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2018


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Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

Tronarp, F., Kersting, H., Särkkä, S., Hennig, P.

ArXiv preprint 2018, arXiv:1810.03440 [stat.ME], October 2018 (article)

Abstract
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consists of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP---which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a Bayesian state estimation problem and all widely-used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers, which were formulated in terms of generating synthetic measurements of the vector field, come out as specific approximations. We derive novel solvers, both Gaussian and non-Gaussian, from the Bayesian state estimation problem posed in this paper and compare them with other probabilistic solvers in illustrative experiments.

pn

link (url) Project Page [BibTex]

2018



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Leveraging Contact Forces for Learning to Grasp

Merzic, H., Bogdanovic, M., Kappler, D., Righetti, L., Bohg, J.

arXiv, September 2018, Submitted to ICRA'19 (article) Submitted

Abstract
Grasping objects under uncertainty remains an open problem in robotics research. This uncertainty is often due to noisy or partial observations of the object pose or shape. To enable a robot to react appropriately to unforeseen effects, it is crucial that it continuously takes sensor feedback into account. While visual feedback is important for inferring a grasp pose and reaching for an object, contact feedback offers valuable information during manipulation and grasp acquisition. In this paper, we use model-free deep reinforcement learning to synthesize control policies that exploit contact sensing to generate robust grasping under uncertainty. We demonstrate our approach on a multi-fingered hand that exhibits more complex finger coordination than the commonly used two- fingered grippers. We conduct extensive experiments in order to assess the performance of the learned policies, with and without contact sensing. While it is possible to learn grasping policies without contact sensing, our results suggest that contact feedback allows for a significant improvement of grasping robustness under object pose uncertainty and for objects with a complex shape.

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video arXiv [BibTex]

video arXiv [BibTex]


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Kernel Recursive ABC: Point Estimation with Intractable Likelihood

Kajihara, T., Kanagawa, M., Yamazaki, K., Fukumizu, K.

Proceedings of the 35th International Conference on Machine Learning, pages: 2405-2414, PMLR, July 2018 (conference)

Abstract
We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why the approach works, showing (for the population setting) that, under a certain assumption, point estimates obtained with this method converge to the true parameter, as recursion proceeds. We have conducted a variety of numerical experiments, including parameter estimation for a real-world pedestrian flow simulator, and show that in most cases our method outperforms existing approaches.

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Paper [BibTex]

Paper [BibTex]


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Robust Physics-based Motion Retargeting with Realistic Body Shapes

Borno, M. A., Righetti, L., Black, M. J., Delp, S. L., Fiume, E., Romero, J.

Computer Graphics Forum, 37, pages: 6:1-12, July 2018 (article)

Abstract
Motion capture is often retargeted to new, and sometimes drastically different, characters. When the characters take on realistic human shapes, however, we become more sensitive to the motion looking right. This means adapting it to be consistent with the physical constraints imposed by different body shapes. We show how to take realistic 3D human shapes, approximate them using a simplified representation, and animate them so that they move realistically using physically-based retargeting. We develop a novel spacetime optimization approach that learns and robustly adapts physical controllers to new bodies and constraints. The approach automatically adapts the motion of the mocap subject to the body shape of a target subject. This motion respects the physical properties of the new body and every body shape results in a different and appropriate movement. This makes it easy to create a varied set of motions from a single mocap sequence by simply varying the characters. In an interactive environment, successful retargeting requires adapting the motion to unexpected external forces. We achieve robustness to such forces using a novel LQR-tree formulation. We show that the simulated motions look appropriate to each character’s anatomy and their actions are robust to perturbations.

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pdf video Project Page Project Page [BibTex]

pdf video Project Page Project Page [BibTex]


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Convergence Rates of Gaussian ODE Filters

Kersting, H., Sullivan, T. J., Hennig, P.

arXiv preprint 2018, arXiv:1807.09737 [math.NA], July 2018 (article)

Abstract
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives a priori as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. We prove worst-case local convergence rates of order $h^{q+1}$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $h^q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyse how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we present explicit formulas for the steady states and show that the posterior confidence intervals are well calibrated in all considered cases that exhibit global convergence---in the sense that they globally contract at the same rate as the truncation error.

pn

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

Kanagawa, M., Hennig, P., Sejdinovic, D., Sriperumbudur, B. K.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

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arXiv [BibTex]

arXiv [BibTex]


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Detailed Dense Inference with Convolutional Neural Networks via Discrete Wavelet Transform

Ma, L., Stueckler, J., Wu, T., Cremers, D.

arxiv, 2018, arXiv:1808.01834 (techreport)

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[BibTex]

[BibTex]


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Numerical Quadrature for Probabilistic Policy Search

Vinogradska, J., Bischoff, B., Achterhold, J., Koller, T., Peters, J.

