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International Journal of Humanoid Robotics 2005年第4期2卷 389-390页

作者： CHENG, GORDON SCHAAL, STEFAN ATKESON, CHRISTOPHER G. JST-ICORP Computational Brain Project ATR Computational Neuroscience Laboratory 2-2-2 Keihanna Science City Soraku-gun Kyoto619-0288 Japan Computational Learning and Motor Control Lab University of Southern California Hedco Neurosciences Building HNB-103 3641 Watt Way Los AngelesCA90089-2520 United States Robotics Institute Carnegie Mellon University 5000 Forbes Avenue PittsburghPA15213 United States

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Movement segmentation and recognition for imitation learning 15

Movement segmentation and recognition for imitation learning

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15th International Conference on Artificial Intelligence and Statistics, AISTATS 2012

作者： Meier, Franziska Theodorou, Evangelos Schaal, Stefan Computational Learning and Motor Control Lab University of Southern California Los Angeles United States Department of Computer Science and Engineering University of Washington Seattle United States Max-Planck-Institute for Intelligent Systems Tübingen Germany

In human movement learning, it is most common to teach constituent elements of complex movements in isolation, before chaining them into complex movements. Segmentation and recognition of observed movement could thus proceed out of this existing knowledge, which is directly compatible with movement generation. In this paper, we address exactly this scenario. We assume that a library of movement primitives has already been taught, and we wish to identify elements of the library in a complex motor act, where the individual elements have been smoothed together, and, occasionally, there might be a movement segment that is not in our library yet. We employ a flexible machine learning representation of movement primitives based on learnable nonlinear attractor system. For the purpose of movement segmentation and recognition, it is possible to reformulate this representation as a controlled linear dynamical system. An Expectation-Maximization algorithm can be developed to estimate the open parameters of a movement primitive from the library, using as input an observed trajectory piece. If no matching primitive from the library can be found, a new primitive is created. This process allows a straightforward sequential segmentation of observed movement into known and new primitives, which are suitable for robot imitation learning. We illustrate our approach with synthetic examples and data collected from human movement.

关键词： Maximum principle

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An Iterative Path Integral Stochastic Optimal control Approach for learning Robotic Tasks

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IFAC Proceedings Volumes 2011年第1期44卷 11594-11601页

作者： Evangelos Theodorou Freek Stulp Jonas Buchli Stefan Schaal Computational Learning and Motor Control Lab University of Southern California USA Department of Advanced Robotics Italian Institute of Technology ATR Computational Neuroscience Laboratories Kyoto 619-0288 Japan

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 P olicy I mprovement with P ath I ntegrals or (PI 2 ) 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.

关键词： Path Integrals Stochastic Optimal control Robotics

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Model-based policy search for automatic tuning of multivariate PID controllers

Model-based policy search for automatic tuning of multivaria...

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2017 IEEE International Conference on Robotics and Automation, ICRA 2017

作者： Doerr, Andreas Nguyen-Tuong, Duy Marco, Alonso Schaal, Stefan Trimpe, Sebastian Bosch Center for Artificial Intelligence Renningen Germany Autonomous Motion Department Max Planck Institute for Intelligent Systems Tübingen Germany Computational Learning and Motor Control Lab University of Southern California Los AngelesCA United States

ISBN: (纸本)9781509046331

PID control architectures are widely used in industrial applications. Despite their low number of open parameters, tuning multiple, coupled PID controllers can become tedious in practice. In this paper, we extend PILCO, a model-based policy search framework, to automatically tune multivariate PID controllers purely based on data observed on an otherwise unknown system. The system's state is extended appropriately to frame the PID policy as a static state feedback policy. This renders PID tuning possible as the solution of a finite horizon optimal control problem without further a priori knowledge. The framework is applied to the task of balancing an inverted pendulum on a seven degree-of-freedom robotic arm, thereby demonstrating its capabilities of fast and data-efficient policy learning, even on complex real world problems. © 2017 IEEE.

