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2019


Thumb xl screenshot 2019 09 12 at 07.43.13
A Learnable Safety Measure

Heim, S., Rohr, A. V., Trimpe, S., Badri-Spröwitz, A.

Conference on Robot Learning, November 2019 (conference) Accepted

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[BibTex]

2019


[BibTex]


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Predictive Triggering for Distributed Control of Resource Constrained Multi-agent Systems

Mastrangelo, J. M., Baumann, D., Trimpe, S.

In Proceedings of the 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems, 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys), September 2019 (inproceedings) Accepted

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arXiv PDF [BibTex]

arXiv PDF [BibTex]


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Event-triggered Pulse Control with Model Learning (if Necessary)

Baumann, D., Solowjow, F., Johansson, K. H., Trimpe, S.

In Proceedings of the American Control Conference, pages: 792-797, American Control Conference (ACC), July 2019 (inproceedings)

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arXiv PDF [BibTex]

arXiv PDF [BibTex]


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Data-driven inference of passivity properties via Gaussian process optimization

Romer, A., Trimpe, S., Allgöwer, F.

In Proceedings of the European Control Conference, European Control Conference (ECC), June 2019 (inproceedings) Accepted

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PDF [BibTex]

PDF [BibTex]


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Trajectory-Based Off-Policy Deep Reinforcement Learning

Doerr, A., Volpp, M., Toussaint, M., Trimpe, S., Daniel, C.

In Proceedings of the International Conference on Machine Learning (ICML), International Conference on Machine Learning (ICML), June 2019 (inproceedings) Accepted

Abstract
Policy gradient methods are powerful reinforcement learning algorithms and have been demonstrated to solve many complex tasks. However, these methods are also data-inefficient, afflicted with high variance gradient estimates, and frequently get stuck in local optima. This work addresses these weaknesses by combining recent improvements in the reuse of off-policy data and exploration in parameter space with deterministic behavioral policies. The resulting objective is amenable to standard neural network optimization strategies like stochastic gradient descent or stochastic gradient Hamiltonian Monte Carlo. Incorporation of previous rollouts via importance sampling greatly improves data-efficiency, whilst stochastic optimization schemes facilitate the escape from local optima. We evaluate the proposed approach on a series of continuous control benchmark tasks. The results show that the proposed algorithm is able to successfully and reliably learn solutions using fewer system interactions than standard policy gradient methods.

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arXiv PDF [BibTex]

arXiv PDF [BibTex]


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Feedback Control Goes Wireless: Guaranteed Stability over Low-power Multi-hop Networks

(Best Paper Award)

Mager, F., Baumann, D., Jacob, R., Thiele, L., Trimpe, S., Zimmerling, M.

In Proceedings of the 10th ACM/IEEE International Conference on Cyber-Physical Systems, pages: 97-108, 10th ACM/IEEE International Conference on Cyber-Physical Systems, April 2019 (inproceedings)

Abstract
Closing feedback loops fast and over long distances is key to emerging applications; for example, robot motion control and swarm coordination require update intervals below 100 ms. Low-power wireless is preferred for its flexibility, low cost, and small form factor, especially if the devices support multi-hop communication. Thus far, however, closed-loop control over multi-hop low-power wireless has only been demonstrated for update intervals on the order of multiple seconds. This paper presents a wireless embedded system that tames imperfections impairing control performance such as jitter or packet loss, and a control design that exploits the essential properties of this system to provably guarantee closed-loop stability for linear dynamic systems. Using experiments on a testbed with multiple cart-pole systems, we are the first to demonstrate the feasibility and to assess the performance of closed-loop control and coordination over multi-hop low-power wireless for update intervals from 20 ms to 50 ms.

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arXiv PDF DOI Project Page [BibTex]

arXiv PDF DOI Project Page [BibTex]

2018


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Deep Reinforcement Learning for Event-Triggered Control

Baumann, D., Zhu, J., Martius, G., Trimpe, S.

In Proceedings of the 57th IEEE International Conference on Decision and Control (CDC), pages: 943-950, 57th IEEE International Conference on Decision and Control (CDC), December 2018 (inproceedings)

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arXiv PDF DOI Project Page Project Page [BibTex]

2018


arXiv PDF DOI Project Page Project Page [BibTex]


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Efficient Encoding of Dynamical Systems through Local Approximations

Solowjow, F., Mehrjou, A., Schölkopf, B., Trimpe, S.

