot arms KATANA, WAM, and LWR. Throughout this thesis we show that the DS-based approach to modeling robot discrete movements can offer a high level of adaptability, reactivity, and robustness almost effortlessly when interacting with dynamic environments

A Dynamical System Approach to Realtime Obstacle Avoidance

This paper presents a novel approach to real-time obstacle avoidance based on dynamical systems (DS) that ensures impenetrability of multiple convex shaped objects. The proposed method can be applied to perform obstacle avoidance in Cartesian and Joint spaces and using both autonomous and non-autonomous DS-based controllers. Obstacle avoidance proceeds by modulating the original dynamics of the controller. The modulation is parameterizable and allows to determine a safety margin and to increase the robot's reactiveness in the face of uncertainty in the localization of the obstacle. The method is validated in simulation on different types of DS including locally and globally asymptotically stable DS, autonomous and non-autonomous DS, limit cycles, and unstable DS. Further, we verify it in several robot experiments on the 7 degrees of freedom Barrett WAM arm

The derivatives of the SEDS optimization cost function and constraints with respect to the learning parameters

This technical report provides supplementary information for the optimization problems defined for Stable Estimator of Dynamical Systems (SEDS). Reading of this report is not necessary for researchers who only want to use SEDS learning algorithm. The report is aimed at helping those persons who want to develop SEDS, or to write their own optimization program. All the formulations reported here are developed for SEDS models; however, they can also be used for general Gaussian Mixture Model (GMM) formulations. In the case of the latter, they should be slightly modified to consider the general form of GMM. Hopefully, the report should be clear enough to help readers in that

Realtime Avoidance of Fast Moving Objects: A Dynamical System-based Approach

In this paper, we provide an extension to our previous approach (Khansari & Billard (2012), Autonomous Robots) to perform obstacle avoidance in the presence of multiple fast moving and rotating obstacles. Our approach leverage on the notion of DS to generate robot motions that are inherently robust to perturbations and can instantly adapt to changes in the target and obstacles' positions in a dynamically moving environments. We validate our method in the challenging experiment of dodging a fast moving and rotating box on the 7-degrees of freedom (DoF) KUKA DLR arm

Learning Stable Non-Linear Dynamical Systems with Gaussian Mixture Models

This paper presents a method for learning 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, called Stable Estimator of Dynamical Systems (SEDS), to learn the parameters of the DS to ensure that all motions follow closely the demonstrations while ultimately reaching in 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 encountered during the motion. The method is evaluated through a set of robot experiments and on a library of human handwriting motions

BM: An Iterative Method to Learn Stable Non-Linear Dynamical Systems with Gaussian Mixture Models

We model the dynamics of non-linear discrete (i.e. point-to- point) robot motions as a time-independent system described by an autonomous dynamical system (DS). We propose an iterative algorithm to estimate the form of the DS through a mixture of Gaussian distributions. We prove that the resulting model is asymptotically stable at the target. We validate the accuracy of the model on a library of 2D human motions and to learn a control policy through human demonstrations for two multi- degrees of freedom robots. We show the real-time adaptation to perturbations of the learned model when controlling the two kinematically-driven robots

Learning Nonlinear Multivariate Dynamics of Motion in Robotic Manipulators [accepted]

Motion imitation requires reproduction of a dynamical signature of a movement, i.e. a robot should be able to encode and reproduce a particular path together with a specific velocity and/or an acceleration profile. Furthermore, a human provides only few demonstrations, that cannot cover all possible contexts in which the robot will need to reproduce the motion autonomously. Therefore, the encoding should be able to efficiently generalize knowledge by generating similar motions in unseen context. This work follows a recent trend in Programming by Demonstration in which the dynamics of the motion is learned. We present an algorithm to estimate multivariate robot motions through a Mixture of Gaussians. The strengths of the proposed encoding are three-fold: i) it allows to generalize a motion to unseen context; ii) it provides fast on-line replanning of the motion in the face of spatio-temporal perturbations; iii) it may embed different types of dynamics, governed by different attractors. The generality of the method to estimate arbitrary nonlinear motion dynamics is demonstrated by accurately estimating a set of known non-linear dynamical systems. The platformindependency and real-time performance of the method are further validated to learn the non-linear motion dynamics of manipulation tasks with different robotic platforms. We provide an experimental comparison of our approach with an related state-of-the-art method

Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module

The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project

Neural Learning of Vector Fields for Encoding Stable Dynamical Systems

Lemme A, Reinhart F, Neumann K, Steil JJ. Neural Learning of Vector Fields for Encoding Stable Dynamical Systems. Neurocomputing. 2014;141:3-14