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283 results (BibTeX)

2010


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Optimality in Neuromuscular Systems

Theodorou, E. A., Valero-Cuevas, F.

In 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2010, clmc (inproceedings)

Abstract
Abstract? We provide an overview of optimal control meth- ods to nonlinear neuromuscular systems and discuss their lim- itations. Moreover we extend current optimal control methods to their application to neuromuscular models with realistically numerous musculotendons; as most prior work is limited to torque-driven systems. Recent work on computational motor control has explored the used of control theory and esti- mation as a conceptual tool to understand the underlying computational principles of neuromuscular systems. After all, successful biological systems regularly meet conditions for stability, robustness and performance for multiple classes of complex tasks. Among a variety of proposed control theory frameworks to explain this, stochastic optimal control has become a dominant framework to the point of being a standard computational technique to reproduce kinematic trajectories of reaching movements (see [12]) In particular, we demonstrate the application of optimal control to a neuromuscular model of the index finger with all seven musculotendons producing a tapping task. Our simu- lations include 1) a muscle model that includes force- length and force-velocity characteristics; 2) an anatomically plausible biomechanical model of the index finger that includes a tendi- nous network for the extensor mechanism and 3) a contact model that is based on a nonlinear spring-damper attached at the end effector of the index finger. We demonstrate that it is feasible to apply optimal control to systems with realistically large state vectors and conclude that, while optimal control is an adequate formalism to create computational models of neuro- musculoskeletal systems, there remain important challenges and limitations that need to be considered and overcome such as contact transitions, curse of dimensionality, and constraints on states and controls.

PDF [BibTex]

2010

PDF [BibTex]


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Reinforcement learning of motor skills in high dimensions: A path integral approach

Theodorou, E., Buchli, J., Schaal, S.

In Robotics and Automation (ICRA), 2010 IEEE International Conference on, pages: 2397-2403, May 2010, clmc (inproceedings)

Abstract
Reinforcement learning (RL) is one of the most general approaches to learning control. Its applicability to complex motor systems, however, has been largely impossible so far due to the computational difficulties that reinforcement learning encounters in high dimensional continuous state-action spaces. In this paper, we derive a novel approach to RL for parameterized control policies based on the framework of stochastic optimal control with path integrals. While solidly grounded in optimal control theory and estimation theory, the update equations for learning are surprisingly simple and have no danger of numerical instabilities as neither matrix inversions nor gradient learning rates are required. Empirical evaluations demonstrate significant performance improvements over gradient-based policy learning and scalability to high-dimensional control problems. Finally, a learning experiment on a robot dog illustrates the functionality of our algorithm in a real-world scenario. We believe that our new algorithm, Policy Improvement with Path Integrals (PI2), offers currently one of the most efficient, numerically robust, and easy to implement algorithms for RL in robotics.

link (url) [BibTex]

link (url) [BibTex]


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Inverse dynamics control of floating base systems using orthogonal decomposition

Mistry, M., Buchli, J., Schaal, S.

In Robotics and Automation (ICRA), 2010 IEEE International Conference on, pages: 3406-3412, May 2010, clmc (inproceedings)

Abstract
Model-based control methods can be used to enable fast, dexterous, and compliant motion of robots without sacrificing control accuracy. However, implementing such techniques on floating base robots, e.g., humanoids and legged systems, is non-trivial due to under-actuation, dynamically changing constraints from the environment, and potentially closed loop kinematics. In this paper, we show how to compute the analytically correct inverse dynamics torques for model-based control of sufficiently constrained floating base rigid-body systems, such as humanoid robots with one or two feet in contact with the environment. While our previous inverse dynamics approach relied on an estimation of contact forces to compute an approximate inverse dynamics solution, here we present an analytically correct solution by using an orthogonal decomposition to project the robot dynamics onto a reduced dimensional space, independent of contact forces. We demonstrate the feasibility and robustness of our approach on a simulated floating base bipedal humanoid robot and an actual robot dog locomoting over rough terrain.

link (url) [BibTex]

link (url) [BibTex]


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Learning Policy Improvements with Path Integrals

Theodorou, E. A., Buchli, J., Schaal, S.

In International Conference on Artificial Intelligence and Statistics (AISTATS 2010), 2010, clmc (inproceedings)

Abstract
With the goal to generate more scalable algo- rithms with higher efficiency and fewer open parameters, reinforcement learning (RL) has recently moved towards combining classi- cal techniques from optimal control and dy- namic programming with modern learning techniques from statistical estimation the- ory. In this vein, this paper suggests the framework of stochastic optimal control with path integrals to derive a novel approach to RL with parametrized policies. While solidly grounded in value function estimation and optimal control based on the stochastic Hamilton-Jacobi-Bellman (HJB) equations, policy improvements can be transformed into an approximation problem of a path inte- gral which has no open parameters other than the exploration noise. The resulting algorithm can be conceived of as model- based, semi-model-based, or even model free, depending on how the learning problem is structured. Our new algorithm demon- strates interesting similarities with previous RL research in the framework of proba- bility matching and provides intuition why the slightly heuristically motivated proba- bility matching approach can actually per- form well. Empirical evaluations demon- strate significant performance improvements over gradient-based policy learning and scal- ability to high-dimensional control problems. We believe that Policy Improvement with Path Integrals (PI2) offers currently one of the most efficient, numerically robust, and easy to implement algorithms for RL based on trajectory roll-outs.

PDF [BibTex]

PDF [BibTex]


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Learning optimal control solutions: a path integral approach

Theodorou, E., Schaal, S.