In Proceedings of the 57th IEEE International Conference on Decision and Control (CDC), pages: 6073 - 6079 , Miami, Fl, USA, December 2018 (inproceedings)

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arXiv PDF DOI Project Page [BibTex]

arXiv PDF DOI Project Page [BibTex]


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Depth Control of Underwater Robots using Sliding Modes and Gaussian Process Regression

Lima, G. S., Bessa, W. M., Trimpe, S.

In Proceeding of the 15th Latin American Robotics Symposium, João Pessoa, Brazil, 15th Latin American Robotics Symposium, November 2018 (inproceedings)

Abstract
The development of accurate control systems for underwater robotic vehicles relies on the adequate compensation for hydrodynamic effects. In this work, a new robust control scheme is presented for remotely operated underwater vehicles. In order to meet both robustness and tracking requirements, sliding mode control is combined with Gaussian process regression. The convergence properties of the closed-loop signals are analytically proven. Numerical results confirm the stronger improved performance of the proposed control scheme.

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[BibTex]

[BibTex]


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Gait learning for soft microrobots controlled by light fields

Rohr, A. V., Trimpe, S., Marco, A., Fischer, P., Palagi, S.

In International Conference on Intelligent Robots and Systems (IROS) 2018, pages: 6199-6206, International Conference on Intelligent Robots and Systems 2018, October 2018 (inproceedings)

Abstract
Soft microrobots based on photoresponsive materials and controlled by light fields can generate a variety of different gaits. This inherent flexibility can be exploited to maximize their locomotion performance in a given environment and used to adapt them to changing environments. However, because of the lack of accurate locomotion models, and given the intrinsic variability among microrobots, analytical control design is not possible. Common data-driven approaches, on the other hand, require running prohibitive numbers of experiments and lead to very sample-specific results. Here we propose a probabilistic learning approach for light-controlled soft microrobots based on Bayesian Optimization (BO) and Gaussian Processes (GPs). The proposed approach results in a learning scheme that is highly data-efficient, enabling gait optimization with a limited experimental budget, and robust against differences among microrobot samples. These features are obtained by designing the learning scheme through the comparison of different GP priors and BO settings on a semisynthetic data set. The developed learning scheme is validated in microrobot experiments, resulting in a 115% improvement in a microrobot’s locomotion performance with an experimental budget of only 20 tests. These encouraging results lead the way toward self-adaptive microrobotic systems based on lightcontrolled soft microrobots and probabilistic learning control.

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arXiv IEEE Xplore DOI Project Page [BibTex]

arXiv IEEE Xplore DOI Project Page [BibTex]


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Learning-Based Robust Model Predictive Control with State-Dependent Uncertainty

Soloperto, R., Müller, M. A., Trimpe, S., Allgöwer, F.

In Proceedings of the IFAC Conference on Nonlinear Model Predictive Control (NMPC), Madison, Wisconsin, USA, 6th IFAC Conference on Nonlinear Model Predictive Control, August 2018 (inproceedings)

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PDF [BibTex]

PDF [BibTex]


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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]

arXiv pdf Project Page [BibTex]


Thumb xl unbenannte pr%c3%a4sentation
Event-triggered Learning for Resource-efficient Networked Control

Solowjow, F., Baumann, D., Garcke, J., Trimpe, S.

In Proceedings of the American Control Conference (ACC), pages: 6506 - 6512, American Control Conference, June 2018 (inproceedings)

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arXiv PDF DOI Project Page [BibTex]

arXiv PDF DOI Project Page [BibTex]


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Evaluating Low-Power Wireless Cyber-Physical Systems

Baumann, D., Mager, F., Singh, H., Zimmerling, M., Trimpe, S.

In Proceedings of the IEEE Workshop on Benchmarking Cyber-Physical Networks and Systems (CPSBench), pages: 13-18, IEEE Workshop on Benchmarking Cyber-Physical Networks and Systems (CPSBench), April 2018 (inproceedings)

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arXiv PDF DOI Project Page [BibTex]

arXiv PDF DOI Project Page [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, May 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]

2017


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On the Design of LQR Kernels for Efficient Controller Learning

Marco, A., Hennig, P., Schaal, S., Trimpe, S.

Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC), pages: 5193-5200, IEEE, IEEE Conference on Decision and Control, December 2017 (conference)

Abstract
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.