IEEE Transactions on Pattern Analysis and Machine Intelligence, pages: 1-1, 2018 (article)

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DOI [BibTex]

DOI [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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Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients

Balles, L., Hennig, P.

In Proceedings of the 35th International Conference on Machine Learning (ICML), 2018 (inproceedings) Accepted

Abstract
The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn't. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the sign of stochastic gradients, whereas the update magnitude is determined by an estimate of their relative variance. We disentangle these two aspects and analyze them in isolation, gaining insight into the mechanisms underlying ADAM. This analysis also extends recent results on adverse effects of ADAM on generalization, isolating the sign aspect as the problematic one. Transferring the variance adaptation to SGD gives rise to a novel method, completing the practitioner's toolbox for problems where ADAM fails.

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper introduces a novel Hilbert space representation of a counterfactual distribution---called counterfactual mean embedding (CME)---with applications in nonparametric causal inference. Counterfactual prediction has become an ubiquitous tool in machine learning applications, such as online advertisement, recommendation systems, and medical diagnosis, whose performance relies on certain interventions. To infer the outcomes of such interventions, we propose to embed the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel. Under appropriate assumptions, the CME allows us to perform causal inference over the entire landscape of the counterfactual distribution. The CME can be estimated consistently from observational data without requiring any parametric assumption about the underlying distributions. We also derive a rate of convergence which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Our framework can deal with not only real-valued outcome, but potentially also more complex and structured outcomes such as images, sequences, and graphs. Lastly, our experimental results on off-policy evaluation tasks demonstrate the advantages of the proposed estimator.

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arXiv [BibTex]

arXiv [BibTex]


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Model-based Kernel Sum Rule: Kernel Bayesian Inference with Probabilistic Models

Nishiyama, Y., Kanagawa, M., Gretton, A., Fukumizu, K.

Arxiv e-prints, arXiv:1409.5178v2 [stat.ML], 2018 (article)

Abstract
Kernel Bayesian inference is a powerful nonparametric approach to performing Bayesian inference in reproducing kernel Hilbert spaces or feature spaces. In this approach, kernel means are estimated instead of probability distributions, and these estimates can be used for subsequent probabilistic operations (as for inference in graphical models) or in computing the expectations of smooth functions, for instance. Various algorithms for kernel Bayesian inference have been obtained by combining basic rules such as the kernel sum rule (KSR), kernel chain rule, kernel product rule and kernel Bayes' rule. However, the current framework only deals with fully nonparametric inference (i.e., all conditional relations are learned nonparametrically), and it does not allow for flexible combinations of nonparametric and parametric inference, which are practically important. Our contribution is in providing a novel technique to realize such combinations. We introduce a new KSR referred to as the model-based KSR (Mb-KSR), which employs the sum rule in feature spaces under a parametric setting. Incorporating the Mb-KSR into existing kernel Bayesian framework provides a richer framework for hybrid (nonparametric and parametric) kernel Bayesian inference. As a practical application, we propose a novel filtering algorithm for state space models based on the Mb-KSR, which combines the nonparametric learning of an observation process using kernel mean embedding and the additive Gaussian noise model for a state transition process. While we focus on additive Gaussian noise models in this study, the idea can be extended to other noise models, such as the Cauchy and alpha-stable noise models.

pn

arXiv [BibTex]

arXiv [BibTex]


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A probabilistic model for the numerical solution of initial value problems

Schober, M., Särkkä, S., Philipp Hennig,

Statistics and Computing, Springer US, 2018 (article)

Abstract
We study connections between ordinary differential equation (ODE) solvers and probabilistic regression methods in statistics. We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics. Adding to this picture, we show that several multistep methods of Nordsieck form can be recast as Kalman filtering on q-times integrated Wiener processes. Doing so provides a family of IVP solvers that return a Gaussian posterior measure, rather than a point estimate. We show that some such methods have low computational overhead, nontrivial convergence order, and that the posterior has a calibrated concentration rate. Additionally, we suggest a step size adaptation algorithm which completes the proposed method to a practically useful implementation, which we experimentally evaluate using a representative set of standard codes in the DETEST benchmark set.

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PDF Code DOI Project Page [BibTex]


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Probabilistic Approaches to Stochastic Optimization

Mahsereci, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Probabilistic Ordinary Differential Equation Solvers — Theory and Applications

Schober, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

ei pn

[BibTex]

[BibTex]


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Learning a Structured Neural Network Policy for a Hopping Task.

Viereck, J., Kozolinsky, J., Herzog, A., Righetti, L.

IEEE Robotics and Automation Letters, 3(4):4092-4099, October 2018 (article)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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The Impact of Robotics and Automation on Working Conditions and Employment [Ethical, Legal, and Societal Issues]

Pham, Q., Madhavan, R., Righetti, L., Smart, W., Chatila, R.

