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2016


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A New Perspective and Extension of the Gaussian Filter

Wüthrich, M., Trimpe, S., Garcia Cifuentes, C., Kappler, D., Schaal, S.

The International Journal of Robotics Research, 35(14):1731-1749, December 2016 (article)

Abstract
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. The GF represents the belief of the current state by a Gaussian distribution, whose mean is an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end, we view the GF as the solution to a constrained optimization problem. From this new perspective, the GF is seen as a special case of a much broader class of filters, obtained by relaxing the constraint on the form of the approximate posterior. On this basis, we outline some conditions which potential generalizations have to satisfy in order to maintain the computational efficiency of the GF. We propose one concrete generalization which corresponds to the standard GF using a pseudo measurement instead of the actual measurement. Extending an existing GF implementation in this manner is trivial. Nevertheless, we show that this small change can have a major impact on the estimation accuracy.

PDF DOI Project Page [BibTex]

2016

PDF DOI Project Page [BibTex]


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Probabilistic Inference for Determining Options in Reinforcement Learning

Daniel, C., van Hoof, H., Peters, J., Neumann, G.

Machine Learning, Special Issue, 104(2):337-357, (Editors: Gärtner, T., Nanni, M., Passerini, A. and Robardet, C.), European Conference on Machine Learning im Machine Learning, Journal Track, 2016, Best Student Paper Award of ECML-PKDD 2016 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Event-based Sampling for Reducing Communication Load in Realtime Human Motion Analysis by Wireless Inertial Sensor Networks

Laidig, D., Trimpe, S., Seel, T.

Current Directions in Biomedical Engineering, 2(1):711-714, De Gruyter, 2016 (article)

PDF DOI [BibTex]

PDF DOI [BibTex]


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Momentum Control with Hierarchical Inverse Dynamics on a Torque-Controlled Humanoid

Herzog, A., Rotella, N., Mason, S., Grimminger, F., Schaal, S., Righetti, L.

Autonomous Robots, 40(3):473-491, 2016 (article)

Abstract
Hierarchical inverse dynamics based on cascades of quadratic programs have been proposed for the control of legged robots. They have important benefits but to the best of our knowledge have never been implemented on a torque controlled humanoid where model inaccuracies, sensor noise and real-time computation requirements can be problematic. Using a reformulation of existing algorithms, we propose a simplification of the problem that allows to achieve real-time control. Momentum-based control is integrated in the task hierarchy and a LQR design approach is used to compute the desired associated closed-loop behavior and improve performance. Extensive experiments on various balancing and tracking tasks show very robust performance in the face of unknown disturbances, even when the humanoid is standing on one foot. Our results demonstrate that hierarchical inverse dynamics together with momentum control can be efficiently used for feedback control under real robot conditions.

link (url) DOI [BibTex]


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Bioinspired Motor Control for Articulated Robots [From the Guest Editors]

Vitiello, Nicola, Ijspeert, Auke J, Schaal, S.

IEEE Robotics {\&} Automation Magazine, 23(1):20-21, 2016 (article)

[BibTex]

[BibTex]

2013


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3-D Object Reconstruction of Symmetric Objects by Fusing Visual and Tactile Sensing

Illonen, J., Bohg, J., Kyrki, V.

The International Journal of Robotics Research, 33(2):321-341, Sage, October 2013 (article)

Abstract
In this work, we propose to reconstruct a complete 3-D model of an unknown object by fusion of visual and tactile information while the object is grasped. Assuming the object is symmetric, a first hypothesis of its complete 3-D shape is generated. A grasp is executed on the object with a robotic manipulator equipped with tactile sensors. Given the detected contacts between the fingers and the object, the initial full object model including the symmetry parameters can be refined. This refined model will then allow the planning of more complex manipulation tasks. The main contribution of this work is an optimal estimation approach for the fusion of visual and tactile data applying the constraint of object symmetry. The fusion is formulated as a state estimation problem and solved with an iterative extended Kalman filter. The approach is validated experimentally using both artificial and real data from two different robotic platforms.

Web DOI Project Page [BibTex]

2013

Web DOI Project Page [BibTex]


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Optimal control of reaching includes kinematic constraints

Mistry, M., Theodorou, E., Schaal, S., Kawato, M.