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arXiv PDF On the Design of LQR Kernels for Efficient Controller Learning - CDC presentation DOI Project Page [BibTex]

2017


arXiv PDF On the Design of LQR Kernels for Efficient Controller Learning - CDC presentation DOI Project Page [BibTex]


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Optimizing Long-term Predictions for Model-based Policy Search

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

Proceedings of 1st Annual Conference on Robot Learning (CoRL), 78, pages: 227-238, (Editors: Sergey Levine and Vincent Vanhoucke and Ken Goldberg), 1st Annual Conference on Robot Learning, November 2017 (conference)

Abstract
We propose a novel long-term optimization criterion to improve the robustness of model-based reinforcement learning in real-world scenarios. Learning a dynamics model to derive a solution promises much greater data-efficiency and reusability compared to model-free alternatives. In practice, however, modelbased RL suffers from various imperfections such as noisy input and output data, delays and unmeasured (latent) states. To achieve higher resilience against such effects, we propose to optimize a generative long-term prediction model directly with respect to the likelihood of observed trajectories as opposed to the common approach of optimizing a dynamics model for one-step-ahead predictions. We evaluate the proposed method on several artificial and real-world benchmark problems and compare it to PILCO, a model-based RL framework, in experiments on a manipulation robot. The results show that the proposed method is competitive compared to state-of-the-art model learning methods. In contrast to these more involved models, our model can directly be employed for policy search and outperforms a baseline method in the robot experiment.

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PDF Project Page [BibTex]

PDF Project Page [BibTex]


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Model-Based Policy Search for Automatic Tuning of Multivariate PID Controllers

Doerr, A., Nguyen-Tuong, D., Marco, A., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 5295-5301, IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (inproceedings)

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PDF arXiv DOI Project Page [BibTex]

PDF arXiv DOI Project Page [BibTex]


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Virtual vs. Real: Trading Off Simulations and Physical Experiments in Reinforcement Learning with Bayesian Optimization

Marco, A., Berkenkamp, F., Hennig, P., Schoellig, A. P., Krause, A., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 1557-1563, IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (inproceedings)

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PDF arXiv ICRA 2017 Spotlight presentation Virtual vs. Real - Video explanation DOI Project Page [BibTex]

PDF arXiv ICRA 2017 Spotlight presentation Virtual vs. Real - Video explanation DOI Project Page [BibTex]


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Pattern Generation for Walking on Slippery Terrains

Khadiv, M., Moosavian, S. A. A., Herzog, A., Righetti, L.

In 2017 5th International Conference on Robotics and Mechatronics (ICROM), Iran, August 2017 (inproceedings)

Abstract
In this paper, we extend state of the art Model Predictive Control (MPC) approaches to generate safe bipedal walking on slippery surfaces. In this setting, we formulate walking as a trade off between realizing a desired walking velocity and preserving robust foot-ground contact. Exploiting this for- mulation inside MPC, we show that safe walking on various flat terrains can be achieved by compromising three main attributes, i. e. walking velocity tracking, the Zero Moment Point (ZMP) modulation, and the Required Coefficient of Friction (RCoF) regulation. Simulation results show that increasing the walking velocity increases the possibility of slippage, while reducing the slippage possibility conflicts with reducing the tip-over possibility of the contact and vice versa.

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link (url) [BibTex]

link (url) [BibTex]

2016


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Predictive and Self Triggering for Event-based State Estimation

Trimpe, S.

In Proceedings of the 55th IEEE Conference on Decision and Control (CDC), pages: 3098-3105, Las Vegas, NV, USA, December 2016 (inproceedings)

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arXiv PDF DOI Project Page [BibTex]

2016


arXiv PDF DOI Project Page [BibTex]


Thumb xl screen shot 2015 12 04 at 15.11.43
Robust Gaussian Filtering using a Pseudo Measurement

Wüthrich, M., Garcia Cifuentes, C., Trimpe, S., Meier, F., Bohg, J., Issac, J., Schaal, S.

In Proceedings of the American Control Conference (ACC), Boston, MA, USA, July 2016 (inproceedings)

Abstract
Most widely-used state estimation algorithms, such as the Extended Kalman Filter and the Unscented Kalman Filter, belong to the family of Gaussian Filters (GF). Unfortunately, GFs fail if the measurement process is modelled by a fat-tailed distribution. This is a severe limitation, because thin-tailed measurement models, such as the analytically-convenient and therefore widely-used Gaussian distribution, are sensitive to outliers. In this paper, we show that mapping the measurements into a specific feature space enables any existing GF algorithm to work with fat-tailed measurement models. We find a feature function which is optimal under certain conditions. Simulation results show that the proposed method allows for robust filtering in both linear and nonlinear systems with measurements contaminated by fat-tailed noise.

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Web link (url) DOI Project Page [BibTex]

Web link (url) DOI Project Page [BibTex]


Thumb xl screen shot 2016 01 19 at 14.48.37
Automatic LQR Tuning Based on Gaussian Process Global Optimization

Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 270-277, IEEE, IEEE International Conference on Robotics and Automation, May 2016 (inproceedings)

Abstract
This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree- of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Results of a two- and four- dimensional tuning problems highlight the method’s potential for automatic controller tuning on robotic platforms.

