Augmented-SVM: Automatic space partitioning for combining multiple non-linear dynamics

Non-linear dynamical systems (DS) have been used extensively for building generative models of human behavior. Their applications range from modeling brain dynamics to encoding motor commands. Many schemes have been proposed for encoding robot motions using dynamical systems with a single attractor placed at a predefined target in state space. Although these enable the robots to react against sudden perturbations without any re-planning, the motions are always directed towards a single target. In this work, we focus on combining several such DS with distinct attractors, resulting in a multi-stable DS. We show its applicability in reach-to-grasp tasks where the attractors represent several grasping points on the target object. While exploiting multiple attractors provides more flexibility in recovering from unseen perturbations, it also increases the complexity of the underlying learning problem. Here we present the \emph{Augmented-SVM} (A-SVM) model which inherits region partitioning ability of the well known SVM classifier and is augmented with novel constraints derived from the individual DS. The new constraints modify the original SVM dual whose optimal solution then results in a new class of support vectors (SV). These new SV ensure that the resulting multi-stable DS incurs minimum deviation from the original dynamics and is stable at each of the attractors within a finite region of attraction. We show, via implementations on a simulated 10 degrees of freedom mobile robotic platform, that the model is capable of real-time motion generation and is able to adapt on-the-fly to perturbations.

Learning Reach-to-Grasp Motions From Human Demonstrations

Ashwini Shukla

Reaching over to grasp an item is arguably the most commonly used motor skill by humans. Even under sudden perturbations, humans seem to react rapidly and adapt their motion to guarantee success. Despite the apparent ease and frequency with which we use this ability, a complete understanding of the underlying mechanisms cannot be claimed. It is partly due to such incomplete knowledge that adaptive robot motion for reaching and grasping under perturbations is not perfectly achieved. In this thesis, we take the discriminative approach for modelling trajectories of reach-to-grasp motion from expert demonstrations. Throughout this thesis, we will employ time-independent (autonomous) flow based representations to learn reactive motion controllers which can then be ported onto robots. This thesis is divided into three main parts. The first part is dedicated to biologically inspired modelling of reach-to-grasp motions with respect to the hand-arm coupling. We build upon previous work in motion modelling using autonomous dynamical systems (DS) and present a coupled dynamical system (CDS) model of these two subsystems. The coupled model ensures satisfaction of the constraints between the hand and the arm subsystems which are critical to the success of a reach-to-grasp task. Moreover, it reduces the complexity of the overall motion planning problem as compared to considering a combined problem for the hand and the arm motion. In the second part we extend the CDS approach to incorporate multiple grasping points. Such a model is beneficial due to the fact that many daily life objects afford multiple grasping locations on their surface. We combine a DS based approach with energy-function learning to learn a multiple attractor dynamical system where the attractors are mapped to the desired grasping points. We present the Augmented-SVM (ASVM) model that combines the classical SVM formulation with gradient constraints arising from the energy function to learn the desired dynamical function for motion generation. In the last part of this thesis, we address the problem of inverse-kinematics and obstacle avoidance by combining our flow-based motion generator with global configuration-space planners. We claim that the two techniques complement each other. On one hand, the fast reactive nature of our flow based motion generator can used to guide the search of a randomly exploring random tree (RRT) based global planner. On the other hand, global planners can efficiently handle arbitrary obstacles and avoid local minima present in the dynamical function learned from demonstrations. We show that combining the information from demonstrations with global planning in the form of a energy-map considerably decreases the computational complexity of state-of-the-art sampling based planners. We believe that this thesis has the following contributions to Robotics and Machine Learning. First, we have developed algorithms for fast and adaptive motion generation for reach-grasp motions. Second, we formulated an extension to the classical SVM formulation that takes into account the gradient information from data. We showed that instead of being limited as a classifier or a regressor, the SVM framework can be used as a more general function approximation technique. Lastly, we have combined our local methods with global approaches for planning to achieve arbitrary obstacle avoidance and considerable reduction in the computation complexity of the global planners.