Journal of Neurophysiology, 2013, clmc (article)

Abstract
We investigate adaptation under a reaching task with an acceleration-based force field perturbation designed to alter the nominal straight hand trajectory in a potentially benign manner:pushing the hand of course in one direction before subsequently restoring towards the target. In this particular task, an explicit strategy to reduce motor effort requires a distinct deviation from the nominal rectilinear hand trajectory. Rather, our results display a clear directional preference during learning, as subjects adapted perturbed curved trajectories towards their initial baselines. We model this behavior using the framework of stochastic optimal control theory and an objective function that trades-of the discordant requirements of 1) target accuracy, 2) motor effort, and 3) desired trajectory. Our work addresses the underlying objective of a reaching movement, and we suggest that robustness, particularly against internal model uncertainly, is as essential to the reaching task as terminal accuracy and energy effciency.

PDF [BibTex]

PDF [BibTex]


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Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors

Ijspeert, A., Nakanishi, J., Pastor, P., Hoffmann, H., Schaal, S.

Neural Computation, (25):328-373, 2013, clmc (article)

Abstract
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 meansof 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.

link (url) [BibTex]

link (url) [BibTex]


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Optimal distribution of contact forces with inverse-dynamics control

Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S.

The International Journal of Robotics Research, 32(3):280-298, March 2013 (article)

Abstract
The development of legged robots for complex environments requires controllers that guarantee both high tracking performance and compliance with the environment. More specifically the control of the contact interaction with the environment is of crucial importance to ensure stable, robust and safe motions. In this contribution we develop an inverse-dynamics controller for floating-base robots under contact constraints that can minimize any combination of linear and quadratic costs in the contact constraints and the commands. Our main result is the exact analytical derivation of the controller. Such a result is particularly relevant for legged robots as it allows us to use torque redundancy to directly optimize contact interactions. For example, given a desired locomotion behavior, we can guarantee the minimization of contact forces to reduce slipping on difficult terrains while ensuring high tracking performance of the desired motion. The main advantages of the controller are its simplicity, computational efficiency and robustness to model inaccuracies. We present detailed experimental results on simulated humanoid and quadruped robots as well as a real quadruped robot. The experiments demonstrate that the controller can greatly improve the robustness of locomotion of the robots.1

link (url) DOI [BibTex]

link (url) DOI [BibTex]

2012


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The Balancing Cube: A Dynamic Sculpture as Test Bed for Distributed Estimation and Control

Trimpe, S., D’Andrea, R.

IEEE Control Systems Magazine, 32(6):48-75, December 2012 (article)

DOI [BibTex]

2012

DOI [BibTex]


Thumb xl thumb screen shot 2012 10 06 at 11.48.38 am
Visual Servoing on Unknown Objects

Gratal, X., Romero, J., Bohg, J., Kragic, D.

Mechatronics, 22(4):423-435, Elsevier, June 2012, Visual Servoing \{SI\} (article)

Abstract
We study visual servoing in a framework of detection and grasping of unknown objects. Classically, visual servoing has been used for applications where the object to be servoed on is known to the robot prior to the task execution. In addition, most of the methods concentrate on aligning the robot hand with the object without grasping it. In our work, visual servoing techniques are used as building blocks in a system capable of detecting and grasping unknown objects in natural scenes. We show how different visual servoing techniques facilitate a complete grasping cycle.

Grasping sequence video Offline calibration video Pdf DOI [BibTex]

Grasping sequence video Offline calibration video Pdf DOI [BibTex]


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Emotionally Assisted Human-Robot Interaction Using a Wearable Device for Reading Facial Expressions

Gruebler, A., Berenz, V., Suzuki, K.

Advanced Robotics, 26(10):1143-1159, 2012 (article)

link (url) DOI [BibTex]


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From Dynamic Movement Primitives to Associative Skill Memories

Pastor, P., Kalakrishnan, M., Meier, F., Stulp, F., Buchli, J., Theodorou, E., Schaal, S.

Robotics and Autonomous Systems, 2012 (article)

Project Page [BibTex]

Project Page [BibTex]


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Autonomous battery management for mobile robots based on risk and gain assessment

Berenz, V., Tanaka, F., Suzuki, K.