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Video PDF DOI Project Page [BibTex]

Video PDF DOI Project Page [BibTex]


Thumb xl screen shot 2016 01 19 at 14.56.20
Depth-based Object Tracking Using a Robust Gaussian Filter

Issac, J., Wüthrich, M., Garcia Cifuentes, C., Bohg, J., Trimpe, S., Schaal, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2016, IEEE, IEEE International Conference on Robotics and Automation, May 2016 (inproceedings)

Abstract
We consider the problem of model-based 3D- tracking of objects given dense depth images as input. Two difficulties preclude the application of a standard Gaussian filter to this problem. First of all, depth sensors are characterized by fat-tailed measurement noise. To address this issue, we show how a recently published robustification method for Gaussian filters can be applied to the problem at hand. Thereby, we avoid using heuristic outlier detection methods that simply reject measurements if they do not match the model. Secondly, the computational cost of the standard Gaussian filter is prohibitive due to the high-dimensional measurement, i.e. the depth image. To address this problem, we propose an approximation to reduce the computational complexity of the filter. In quantitative experiments on real data we show how our method clearly outperforms the standard Gaussian filter. Furthermore, we compare its performance to a particle-filter-based tracking method, and observe comparable computational efficiency and improved accuracy and smoothness of the estimates.

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Video Bayesian Object Tracking Library Bayesian Filtering Framework Object Tracking Dataset link (url) DOI Project Page [BibTex]

Video Bayesian Object Tracking Library Bayesian Filtering Framework Object Tracking Dataset link (url) DOI Project Page [BibTex]


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Communication Rate Analysis for Event-based State Estimation

(Best student paper finalist)

Ebner, S., Trimpe, S.

In Proceedings of the 13th International Workshop on Discrete Event Systems, May 2016 (inproceedings)

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PDF DOI [BibTex]

PDF DOI [BibTex]


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Inertial Sensor-Based Humanoid Joint State Estimation

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

In 2016 IEEE International Conference on Robotics and Automation (ICRA), pages: 1825-1831, IEEE, Stockholm, Sweden, 2016 (inproceedings)

Abstract
This work presents methods for the determination of a humanoid robot's joint velocities and accelerations directly from link-mounted Inertial Measurement Units (IMUs) each containing a three-axis gyroscope and a three-axis accelerometer. No information about the global pose of the floating base or its links is required and precise knowledge of the link IMU poses is not necessary due to presented calibration routines. Additionally, a filter is introduced to fuse gyroscope angular velocities with joint position measurements and compensate the computed joint velocities for time-varying gyroscope biases. The resulting joint velocities are subject to less noise and delay than filtered velocities computed from numerical differentiation of joint potentiometer signals, leading to superior performance in joint feedback control as demonstrated in experiments performed on a SARCOS hydraulic humanoid.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Stepping Stabilization Using a Combination of DCM Tracking and Step Adjustment

Khadiv, M., Kleff, S., Herzog, A., Moosavian, S. A. A., Schaal, S., Righetti, L.

In 2016 4th International Conference on Robotics and Mechatronics (ICROM), pages: 130-135, IEEE, Teheran, Iran, 2016 (inproceedings)

Abstract
In this paper, a method for stabilizing biped robots stepping by a combination of Divergent Component of Motion (DCM) tracking and step adjustment is proposed. In this method, the DCM trajectory is generated, consistent with the predefined footprints. Furthermore, a swing foot trajectory modification strategy is proposed to adapt the landing point, using DCM measurement. In order to apply the generated trajectories to the full robot, a Hierarchical Inverse Dynamics (HID) is employed. The HID enables us to use different combinations of the DCM tracking and step adjustment for stabilizing different biped robots. Simulation experiments on two scenarios for two different simulated robots, one with active ankles and the other with passive ankles, are carried out. Simulation results demonstrate the effectiveness of the proposed method for robots with both active and passive ankles.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Structured contact force optimization for kino-dynamic motion generation

Herzog, A., Schaal, S., Righetti, L.