In Abstracts of Neural Control of Movement Conference (NCM 2010), Naples, Florida, 2010, 2010, clmc (inproceedings)

Abstract
Investigating principles of human motor control in the framework of optimal control has had a long tradition in neural control of movement, and has recently experienced a new surge of investigations. Ideally, optimal control problems are addresses as a reinforcement learning (RL) problem, which would allow to investigate both the process of acquiring an optimal control solution as well as the solution itself. Unfortunately, the applicability of RL to complex neural and biomechanics systems has been largely impossible so far due to the computational difficulties that arise in high dimensional continuous state-action spaces. As a way out, research has focussed on computing optimal control solutions based on iterative optimal control methods that are based on linear and quadratic approximations of dynamical models and cost functions. These methods require perfect knowledge of the dynamics and cost functions while they are based on gradient and Newton optimization schemes. Their applicability is also restricted to low dimensional problems due to problematic convergence in high dimensions. Moreover, the process of computing the optimal solution is removed from the learning process that might be plausible in biology. In this work, we present a new reinforcement learning method for learning optimal control solutions or motor control. This method, based on the framework of stochastic optimal control with path integrals, has a very solid theoretical foundation, while resulting in surprisingly simple learning algorithms. It is also possible to apply this approach without knowledge of the system model, and to use a wide variety of complex nonlinear cost functions for optimization. We illustrate the theoretical properties of this approach and its applicability to learning motor control tasks for reaching movements and locomotion studies. We discuss its applicability to learning desired trajectories, variable stiffness control (co-contraction), and parameterized control policies. We also investigate the applicability to signal dependent noise control systems. We believe that the suggested method offers one of the easiest to use approaches to learning optimal control suggested in the literature so far, which makes it ideally suited for computational investigations of biological motor control.

[BibTex]

[BibTex]


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Reinforcement learning of full-body humanoid motor skills

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

In Humanoid Robots (Humanoids), 2010 10th IEEE-RAS International Conference on, pages: 405-410, December 2010, clmc (inproceedings)

Abstract
Applying reinforcement learning to humanoid robots is challenging because humanoids have a large number of degrees of freedom and state and action spaces are continuous. Thus, most reinforcement learning algorithms would become computationally infeasible and require a prohibitive amount of trials to explore such high-dimensional spaces. In this paper, we present a probabilistic reinforcement learning approach, which is derived from the framework of stochastic optimal control and path integrals. The algorithm, called Policy Improvement with Path Integrals (PI2), has a surprisingly simple form, has no open tuning parameters besides the exploration noise, is model-free, and performs numerically robustly in high dimensional learning problems. We demonstrate how PI2 is able to learn full-body motor skills on a 34-DOF humanoid robot. To demonstrate the generality of our approach, we also apply PI2 in the context of variable impedance control, where both planned trajectories and gain schedules for each joint are optimized simultaneously.

link (url) [BibTex]

link (url) [BibTex]


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Fast, robust quadruped locomotion over challenging terrain

Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., Schaal, S.

In Robotics and Automation (ICRA), 2010 IEEE International Conference on, pages: 2665-2670, May 2010, clmc (inproceedings)

Abstract
We present a control architecture for fast quadruped locomotion over rough terrain. We approach the problem by decomposing it into many sub-systems, in which we apply state-of-the-art learning, planning, optimization and control techniques to achieve robust, fast locomotion. Unique features of our control strategy include: (1) a system that learns optimal foothold choices from expert demonstration using terrain templates, (2) a body trajectory optimizer based on the Zero-Moment Point (ZMP) stability criterion, and (3) a floating-base inverse dynamics controller that, in conjunction with force control, allows for robust, compliant locomotion over unperceived obstacles. We evaluate the performance of our controller by testing it on the LittleDog quadruped robot, over a wide variety of rough terrain of varying difficulty levels. We demonstrate the generalization ability of this controller by presenting test results from an independent external test team on terrains that have never been shown to us.

link (url) [BibTex]

link (url) [BibTex]


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Inverse dynamics with optimal distribution of ground reaction forces for legged robots

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

In Proceedings of the international conference on climbing and walking robots (CLAWAR) 2010, Nagoya, Japan, Aug.31-Sept.3, 2010, clmc (inproceedings)

Abstract
The control of the interaction of legged robots with their environment is of crucial importance in the design of locomotion controllers. We need to control the effects of the robots movement on the contact reaction forces to prevent slipping, for example. In this contribution, we extend a recent inverse dynamics algorithm for floating base robots to optimize the distribution of contact forces while achieving precise trajectory tracking. The resulting controller is algorithmically simple as compared to other approaches. Numerical simulations show that this result significantly increases the range of possible movements of a humanoid robot as compared to the previous inverse dynamics algorithm. We also present a simplification of the result for practical use on a real robot. Such an algorithm becomes particularly relevant for agile locomotion of robots on difficult terrains where the contacts with the environment are critical, such as walking over rough or slippery terrain

link (url) [BibTex]

link (url) [BibTex]


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Constrained accelerations for controlled geometric reduction: Sagittal-plane decoupling for bipedal locomotion

Gregg, R. D., Righetti, L., Buchli, J., Schaal, S.

