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2015


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Distributed Event-based State Estimation

Trimpe, S.

Max Planck Institute for Intelligent Systems, November 2015 (techreport)

Abstract
An event-based state estimation approach for reducing communication in a networked control system is proposed. Multiple distributed sensor-actuator-agents observe a dynamic process and sporadically exchange their measurements and inputs over a bus network. Based on these data, each agent estimates the full state of the dynamic system, which may exhibit arbitrary inter-agent couplings. Local event-based protocols ensure that data is transmitted only when necessary to meet a desired estimation accuracy. This event-based scheme is shown to mimic a centralized Luenberger observer design up to guaranteed bounds, and stability is proven in the sense of bounded estimation errors for bounded disturbances. The stability result extends to the distributed control system that results when the local state estimates are used for distributed feedback control. Simulation results highlight the benefit of the event-based approach over classical periodic ones in reducing communication requirements.

arXiv [BibTex]

2015

arXiv [BibTex]


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Active Reward Learning with a Novel Acquisition Function

Daniel, C., Kroemer, O., Viering, M., Metz, J., Peters, J.

Autonomous Robots, 39(3):389-405, 2015 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Movement Primitive Attractor Goals and Sequential Skills from Kinesthetic Demonstrations

Manschitz, S., Kober, J., Gienger, M., Peters, J.

Robotics and Autonomous Systems, 74, Part A, pages: 97-107, 2015 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Bayesian Optimization for Learning Gaits under Uncertainty

Calandra, R., Seyfarth, A., Peters, J., Deisenroth, M.

Annals of Mathematics and Artificial Intelligence, pages: 1-19, 2015 (article)

DOI [BibTex]

DOI [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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Learning and Optimization with Submodular Functions

Sankaran, B., Ghazvininejad, M., He, X., Kale, D., Cohen, L.

ArXiv, May 2013 (techreport)

Abstract
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast under the umbrella of convexity or submodularity. In this report we will study design and optimization over a common class of functions called submodular functions. Set functions, and specifically submodular set functions, characterize a wide variety of naturally occurring optimization problems, and the property of submodularity of set functions has deep theoretical consequences with wide ranging applications. Informally, the property of submodularity of set functions concerns the intuitive principle of diminishing returns. This property states that adding an element to a smaller set has more value than adding it to a larger set. Common examples of submodular monotone functions are entropies, concave functions of cardinality, and matroid rank functions; non-monotone examples include graph cuts, network flows, and mutual information. In this paper we will review the formal definition of submodularity; the optimization of submodular functions, both maximization and minimization; and finally discuss some applications in relation to learning and reasoning using submodular functions.

arxiv link (url) [BibTex]

arxiv link (url) [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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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]

2012

Project Page [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]

2005


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Composite adaptive control with locally weighted statistical learning

Nakanishi, J., Farrell, J. A., Schaal, S.

Neural Networks, 18(1):71-90, January 2005, clmc (article)

Abstract
This paper introduces a provably stable learning adaptive control framework with statistical learning. The proposed algorithm employs nonlinear function approximation with automatic growth of the learning network according to the nonlinearities and the working domain of the control system. The unknown function in the dynamical system is approximated by piecewise linear models using a nonparametric regression technique. Local models are allocated as necessary and their parameters are optimized on-line. Inspired by composite adaptive control methods, the proposed learning adaptive control algorithm uses both the tracking error and the estimation error to update the parameters. We first discuss statistical learning of nonlinear functions, and motivate our choice of the locally weighted learning framework. Second, we begin with a class of first order SISO systems for theoretical development of our learning adaptive control framework, and present a stability proof including a parameter projection method that is needed to avoid potential singularities during adaptation. Then, we generalize our adaptive controller to higher order SISO systems, and discuss further extension to MIMO problems. Finally, we evaluate our theoretical control framework in numerical simulations to illustrate the effectiveness of the proposed learning adaptive controller for rapid convergence and high accuracy of control.

link (url) [BibTex]

2005

link (url) [BibTex]


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A model of smooth pursuit based on learning of the target dynamics using only retinal signals

Shibata, T., Tabata, H., Schaal, S., Kawato, M.

Neural Networks, 18, pages: 213-225, 2005, clmc (article)

Abstract
While the predictive nature of the primate smooth pursuit system has been evident through several behavioural and neurophysiological experiments, few models have attempted to explain these results comprehensively. The model we propose in this paper in line with previous models employing optimal control theory; however, we hypothesize two new issues: (1) the medical superior temporal (MST) area in the cerebral cortex implements a recurrent neural network (RNN) in order to predict the current or future target velocity, and (2) a forward model of the target motion is acquired by on-line learning. We use stimulation studies to demonstrate how our new model supports these hypotheses.

link (url) [BibTex]

link (url) [BibTex]


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Linear and Nonlinear Estimation models applied to Hemodynamic Model

Theodorou, E.

Technical Report-2005-1, Computational Action and Vision Lab University of Minnesota, 2005, clmc (techreport)

Abstract
The relation between BOLD signal and neural activity is still poorly understood. The Gaussian Linear Model known as GLM is broadly used in many fMRI data analysis for recovering the underlying neural activity. Although GLM has been proved to be a really useful tool for analyzing fMRI data it can not be used for describing the complex biophysical process of neural metabolism. In this technical report we make use of a system of Stochastic Differential Equations that is based on Buxton model [1] for describing the underlying computational principles of hemodynamic process. Based on this SDE we built a Kalman Filter estimator so as to estimate the induced neural signal as well as the blood inflow under physiologic and sensor noise. The performance of Kalman Filter estimator is investigated under different physiologic noise characteristics and measurement frequencies.

PDF [BibTex]

PDF [BibTex]


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Parametric and Non-Parametric approaches for nonlinear tracking of moving objects

Hidaka, Y, Theodorou, E.

