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2018


Probabilistic Recurrent State-Space Models
Probabilistic Recurrent State-Space Models

Doerr, A., Daniel, C., Schiegg, M., Nguyen-Tuong, D., Schaal, S., Toussaint, M., Trimpe, S.

In Proceedings of the International Conference on Machine Learning (ICML), International Conference on Machine Learning (ICML), July 2018 (inproceedings)

Abstract
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g., LSTMs) proved extremely successful in modeling complex time-series data. Fully probabilistic SSMs, however, unfortunately often prove hard to train, even for smaller problems. To overcome this limitation, we propose a scalable initialization and training algorithm based on doubly stochastic variational inference and Gaussian processes. In the variational approximation we propose in contrast to related approaches to fully capture the latent state temporal correlations to allow for robust training.

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arXiv pdf Project Page [BibTex]

2018


arXiv pdf Project Page [BibTex]


Online Learning of a Memory for Learning Rates
Online Learning of a Memory for Learning Rates

(nominated for best paper award)

Meier, F., Kappler, D., Schaal, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2018, IEEE, International Conference on Robotics and Automation, May 2018, accepted (inproceedings)

Abstract
The promise of learning to learn for robotics rests on the hope that by extracting some information about the learning process itself we can speed up subsequent similar learning tasks. Here, we introduce a computationally efficient online meta-learning algorithm that builds and optimizes a memory model of the optimal learning rate landscape from previously observed gradient behaviors. While performing task specific optimization, this memory of learning rates predicts how to scale currently observed gradients. After applying the gradient scaling our meta-learner updates its internal memory based on the observed effect its prediction had. Our meta-learner can be combined with any gradient-based optimizer, learns on the fly and can be transferred to new optimization tasks. In our evaluations we show that our meta-learning algorithm speeds up learning of MNIST classification and a variety of learning control tasks, either in batch or online learning settings.

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pdf video code [BibTex]

pdf video code [BibTex]


Learning Sensor Feedback Models from Demonstrations via Phase-Modulated Neural Networks
Learning Sensor Feedback Models from Demonstrations via Phase-Modulated Neural Networks

Sutanto, G., Su, Z., Schaal, S., Meier, F.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2018, IEEE, International Conference on Robotics and Automation, May 2018 (inproceedings)

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pdf video [BibTex]

pdf video [BibTex]


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On Time Optimization of Centroidal Momentum Dynamics

Ponton, B., Herzog, A., Del Prete, A., Schaal, S., Righetti, L.

In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 5776-5782, IEEE, Brisbane, Australia, 2018 (inproceedings)

Abstract
Recently, the centroidal momentum dynamics has received substantial attention to plan dynamically consistent motions for robots with arms and legs in multi-contact scenarios. However, it is also non convex which renders any optimization approach difficult and timing is usually kept fixed in most trajectory optimization techniques to not introduce additional non convexities to the problem. But this can limit the versatility of the algorithms. In our previous work, we proposed a convex relaxation of the problem that allowed to efficiently compute momentum trajectories and contact forces. However, our approach could not minimize a desired angular momentum objective which seriously limited its applicability. Noticing that the non-convexity introduced by the time variables is of similar nature as the centroidal dynamics one, we propose two convex relaxations to the problem based on trust regions and soft constraints. The resulting approaches can compute time-optimized dynamically consistent trajectories sufficiently fast to make the approach realtime capable. The performance of the algorithm is demonstrated in several multi-contact scenarios for a humanoid robot. In particular, we show that the proposed convex relaxation of the original problem finds solutions that are consistent with the original non-convex problem and illustrate how timing optimization allows to find motion plans that would be difficult to plan with fixed timing † †Implementation details and demos can be found in the source code available at https://git-amd.tuebingen.mpg.de/bponton/timeoptimization.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Unsupervised Contact Learning for Humanoid Estimation and Control

Rotella, N., Schaal, S., Righetti, L.

In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 411-417, IEEE, Brisbane, Australia, 2018 (inproceedings)

Abstract
This work presents a method for contact state estimation using fuzzy clustering to learn contact probability for full, six-dimensional humanoid contacts. The data required for training is solely from proprioceptive sensors - endeffector contact wrench sensors and inertial measurement units (IMUs) - and the method is completely unsupervised. The resulting cluster means are used to efficiently compute the probability of contact in each of the six endeffector degrees of freedom (DoFs) independently. This clustering-based contact probability estimator is validated in a kinematics-based base state estimator in a simulation environment with realistic added sensor noise for locomotion over rough, low-friction terrain on which the robot is subject to foot slip and rotation. The proposed base state estimator which utilizes these six DoF contact probability estimates is shown to perform considerably better than that which determines kinematic contact constraints purely based on measured normal force.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Task-Specific Dynamics to Improve Whole-Body Control

Gams, A., Mason, S., Ude, A., Schaal, S., Righetti, L.