In Humanoid Robots (Humanoids), 2010 10th IEEE-RAS International Conference on, pages: 1-7, December 2010, clmc (inproceedings)

Abstract
Energy-shaping control methods have produced strong theoretical results for asymptotically stable 3D bipedal dynamic walking in the literature. In particular, geometric controlled reduction exploits robot symmetries to control momentum conservation laws that decouple the sagittal-plane dynamics, which are easier to stabilize. However, the associated control laws require high-dimensional matrix inverses multiplied with complicated energy-shaping terms, often making these control theories difficult to apply to highly-redundant humanoid robots. This paper presents a first step towards the application of energy-shaping methods on real robots by casting controlled reduction into a framework of constrained accelerations for inverse dynamics control. By representing momentum conservation laws as constraints in acceleration space, we construct a general expression for desired joint accelerations that render the constraint surface invariant. By appropriately choosing an orthogonal projection, we show that the unconstrained (reduced) dynamics are decoupled from the constrained dynamics. Any acceleration-based controller can then be used to stabilize this planar subsystem, including passivity-based methods. The resulting control law is surprisingly simple and represents a practical way to employ control theoretic stability results in robotic platforms. Simulated walking of a 3D compass-gait biped show correspondence between the new and original controllers, and simulated motions of a 16-DOF humanoid demonstrate the applicability of this method.

link (url) [BibTex]

link (url) [BibTex]


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Variable impedance control - a reinforcement learning approach

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

In Robotics Science and Systems (2010), Zaragoza, Spain, June 27-30, 2010, clmc (inproceedings)

Abstract
One of the hallmarks of the performance, versatility, and robustness of biological motor control is the ability to adapt the impedance of the overall biomechanical system to different task requirements and stochastic disturbances. A transfer of this principle to robotics is desirable, for instance to enable robots to work robustly and safely in everyday human environments. It is, however, not trivial to derive variable impedance controllers for practical high DOF robotic tasks. In this contribution, we accomplish such gain scheduling with a reinforcement learning approach algorithm, PI2 (Policy Improvement with Path Integrals). PI2 is a model-free, sampling based learning method derived from first principles of optimal control. The PI2 algorithm requires no tuning of algorithmic parameters besides the exploration noise. The designer can thus fully focus on cost function design to specify the task. From the viewpoint of robotics, a particular useful property of PI2 is that it can scale to problems of many DOFs, so that RL on real robotic systems becomes feasible. We sketch the PI2 algorithm and its theoretical properties, and how it is applied to gain scheduling. We evaluate our approach by presenting results on two different simulated robotic systems, a 3-DOF Phantom Premium Robot and a 6-DOF Kuka Lightweight Robot. We investigate tasks where the optimal strategy requires both tuning of the impedance of the end-effector, and tuning of a reference trajectory. The results show that we can use path integral based RL not only for planning but also to derive variable gain feedback controllers in realistic scenarios. Thus, the power of variable impedance control is made available to a wide variety of robotic systems and practical applications.

link (url) [BibTex]

link (url) [BibTex]

2009


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A Limiting Property of the Matrix Exponential with Application to Multi-loop Control

Trimpe, S., D’Andrea, R.

In Proceedings of the Joint 48th IEEE Conference on Decision (CDC) and Control and 28th Chinese Control Conference, 2009 (inproceedings)

PDF DOI [BibTex]

2009

PDF DOI [BibTex]


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Sensory-objects network driven by intrinsic motivation for survival abilities

Berenz, V., Suzuki, K.

In Robotics and Biomimetics (ROBIO), 2009 IEEE International Conference on, pages: 871-876, 2009 (inproceedings)

DOI [BibTex]

DOI [BibTex]


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Modelling the interplay of central pattern generation and sensory feedback in the neuromuscular control of running

Daley, M., Righetti, L., Ijspeert, A.

In Comparative Biochemistry and Physiology - Part A: Molecular & Integrative Physiology. Annual Main Meeting for the Society for Experimental Biology, Glasgow, Scotland, 2009 (inproceedings)

[BibTex]

[BibTex]


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Compliant Leg Design for a Quadruped Robot

Sproewitz, A., Fremerey, M., Karakasiliotis, K., Rutishauser, S., Righetti, L., Ijspeert, A.

In Proceedings of Dynamic Walking 2009, Vancouver, Canada, 2009 (inproceedings)

[BibTex]

[BibTex]


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Grasping familiar objects using shape context

Bohg, J., Kragic, D.

In Advanced Robotics, 2009. ICAR 2009. International Conference on, pages: 1-6, 2009 (inproceedings)

Abstract
We present work on vision based robotic grasping. The proposed method relies on extracting and representing the global contour of an object in a monocular image. A suitable grasp is then generated using a learning framework where prototypical grasping points are learned from several examples and then used on novel objects. For representation purposes, we apply the concept of shape context and for learning we use a supervised learning approach in which the classifier is trained with labeled synthetic images. Our results show that a combination of a descriptor based on shape context with a non-linear classification algorithm leads to a stable detection of grasping points for a variety of objects. Furthermore, we will show how our representation supports the inference of a full grasp configuration.

pdf slides [BibTex]

pdf slides [BibTex]


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Path integral-based stochastic optimal control for rigid body dynamics

Theodorou, E. A., Buchli, J., Schaal, S.

In Adaptive Dynamic Programming and Reinforcement Learning, 2009. ADPRL ’09. IEEE Symposium on, pages: 219-225, 2009, clmc (inproceedings)

Abstract
Recent advances on path integral stochastic optimal control [1],[2] provide new insights in the optimal control of nonlinear stochastic systems which are linear in the controls, with state independent and time invariant control transition matrix. Under these assumptions, the Hamilton-Jacobi-Bellman (HJB) equation is formulated and linearized with the use of the logarithmic transformation of the optimal value function. The resulting HJB is a linear second order partial differential equation which is solved by an approximation based on the Feynman-Kac formula [3]. In this work we review the theory of path integral control and derive the linearized HJB equation for systems with state dependent control transition matrix. In addition we derive the path integral formulation for the general class of systems with state dimensionality that is higher than the dimensionality of the controls. Furthermore, by means of a modified inverse dynamics controller, we apply path integral stochastic optimal control over the new control space. Simulations illustrate the theoretical results. Future developments and extensions are discussed.

link (url) [BibTex]

link (url) [BibTex]


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Learning locomotion over rough terrain using terrain templates

Kalakrishnan, M., Buchli, J., Pastor, P., Schaal, S.