关键词： Inverted pendulum

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Stochastic differential dynamic programming

Stochastic differential dynamic programming

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作者： Theodorou, Evangelos Tassa, Yuval Todorov, Emo Departments of Computer Science and Neuroscience Computational Learning and Motor Control Lab. University of Southern California United States Interdisciplinary Center for Neural Computation Hebrew University Jerusalem Israel Department of Computer Science and Engineering University of Washington Seattle WA United States

ISBN: (纸本)9781424474264

Although there has been a significant amount of work in the area of stochastic optimal control theory towards the development of new algorithms, the problem of how to control a stochastic nonlinear system remains an open research topic. Recent iterative linear quadratic optimal control methods iLQG [1], [2] handle control and state multiplicative noise while they are derived based on first order approximation of dynamics. On the other hand, methods such as Differential Dynamic Programming expand the dynamics up to the second order but so far they can handle nonlinear systems with additive noise. In this work we present a generalization of the classic Differential Dynamic Programming algorithm. We assume the existence of state and control multiplicative process noise, and proceed to derive the second-order expansion of the cost-to-go. We find the correction terms that arise from the stochastic assumption. Despite having quartic and cubic terms in the initial expression, we show that these vanish, leaving us with the same quadratic structure as standard DDP. © 2010 AACC.

关键词： Additive noise

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Unsupervised Contact learning for Humanoid Estimation and control

Unsupervised Contact Learning for Humanoid Estimation and Co...

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IEEE International Conference on Robotics and Automation (ICRA)

作者： Nicholas Rotella Stefan Schaal Ludovic Righetti Computational Learning and Motor Control Lab University of Southern California Los Angeles California New York University New York New York

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.

关键词： Friction Sensors Force Foot State estimation computational modeling

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On the Design of LQR Kernels for Efficient controller learning

On the Design of LQR Kernels for Efficient Controller Learni...

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IEEE Annual Conference on Decision and control

作者： Alonso Marco Philipp Hennig Stefan Schaal Sebastian Trimpe Max Planck Institute for Intelligent Systems Tübingen Germany Computational Learning and Motor Control Lab University of Southern California Los Angeles USA

Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point and finding the global optimum, BO relies on a probabilistic description of the latent objective function, typically a Gaussian process (GP). As is shown herein, GPs with a common kernel choice can, however, lead to poor learning outcomes on standard quadratic control problems. For a first-order system, we construct two kernels that specifically leverage the structure of the well-known Linear Quadratic Regulator (LQR), yet retain the flexibility of Bayesian nonparametric learning. Simulations of uncertain linear and nonlinear systems demonstrate that the LQR kernels yield superior learning performance.

关键词： Kernel Bayes methods Optimization Standards Adaptive control Nonlinear dynamical systems Optimal control

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An MPC Walking Framework With External Contact Forces

An MPC Walking Framework With External Contact Forces

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IEEE International Conference on Robotics and Automation

作者： Sean Mason Nicholas Rotella Stefan Schaal Ludovic Righetti Computational Learning and Motor Control Lab University of Southern California Los Angeles California Tandon School of Engineering New York University New York USA

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 (< 1kHz). Simulations show that the presented walking control scheme can withstand disturbances 2-3× larger with the additional force provided by a hand contact.

关键词： Optimization Force Legged locomotion Trajectory Friction Dynamics

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control of legged robots with optimal distribution of contact forces

Control of legged robots with optimal distribution of contac...

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2011 11th IEEE-RAS International Conference on Humanoid Robots, HUMANOIDS 2011

作者： Righetti, Ludovic Buchli, Jonas Mistry, Michael Schaal, Stefan Computational Learning and Motor Control Lab. University of Southern California Los Angeles CA 90089 United States Max Planck Institute for Intelligent Systems Tübingen Germany Dept. of Advanced Robotics Italian Institute of Technology Genoa Italy Disney Research Pittsburgh Pittsburgh PA 15213 United States

ISBN: (纸本)9781612848679

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. © 2011 IEEE.

关键词： controllers

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On the design of LQR kernels for efficient controller learning

arXiv

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arXiv 2017年

作者： Marco, Alonso Hennig, Philipp Schaal, Stefan Trimpe, Sebastian Max Planck Institute for Intelligent Systems Tübingen72076 Germany Computational Learning and Motor Control Lab University of Southern California Los Angeles United States

关键词： controllers

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