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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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Softness, Warmth, and Responsiveness Improve Robot Hugs

Block, A. E., Kuchenbecker, K. J.

International Journal of Social Robotics, 11(1):49-64, October 2018 (article)

Abstract
Hugs are one of the first forms of contact and affection humans experience. Due to their prevalence and health benefits, roboticists are naturally interested in having robots one day hug humans as seamlessly as humans hug other humans. This project's purpose is to evaluate human responses to different robot physical characteristics and hugging behaviors. Specifically, we aim to test the hypothesis that a soft, warm, touch-sensitive PR2 humanoid robot can provide humans with satisfying hugs by matching both their hugging pressure and their hugging duration. Thirty relatively young and rather technical participants experienced and evaluated twelve hugs with the robot, divided into three randomly ordered trials that focused on physical robot characteristics (single factor, three levels) and nine randomly ordered trials with low, medium, and high hug pressure and duration (two factors, three levels each). Analysis of the results showed that people significantly prefer soft, warm hugs over hard, cold hugs. Furthermore, users prefer hugs that physically squeeze them and release immediately when they are ready for the hug to end. Taking part in the experiment also significantly increased positive user opinions of robots and robot use.

hi

link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Task-Driven PCA-Based Design Optimization of Wearable Cutaneous Devices

Pacchierotti, C., Young, E. M., Kuchenbecker, K. J.

IEEE Robotics and Automation Letters, 3(3):2214-2221, July 2018, Presented at ICRA 2018 (article)

Abstract
Small size and low weight are critical requirements for wearable and portable haptic interfaces, making it essential to work toward the optimization of their sensing and actuation systems. This paper presents a new approach for task-driven design optimization of fingertip cutaneous haptic devices. Given one (or more) target tactile interactions to render and a cutaneous device to optimize, we evaluate the minimum number and best configuration of the device’s actuators to minimize the estimated haptic rendering error. First, we calculate the motion needed for the original cutaneous device to render the considered target interaction. Then, we run a principal component analysis (PCA) to search for possible couplings between the original motor inputs, looking also for the best way to reconfigure them. If some couplings exist, we can re-design our cutaneous device with fewer motors, optimally configured to render the target tactile sensation. The proposed approach is quite general and can be applied to different tactile sensors and cutaneous devices. We validated it using a BioTac tactile sensor and custom plate-based 3-DoF and 6-DoF fingertip cutaneous devices, considering six representative target tactile interactions. The algorithm was able to find couplings between each device’s motor inputs, proving it to be a viable approach to optimize the design of wearable and portable cutaneous devices. Finally, we present two examples of optimized designs for our 3-DoF fingertip cutaneous device.

hi

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning an Approximate Model Predictive Controller with Guarantees

Hertneck, M., Koehler, J., Trimpe, S., Allgöwer, F.

IEEE Control Systems Letters, 2(3):543-548, July 2018 (article)

Abstract
A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding’s Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.

ics

arXiv PDF DOI [BibTex]

arXiv PDF DOI [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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Teaching a Robot Bimanual Hand-Clapping Games via Wrist-Worn IMUs

Fitter, N. T., Kuchenbecker, K. J.

Frontiers in Robotics and Artificial Intelligence, 5(85), July 2018 (article)

Abstract
Colleagues often shake hands in greeting, friends connect through high fives, and children around the world rejoice in hand-clapping games. As robots become more common in everyday human life, they will have the opportunity to join in these social-physical interactions, but few current robots are intended to touch people in friendly ways. This article describes how we enabled a Baxter Research Robot to both teach and learn bimanual hand-clapping games with a human partner. Our system monitors the user's motions via a pair of inertial measurement units (IMUs) worn on the wrists. We recorded a labeled library of 10 common hand-clapping movements from 10 participants; this dataset was used to train an SVM classifier to automatically identify hand-clapping motions from previously unseen participants with a test-set classification accuracy of 97.0%. Baxter uses these sensors and this classifier to quickly identify the motions of its human gameplay partner, so that it can join in hand-clapping games. This system was evaluated by N = 24 naïve users in an experiment that involved learning sequences of eight motions from Baxter, teaching Baxter eight-motion game patterns, and completing a free interaction period. The motion classification accuracy in this less structured setting was 85.9%, primarily due to unexpected variations in motion timing. The quantitative task performance results and qualitative participant survey responses showed that learning games from Baxter was significantly easier than teaching games to Baxter, and that the teaching role caused users to consider more teamwork aspects of the gameplay. Over the course of the experiment, people felt more understood by Baxter and became more willing to follow the example of the robot. Users felt uniformly safe interacting with Baxter, and they expressed positive opinions of Baxter and reported fun interacting with the robot. Taken together, the results indicate that this robot achieved credible social-physical interaction with humans and that its ability to both lead and follow systematically changed the human partner's experience.

hi

DOI [BibTex]

DOI [BibTex]


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Oncilla robot: a versatile open-source quadruped research robot with compliant pantograph legs

Sproewitz, A., Tuleu, A., Ajallooeian, M., Vespignani, M., Moeckel, R., Eckert, P., D’Haene, M., Degrave, J., Nordmann, A., Schrauwen, B., Steil, J., Ijspeert, A. J.