In 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages: 2703-2710, IEEE, Daejeon, South Korea, 2016 (inproceedings)

Abstract
Optimal control approaches in combination with trajectory optimization have recently proven to be a promising control strategy for legged robots. Computationally efficient and robust algorithms were derived using simplified models of the contact interaction between robot and environment such as the linear inverted pendulum model (LIPM). However, as humanoid robots enter more complex environments, less restrictive models become increasingly important. As we leave the regime of linear models, we need to build dedicated solvers that can compute interaction forces together with consistent kinematic plans for the whole-body. In this paper, we address the problem of planning robot motion and interaction forces for legged robots given predefined contact surfaces. The motion generation process is decomposed into two alternating parts computing force and motion plans in coherence. We focus on the properties of the momentum computation leading to sparse optimal control formulations to be exploited by a dedicated solver. In our experiments, we demonstrate that our motion generation algorithm computes consistent contact forces and joint trajectories for our humanoid robot. We also demonstrate the favorable time complexity due to our formulation and composition of the momentum equations.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Balancing and Walking Using Full Dynamics LQR Control With Contact Constraints

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

In 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pages: 63-68, IEEE, Cancun, Mexico, 2016 (inproceedings)

Abstract
Torque control algorithms which consider robot dynamics and contact constraints are important for creating dynamic behaviors for humanoids. As computational power increases, algorithms tend to also increase in complexity. However, it is not clear how much complexity is really required to create controllers which exhibit good performance. In this paper, we study the capabilities of a simple approach based on contact consistent LQR controllers designed around key poses to control various tasks on a humanoid robot. We present extensive experimental results on a hydraulic, torque controlled humanoid performing balancing and stepping tasks. This feedback control approach captures the necessary synergies between the DoFs of the robot to guarantee good control performance. We show that for the considered tasks, it is only necessary to re-linearize the dynamics of the robot at different contact configurations and that increasing the number of LQR controllers along desired trajectories does not improve performance. Our result suggest that very simple controllers can yield good performance competitive with current state of the art, but more complex, optimization-based whole-body controllers. A video of the experiments can be found at https://youtu.be/5T08CNKV1hw.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Step Timing Adjustement: a Step toward Generating Robust Gaits

Khadiv, M., Herzog, A., Moosavian, S. A. A., Righetti, L.

In 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pages: 35-42, IEEE, Cancun, Mexico, 2016 (inproceedings)

Abstract
Step adjustment for humanoid robots has been shown to improve robustness in gaits. However, step duration adaptation is often neglected in control strategies. In this paper, we propose an approach that combines both step location and timing adjustment for generating robust gaits. In this approach, step location and step timing are decided, based on feedback from the current state of the robot. The proposed approach is comprised of two stages. In the first stage, the nominal step location and step duration for the next step or a previewed number of steps are specified. In this stage which is done at the start of each step, the main goal is to specify the best step length and step duration for a desired walking speed. The second stage deals with finding the best landing point and landing time of the swing foot at each control cycle. In this stage, stability of the gaits is preserved by specifying a desired offset between the swing foot landing point and the Divergent Component of Motion (DCM) at the end of current step. After specifying the landing point of the swing foot at a desired time, the swing foot trajectory is regenerated at each control cycle to realize desired landing properties. Simulation on different scenarios shows the robustness of the generated gaits from our proposed approach compared to the case where no timing adjustment is employed.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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On the Effects of Measurement Uncertainty in Optimal Control of Contact Interactions

Ponton, B., Schaal, S., Righetti, L.

In The 12th International Workshop on the Algorithmic Foundations of Robotics WAFR, Berkeley, USA, 2016 (inproceedings)

Abstract
Stochastic Optimal Control (SOC) typically considers noise only in the process model, i.e. unknown disturbances. However, in many robotic applications involving interaction with the environment, such as locomotion and manipulation, uncertainty also comes from lack of precise knowledge of the world, which is not an actual disturbance. We analyze the effects of also considering noise in the measurement model, by devel- oping a SOC algorithm based on risk-sensitive control, that includes the dynamics of an observer in such a way that the control law explicitly de- pends on the current measurement uncertainty. In simulation results on a simple 2D manipulator, we have observed that measurement uncertainty leads to low impedance behaviors, a result in contrast with the effects of process noise that creates stiff behaviors. This suggests that taking into account measurement uncertainty could be a potentially very interesting way to approach problems involving uncertain contact interactions.