In Hua, IEEE, Beijing, China, November 2018 (inproceedings)

Abstract
In task-based inverse dynamics control, reference accelerations used to follow a desired plan can be broken down into feedforward and feedback trajectories. The feedback term accounts for tracking errors that are caused from inaccurate dynamic models or external disturbances. On underactuated, free-floating robots, such as humanoids, high feedback terms can be used to improve tracking accuracy; however, this can lead to very stiff behavior or poor tracking accuracy due to limited control bandwidth. In this paper, we show how to reduce the required contribution of the feedback controller by incorporating learned task-space reference accelerations. Thus, we i) improve the execution of the given specific task, and ii) offer the means to reduce feedback gains, providing for greater compliance of the system. With a systematic approach we also reduce heuristic tuning of the model parameters and feedback gains, often present in real-world experiments. In contrast to learning task-specific joint-torques, which might produce a similar effect but can lead to poor generalization, our approach directly learns the task-space dynamics of the center of mass of a humanoid robot. Simulated and real-world results on the lower part of the Sarcos Hermes humanoid robot demonstrate the applicability of the approach.

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link (url) [BibTex]

link (url) [BibTex]


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An MPC Walking Framework With External Contact Forces

Mason, S., Rotella, N., Schaal, S., Righetti, L.

In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 1785-1790, IEEE, Brisbane, Australia, May 2018 (inproceedings)

Abstract
In this work, we present an extension to a linear Model Predictive Control (MPC) scheme that plans external contact forces for the robot when given multiple contact locations and their corresponding friction cone. To this end, we set up a two-step optimization problem. In the first optimization, we compute the Center of Mass (CoM) trajectory, foot step locations, and introduce slack variables to account for violating the imposed constraints on the Zero Moment Point (ZMP). We then use the slack variables to trigger the second optimization, in which we calculate the optimal external force that compensates for the ZMP tracking error. This optimization considers multiple contacts positions within the environment by formulating the problem as a Mixed Integer Quadratic Program (MIQP) that can be solved at a speed between 100-300 Hz. Once contact is created, the MIQP reduces to a single Quadratic Program (QP) that can be solved in real-time ({\textless}; 1kHz). Simulations show that the presented walking control scheme can withstand disturbances 2-3× larger with the additional force provided by a hand contact.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2013


Probabilistic Object Tracking Using a Range Camera
Probabilistic Object Tracking Using a Range Camera

Wüthrich, M., Pastor, P., Kalakrishnan, M., Bohg, J., Schaal, S.

In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 3195-3202, IEEE, November 2013 (inproceedings)

Abstract
We address the problem of tracking the 6-DoF pose of an object while it is being manipulated by a human or a robot. We use a dynamic Bayesian network to perform inference and compute a posterior distribution over the current object pose. Depending on whether a robot or a human manipulates the object, we employ a process model with or without knowledge of control inputs. Observations are obtained from a range camera. As opposed to previous object tracking methods, we explicitly model self-occlusions and occlusions from the environment, e.g, the human or robotic hand. This leads to a strongly non-linear observation model and additional dependencies in the Bayesian network. We employ a Rao-Blackwellised particle filter to compute an estimate of the object pose at every time step. In a set of experiments, we demonstrate the ability of our method to accurately and robustly track the object pose in real-time while it is being manipulated by a human or a robot.

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arXiv Video Code Video DOI Project Page [BibTex]

2013


arXiv Video Code Video DOI Project Page [BibTex]


Hypothesis Testing Framework for Active Object Detection
Hypothesis Testing Framework for Active Object Detection

Sankaran, B., Atanasov, N., Le Ny, J., Koletschka, T., Pappas, G., Daniilidis, K.

In IEEE International Conference on Robotics and Automation (ICRA), May 2013, clmc (inproceedings)

Abstract
One of the central problems in computer vision is the detection of semantically important objects and the estimation of their pose. Most of the work in object detection has been based on single image processing and its performance is limited by occlusions and ambiguity in appearance and geometry. This paper proposes an active approach to object detection by controlling the point of view of a mobile depth camera. When an initial static detection phase identifies an object of interest, several hypotheses are made about its class and orientation. The sensor then plans a sequence of view-points, which balances the amount of energy used to move with the chance of identifying the correct hypothesis. We formulate an active M-ary hypothesis testing problem, which includes sensor mobility, and solve it using a point-based approximate POMDP algorithm. The validity of our approach is verified through simulation and experiments with real scenes captured by a kinect sensor. The results suggest a significant improvement over static object detection.

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pdf [BibTex]

pdf [BibTex]


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Action and Goal Related Decision Variables Modulate the Competition Between Multiple Potential Targets

Enachescu, V, Christopoulos, Vassilios N, Schrater, P. R., Schaal, S.

In Abstracts of Neural Control of Movement Conference (NCM 2013), February 2013 (inproceedings)

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[BibTex]

[BibTex]


Fusing visual and tactile sensing for 3-D object reconstruction while grasping
Fusing visual and tactile sensing for 3-D object reconstruction while grasping

Ilonen, J., Bohg, J., Kyrki, V.

In IEEE International Conference on Robotics and Automation (ICRA), pages: 3547-3554, 2013 (inproceedings)

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 from a single view. This initial model is used to plan a grasp on the object which is then executed with a robotic manipulator equipped with tactile sensors. Given the detected contacts between the fingers and the object, the 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.

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DOI Project Page [BibTex]

DOI Project Page [BibTex]


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AGILITY – Dynamic Full Body Locomotion and Manipulation with Autonomous Legged Robots

Hutter, M., Bloesch, M., Buchli, J., Semini, C., Bazeille, S., Righetti, L., Bohg, J.