In Intelligent Robots and Systems, 2009. IROS 2009. IEEE/RSJ International Conference on, pages: 167-172, 2009, clmc (inproceedings)

Abstract
We address the problem of foothold selection in robotic legged locomotion over very rough terrain. The difficulty of the problem we address here is comparable to that of human rock-climbing, where foot/hand-hold selection is one of the most critical aspects. Previous work in this domain typically involves defining a reward function over footholds as a weighted linear combination of terrain features. However, a significant amount of effort needs to be spent in designing these features in order to model more complex decision functions, and hand-tuning their weights is not a trivial task. We propose the use of terrain templates, which are discretized height maps of the terrain under a foothold on different length scales, as an alternative to manually designed features. We describe an algorithm that can simultaneously learn a small set of templates and a foothold ranking function using these templates, from expert-demonstrated footholds. Using the LittleDog quadruped robot, we experimentally show that the use of terrain templates can produce complex ranking functions with higher performance than standard terrain features, and improved generalization to unseen terrain.

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Compact models of motor primitive variations for predictible reaching and obstacle avoidance

Stulp, F., Oztop, E., Pastor, P., Beetz, M., Schaal, S.

In IEEE-RAS International Conference on Humanoid Robots (Humanoids 2009), Paris, Dec.7-10, 2009, clmc (inproceedings)

Abstract
over and over again. This regularity allows humans and robots to reuse existing solutions for known recurring tasks. We expect that reusing a set of standard solutions to solve similar tasks will facilitate the design and on-line adaptation of the control systems of robots operating in human environments. In this paper, we derive a set of standard solutions for reaching behavior from human motion data. We also derive stereotypical reaching trajectories for variations of the task, in which obstacles are present. These stereotypical trajectories are then compactly represented with Dynamic Movement Primitives. On the humanoid robot Sarcos CB, this approach leads to reproducible, predictable, and human-like reaching motions.

link (url) [BibTex]

link (url) [BibTex]


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Human optimization strategies under reward feedback

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

In Abstracts of Neural Control of Movement Conference (NCM 2009), Waikoloa, Hawaii, 2009, 2009, clmc (inproceedings)

Abstract
Many hypothesis on human movement generation have been cast into an optimization framework, implying that movements are adapted to optimize a single quantity, like, e.g., jerk, end-point variance, or control cost. However, we still do not understand how humans actually learn when given only a cost or reward feedback at the end of a movement. Such a reinforcement learning setting has been extensively explored theoretically in engineering and computer science, but in human movement control, hardly any experiment studied movement learning under reward feedback. We present experiments probing which computational strategies humans use to optimize a movement under a continuous reward function. We present two experimental paradigms. The first paradigm mimics a ball-hitting task. Subjects (n=12) sat in front of a computer screen and moved a stylus on a tablet towards an unknown target. This target was located on a line that the subjects had to cross. During the movement, visual feedback was suppressed. After the movement, a reward was displayed graphically as a colored bar. As reward, we used a Gaussian function of the distance between the target location and the point of line crossing. We chose such a function since in sensorimotor tasks, the cost or loss function that humans seem to represent is close to an inverted Gaussian function (Koerding and Wolpert 2004). The second paradigm mimics pocket billiards. On the same experimental setup as above, the computer screen displayed a pocket (two bars), a white disk, and a green disk. The goal was to hit with the white disk the green disk (as in a billiard collision), such that the green disk moved into the pocket. Subjects (n=8) manipulated with the stylus the white disk to effectively choose start point and movement direction. Reward feedback was implicitly given as hitting or missing the pocket with the green disk. In both paradigms, subjects increased the average reward over trials. The surprising result was that in these experiments, humans seem to prefer a strategy that uses a reward-weighted average over previous movements instead of gradient ascent. The literature on reinforcement learning is dominated by gradient-ascent methods. However, our computer simulations and theoretical analysis revealed that reward-weighted averaging is the more robust choice given the amount of movement variance observed in humans. Apparently, humans choose an optimization strategy that is suitable for their own movement variance.

[BibTex]

[BibTex]


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Learning and generalization of motor skills by learning from demonstration

Pastor, P., Hoffmann, H., Asfour, T., Schaal, S.

In International Conference on Robotics and Automation (ICRA2009), Kobe, Japan, May 12-19, 2009, 2009, clmc (inproceedings)

Abstract
We provide a general approach for learning robotic motor skills from human demonstration. To represent an observed movement, a non-linear differential equation is learned such that it reproduces this movement. Based on this representation, we build a library of movements by labeling each recorded movement according to task and context (e.g., grasping, placing, and releasing). Our differential equation is formulated such that generalization can be achieved simply by adapting a start and a goal parameter in the equation to the desired position values of a movement. For object manipulation, we present how our framework extends to the control of gripper orientation and finger position. The feasibility of our approach is demonstrated in simulation as well as on a real robot. The robot learned a pick-and-place operation and a water-serving task and could generalize these tasks to novel situations.

link (url) [BibTex]

link (url) [BibTex]


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Compliant quadruped locomotion over rough terrain

Buchli, J., Kalakrishnan, M., Mistry, M., Pastor, P., Schaal, S.