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link (url) [BibTex]

link (url) [BibTex]


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A Convex Model of Momentum Dynamics for Multi-Contact Motion Generation

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

In 2016 IEEE-RAS 16th International Conference on Humanoid Robots Humanoids, pages: 842-849, IEEE, Cancun, Mexico, 2016 (inproceedings)

Abstract
Linear models for control and motion generation of humanoid robots have received significant attention in the past years, not only due to their well known theoretical guarantees, but also because of practical computational advantages. However, to tackle more challenging tasks and scenarios such as locomotion on uneven terrain, a more expressive model is required. In this paper, we are interested in contact interaction-centered motion optimization based on the momentum dynamics model. This model is non-linear and non-convex; however, we find a relaxation of the problem that allows us to formulate it as a single convex quadratically-constrained quadratic program (QCQP) that can be very efficiently optimized and is useful for multi-contact planning. This convex model is then coupled to the optimization of end-effector contact locations using a mixed integer program, which can also be efficiently solved. This becomes relevant e.g. to recover from external pushes, where a predefined stepping plan is likely to fail and an online adaptation of the contact location is needed. The performance of our algorithm is demonstrated in several multi-contact scenarios for a humanoid robot.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2015


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Automatic LQR Tuning Based on Gaussian Process Optimization: Early Experimental Results

Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S.

Machine Learning in Planning and Control of Robot Motion Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems (iROS), pages: , , Machine Learning in Planning and Control of Robot Motion Workshop, October 2015 (conference)

Abstract
This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree-of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Preliminary results of a low-dimensional tuning problem highlight the method’s potential for automatic controller tuning on robotic platforms.

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PDF DOI Project Page [BibTex]

2015


PDF DOI Project Page [BibTex]


Thumb xl screen shot 2015 08 22 at 21.47.37
Direct Loss Minimization Inverse Optimal Control

Doerr, A., Ratliff, N., Bohg, J., Toussaint, M., Schaal, S.

In Proceedings of Robotics: Science and Systems, Rome, Italy, Robotics: Science and Systems XI, July 2015 (inproceedings)

Abstract
Inverse Optimal Control (IOC) has strongly impacted the systems engineering process, enabling automated planner tuning through straightforward and intuitive demonstration. The most successful and established applications, though, have been in lower dimensional problems such as navigation planning where exact optimal planning or control is feasible. In higher dimensional systems, such as humanoid robots, research has made substantial progress toward generalizing the ideas to model free or locally optimal settings, but these systems are complicated to the point where demonstration itself can be difficult. Typically, real-world applications are restricted to at best noisy or even partial or incomplete demonstrations that prove cumbersome in existing frameworks. This work derives a very flexible method of IOC based on a form of Structured Prediction known as Direct Loss Minimization. The resulting algorithm is essentially Policy Search on a reward function that rewards similarity to demonstrated behavior (using Covariance Matrix Adaptation (CMA) in our experiments). Our framework blurs the distinction between IOC, other forms of Imitation Learning, and Reinforcement Learning, enabling us to derive simple, versatile, and practical algorithms that blend imitation and reinforcement signals into a unified framework. Our experiments analyze various aspects of its performance and demonstrate its efficacy on conveying preferences for motion shaping and combined reach and grasp quality optimization.

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PDF Video Project Page [BibTex]

PDF Video Project Page [BibTex]


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LMI-Based Synthesis for Distributed Event-Based State Estimation

Muehlebach, M., Trimpe, S.

In Proceedings of the American Control Conference, July 2015 (inproceedings)

Abstract
This paper presents an LMI-based synthesis procedure for distributed event-based state estimation. Multiple agents observe and control a dynamic process by sporadically exchanging data over a broadcast network according to an event-based protocol. In previous work [1], the synthesis of event-based state estimators is based on a centralized design. In that case three different types of communication are required: event-based communication of measurements, periodic reset of all estimates to their joint average, and communication of inputs. The proposed synthesis problem eliminates the communication of inputs as well as the periodic resets (under favorable circumstances) by accounting explicitly for the distributed structure of the control system.

am ics

PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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Guaranteed H2 Performance in Distributed Event-Based State Estimation

Muehlebach, M., Trimpe, S.

In Proceeding of the First International Conference on Event-based Control, Communication, and Signal Processing, June 2015 (inproceedings)

am ics

PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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On the Choice of the Event Trigger in Event-based Estimation

Trimpe, S., Campi, M.

In Proceeding of the First International Conference on Event-based Control, Communication, and Signal Processing, June 2015 (inproceedings)

am ics

PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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Event-based Estimation and Control for Remote Robot Operation with Reduced Communication

Trimpe, S., Buchli, J.

In Proceedings of the IEEE International Conference on Robotics and Automation, May 2015 (inproceedings)

Abstract
An event-based communication framework for remote operation of a robot via a bandwidth-limited network is proposed. The robot sends state and environment estimation data to the operator, and the operator transmits updated control commands or policies to the robot. Event-based communication protocols are designed to ensure that data is transmitted only when required: the robot sends new estimation data only if this yields a significant information gain at the operator, and the operator transmits an updated control policy only if this comes with a significant improvement in control performance. The developed framework is modular and can be used with any standard estimation and control algorithms. Simulation results of a robotic arm highlight its potential for an efficient use of limited communication resources, for example, in disaster response scenarios such as the DARPA Robotics Challenge.