In 2013 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), pages: 1-4, IEEE, Linköping, Sweden, 2013 (inproceedings)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Objective Functions for Manipulation

Kalakrishnan, M., Pastor, P., Righetti, L., Schaal, S.

In 2013 IEEE International Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

Abstract
We present an approach to learning objective functions for robotic manipulation based on inverse reinforcement learning. Our path integral inverse reinforcement learning algorithm can deal with high-dimensional continuous state-action spaces, and only requires local optimality of demonstrated trajectories. We use L 1 regularization in order to achieve feature selection, and propose an efficient algorithm to minimize the resulting convex objective function. We demonstrate our approach by applying it to two core problems in robotic manipulation. First, we learn a cost function for redundancy resolution in inverse kinematics. Second, we use our method to learn a cost function over trajectories, which is then used in optimization-based motion planning for grasping and manipulation tasks. Experimental results show that our method outperforms previous algorithms in high-dimensional settings.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Task Error Models for Manipulation

Pastor, P., Kalakrishnan, M., Binney, J., Kelly, J., Righetti, L., Sukhatme, G. S., Schaal, S.

In 2013 IEEE Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

Abstract
Precise kinematic forward models are important for robots to successfully perform dexterous grasping and manipulation tasks, especially when visual servoing is rendered infeasible due to occlusions. A lot of research has been conducted to estimate geometric and non-geometric parameters of kinematic chains to minimize reconstruction errors. However, kinematic chains can include non-linearities, e.g. due to cable stretch and motor-side encoders, that result in significantly different errors for different parts of the state space. Previous work either does not consider such non-linearities or proposes to estimate non-geometric parameters of carefully engineered models that are robot specific. We propose a data-driven approach that learns task error models that account for such unmodeled non-linearities. We argue that in the context of grasping and manipulation, it is sufficient to achieve high accuracy in the task relevant state space. We identify this relevant state space using previously executed joint configurations and learn error corrections for those. Therefore, our system is developed to generate subsequent executions that are similar to previous ones. The experiments show that our method successfully captures the non-linearities in the head kinematic chain (due to a counterbalancing spring) and the arm kinematic chains (due to cable stretch) of the considered experimental platform, see Fig. 1. The feasibility of the presented error learning approach has also been evaluated in independent DARPA ARM-S testing contributing to successfully complete 67 out of 72 grasping and manipulation tasks.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2011


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STOMP: Stochastic trajectory optimization for motion planning

Kalakrishnan, M., Chitta, S., Theodorou, E., Pastor, P., Schaal, S.

In IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9-13, 2011, clmc (inproceedings)

Abstract
We present a new approach to motion planning using a stochastic trajectory optimization framework. The approach relies on generating noisy trajectories to explore the space around an initial (possibly infeasible) trajectory, which are then combined to produced an updated trajectory with lower cost. A cost function based on a combination of obstacle and smoothness cost is optimized in each iteration. No gradient information is required for the particular optimization algorithm that we use and so general costs for which derivatives may not be available (e.g. costs corresponding to constraints and motor torques) can be included in the cost function. We demonstrate the approach both in simulation and on a dual-arm mobile manipulation system for unconstrained and constrained tasks. We experimentally show that the stochastic nature of STOMP allows it to overcome local minima that gradient-based optimizers like CHOMP can get stuck in.

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link (url) Project Page [BibTex]

2011


link (url) Project Page [BibTex]


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Development of a Low-Pressure Fluidic Servo-Valve for Wearable Haptic Interfaces and Lightweight Robotic Systems"

Folgheraiter, M., Jordan, M., Benitez, L. M. V., Grimminger, F., Schmidt, S., Albiez, J., Kirchner, F.

In Informatics in Control, Automation and Robotics, pages: 239-252, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011 (inproceedings)

Abstract
This document presents a low-pressure servo-valve specifically designed for haptic interfaces and lightweight robotic applications. The device is able to work with hydraulic and pneumatic fluidic sources, operating within a pressure range of (0{\thinspace}−{\thinspace}50 {\textperiodcentered}105Pa). All sensors and electronics were integrated inside the body of the valve, reducing the need for external circuits. Positioning repeatability as well as the capability to fine modulate the hydraulic flow were measured and verified. Furthermore, the static and dynamic behavior of the valve were evaluated for different working conditions, and a non-linear model identified using a recursive Hammerstein-Wiener parameter adaptation algorithm.

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DOI [BibTex]

DOI [BibTex]


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Path Integral Control and Bounded Rationality

Braun, D. A., Ortega, P. A., Theodorou, E., Schaal, S.