Technical Report-2005-1, 2005, clmc (article)

PDF [BibTex]

PDF [BibTex]

2002


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Forward models in visuomotor control

Mehta, B., Schaal, S.

J Neurophysiol, 88(2):942-53, August 2002, clmc (article)

Abstract
In recent years, an increasing number of research projects investigated whether the central nervous system employs internal models in motor control. While inverse models in the control loop can be identified more readily in both motor behavior and the firing of single neurons, providing direct evidence for the existence of forward models is more complicated. In this paper, we will discuss such an identification of forward models in the context of the visuomotor control of an unstable dynamic system, the balancing of a pole on a finger. Pole balancing imposes stringent constraints on the biological controller, as it needs to cope with the large delays of visual information processing while keeping the pole at an unstable equilibrium. We hypothesize various model-based and non-model-based control schemes of how visuomotor control can be accomplished in this task, including Smith Predictors, predictors with Kalman filters, tapped-delay line control, and delay-uncompensated control. Behavioral experiments with human participants allow exclusion of most of the hypothesized control schemes. In the end, our data support the existence of a forward model in the sensory preprocessing loop of control. As an important part of our research, we will provide a discussion of when and how forward models can be identified and also the possible pitfalls in the search for forward models in control.

link (url) [BibTex]

2002

link (url) [BibTex]


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Scalable techniques from nonparameteric statistics for real-time robot learning

Schaal, S., Atkeson, C. G., Vijayakumar, S.

Applied Intelligence, 17(1):49-60, 2002, clmc (article)

Abstract
Locally weighted learning (LWL) is a class of techniques from nonparametric statistics that provides useful representations and training algorithms for learning about complex phenomena during autonomous adaptive control of robotic systems. This paper introduces several LWL algorithms that have been tested successfully in real-time learning of complex robot tasks. We discuss two major classes of LWL, memory-based LWL and purely incremental LWL that does not need to remember any data explicitly. In contrast to the traditional belief that LWL methods cannot work well in high-dimensional spaces, we provide new algorithms that have been tested on up to 90 dimensional learning problems. The applicability of our LWL algorithms is demonstrated in various robot learning examples, including the learning of devil-sticking, pole-balancing by a humanoid robot arm, and inverse-dynamics learning for a seven and a 30 degree-of-freedom robot. In all these examples, the application of our statistical neural networks techniques allowed either faster or more accurate acquisition of motor control than classical control engineering.

link (url) [BibTex]

link (url) [BibTex]

1999


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Is imitation learning the route to humanoid robots?

Schaal, S.

Trends in Cognitive Sciences, 3(6):233-242, 1999, clmc (article)

Abstract
This review will focus on two recent developments in artificial intelligence and neural computation: learning from imitation and the development of humanoid robots. It will be postulated that the study of imitation learning offers a promising route to gain new insights into mechanisms of perceptual motor control that could ultimately lead to the creation of autonomous humanoid robots. This hope is justified because imitation learning channels research efforts towards three important issues: efficient motor learning, the connection between action and perception, and modular motor control in form of movement primitives. In order to make these points, first, a brief review of imitation learning will be given from the view of psychology and neuroscience. In these fields, representations and functional connections between action and perception have been explored that contribute to the understanding of motor acts of other beings. The recent discovery that some areas in the primate brain are active during both movement perception and execution provided a first idea of the possible neural basis of imitation. Secondly, computational approaches to imitation learning will be described, initially from the perspective of traditional AI and robotics, and then with a focus on neural network models and statistical learning research. Parallels and differences between biological and computational approaches to imitation will be highlighted. The review will end with an overview of current projects that actually employ imitation learning for humanoid robots.

link (url) [BibTex]

1999

link (url) [BibTex]


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Segmentation of endpoint trajectories does not imply segmented control

Sternad, D., Schaal, D.

Experimental Brain Research, 124(1):118-136, 1999, clmc (article)

Abstract
While it is generally assumed that complex movements consist of a sequence of simpler units, the quest to define these units of action, or movement primitives, still remains an open question. In this context, two hypotheses of movement segmentation of endpoint trajectories in 3D human drawing movements are re-examined: (1) the stroke-based segmentation hypothesis based on the results that the proportionality coefficient of the 2/3 power law changes discontinuously with each new â??strokeâ?, and (2) the segmentation hypothesis inferred from the observation of piecewise planar endpoint trajectories of 3D drawing movements. In two experiments human subjects performed a set of elliptical and figure-8 patterns of different sizes and orientations using their whole arm in 3D. The kinematic characteristics of the endpoint trajectories and the seven joint angles of the arm were analyzed. While the endpoint trajectories produced similar segmentation features as reported in the literature, analyses of the joint angles show no obvious segmentation but rather continuous oscillatory patterns. By approximating the joint angle data of human subjects with sinusoidal trajectories, and by implementing this model on a 7-degree-of-freedom anthropomorphic robot arm, it is shown that such a continuous movement strategy can produce exactly the same features as observed by the above segmentation hypotheses. The origin of this apparent segmentation of endpoint trajectories is traced back to the nonlinear transformations of the forward kinematics of human arms. The presented results demonstrate that principles of discrete movement generation may not be reconciled with those of rhythmic movement as easily as has been previously suggested, while the generalization of nonlinear pattern generators to arm movements can offer an interesting alternative to approach the question of units of action.

link (url) [BibTex]

link (url) [BibTex]

1992


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Ins CAD integrierte Kostenkalkulation (CAD-Integrated Cost Calculation)

Ehrlenspiel, K., Schaal, S.

Konstruktion 44, 12, pages: 407-414, 1992, clmc (article)

[BibTex]

1992

[BibTex]