Artif. Intell. Rev., 37(3):217-237, 2012 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Model-free reinforcement learning of impedance control in stochastic environments

Stulp, Freek, Buchli, Jonas, Ellmer, Alice, Mistry, Michael, Theodorou, Evangelos A., Schaal, S.

Autonomous Mental Development, IEEE Transactions on, 4(4):330-341, 2012 (article)

[BibTex]

[BibTex]


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Reinforcement Learning with Sequences of Motion Primitives for Robust Manipulation

Stulp, F., Theodorou, E., Schaal, S.

IEEE Transactions on Robotics, 2012 (article)

[BibTex]

[BibTex]

2008


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Learning to control in operational space

Peters, J., Schaal, S.

International Journal of Robotics Research, 27, pages: 197-212, 2008, clmc (article)

Abstract
One of the most general frameworks for phrasing control problems for complex, redundant robots is operational space control. However, while this framework is of essential importance for robotics and well-understood from an analytical point of view, it can be prohibitively hard to achieve accurate control in face of modeling errors, which are inevitable in com- plex robots, e.g., humanoid robots. In this paper, we suggest a learning approach for opertional space control as a direct inverse model learning problem. A first important insight for this paper is that a physically cor- rect solution to the inverse problem with redundant degrees-of-freedom does exist when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component for our work is based on the insight that many operational space controllers can be understood in terms of a constrained optimal control problem. The cost function as- sociated with this optimal control problem allows us to formulate a learn- ing algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller. From the machine learning point of view, this learning problem corre- sponds to a reinforcement learning problem that maximizes an immediate reward. We employ an expectation-maximization policy search algorithm in order to solve this problem. Evaluations on a three degrees of freedom robot arm are used to illustrate the suggested approach. The applica- tion to a physically realistic simulator of the anthropomorphic SARCOS Master arm demonstrates feasibility for complex high degree-of-freedom robots. We also show that the proposed method works in the setting of learning resolved motion rate control on real, physical Mitsubishi PA-10 medical robotics arm.

link (url) DOI [BibTex]

2008

link (url) DOI [BibTex]


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Adaptation to a sub-optimal desired trajectory

M. Mistry, E. A. G. L. T. Y. S. S. M. K.

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

PDF [BibTex]

PDF [BibTex]


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Operational space control: A theoretical and emprical comparison

Nakanishi, J., Cory, R., Mistry, M., Peters, J., Schaal, S.

International Journal of Robotics Research, 27(6):737-757, 2008, clmc (article)

Abstract
Dexterous manipulation with a highly redundant movement system is one of the hallmarks of hu- man motor skills. From numerous behavioral studies, there is strong evidence that humans employ compliant task space control, i.e., they focus control only on task variables while keeping redundant degrees-of-freedom as compliant as possible. This strategy is robust towards unknown disturbances and simultaneously safe for the operator and the environment. The theory of operational space con- trol in robotics aims to achieve similar performance properties. However, despite various compelling theoretical lines of research, advanced operational space control is hardly found in actual robotics imple- mentations, in particular new kinds of robots like humanoids and service robots, which would strongly profit from compliant dexterous manipulation. To analyze the pros and cons of different approaches to operational space control, this paper focuses on a theoretical and empirical evaluation of different methods that have been suggested in the literature, but also some new variants of operational space controllers. We address formulations at the velocity, acceleration and force levels. First, we formulate all controllers in a common notational framework, including quaternion-based orientation control, and discuss some of their theoretical properties. Second, we present experimental comparisons of these approaches on a seven-degree-of-freedom anthropomorphic robot arm with several benchmark tasks. As an aside, we also introduce a novel parameter estimation algorithm for rigid body dynamics, which ensures physical consistency, as this issue was crucial for our successful robot implementations. Our extensive empirical results demonstrate that one of the simplified acceleration-based approaches can be advantageous in terms of task performance, ease of parameter tuning, and general robustness and compliance in face of inevitable modeling errors.

link (url) [BibTex]

link (url) [BibTex]


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A library for locally weighted projection regression

Klanke, S., Vijayakumar, S., Schaal, S.