In IEEE Symposium on Adaptive Dynamic Programming And Reinforcement Learning (ADPRL), 2011, clmc (inproceedings)

Abstract
Path integral methods [7], [15],[1] have recently been shown to be applicable to a very general class of optimal control problems. Here we examine the path integral formalism from a decision-theoretic point of view, since an optimal controller can always be regarded as an instance of a perfectly rational decision-maker that chooses its actions so as to maximize its expected utility [8]. The problem with perfect rationality is, however, that finding optimal actions is often very difficult due to prohibitive computational resource costs that are not taken into account. In contrast, a bounded rational decision-maker has only limited resources and therefore needs to strike some compromise between the desired utility and the required resource costs [14]. In particular, we suggest an information-theoretic measure of resource costs that can be derived axiomatically [11]. As a consequence we obtain a variational principle for choice probabilities that trades off maximizing a given utility criterion and avoiding resource costs that arise due to deviating from initially given default choice probabilities. The resulting bounded rational policies are in general probabilistic. We show that the solutions found by the path integral formalism are such bounded rational policies. Furthermore, we show that the same formalism generalizes to discrete control problems, leading to linearly solvable bounded rational control policies in the case of Markov systems. Importantly, Bellman?s optimality principle is not presupposed by this variational principle, but it can be derived as a limit case. This suggests that the information- theoretic formalization of bounded rationality might serve as a general principle in control design that unifies a number of recently reported approximate optimal control methods both in the continuous and discrete domain.

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PDF [BibTex]

PDF [BibTex]


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Skill learning and task outcome prediction for manipulation

Pastor, P., Kalakrishnan, M., Chitta, S., Theodorou, E., Schaal, S.

In IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9-13, 2011, clmc (inproceedings)

Abstract
Learning complex motor skills for real world tasks is a hard problem in robotic manipulation that often requires painstaking manual tuning and design by a human expert. In this work, we present a Reinforcement Learning based approach to acquiring new motor skills from demonstration. Our approach allows the robot to learn fine manipulation skills and significantly improve its success rate and skill level starting from a possibly coarse demonstration. Our approach aims to incorporate task domain knowledge, where appropriate, by working in a space consistent with the constraints of a specific task. In addition, we also present an approach to using sensor feedback to learn a predictive model of the task outcome. This allows our system to learn the proprioceptive sensor feedback needed to monitor subsequent executions of the task online and abort execution in the event of predicted failure. We illustrate our approach using two example tasks executed with the PR2 dual-arm robot: a straight and accurate pool stroke and a box flipping task using two chopsticks as tools.

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link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


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An Iterative Path Integral Stochastic Optimal Control Approach for Learning Robotic Tasks

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

In Proceedings of the 18th World Congress of the International Federation of Automatic Control, 2011, clmc (inproceedings)

Abstract
Recent work on path integral stochastic optimal control theory Theodorou et al. (2010a); Theodorou (2011) has shown promising results in planning and control of nonlinear systems in high dimensional state spaces. The path integral control framework relies on the transformation of the nonlinear Hamilton Jacobi Bellman (HJB) partial differential equation (PDE) into a linear PDE and the approximation of its solution via the use of the Feynman Kac lemma. In this work, we are reviewing the generalized version of path integral stochastic optimal control formalism Theodorou et al. (2010a), used for optimal control and planing of stochastic dynamical systems with state dependent control and diffusion matrices. Moreover we present the iterative path integral control approach, the so called Policy Improvement with Path Integrals or (PI2 ) which is capable of scaling in high dimensional robotic control problems. Furthermore we present a convergence analysis of the proposed algorithm and we apply the proposed framework to a variety of robotic tasks. Finally with the goal to perform locomotion the iterative path integral control is applied for learning nonlinear limit cycle attractors with adjustable land scape.

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PDF [BibTex]

PDF [BibTex]


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Learning Force Control Policies for Compliant Manipulation

Kalakrishnan, M., Righetti, L., Pastor, P., Schaal, S.

In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 4639-4644, IEEE, San Francisco, USA, sep 2011 (inproceedings)

Abstract
Developing robots capable of fine manipulation skills is of major importance in order to build truly assistive robots. These robots need to be compliant in their actuation and control in order to operate safely in human environments. Manipulation tasks imply complex contact interactions with the external world, and involve reasoning about the forces and torques to be applied. Planning under contact conditions is usually impractical due to computational complexity, and a lack of precise dynamics models of the environment. We present an approach to acquiring manipulation skills on compliant robots through reinforcement learning. The initial position control policy for manipulation is initialized through kinesthetic demonstration. We augment this policy with a force/torque profile to be controlled in combination with the position trajectories. We use the Policy Improvement with Path Integrals (PI2) algorithm to learn these force/torque profiles by optimizing a cost function that measures task success. We demonstrate our approach on the Barrett WAM robot arm equipped with a 6-DOF force/torque sensor on two different manipulation tasks: opening a door with a lever door handle, and picking up a pen off the table. We show that the learnt force control policies allow successful, robust execution of the tasks.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Control of legged robots with optimal distribution of contact forces

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

In 2011 11th IEEE-RAS International Conference on Humanoid Robots, pages: 318-324, IEEE, Bled, Slovenia, 2011 (inproceedings)

Abstract
The development of agile and safe humanoid robots require controllers that guarantee both high tracking performance and compliance with the environment. More specifically, the control of contact interaction is of crucial importance for robots that will actively interact with their environment. Model-based controllers such as inverse dynamics or operational space control are very appealing as they offer both high tracking performance and compliance. However, while widely used for fully actuated systems such as manipulators, they are not yet standard controllers for legged robots such as humanoids. Indeed such robots are fundamentally different from manipulators as they are underactuated due to their floating-base and subject to switching contact constraints. In this paper we present an inverse dynamics controller for legged robots that use torque redundancy to create an optimal distribution of contact constraints. The resulting controller is able to minimize, given a desired motion, any quadratic cost of the contact constraints at each instant of time. In particular we show how this can be used to minimize tangential forces during locomotion, therefore significantly improving the locomotion of legged robots on difficult terrains. In addition to the theoretical result, we present simulations of a humanoid and a quadruped robot, as well as experiments on a real quadruped robot that demonstrate the advantages of the controller.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Motion Primitive Goals for Robust Manipulation

Stulp, F., Theodorou, E., Kalakrishnan, M., Pastor, P., Righetti, L., Schaal, S.

