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

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

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

Learning modular policies for robotics

A promising idea for scaling robot learning to more complex tasks is to use elemental behaviors as building blocks to compose more complex behavior. Ideally, such building blocks are used in combination with a learning algorithm that is able to learn to select, adapt, sequence and co-activate the building blocks. While there has been a lot of work on approaches that support one of these requirements, no learning algorithm exists that unifies all these properties in one framework. In this paper we present our work on a unified approach for learning such a modular control architecture. We introduce new policy search algorithms that are based on information-theoretic principles and are able to learn to select, adapt and sequence the building blocks. Furthermore, we developed a new representation for the individual building block that supports co-activation and principled ways for adapting the movement. Finally, we summarize our experiments for learning modular control architectures in simulation and with real robots

Robot Learning with Task-Parameterized Generative Models

Task-parameterized models provide a representation of movement/behavior that can adapt to a set of task parameters describing the current situation encountered by the robot, such as location of objects or landmarks in its workspace. This paper gives an overview of the task-parameterized Gaussian mixture model (TP-GMM) introduced in previous publications, and introduces a number of extensions and ongoing challenges required to move the approach toward unconstrained environments. In particular, it discusses its generalization capability and the handling of movements with a high number of degrees of freedom. It then shows that the method is not restricted to movements in task space, but that it can also be exploited to handle constraints in joint space, including priority constraints