EPFL2014

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

Modeling diversity by strange attractors with application to temporal pattern recognition

Oscar De Feo

This thesis belongs to the general discipline of establishing black-box models from real-word data, more precisely, from measured time-series. This is an old subject and a large amount of papers and books has been written about it. The main difficulty is to express the diversity of data that has essentially the same origin without creating confusion with data that has a different origin. Normally, the diversity of time-series is modeled by a stochastic process, such as filtered white noise. Often, it is reasonable to assume that the time series is generated by a deterministic dynamical system rather than a stochastic process. In this case, the diversity of the data is expressed by the variability of the parameters of the dynamical system. The parameter variability itself is then, once again, modeled by a stochastic process. In both cases the diversity is generated by some form of exogenous noise. In this thesis a further step has been taken. A single chaotic dynamical system is used to model the data and their diversity. Indeed, a chaotic system produces a whole family of trajectories that are different but nonetheless very similar. It is believed that chaotic dynamics not only are a convenient means to represent diversity but that in many cases the origin of diversity stems actually from chaotic dynamic. Since the approach of this thesis explores completely new grounds the most suitable kind of data is considered, namely approximately periodic signals. In nature such time-series are rather common, in particular the physiological signal of living beings, such as the electrocardiograms (ECG), parts of speech signals, electroencephalograms (EEG), etc. Since there are strong arguments in favor of the chaotic nature of these signals, they appear to be the best candidates for modeling diversity by chaos. It should be stressed however, that the modeling approach pursued in this thesis is thought to be quite general and not limited to signals produced by chaotic dynamics in nature. The intended application of the modeling effort in this thesis is temporal signal classification. The reason for this is twofold. Firstly, classification is one of the basic building block of any cognitive system. Secondly, the recently studied phenomenon of synchronization of chaotic systems suggests a way to test a signal against its chaotic model. The essential content of this work can now be formulated as follows. Thesis: The diversity of approximately periodic signals found in nature can be modeled by means of chaotic dynamics. This kind of modeling technique, together with selective properties of the synchronization of chaotic systems, can be exploited for pattern recognition purposes. This Thesis is advocated by means of the following five points. Models of randomness (Chapter 2) It is argued that the randomness observed in nature is not necessarily the result of exogenous noise, but it could be endogenally generated by deterministic chaotic dynamics. The diversity of real signals is compared with signals produced by the most common chaotic systems. Qualitative resonance (Chapter 3) The behavior of chaotic systems forced by periodic or approximately periodic input signals is studied theoretically and by numerical simulation. It is observed that the chaotic system "locks" approximately to an input signal that is related to its internal chaotic dynamic. In contrast to this, its chaotic behavior is reinforced when the input signal has nothing to do with its internal dynamics. This new phenomenon is called "qualitative resonance". Modeling and recognizing (Chapter 4) In this chapter qualitative resonance is used for pattern recognition. The core of the method is a chaotic dynamical system that is able to reproduce the class of time-series that is to be recognized. This model is excited in a suitable way by an input signal such that qualitative resonance is realized. This means that if the input signal belongs to the modeled class of time-series, the system approximately "locks" into it. If not, the trajectory of the system and the input signal remain unrelated. Automated design of the recognizer (Chapters 5 and 6) For the kind of signals considered in this thesis a systematic design method of the recognizer is presented. The model used is a system of Lur'e type, i.e. a model where the linear dynamic and nonlinear static part are separated. The identification of the model parameters from the given data proceed iteratively, adapting in turn the linear and the nonlinear part. Thus, the difficult nonlinear dynamical system identification task is decomposed into the easier problems of linear dynamical and nonlinear static system identification. The way to apply the approximately periodic input signal in order to realize qualitative resonance is chosen with the help of periodic control theory. Validation (Chapter 7) The pattern recognition method has been validated on the following examples — A synthetic example — Laboratory measurement from Colpitts oscillator — ECG — EEG — Vowels of a speech signals In the first four cases a binary classification and in the last example a classification with five classes was performed. To the best of the knowledge of the author the recognition method is original. Chaotic systems have been already used to produce pseudo-noise and to model signal diversity. Also, parameter identification of chaotic systems has been already carried out. However, the direct establishment of the model from the given data and its subsequent use for classification based on the phenomenon of qualitative resonance is entirely new.

EPFL2001