In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 325-331, IEEE, San Francisco, USA, sep 2011 (inproceedings)

Abstract
Applying model-free reinforcement learning to manipulation remains challenging for several reasons. First, manipulation involves physical contact, which causes discontinuous cost functions. Second, in manipulation, the end-point of the movement must be chosen carefully, as it represents a grasp which must be adapted to the pose and shape of the object. Finally, there is uncertainty in the object pose, and even the most carefully planned movement may fail if the object is not at the expected position. To address these challenges we 1) present a simplified, computationally more efficient version of our model-free reinforcement learning algorithm PI2; 2) extend PI2 so that it simultaneously learns shape parameters and goal parameters of motion primitives; 3) use shape and goal learning to acquire motion primitives that are robust to object pose uncertainty. We evaluate these contributions on a manipulation platform consisting of a 7-DOF arm with a 4-DOF hand.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Inverse Dynamics Control of Floating-Base Robots with External Constraints: a Unified View

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

In 2011 IEEE International Conference on Robotics and Automation, pages: 1085-1090, IEEE, Shanghai, China, 2011 (inproceedings)

Abstract
Inverse dynamics controllers and operational space controllers have proved to be very efficient for compliant control of fully actuated robots such as fixed base manipulators. However legged robots such as humanoids are inherently different as they are underactuated and subject to switching external contact constraints. Recently several methods have been proposed to create inverse dynamics controllers and operational space controllers for these robots. In an attempt to compare these different approaches, we develop a general framework for inverse dynamics control and show that these methods lead to very similar controllers. We are then able to greatly simplify recent whole-body controllers based on operational space approaches using kinematic projections, bringing them closer to efficient practical implementations. We also generalize these controllers such that they can be optimal under an arbitrary quadratic cost in the commands.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Movement segmentation using a primitive library

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

In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011), Sept. 25-30, San Francisco, CA, 2011, clmc (inproceedings)

Abstract
Segmenting complex movements into a sequence of primitives remains a difficult problem with many applications in the robotics and vision communities. In this work, we show how the movement segmentation problem can be reduced to a sequential movement recognition problem. To this end, we reformulate the orig-inal Dynamic Movement Primitive (DMP) formulation as a linear dynamical sys-tem with control inputs. Based on this new formulation, we develop an Expecta-tion-Maximization algorithm to estimate the duration and goal position of a par-tially observed trajectory. With the help of this algorithm and the assumption that a library of movement primitives is present, we present a movement seg-mentation framework. We illustrate the usefulness of the new DMP formulation on the two applications of online movement recognition and movement segmen-tation.

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link (url) [BibTex]

link (url) [BibTex]


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Operational Space Control of Constrained and Underactuated Systems

Mistry, M., Righetti, L.

In Proceedings of Robotics: Science and Systems, Los Angeles, CA, USA, June 2011 (inproceedings)

Abstract
The operational space formulation (Khatib, 1987), applied to rigid-body manipulators, describes how to decouple task-space and null-space dynamics, and write control equations that correspond only to forces at the end-effector or, alternatively, only to motion within the null-space. We would like to apply this useful theory to modern humanoids and other legged systems, for manipulation or similar tasks, however these systems present additional challenges due to their underactuated floating bases and contact states that can dynamically change. In recent work, Sentis et al. derived controllers for such systems by implementing a task Jacobian projected into a space consistent with the supporting constraints and underactuation (the so called "support consistent reduced Jacobian"). Here, we take a new approach to derive operational space controllers for constrained underactuated systems, by first considering the operational space dynamics within "projected inverse-dynamics" (Aghili, 2005), and subsequently resolving underactuation through the addition of dynamically consistent control torques. Doing so results in a simplified control solution compared with previous results, and importantly yields several new insights into the underlying problem of operational space control in constrained environments: 1) Underactuated systems, such as humanoid robots, cannot in general completely decouple task and null-space dynamics. However, 2) there may exist an infinite number of control solutions to realize desired task-space dynamics, and 3) these solutions involve the addition of dynamically consistent null-space motion or constraint forces (or combinations of both). In light of these findings, we present several possible control solutions, with varying optimization criteria, and highlight some of their practical consequences.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Online movement adaptation based on previous sensor experiences

Pastor, P., Righetti, L., Kalakrishnan, M., Schaal, S.