Frontiers in Robotics and AI, 5(67), June 2018, arXiv: 1803.06259 (article)

Abstract
We present Oncilla robot, a novel mobile, quadruped legged locomotion machine. This large-cat sized, 5.1 robot is one of a kind of a recent, bioinspired legged robot class designed with the capability of model-free locomotion control. Animal legged locomotion in rough terrain is clearly shaped by sensor feedback systems. Results with Oncilla robot show that agile and versatile locomotion is possible without sensory signals to some extend, and tracking becomes robust when feedback control is added (Ajaoolleian 2015). By incorporating mechanical and control blueprints inspired from animals, and by observing the resulting robot locomotion characteristics, we aim to understand the contribution of individual components. Legged robots have a wide mechanical and control design parameter space, and a unique potential as research tools to investigate principles of biomechanics and legged locomotion control. But the hardware and controller design can be a steep initial hurdle for academic research. To facilitate the easy start and development of legged robots, Oncilla-robot's blueprints are available through open-source. [...]

dlg

link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Haptics and Haptic Interfaces

Kuchenbecker, K. J.

In Encyclopedia of Robotics, (Editors: Marcelo H. Ang and Oussama Khatib and Bruno Siciliano), Springer, May 2018 (incollection)

Abstract
Haptics is an interdisciplinary field that seeks to both understand and engineer touch-based interaction. Although a wide range of systems and applications are being investigated, haptics researchers often concentrate on perception and manipulation through the human hand. A haptic interface is a mechatronic system that modulates the physical interaction between a human and his or her tangible surroundings. Haptic interfaces typically involve mechanical, electrical, and computational layers that work together to sense user motions or forces, quickly process these inputs with other information, and physically respond by actuating elements of the user’s surroundings, thereby enabling him or her to act on and feel a remote and/or virtual environment.

hi

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Impact of Trunk Orientation for Dynamic Bipedal Locomotion

Drama, O.

Dynamic Walking Conference, May 2018 (talk)

Abstract
Impact of trunk orientation for dynamic bipedal locomotion My research revolves around investigating the functional demands of bipedal running, with focus on stabilizing trunk orientation. When we think about postural stability, there are two critical questions we need to answer: What are the necessary and sufficient conditions to achieve and maintain trunk stability? I am concentrating on how morphology affects control strategies in achieving trunk stability. In particular, I denote the trunk pitch as the predominant morphology parameter and explore the requirements it imposes on a chosen control strategy. To analyze this, I use a spring loaded inverted pendulum model extended with a rigid trunk, which is actuated by a hip motor. The challenge for the controller design here is to have a single hip actuator to achieve two coupled tasks of moving the legs to generate motion and stabilizing the trunk. I enforce orthograde and pronograde postures and aim to identify the effect of these trunk orientations on the hip torque and ground reaction profiles for different control strategies.

dlg

Impact of trunk orientation for dynamic bipedal locomotion [DW 2018] link (url) Project Page [BibTex]


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Automatically Rating Trainee Skill at a Pediatric Laparoscopic Suturing Task

Oquendo, Y. A., Riddle, E. W., Hiller, D., Blinman, T. A., Kuchenbecker, K. J.

Surgical Endoscopy, 32(4):1840-1857, April 2018 (article)

hi

DOI [BibTex]

DOI [BibTex]


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Distributed Event-Based State Estimation for Networked Systems: An LMI Approach

Muehlebach, M., Trimpe, S.

IEEE Transactions on Automatic Control, 63(1):269-276, January 2018 (article)

am ics

arXiv (extended version) DOI Project Page [BibTex]

arXiv (extended version) DOI 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.

pn

arXiv [BibTex]

arXiv [BibTex]


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Immersive Low-Cost Virtual Reality Treatment for Phantom Limb Pain: Evidence from Two Cases

Ambron, E., Miller, A., Kuchenbecker, K. J., Buxbaum, L. J., Coslett, H. B.

Frontiers in Neurology, 9(67):1-7, 2018 (article)

hi

DOI Project Page [BibTex]

DOI 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.

ei pn

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.

pn

PDF Code DOI Project Page [BibTex]

2015


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Lernende Roboter

Trimpe, S.

In Jahrbuch der Max-Planck-Gesellschaft, Max Planck Society, May 2015, (popular science article in German) (inbook)

am ics

link (url) [BibTex]

2015


link (url) [BibTex]


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Probabilistic Interpretation of Linear Solvers

Hennig, P.

SIAM Journal on Optimization, 25(1):234-260, 2015 (article)

ei pn

Web PDF link (url) DOI [BibTex]

Web PDF link (url) DOI [BibTex]


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Exciting Engineered Passive Dynamics in a Bipedal Robot

Renjewski, D., Spröwitz, A., Peekema, A., Jones, M., Hurst, J.

{IEEE Transactions on Robotics and Automation}, 31(5):1244-1251, IEEE, New York, NY, 2015 (article)

Abstract
A common approach in designing legged robots is to build fully actuated machines and control the machine dynamics entirely in soft- ware, carefully avoiding impacts and expending a lot of energy. However, these machines are outperformed by their human and animal counterparts. Animals achieve their impressive agility, efficiency, and robustness through a close integration of passive dynamics, implemented through mechanical components, and neural control. Robots can benefit from this same integrated approach, but a strong theoretical framework is required to design the passive dynamics of a machine and exploit them for control. For this framework, we use a bipedal spring–mass model, which has been shown to approximate the dynamics of human locomotion. This paper reports the first implementation of spring–mass walking on a bipedal robot. We present the use of template dynamics as a control objective exploiting the engineered passive spring–mass dynamics of the ATRIAS robot. The results highlight the benefits of combining passive dynamics with dynamics-based control and open up a library of spring–mass model-based control strategies for dynamic gait control of robots.

dlg

link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Probabilistic numerics and uncertainty in computations

Hennig, P., Osborne, M. A., Girolami, M.

Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2179), 2015 (article)

Abstract
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

ei pn

PDF DOI [BibTex]

PDF DOI [BibTex]