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PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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A New Perspective and Extension of the Gaussian Filter

Wüthrich, M., Trimpe, S., Kappler, D., Schaal, S.

In Robotics: Science and Systems, 2015 (inproceedings)

Abstract
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the mean being an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependencies in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end we view the GF from a variational-inference perspective, and analyze how restrictions on the form of the belief can be relaxed while maintaining simplicity and efficiency. This analysis provides a basis for generalizations of the GF. We propose one such generalization which coincides with a GF using a virtual measurement, obtained by applying a nonlinear function to the actual measurement. Numerical experiments show that the proposed Feature Gaussian Filter (FGF) can have a substantial performance advantage over the standard GF for systems with nonlinear observation models.

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Web PDF Project Page [BibTex]


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Trajectory generation for multi-contact momentum control

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

In 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), pages: 874-880, IEEE, Seoul, South Korea, 2015 (inproceedings)

Abstract
Simplified models of the dynamics such as the linear inverted pendulum model (LIPM) have proven to perform well for biped walking on flat ground. However, for more complex tasks the assumptions of these models can become limiting. For example, the LIPM does not allow for the control of contact forces independently, is limited to co-planar contacts and assumes that the angular momentum is zero. In this paper, we propose to use the full momentum equations of a humanoid robot in a trajectory optimization framework to plan its center of mass, linear and angular momentum trajectories. The model also allows for planning desired contact forces for each end-effector in arbitrary contact locations. We extend our previous results on linear quadratic regulator (LQR) design for momentum control by computing the (linearized) optimal momentum feedback law in a receding horizon fashion. The resulting desired momentum and the associated feedback law are then used in a hierarchical whole body control approach. Simulation experiments show that the approach is computationally fast and is able to generate plans for locomotion on complex terrains while demonstrating good tracking performance for the full humanoid control.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Humanoid Momentum Estimation Using Sensed Contact Wrenches

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

In 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), pages: 556-563, IEEE, Seoul, South Korea, 2015 (inproceedings)

Abstract
This work presents approaches for the estimation of quantities important for the control of the momentum of a humanoid robot. In contrast to previous approaches which use simplified models such as the Linear Inverted Pendulum Model, we present estimators based on the momentum dynamics of the robot. By using this simple yet dynamically-consistent model, we avoid the issues of using simplified models for estimation. We develop an estimator for the center of mass and full momentum which can be reformulated to estimate center of mass offsets as well as external wrenches applied to the robot. The observability of these estimators is investigated and their performance is evaluated in comparison to previous approaches.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2014


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A Self-Tuning LQR Approach Demonstrated on an Inverted Pendulum

Trimpe, S., Millane, A., Doessegger, S., D’Andrea, R.

In Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, 2014 (inproceedings)

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PDF Supplementary material DOI [BibTex]

2014


PDF Supplementary material DOI [BibTex]


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Stability Analysis of Distributed Event-Based State Estimation

Trimpe, S.

In Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles, CA, 2014 (inproceedings)

Abstract
An approach for distributed and event-based state estimation that was proposed in previous work [1] is analyzed and extended to practical networked systems in this paper. Multiple sensor-actuator-agents observe a dynamic process, sporadically exchange their measurements over a broadcast network according to an event-based protocol, and estimate the process state from the received data. The event-based approach was shown in [1] to mimic a centralized Luenberger observer up to guaranteed bounds, under the assumption of identical estimates on all agents. This assumption, however, is unrealistic (it is violated by a single packet drop or slight numerical inaccuracy) and removed herein. By means of a simulation example, it is shown that non-identical estimates can actually destabilize the overall system. To achieve stability, the event-based communication scheme is supplemented by periodic (but infrequent) exchange of the agentsâ?? estimates and reset to their joint average. When the local estimates are used for feedback control, the stability guarantee for the estimation problem extends to the event-based control system.

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PDF Supplementary material DOI Project Page [BibTex]

PDF Supplementary material DOI Project Page [BibTex]


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Dual Execution of Optimized Contact Interaction Trajectories

Toussaint, M., Ratliff, N., Bohg, J., Righetti, L., Englert, P., Schaal, S.