In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 365-371, IEEE, San Francisco, USA, sep 2011 (inproceedings)

Abstract
Personal robots can only become widespread if they are capable of safely operating among humans. In uncertain and highly dynamic environments such as human households, robots need to be able to instantly adapt their behavior to unforseen events. In this paper, we propose a general framework to achieve very contact-reactive motions for robotic grasping and manipulation. Associating stereotypical movements to particular tasks enables our system to use previous sensor experiences as a predictive model for subsequent task executions. We use dynamical systems, named Dynamic Movement Primitives (DMPs), to learn goal-directed behaviors from demonstration. We exploit their dynamic properties by coupling them with the measured and predicted sensor traces. This feedback loop allows for online adaptation of the movement plan. Our system can create a rich set of possible motions that account for external perturbations and perception uncertainty to generate truly robust behaviors. As an example, we present an application to grasping with the WAM robot arm.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Additional DOFs and sensors for bio-inspired locomotion: Towards active spine, ankle joints, and feet for a quadruped robot

Kuehn, D., Grimminger, F., Beinersdorf, F., Bernhard, F., Burchardt, A., Schilling, M., Simnofske, M., Stark, T., Zenzes, M., Kirchner, F.

In 2011 IEEE International Conference on Robotics and Biomimetics, pages: 2780-2786, December 2011 (inproceedings)

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DOI [BibTex]

DOI [BibTex]


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Learning to grasp under uncertainty

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

In Robotics and Automation (ICRA), 2011 IEEE International Conference on, Shanghai, China, May 9-13, 2011, clmc (inproceedings)

Abstract
We present an approach that enables robots to learn motion primitives that are robust towards state estimation uncertainties. During reaching and preshaping, the robot learns to use fine manipulation strategies to maneuver the object into a pose at which closing the hand to perform the grasp is more likely to succeed. In contrast, common assumptions in grasp planning and motion planning for reaching are that these tasks can be performed independently, and that the robot has perfect knowledge of the pose of the objects in the environment. We implement our approach using Dynamic Movement Primitives and the probabilistic model-free reinforcement learning algorithm Policy Improvement with Path Integrals (PI2 ). The cost function that PI2 optimizes is a simple boolean that penalizes failed grasps. The key to acquiring robust motion primitives is to sample the actual pose of the object from a distribution that represents the state estimation uncertainty. During learning, the robot will thus optimize the chance of grasping an object from this distribution, rather than at one specific pose. In our empirical evaluation, we demonstrate how the motion primitives become more robust when grasping simple cylindrical objects, as well as more complex, non-convex objects. We also investigate how well the learned motion primitives generalize towards new object positions and other state estimation uncertainty distributions.

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link (url) [BibTex]

link (url) [BibTex]

2010


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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.

am

link (url) [BibTex]

2010


link (url) [BibTex]


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Relative Entropy Policy Search

Peters, J., Mülling, K., Altun, Y.

In Proceedings of the Twenty-Fourth National Conference on Artificial Intelligence, pages: 1607-1612, (Editors: Fox, M. , D. Poole), AAAI Press, Menlo Park, CA, USA, Twenty-Fourth National Conference on Artificial Intelligence (AAAI-10), July 2010 (inproceedings)

Abstract
Policy search is a successful approach to reinforcement learning. However, policy improvements often result in the loss of information. Hence, it has been marred by premature convergence and implausible solutions. As first suggested in the context of covariant policy gradients (Bagnell and Schneider 2003), many of these problems may be addressed by constraining the information loss. In this paper, we continue this path of reasoning and suggest the Relative Entropy Policy Search (REPS) method. The resulting method differs significantly from previous policy gradient approaches and yields an exact update step. It works well on typical reinforcement learning benchmark problems.

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PDF Web [BibTex]

PDF Web [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.

am

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.

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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.

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link (url) [BibTex]

link (url) [BibTex]


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Are reaching movements planned in kinematic or dynamic coordinates?

Ellmer, A., Schaal, S.

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

Abstract
Whether human reaching movements are planned and optimized in kinematic (task space) or dynamic (joint or muscle space) coordinates is still an issue of debate. The first hypothesis implies that a planner produces a desired end-effector position at each point in time during the reaching movement, whereas the latter hypothesis includes the dynamics of the muscular-skeletal control system to produce a continuous end-effector trajectory. Previous work by Wolpert et al (1995) showed that when subjects were led to believe that their straight reaching paths corresponded to curved paths as shown on a computer screen, participants adapted the true path of their hand such that they would visually perceive a straight line in visual space, despite that they actually produced a curved path. These results were interpreted as supporting the stance that reaching trajectories are planned in kinematic coordinates. However, this experiment could only demonstrate that adaptation to altered paths, i.e. the position of the end-effector, did occur, but not that the precise timing of end-effector position was equally planned, i.e., the trajectory. Our current experiment aims at filling this gap by explicitly testing whether position over time, i.e. velocity, is a property of reaching movements that is planned in kinematic coordinates. In the current experiment, the velocity profiles of cursor movements corresponding to the participant's hand motions were skewed either to the left or to the right; the path itself was left unaltered. We developed an adaptation paradigm, where the skew of the velocity profile was introduced gradually and participants reported no awareness of any manipulation. Preliminary results indicate that the true hand motion of participants did not alter, i.e. there was no adaptation so as to counterbalance the introduced skew. However, for some participants, peak hand velocities were lowered for higher skews, which suggests that participants interpreted the manipulation as mere noise due to variance in their own movement. 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 systematic adaptation under such transformation, but did demonstrate an effect that is more in accordance that subjects could not perceive the manipulation and rather interpreted as an increase of noise.

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[BibTex]

[BibTex]


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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.