Journal of Machine Learning Research, 9, pages: 623-626, 2008, clmc (article)

Abstract
In this paper we introduce an improved implementation of locally weighted projection regression (LWPR), a supervised learning algorithm that is capable of handling high-dimensional input data. As the key features, our code supports multi-threading, is available for multiple platforms, and provides wrappers for several programming languages.

link (url) [BibTex]

link (url) [BibTex]


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Optimization strategies in human reinforcement learning

Hoffmann, H., Theodorou, E., Schaal, S.

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

PDF [BibTex]

PDF [BibTex]

2003


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Computational approaches to motor learning by imitation

Schaal, S., Ijspeert, A., Billard, A.

Philosophical Transaction of the Royal Society of London: Series B, Biological Sciences, 358(1431):537-547, 2003, clmc (article)

Abstract
Movement imitation requires a complex set of mechanisms that map an observed movement of a teacher onto one's own movement apparatus. Relevant problems include movement recognition, pose estimation, pose tracking, body correspondence, coordinate transformation from external to egocentric space, matching of observed against previously learned movement, resolution of redundant degrees-of-freedom that are unconstrained by the observation, suitable movement representations for imitation, modularization of motor control, etc. All of these topics by themselves are active research problems in computational and neurobiological sciences, such that their combination into a complete imitation system remains a daunting undertaking - indeed, one could argue that we need to understand the complete perception-action loop. As a strategy to untangle the complexity of imitation, this paper will examine imitation purely from a computational point of view, i.e. we will review statistical and mathematical approaches that have been suggested for tackling parts of the imitation problem, and discuss their merits, disadvantages and underlying principles. Given the focus on action recognition of other contributions in this special issue, this paper will primarily emphasize the motor side of imitation, assuming that a perceptual system has already identified important features of a demonstrated movement and created their corresponding spatial information. Based on the formalization of motor control in terms of control policies and their associated performance criteria, useful taxonomies of imitation learning can be generated that clarify different approaches and future research directions.

link (url) [BibTex]

2003

link (url) [BibTex]

1998


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Constructive incremental learning from only local information

Schaal, S., Atkeson, C. G.

Neural Computation, 10(8):2047-2084, 1998, clmc (article)

Abstract
We introduce a constructive, incremental learning system for regression problems that models data by means of spatially localized linear models. In contrast to other approaches, the size and shape of the receptive field of each locally linear model as well as the parameters of the locally linear model itself are learned independently, i.e., without the need for competition or any other kind of communication. Independent learning is accomplished by incrementally minimizing a weighted local cross validation error. As a result, we obtain a learning system that can allocate resources as needed while dealing with the bias-variance dilemma in a principled way. The spatial localization of the linear models increases robustness towards negative interference. Our learning system can be interpreted as a nonparametric adaptive bandwidth smoother, as a mixture of experts where the experts are trained in isolation, and as a learning system which profits from combining independent expert knowledge on the same problem. This paper illustrates the potential learning capabilities of purely local learning and offers an interesting and powerful approach to learning with receptive fields. 

link (url) [BibTex]

1998

link (url) [BibTex]


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Local adaptive subspace regression

Vijayakumar, S., Schaal, S.

Neural Processing Letters, 7(3):139-149, 1998, clmc (article)

Abstract
Incremental learning of sensorimotor transformations in high dimensional spaces is one of the basic prerequisites for the success of autonomous robot devices as well as biological movement systems. So far, due to sparsity of data in high dimensional spaces, learning in such settings requires a significant amount of prior knowledge about the learning task, usually provided by a human expert. In this paper we suggest a partial revision of the view. Based on empirical studies, we observed that, despite being globally high dimensional and sparse, data distributions from physical movement systems are locally low dimensional and dense. Under this assumption, we derive a learning algorithm, Locally Adaptive Subspace Regression, that exploits this property by combining a dynamically growing local dimensionality reduction technique  as a preprocessing step with a nonparametric learning technique, locally weighted regression, that also learns the region of validity of the regression. The usefulness of the algorithm and the validity of its assumptions are illustrated for a synthetic data set, and for data of the inverse dynamics of human arm movements and an actual 7 degree-of-freedom anthropomorphic robot arm. 

link (url) [BibTex]

link (url) [BibTex]