In Intelligent Robots and Systems, 2009. IROS 2009. IEEE/RSJ International Conference on, pages: 814-820, 2009, clmc (inproceedings)

Abstract
Many critical elements for statically stable walking for legged robots have been known for a long time, including stability criteria based on support polygons, good foothold selection, recovery strategies to name a few. All these criteria have to be accounted for in the planning as well as the control phase. Most legged robots usually employ high gain position control, which means that it is crucially important that the planned reference trajectories are a good match for the actual terrain, and that tracking is accurate. Such an approach leads to conservative controllers, i.e. relatively low speed, ground speed matching, etc. Not surprisingly such controllers are not very robust - they are not suited for the real world use outside of the laboratory where the knowledge of the world is limited and error prone. Thus, to achieve robust robotic locomotion in the archetypical domain of legged systems, namely complex rough terrain, where the size of the obstacles are in the order of leg length, additional elements are required. A possible solution to improve the robustness of legged locomotion is to maximize the compliance of the controller. While compliance is trivially achieved by reduced feedback gains, for terrain requiring precise foot placement (e.g. climbing rocks, walking over pegs or cracks) compliance cannot be introduced at the cost of inferior tracking. Thus, model-based control and - in contrast to passive dynamic walkers - active balance control is required. To achieve these objectives, in this paper we add two crucial elements to legged locomotion, i.e., floating-base inverse dynamics control and predictive force control, and we show that these elements increase robustness in face of unknown and unanticipated perturbations (e.g. obstacles). Furthermore, we introduce a novel line-based COG trajectory planner, which yields a simpler algorithm than traditional polygon based methods and creates the appropriate input to our control system.We show results from bot- h simulation and real world of a robotic dog walking over non-perceived obstacles and rocky terrain. The results prove the effectivity of the inverse dynamics/force controller. The presented results show that we have all elements needed for robust all-terrain locomotion, which should also generalize to other legged systems, e.g., humanoid robots.

link (url) [BibTex]

link (url) [BibTex]


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Inertial parameter estimation of floating-base humanoid systems using partial force sensing

Mistry, M., Schaal, S., Yamane, K.

In IEEE-RAS International Conference on Humanoid Robots (Humanoids 2009), Paris, Dec.7-10, 2009, clmc (inproceedings)

Abstract
Recently, several controllers have been proposed for humanoid robots which rely on full-body dynamic models. The estimation of inertial parameters from data is a critical component for obtaining accurate models for control. However, floating base systems, such as humanoid robots, incur added challenges to this task (e.g. contact forces must be measured, contact states can change, etc.) In this work, we outline a theoretical framework for whole body inertial parameter estimation, including the unactuated floating base. Using a least squares minimization approach, conducted within the nullspace of unmeasured degrees of freedom, we are able to use a partial force sensor set for full-body estimation, e.g. using only joint torque sensors, allowing for estimation when contact force measurement is unavailable or unreliable (e.g. due to slipping, rolling contacts, etc.). We also propose how to determine the theoretical minimum force sensor set for full body estimation, and discuss the practical limitations of doing so.

link (url) [BibTex]

link (url) [BibTex]

2008


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Passive compliant quadruped robot using central pattern generators for locomotion control

Rutishauser, S., Sproewitz, A., Righetti, L., Ijspeert, A.

In 2008 IEEE International Conference on Biomedical Robotics and Biomechatronics, pages: 710-715, 2008 (inproceedings)

[BibTex]

2008

[BibTex]


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Experimental Study of Limit Cycle and Chaotic Controllers for the Locomotion of Centipede Robots

Matthey, L., Righetti, L., Ijspeert, A.

In Proceedings of the 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 1860-1865, 2008 (inproceedings)

[BibTex]

[BibTex]


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A Dynamical System for Online Learning of Periodic Movements of Unknown Waveform and Frequency

Gams, A., Righetti, L., Ijspeert, A., Lenarčič, J.

In 2008 IEEE International Conference on Biomedical Robotics and Biomechatronics, pages: 85-90, 2008 (inproceedings)

[BibTex]

[BibTex]


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Adaptive frequency oscillators and applications

Righetti, L., Buchli, J., Ijspeert, A.

In Proceedings of the 1st International Workshop on Nonlinear Dynamics and Synchronization, 2008 (inproceedings)

[BibTex]

[BibTex]


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Quadruped locomotion: from infants crawling to the design of pattern generators for quadruped robots

Righetti, L., Ijspeert, A.

In Proceedings of the 4th International Symposium on Adaptive Motion in Animals and Machines – AMAM 2008, 2008 (inproceedings)

[BibTex]

[BibTex]


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A modular bio-inspired architecture for movement generation for the infant-like robot iCub

Degallier, S., Righetti, L., Natale, L., Nori, F., Metta, G., Ijspeert, A.

In 2008 IEEE International Conference on Biomedical Robotics and Biomechatronics, pages: 795-800, 2008 (inproceedings)

[BibTex]

[BibTex]


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Human movement generation based on convergent flow fields: A computational model and a behavioral experiment

Hoffmann, H., Schaal, S.

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

link (url) [BibTex]

link (url) [BibTex]


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Movement reproduction and obstacle avoidance with dynamic movement primitives and potential fields

Park, D., Hoffmann, H., Pastor, P., Schaal, S.