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PDF [BibTex]

PDF [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.

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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.

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[BibTex]

[BibTex]


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A highly integrated low pressure fluid servo-valve for applications in wearable robotic systems

Folgheraiter, M., Jordan, M., Vaca Benitez, L. M., Grimminger, F., Schmidt, S., Albiez, J., Kirchner, F.

In ICINCO 2010 - Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics, 2, pages: 72-78, 2010 (inproceedings)

Abstract
In this paper an innovative low pressure servo-valve is presented. The device was designed with the main aim to be easily integrable into complex hydraulic/pneumatic actuation systems, and to operate at relatively low pressure (<50·105Pa). Characteristics like compactness, lightweight, high bandwidth, and autonomous sensory capability, where considered during the design process in order to achieve a device that fulfills the basic requirements for a wearable robotic system. Preliminary results about the prototype performances are presented here, in particular its dynamic behavior was measured for different working conditions, and a non-linear model identified using a recursive Hammerstein-Wiener parameter adaptation algorithm.

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[BibTex]

[BibTex]


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Constrained Accelerations for Controlled Geometric Reduction: Sagittal-Plane Decoupling for Bipedal Locomotion

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

In 2010 10th IEEE-RAS International Conference on Humanoid Robots, pages: 1-7, IEEE, Nashville, USA, 2010 (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.

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link (url) DOI [BibTex]

link (url) DOI [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.

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link (url) [BibTex]

link (url) [BibTex]


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

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

In Proceedings of the 13th International Conference on Climbing and Walking Robots (CLAWAR), pages: 580-587, Nagoya, Japan, sep 2010 (inproceedings)

Abstract
Contact interaction with the environment is crucial in the design of locomotion controllers for legged robots, to prevent slipping for example. Therefore, it is of great importance to be able to control the effects of the robots movements on the contact reaction forces. 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 where no inversion of the inertia matrix is needed which is particularly relevant for practical use on a real robot. Such an algorithm becomes interesting for agile locomotion of robots on difficult terrains where the contacts with the environment are critical, such as walking over rough or slippery terrain.

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DOI [BibTex]

DOI [BibTex]


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Effects of Wheel Synchronization for the Hybrid Leg-Wheel Robot Asguard

Babu, A., Joyeux, S., Schwendner, J., Grimminger, F.

In Proceedings of International Symposium on Artificial Intelligence, Robotics and Automation in Space. International Symposium on Artificial Intelligence, Robotics and Automation in Space (iSAIRAS-10), August 29-September 1, Sapporo, Japan, August 2010 (inproceedings)

am

[BibTex]

[BibTex]

2000


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Reciprocal excitation between biological and robotic research

Schaal, S., Sternad, D., Dean, W., Kotoska, S., Osu, R., Kawato, M.

In Sensor Fusion and Decentralized Control in Robotic Systems III, Proceedings of SPIE, 4196, pages: 30-40, Boston, MA, Nov.5-8, 2000, November 2000, clmc (inproceedings)

Abstract
While biological principles have inspired researchers in computational and engineering research for a long time, there is still rather limited knowledge flow back from computational to biological domains. This paper presents examples of our work where research on anthropomorphic robots lead us to new insights into explaining biological movement phenomena, starting from behavioral studies up to brain imaging studies. Our research over the past years has focused on principles of trajectory formation with nonlinear dynamical systems, on learning internal models for nonlinear control, and on advanced topics like imitation learning. The formal and empirical analyses of the kinematics and dynamics of movements systems and the tasks that they need to perform lead us to suggest principles of motor control that later on we found surprisingly related to human behavior and even brain activity.

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link (url) [BibTex]

2000


link (url) [BibTex]


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Nonlinear dynamical systems as movement primitives

Schaal, S., Kotosaka, S., Sternad, D.

In Humanoids2000, First IEEE-RAS International Conference on Humanoid Robots, CD-Proceedings, Cambridge, MA, September 2000, clmc (inproceedings)

Abstract
This paper explores the idea to create complex human-like movements from movement primitives based on nonlinear attractor dynamics. Each degree-of-freedom of a limb is assumed to have two independent abilities to create movement, one through a discrete dynamic system, and one through a rhythmic system. The discrete system creates point-to-point movements based on internal or external target specifications. The rhythmic system can add an additional oscillatory movement relative to the current position of the discrete system. In the present study, we develop appropriate dynamic systems that can realize the above model, motivate the particular choice of the systems from a biological and engineering point of view, and present simulation results of the performance of such movement primitives. The model was implemented for a drumming task on a humanoid robot

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link (url) [BibTex]

link (url) [BibTex]


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Real Time Learning in Humanoids: A challenge for scalability of Online Algorithms

Vijayakumar, S., Schaal, S.