IEEE Robotics and Automation Magazine, 25(2):126-128, June 2018 (article)

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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]


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Lethal Autonomous Weapon Systems [Ethical, Legal, and Societal Issues]

Righetti, L., Pham, Q., Madhavan, R., Chatila, R.

IEEE Robotics \& Automation Magazine, 25(1):123-126, March 2018 (article)

Abstract
The topic of lethal autonomous weapon systems has recently caught public attention due to extensive news coverage and apocalyptic declarations from famous scientists and technologists. Weapon systems with increasing autonomy are being developed due to fast improvements in machine learning, robotics, and automation in general. These developments raise important and complex security, legal, ethical, societal, and technological issues that are being extensively discussed by scholars, nongovernmental organizations (NGOs), militaries, governments, and the international community. Unfortunately, the robotics community has stayed out of the debate, for the most part, despite being the main provider of autonomous technologies. In this column, we review the main issues raised by the increase of autonomy in weapon systems and the state of the international discussion. We argue that the robotics community has a fundamental role to play in these discussions, for its own sake, to provide the often-missing technical expertise necessary to frame the debate and promote technological development in line with the IEEE Robotics and Automation Society (RAS) objective of advancing technology to benefit humanity.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Active Uncertainty Calibration in Bayesian ODE Solvers

Kersting, H., Hennig, P.

Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence (UAI), pages: 309-318, (Editors: Ihler, A. and Janzing, D.), AUAI Press, June 2016 (conference)

Abstract
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al.~introduced a sampling-based class of methods that are `well-calibrated' in a specific sense. But the computational cost of these methods is significantly above that of classic methods. On the other hand, Schober et al.~pointed out a precise connection between classic Runge-Kutta ODE solvers and Gaussian filters, which gives only a rough probabilistic calibration, but at negligible cost overhead. By formulating the solution of ODEs as approximate inference in linear Gaussian SDEs, we investigate a range of probabilistic ODE solvers, that bridge the trade-off between computational cost and probabilistic calibration, and identify the inaccurate gradient measurement as the crucial source of uncertainty. We propose the novel filtering-based method Bayesian Quadrature filtering (BQF) which uses Bayesian quadrature to actively learn the imprecision in the gradient measurement by collecting multiple gradient evaluations.

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link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


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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]


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Batch Bayesian Optimization via Local Penalization

González, J., Dai, Z., Hennig, P., Lawrence, N.

Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), 51, pages: 648-657, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C.), May 2016 (conference)

ei pn

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Probabilistic Approximate Least-Squares

Bartels, S., Hennig, P.

Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), 51, pages: 676-684, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C. ), May 2016 (conference)

Abstract
Least-squares and kernel-ridge / Gaussian process regression are among the foundational algorithms of statistics and machine learning. Famously, the worst-case cost of exact nonparametric regression grows cubically with the data-set size; but a growing number of approximations have been developed that estimate good solutions at lower cost. These algorithms typically return point estimators, without measures of uncertainty. Leveraging recent results casting elementary linear algebra operations as probabilistic inference, we propose a new approximate method for nonparametric least-squares that affords a probabilistic uncertainty estimate over the error between the approximate and exact least-squares solution (this is not the same as the posterior variance of the associated Gaussian process regressor). This allows estimating the error of the least-squares solution on a subset of the data relative to the full-data solution. The uncertainty can be used to control the computational effort invested in the approximation. Our algorithm has linear cost in the data-set size, and a simple formal form, so that it can be implemented with a few lines of code in programming languages with linear algebra functionality.

ei pn

link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


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Gaussian Process-Based Predictive Control for Periodic Error Correction

Klenske, E. D., Zeilinger, M., Schölkopf, B., Hennig, P.

IEEE Transactions on Control Systems Technology , 24(1):110-121, 2016 (article)

ei pn

PDF DOI [BibTex]

PDF DOI [BibTex]


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Dual Control for Approximate Bayesian Reinforcement Learning

Klenske, E. D., Hennig, P.

Journal of Machine Learning Research, 17(127):1-30, 2016 (article)

ei pn

PDF link (url) [BibTex]

PDF 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]


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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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Momentum Control with Hierarchical Inverse Dynamics on a Torque-Controlled Humanoid

Herzog, A., Rotella, N., Mason, S., Grimminger, F., Schaal, S., Righetti, L.