In IEEE International Conference on Humanoid Robots, 2008., 2008, clmc (inproceedings)

PDF [BibTex]

PDF [BibTex]


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The dual role of uncertainty in force field learning

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

In Abstracts of the Eighteenth Annual Meeting of Neural Control of Movement (NCM), Naples, Florida, April 29-May 4, 2008, clmc (inproceedings)

Abstract
Force field experiments have been a successful paradigm for studying the principles of planning, execution, and learning in human arm movements. Subjects have been shown to cope with the disturbances generated by force fields by learning internal models of the underlying dynamics to predict disturbance effects or by increasing arm impedance (via co-contraction) if a predictive approach becomes infeasible. Several studies have addressed the issue uncertainty in force field learning. Scheidt et al. demonstrated that subjects exposed to a viscous force field of fixed structure but varying strength (randomly changing from trial to trial), learn to adapt to the mean disturbance, regardless of the statistical distribution. Takahashi et al. additionally show a decrease in strength of after-effects after learning in the randomly varying environment. Thus they suggest that the nervous system adopts a dual strategy: learning an internal model of the mean of the random environment, while simultaneously increasing arm impedance to minimize the consequence of errors. In this study, we examine what role variance plays in the learning of uncertain force fields. We use a 7 degree-of-freedom exoskeleton robot as a manipulandum (Sarcos Master Arm, Sarcos, Inc.), and apply a 3D viscous force field of fixed structure and strength randomly selected from trial to trial. Additionally, in separate blocks of trials, we alter the variance of the randomly selected strength multiplier (while keeping a constant mean). In each block, after sufficient learning has occurred, we apply catch trials with no force field and measure the strength of after-effects. As expected in higher variance cases, results show increasingly smaller levels of after-effects as the variance is increased, thus implying subjects choose the robust strategy of increasing arm impedance to cope with higher levels of uncertainty. Interestingly, however, subjects show an increase in after-effect strength with a small amount of variance as compared to the deterministic (zero variance) case. This result implies that a small amount of variability aides in internal model formation, presumably a consequence of the additional amount of exploration conducted in the workspace of the task.

[BibTex]

[BibTex]


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Dynamic movement primitives for movement generation motivated by convergent force fields in frog

Hoffmann, H., Pastor, P., Schaal, S.

In Adaptive Motion of Animals and Machines (AMAM), 2008, clmc (inproceedings)

PDF [BibTex]

PDF [BibTex]


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Behavioral experiments on reinforcement learning in human motor control

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

In Abstracts of the Eighteenth Annual Meeting of Neural Control of Movement (NCM), Naples, Florida, April 29-May 4, 2008, clmc (inproceedings)

Abstract
Reinforcement learning (RL) - learning solely based on reward or cost feedback - is widespread in robotics control and has been also suggested as computational model for human motor control. In human motor control, however, hardly any experiment studied reinforcement learning. Here, we study learning based on visual cost feedback in a reaching task and did three experiments: (1) to establish a simple enough experiment for RL, (2) to study spatial localization of RL, and (3) to study the dependence of RL on the cost function. In experiment (1), subjects sit in front of a drawing tablet and look at a screen onto which the drawing pen's position is projected. Beginning from a start point, their task is to move with the pen through a target point presented on screen. Visual feedback about the pen's position is given only before movement onset. At the end of a movement, subjects get visual feedback only about the cost of this trial. We choose as cost the squared distance between target and virtual pen position at the target line. Above a threshold value, the cost was fixed at this value. In the mapping of the pen's position onto the screen, we added a bias (unknown to subject) and Gaussian noise. As result, subjects could learn the bias, and thus, showed reinforcement learning. In experiment (2), we randomly altered the target position between three different locations (three different directions from start point: -45, 0, 45). For each direction, we chose a different bias. As result, subjects learned all three bias values simultaneously. Thus, RL can be spatially localized. In experiment (3), we varied the sensitivity of the cost function by multiplying the squared distance with a constant value C, while keeping the same cut-off threshold. As in experiment (2), we had three target locations. We assigned to each location a different C value (this assignment was randomized between subjects). Since subjects learned the three locations simultaneously, we could directly compare the effect of the different cost functions. As result, we found an optimal C value; if C was too small (insensitive cost), learning was slow; if C was too large (narrow cost valley), the exploration time was longer and learning delayed. Thus, reinforcement learning in human motor control appears to be sen

[BibTex]

[BibTex]


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Movement generation by learning from demonstration and generalization to new targets

Pastor, P., Hoffmann, H., Schaal, S.

In Adaptive Motion of Animals and Machines (AMAM), 2008, clmc (inproceedings)

PDF [BibTex]

PDF [BibTex]


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Combining dynamic movement primitives and potential fields for online obstacle avoidance

Park, D., Hoffmann, H., Schaal, S.

In Adaptive Motion of Animals and Machines (AMAM), Cleveland, Ohio, 2008, 2008, clmc (inproceedings)

link (url) [BibTex]

link (url) [BibTex]


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Computational model for movement learning under uncertain cost

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

In Abstracts of the Society of Neuroscience Meeting (SFN 2008), Washington, DC 2008, 2008, clmc (inproceedings)