In 2014 IEEE/RSJ Conference on Intelligent Robots and Systems, pages: 47-54, IEEE, Chicago, USA, 2014 (inproceedings)

Abstract
Efficient manipulation requires contact to reduce uncertainty. The manipulation literature refers to this as funneling: a methodology for increasing reliability and robustness by leveraging haptic feedback and control of environmental interaction. However, there is a fundamental gap between traditional approaches to trajectory optimization and this concept of robustness by funneling: traditional trajectory optimizers do not discover force feedback strategies. From a POMDP perspective, these behaviors could be regarded as explicit observation actions planned to sufficiently reduce uncertainty thereby enabling a task. While we are sympathetic to the full POMDP view, solving full continuous-space POMDPs in high-dimensions is hard. In this paper, we propose an alternative approach in which trajectory optimization objectives are augmented with new terms that reward uncertainty reduction through contacts, explicitly promoting funneling. This augmentation shifts the responsibility of robustness toward the actual execution of the optimized trajectories. Directly tracing trajectories through configuration space would lose all robustness-dual execution achieves robustness by devising force controllers to reproduce the temporal interaction profile encoded in the dual solution of the optimization problem. This work introduces dual execution in depth and analyze its performance through robustness experiments in both simulation and on a real-world robotic platform.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Balancing experiments on a torque-controlled humanoid with hierarchical inverse dynamics

Herzog, A., Righetti, L., Grimminger, F., Pastor, P., Schaal, S.

In 2014 IEEE/RSJ Conference on Intelligent Robots and Systems, pages: 981-988, IEEE, Chicago, USA, 2014 (inproceedings)

Abstract
Recently several hierarchical inverse dynamics controllers based on cascades of quadratic programs have been proposed for application on torque controlled robots. They have important theoretical benefits but have never been implemented on a torque controlled robot where model inaccuracies and real-time computation requirements can be problematic. In this contribution we present an experimental evaluation of these algorithms in the context of balance control for a humanoid robot. The presented experiments demonstrate the applicability of the approach under real robot conditions (i.e. model uncertainty, estimation errors, etc). We propose a simplification of the optimization problem that allows us to decrease computation time enough to implement it in a fast torque control loop. We implement a momentum-based balance controller which shows robust performance in face of unknown disturbances, even when the robot is standing on only one foot. In a second experiment, a tracking task is evaluated to demonstrate the performance of the controller with more complicated hierarchies. Our results show that hierarchical inverse dynamics controllers can be used for feedback control of humanoid robots and that momentum-based balance control can be efficiently implemented on a real robot.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Full Dynamics LQR Control of a Humanoid Robot: An Experimental Study on Balancing and Squatting

Mason, S., Righetti, L., Schaal, S.

In 2014 IEEE-RAS International Conference on Humanoid Robots, pages: 374-379, IEEE, Madrid, Spain, 2014 (inproceedings)

Abstract
Humanoid robots operating in human environments require whole-body controllers that can offer precise tracking and well-defined disturbance rejection behavior. In this contribution, we propose an experimental evaluation of a linear quadratic regulator (LQR) using a linearization of the full robot dynamics together with the contact constraints. The advantage of the controller is that it explicitly takes into account the coupling between the different joints to create optimal feedback controllers for whole-body control. We also propose a method to explicitly regulate other tasks of interest, such as the regulation of the center of mass of the robot or its angular momentum. In order to evaluate the performance of linear optimal control designs in a real-world scenario (model uncertainty, sensor noise, imperfect state estimation, etc), we test the controllers in a variety of tracking and balancing experiments on a torque controlled humanoid (e.g. balancing, split plane balancing, squatting, pushes while squatting, and balancing on a wheeled platform). The proposed control framework shows a reliable push recovery behavior competitive with more sophisticated balance controllers, rejecting impulses up to 11.7 Ns with peak forces of 650 N, with the added advantage of great computational simplicity. Furthermore, the controller is able to track squatting trajectories up to 1 Hz without relinearization, suggesting that the linearized dynamics is sufficient for significant ranges of motion.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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State Estimation for a Humanoid Robot

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

In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 952-958, IEEE, Chicago, USA, 2014 (inproceedings)

Abstract
This paper introduces a framework for state estimation on a humanoid robot platform using only common proprioceptive sensors and knowledge of leg kinematics. The presented approach extends that detailed in prior work on a point-foot quadruped platform by adding the rotational constraints imposed by the humanoid's flat feet. As in previous work, the proposed Extended Kalman Filter accommodates contact switching and makes no assumptions about gait or terrain, making it applicable on any humanoid platform for use in any task. A nonlinear observability analysis is performed on both the point-foot and flat-foot filters and it is concluded that the addition of rotational constraints significantly simplifies singular cases and improves the observability characteristics of the system. Results on a simulated walking dataset demonstrate the performance gain of the flat-foot filter as well as confirm the results of the presented observability analysis.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]