Autonomous Robots, 40(3):473-491, 2016 (article)

Abstract
Hierarchical inverse dynamics based on cascades of quadratic programs have been proposed for the control of legged robots. They have important benefits but to the best of our knowledge have never been implemented on a torque controlled humanoid where model inaccuracies, sensor noise and real-time computation requirements can be problematic. Using a reformulation of existing algorithms, we propose a simplification of the problem that allows to achieve real-time control. Momentum-based control is integrated in the task hierarchy and a LQR design approach is used to compute the desired associated closed-loop behavior and improve performance. Extensive experiments on various balancing and tracking tasks show very robust performance in the face of unknown disturbances, even when the humanoid is standing on one foot. Our results demonstrate that hierarchical inverse dynamics together with momentum control can be efficiently used for feedback control under real robot conditions.

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link (url) 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]

2006


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Dynamic Hebbian learning in adaptive frequency oscillators

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

Physica D: Nonlinear Phenomena, 216(2):269-281, 2006 (article)

Abstract
Nonlinear oscillators are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for oscillators which adapts their frequency to the frequency of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of oscillators, from phase oscillators to relaxation oscillators and strange attractors with a generic learning rule. One major feature of our learning rule is that the oscillators constructed can adapt their frequency without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive oscillator. The convergence of the learning is proved for the Hopf oscillator, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic oscillators like relaxation oscillators and strange attractors.

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link (url) DOI [BibTex]

2006


link (url) DOI [BibTex]


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Movement generation using dynamical systems : a humanoid robot performing a drumming task

Degallier, S., Santos, C. P., Righetti, L., Ijspeert, A.

In 2006 6th IEEE-RAS International Conference on Humanoid Robots, pages: 512-517, IEEE, Genova, Italy, 2006 (inproceedings)

Abstract
The online generation of trajectories in humanoid robots remains a difficult problem. In this contribution, we present a system that allows the superposition, and the switch between, discrete and rhythmic movements. Our approach uses nonlinear dynamical systems for generating trajectories online and in real time. Our goal is to make use of attractor properties of dynamical systems in order to provide robustness against small perturbations and to enable online modulation of the trajectories. The system is demonstrated on a humanoid robot performing a drumming task.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Engineering Entrainment and Adaptation in Limit Cycle Systems – From biological inspiration to applications in robotics

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

Biological Cybernetics, 95(6):645-664, December 2006 (article)

Abstract
Periodic behavior is key to life and is observed in multiple instances and at multiple time scales in our metabolism, our natural environment, and our engineered environment. A natural way of modeling or generating periodic behavior is done by using oscillators, i.e., dynamical systems that exhibit limit cycle behavior. While there is extensive literature on methods to analyze such dynamical systems, much less work has been done on methods to synthesize an oscillator to exhibit some specific desired characteristics. The goal of this article is twofold: (1) to provide a framework for characterizing and designing oscillators and (2) to review how classes of well-known oscillators can be understood and related to this framework. The basis of the framework is to characterize oscillators in terms of their fundamental temporal and spatial behavior and in terms of properties that these two behaviors can be designed to exhibit. This focus on fundamental properties is important because it allows us to systematically compare a large variety of oscillators that might at first sight appear very different from each other. We identify several specifications that are useful for design, such as frequency-locking behavior, phase-locking behavior, and specific output signal shape. We also identify two classes of design methods by which these specifications can be met, namely offline methods and online methods. By relating these specifications to our framework and by presenting several examples of how oscillators have been designed in the literature, this article provides a useful methodology and toolbox for designing oscillators for a wide range of purposes. In particular, the focus on synthesis of limit cycle dynamical systems should be useful both for engineering and for computational modeling of physical or biological phenomena.

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link (url) DOI [BibTex]


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Design methodologies for central pattern generators: an application to crawling humanoids

Righetti, L., Ijspeert, A.

In Proceedings of Robotics: Science and Systems, Philadelphia, USA, August 2006 (inproceedings)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Programmable central pattern generators: an application to biped locomotion control

Righetti, L., Ijspeert, A.

In Proceedings of the IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., pages: 1585-1590, IEEE, 2006 (inproceedings)

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[BibTex]

[BibTex]

2003


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Evolution of Fault-tolerant Self-replicating Structures

Righetti, L., Shokur, S., Capcarre, M.

In Advances in Artificial Life, pages: 278-288, Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2003 (inproceedings)

Abstract
Designed and evolved self-replicating structures in cellular automata have been extensively studied in the past as models of Artificial Life. However, CAs, unlike their biological counterpart, are very brittle: any faulty cell usually leads to the complete destruction of any emerging structures, let alone self-replicating structures. A way to design fault-tolerant structures based on error-correcting-code has been presented recently [1], but it required a cumbersome work to be put into practice. In this paper, we get back to the original inspiration for these works, nature, and propose a way to evolve self-replicating structures, faults here being only an idiosyncracy of the environment.

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link (url) DOI [BibTex]

2003


link (url) DOI [BibTex]