Abstract
Stochastic optimal control is a framework for computing control commands that lead to an optimal behavior under a given cost. Despite the long history of optimal control in engineering, it has been only recently applied to describe human motion. So far, stochastic optimal control has been mainly used in tasks that are already learned, such as reaching to a target. For learning, however, there are only few cases where optimal control has been applied. The main assumptions of stochastic optimal control that restrict its application to tasks after learning are the a priori knowledge of (1) a quadratic cost function (2) a state space model that captures the kinematics and/or dynamics of musculoskeletal system and (3) a measurement equation that models the proprioceptive and/or exteroceptive feedback. Under these assumptions, a sequence of control gains is computed that is optimal with respect to the prespecified cost function. In our work, we relax the assumption of the a priori known cost function and provide a computational framework for modeling tasks that involve learning. Typically, a cost function consists of two parts: one part that models the task constraints, like squared distance to goal at movement endpoint, and one part that integrates over the squared control commands. In learning a task, the first part of this cost function will be adapted. We use an expectation-maximization scheme for learning: the expectation step optimizes the task constraints through gradient descent of a reward function and the maximizing step optimizes the control commands. Our computational model is tested and compared with data given from a behavioral experiment. In this experiment, subjects sit in front of a drawing tablet and look at a screen onto which the drawing-pen's position is projected. Beginning from a start point, their task is to move with the pen through a target point presented on screen. Visual feedback about the pen's position is given only before movement onset. At the end of a movement, subjects get visual feedback only about the cost of this trial. In the mapping of the pen's position onto the screen, we added a bias (unknown to subject) and Gaussian noise. Therefore the cost is a function of this bias. The subjects were asked to reach to the target and minimize this cost over trials. In this behavioral experiment, subjects could learn the bias and thus showed reinforcement learning. With our computational model, we could model the learning process over trials. Particularly, the dependence on parameters of the reward function (Gaussian width) and the modulation of movement variance over time were similar in experiment and model.

[BibTex]

[BibTex]


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A Bayesian approach to empirical local linearizations for robotics

Ting, J., D’Souza, A., Vijayakumar, S., Schaal, S.

In International Conference on Robotics and Automation (ICRA2008), Pasadena, CA, USA, May 19-23, 2008, 2008, clmc (inproceedings)

Abstract
Local linearizations are ubiquitous in the control of robotic systems. Analytical methods, if available, can be used to obtain the linearization, but in complex robotics systems where the the dynamics and kinematics are often not faithfully obtainable, empirical linearization may be preferable. In this case, it is important to only use data for the local linearization that lies within a ``reasonable'' linear regime of the system, which can be defined from the Hessian at the point of the linearization -- a quantity that is not available without an analytical model. We introduce a Bayesian approach to solve statistically what constitutes a ``reasonable'' local regime. We approach this problem in the context local linear regression. In contrast to previous locally linear methods, we avoid cross-validation or complex statistical hypothesis testing techniques to find the appropriate local regime. Instead, we treat the parameters of the local regime probabilistically and use approximate Bayesian inference for their estimation. This approach results in an analytical set of iterative update equations that are easily implemented on real robotics systems for real-time applications. As in other locally weighted regressions, our algorithm also lends itself to complete nonlinear function approximation for learning empirical internal models. We sketch the derivation of our Bayesian method and provide evaluations on synthetic data and actual robot data where the analytical linearization was known.

link (url) [BibTex]

link (url) [BibTex]


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Do humans plan continuous trajectories in kinematic coordinates?

Hoffmann, H., Schaal, S.

In Abstracts of the Society of Neuroscience Meeting (SFN 2008), Washington, DC 2008, 2008, clmc (inproceedings)

Abstract
The planning and execution of human arm movements is still unresolved. An ongoing controversy is whether we plan a movement in kinematic coordinates and convert these coordinates with an inverse internal model into motor commands (like muscle activation) or whether we combine a few muscle synergies or equilibrium points to move a hand, e.g., between two targets. The first hypothesis implies that a planner produces a desired end-effector position for all time points; the second relies on the dynamics of the muscular-skeletal system for a given control command to produce a continuous end-effector trajectory. To distinguish between these two possibilities, we use a visuomotor adaptation experiment. Subjects moved a pen on a graphics tablet and observed the pen's mapped position onto a screen (subjects quickly adapted to this mapping). The task was to move a cursor between two points in a given time window. In the adaptation test, we manipulated the velocity profile of the cursor feedback such that the shape of the trajectories remained unchanged (for straight paths). If humans would use a kinematic plan and map at each time the desired end-effector position onto control commands, subjects should adapt to the above manipulation. In a similar experiment, Wolpert et al (1995) showed adaptation to changes in the curvature of trajectories. This result, however, cannot rule out a shift of an equilibrium point or an additional synergy activation between start and end point of a movement. In our experiment, subjects did two sessions, one control without and one with velocity-profile manipulation. To skew the velocity profile of the cursor trajectory, we added to the current velocity, v, the function 0.8*v*cos(pi + pi*x), where x is the projection of the cursor position onto the start-goal line divided by the distance start to goal (x=0 at the start point). As result, subjects did not adapt to this manipulation: for all subjects, the true hand motion was not significantly modified in a direction consistent with adaptation, despite that the visually presented motion differed significantly from the control motion. One may still argue that this difference in motion was insufficient to be processed visually. Thus, as a control experiment, we replayed control and modified motions to the subjects and asked which of the two motions appeared 'more natural'. Subjects chose the unperturbed motion as more natural significantly better than chance. In summary, for a visuomotor transformation task, the hypothesis of a planned continuous end-effector trajectory predicts adaptation to a modified velocity profile. The current experiment found no adaptation under such transformation.

[BibTex]

[BibTex]

2007


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Less Conservative Polytopic LPV Models for Charge Control by Combining Parameter Set Mapping and Set Intersection

Kwiatkowski, A., Trimpe, S., Werner, H.