In Humanoids2000, First IEEE-RAS International Conference on Humanoid Robots, CD-Proceedings, Cambridge, MA, September 2000, clmc (inproceedings)

Abstract
While recent research in neural networks and statistical learning has focused mostly on learning from finite data sets without stringent constraints on computational efficiency, there is an increasing number of learning problems that require real-time performance from an essentially infinite stream of incrementally arriving data. This paper demonstrates how even high-dimensional learning problems of this kind can successfully be dealt with by techniques from nonparametric regression and locally weighted learning. As an example, we describe the application of one of the most advanced of such algorithms, Locally Weighted Projection Regression (LWPR), to the on-line learning of the inverse dynamics model of an actual seven degree-of-freedom anthropomorphic robot arm. LWPR's linear computational complexity in the number of input dimensions, its inherent mechanisms of local dimensionality reduction, and its sound learning rule based on incremental stochastic leave-one-out cross validation allows -- to our knowledge for the first time -- implementing inverse dynamics learning for such a complex robot with real-time performance. In our sample task, the robot acquires the local inverse dynamics model needed to trace a figure-8 in only 60 seconds of training.

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link (url) [BibTex]

link (url) [BibTex]


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Synchronized robot drumming by neural oscillator

Kotosaka, S., Schaal, S.

In The International Symposium on Adaptive Motion of Animals and Machines, Montreal, Canada, August 2000, clmc (inproceedings)

Abstract
Sensory-motor integration is one of the key issues in robotics. In this paper, we propose an approach to rhythmic arm movement control that is synchronized with an external signal based on exploiting a simple neural oscillator network. Trajectory generation by the neural oscillator is a biologically inspired method that can allow us to generate a smooth and continuous trajectory. The parameter tuning of the oscillators is used to generate a synchronized movement with wide intervals. We adopted the method for the drumming task as an example task. By using this method, the robot can realize synchronized drumming with wide drumming intervals in real time. The paper also shows the experimental results of drumming by a humanoid robot.

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link (url) [BibTex]

link (url) [BibTex]


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Real-time robot learning with locally weighted statistical learning

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

In International Conference on Robotics and Automation (ICRA2000), San Francisco, April 2000, 2000, clmc (inproceedings)

Abstract
Locally weighted learning (LWL) is a class of statistical learning techniques 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 beliefs that LWL methods cannot work well in high-dimensional spaces, we provide new algorithms that have been tested in up to 50 dimensional learning problems. The applicability of our LWL algorithms is demonstrated in various robot learning examples, including the learning of devil-sticking, pole-balancing of a humanoid robot arm, and inverse-dynamics learning for a seven degree-of-freedom robot.

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link (url) [BibTex]

link (url) [BibTex]


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Fast learning of biomimetic oculomotor control with nonparametric regression networks

Shibata, T., Schaal, S.

In International Conference on Robotics and Automation (ICRA2000), pages: 3847-3854, San Francisco, April 2000, 2000, clmc (inproceedings)

Abstract
Accurate oculomotor control is one of the essential pre-requisites of successful visuomotor coordination. Given the variable nonlinearities of the geometry of binocular vision as well as the possible nonlinearities of the oculomotor plant, it is desirable to accomplish accurate oculomotor control through learning approaches. In this paper, we investigate learning control for a biomimetic active vision system mounted on a humanoid robot. By combining a biologically inspired cerebellar learning scheme with a state-of-the-art statistical learning network, our robot system is able to acquire high performance visual stabilization reflexes after about 40 seconds of learning despite significant nonlinearities and processing delays in the system.

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link (url) [BibTex]

link (url) [BibTex]


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Locally weighted projection regression: An O(n) algorithm for incremental real time learning in high dimensional spaces

Vijayakumar, S., Schaal, S.

In Proceedings of the Seventeenth International Conference on Machine Learning (ICML 2000), 1, pages: 288-293, Stanford, CA, 2000, clmc (inproceedings)

Abstract
Locally weighted projection regression is a new algorithm that achieves nonlinear function approximation in high dimensional spaces with redundant and irrelevant input dimensions. At its core, it uses locally linear models, spanned by a small number of univariate regressions in selected directions in input space. This paper evaluates different methods of projection regression and derives a nonlinear function approximator based on them. This nonparametric local learning system i) learns rapidly with second order learning methods based on incremental training, ii) uses statistically sound stochastic cross validation to learn iii) adjusts its weighting kernels based on local information only, iv) has a computational complexity that is linear in the number of inputs, and v) can deal with a large number of - possibly redundant - inputs, as shown in evaluations with up to 50 dimensional data sets. To our knowledge, this is the first truly incremental spatially localized learning method to combine all these properties.

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link (url) [BibTex]

link (url) [BibTex]


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Inverse kinematics for humanoid robots

Tevatia, G., Schaal, S.

In International Conference on Robotics and Automation (ICRA2000), pages: 294-299, San Fransisco, April 24-28, 2000, 2000, clmc (inproceedings)

Abstract
Real-time control of the endeffector of a humanoid robot in external coordinates requires computationally efficient solutions of the inverse kinematics problem. In this context, this paper investigates methods of resolved motion rate control (RMRC) that employ optimization criteria to resolve kinematic redundancies. In particular we focus on two established techniques, the pseudo inverse with explicit optimization and the extended Jacobian method. We prove that the extended Jacobian method includes pseudo-inverse methods as a special solution. In terms of computational complexity, however, pseudo-inverse and extended Jacobian differ significantly in favor of pseudo-inverse methods. Employing numerical estimation techniques, we introduce a computationally efficient version of the extended Jacobian with performance comparable to the original version . Our results are illustrated in simulation studies with a multiple degree-of-freedom robot, and were tested on a 30 degree-of-freedom robot. 

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link (url) [BibTex]

link (url) [BibTex]