In Proceedings of the 46th IEEE Conference on Decision and Control, 2007 (inproceedings)

DOI [BibTex]

2007

DOI [BibTex]


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Lower body realization of the baby humanoid - ‘iCub’

Tsagarakis, N., Becchi, F., Righetti, L., Ijspeert, A., Caldwell, D.

In IEEE/RSJ International Conference on Intelligent Robots and Systems, 2007. IROS 2007., pages: 3616-3622, 2007 (inproceedings)

[BibTex]

[BibTex]


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Hand placement during quadruped locomotion in a humanoid robot: A dynamical system approach

Degallier, S., Righetti, L., Ijspeert, A.

In IEEE/RSJ International Conference on Intelligent Robots and Systems, 2007. IROS 2007., pages: 2047-2052, 2007 (inproceedings)

[BibTex]

[BibTex]


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Uncertain 3D Force Fields in Reaching Movements: Do Humans Favor Robust or Average Performance?

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

In Abstracts of the 37th Meeting of the Society of Neuroscience, 2007, clmc (inproceedings)

PDF [BibTex]

PDF [BibTex]


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Towards Machine Learning of Motor Skills

Peters, J., Schaal, S., Schölkopf, B.

In Proceedings of Autonome Mobile Systeme (AMS), pages: 138-144, (Editors: K Berns and T Luksch), 2007, clmc (inproceedings)

Abstract
Autonomous robots that can adapt to novel situations has been a long standing vision of robotics, artificial intelligence, and cognitive sciences. Early approaches to this goal during the heydays of artificial intelligence research in the late 1980s, however, made it clear that an approach purely based on reasoning or human insights would not be able to model all the perceptuomotor tasks that a robot should fulfill. Instead, new hope was put in the growing wake of machine learning that promised fully adaptive control algorithms which learn both by observation and trial-and-error. However, to date, learning techniques have yet to fulfill this promise as only few methods manage to scale into the high-dimensional domains of manipulator robotics, or even the new upcoming trend of humanoid robotics, and usually scaling was only achieved in precisely pre-structured domains. In this paper, we investigate the ingredients for a general approach to motor skill learning in order to get one step closer towards human-like performance. For doing so, we study two ma jor components for such an approach, i.e., firstly, a theoretically well-founded general approach to representing the required control structures for task representation and execution and, secondly, appropriate learning algorithms which can be applied in this setting.

PDF DOI [BibTex]

PDF DOI [BibTex]


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Applying the episodic natural actor-critic architecture to motor primitive learning

Peters, J., Schaal, S.

In Proceedings of the 2007 European Symposium on Artificial Neural Networks (ESANN), Bruges, Belgium, April 25-27, 2007, clmc (inproceedings)

Abstract
In this paper, we investigate motor primitive learning with the Natural Actor-Critic approach. The Natural Actor-Critic consists out of actor updates which are achieved using natural stochastic policy gradients while the critic obtains the natural policy gradient by linear regression. We show that this architecture can be used to learn the Òbuilding blocks of movement generationÓ, called motor primitives. Motor primitives are parameterized control policies such as splines or nonlinear differential equations with desired attractor properties. We show that our most modern algorithm, the Episodic Natural Actor-Critic outperforms previous algorithms by at least an order of magnitude. We demonstrate the efficiency of this reinforcement learning method in the application of learning to hit a baseball with an anthropomorphic robot arm.

link (url) [BibTex]

link (url) [BibTex]


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A computational model of human trajectory planning based on convergent flow fields

Hoffman, H., Schaal, S.

In Abstracts of the 37st Meeting of the Society of Neuroscience, San Diego, CA, Nov. 3-7, 2007, clmc (inproceedings)

Abstract
A popular computational model suggests that smooth reaching movements are generated in humans by minimizing a difference vector between hand and target in visual coordinates (Shadmehr and Wise, 2005). To achieve such a task, the optimal joint accelerations may be pre-computed. However, this pre-planning is inflexible towards perturbations of the limb, and there is strong evidence that reaching movements can be modified on-line at any moment during the movement. Thus, next-state planning models (Bullock and Grossberg, 1988) have been suggested that compute the current control command from a function of the goal state such that the overall movement smoothly converges to the goal (see Shadmehr and Wise (2005) for an overview). So far, these models have been restricted to simple point-to-point reaching movements with (approximately) straight trajectories. Here, we present a computational model for learning and executing arbitrary trajectories that combines ideas from pattern generation with dynamic systems and the observation of convergent force fields, which control a frog leg after spinal stimulation (Giszter et al., 1993). In our model, we incorporate the following two observations: first, the orientation of vectors in a force field is invariant over time, but their amplitude is modulated by a time-varying function, and second, two force fields add up when stimulated simultaneously (Giszter et al., 1993). This addition of convergent force fields varying over time results in a virtual trajectory (a moving equilibrium point) that correlates with the actual leg movement (Giszter et al., 1993). Our next-state planner is a set of differential equations that provide the desired end-effector or joint accelerations using feedback of the current state of the limb. These accelerations can be interpreted as resulting from a damped spring that links the current limb position with a virtual trajectory. This virtual trajectory can be learned to realize any desired limb trajectory and velocity profile, and learning is efficient since the time-modulated sum of convergent force fields equals a sum of weighted basis functions (Gaussian time pulses). Thus, linear algebra is sufficient to compute these weights, which correspond to points on the virtual trajectory. During movement execution, the differential equation corrects automatically for perturbations and brings back smoothly the limb towards the goal. Virtual trajectories can be rescaled and added allowing to build a set of movement primitives to describe movements more complex than previously learned. We demonstrate the potential of the suggested model by learning and generating a wide variety of movements.

[BibTex]

[BibTex]