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Trunk pitch oscillations for energy trade-offs in bipedal running birds and robots
Trunk pitch oscillations for energy trade-offs in bipedal running birds and robots

Drama, Ö., Badri-Spröwitz, A.

Bioinspiration & Biomimetics, 15(3), March 2020 (article)

Abstract
Bipedal animals have diverse morphologies and advanced locomotion abilities. Terrestrial birds, in particular, display agile, efficient, and robust running motion, in which they exploit the interplay between the body segment masses and moment of inertias. On the other hand, most legged robots are not able to generate such versatile and energy-efficient motion and often disregard trunk movements as a means to enhance their locomotion capabilities. Recent research investigated how trunk motions affect the gait characteristics of humans, but there is a lack of analysis across different bipedal morphologies. To address this issue, we analyze avian running based on a spring-loaded inverted pendulum model with a pronograde (horizontal) trunk. We use a virtual point based control scheme and modify the alignment of the ground reaction forces to assess how our control strategy influences the trunk pitch oscillations and energetics of the locomotion. We derive three potential key strategies to leverage trunk pitch motions that minimize either the energy fluctuations of the center of mass or the work performed by the hip and leg. We suggest how these strategies could be used in legged robotics.

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Youtube Video link (url) DOI [BibTex]

Youtube Video link (url) DOI [BibTex]


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Analytical classical density functionals from an equation learning network

Lin, S., Martius, G., Oettel, M.

The Journal of Chemical Physics, 152(2):021102, 2020, arXiv preprint \url{https://arxiv.org/abs/1910.12752} (article)

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Preprint_PDF DOI [BibTex]

Preprint_PDF DOI [BibTex]


Effective Viscous Damping Enables Morphological Computation in Legged Locomotion
Effective Viscous Damping Enables Morphological Computation in Legged Locomotion

Mo, A., Izzi, F., Haeufle, D. F. B., Badri-Spröwitz, A.

2020 (article) In revision

Abstract
Muscle models and animal observations suggest that physical damping is beneficial for stabilization. Still, only a few implementations of mechanical damping exist in compliant robotic legged locomotion. It remains unclear how physical damping can be exploited for locomotion tasks, while its advantages as sensor-free, adaptive force- and negative work-producing actuators are promising. In a simplified numerical leg model, we studied the energy dissipation from viscous and Coulomb damping during vertical drops with ground-level perturbations. A parallel spring-damper is engaged between touch-down and mid-stance, and its damper auto-disengages during mid-stance and takeoff. Our simulations indicate that an adjustable and viscous damper is desired. In hardware we explored effective viscous damping and adjustability and quantified the dissipated energy. We tested two mechanical, leg-mounted damping mechanisms; a commercial hydraulic damper, and a custom-made pneumatic damper. The pneumatic damper exploits a rolling diaphragm with an adjustable orifice, minimizing Coulomb damping effects while permitting adjustable resistance. Experimental results show that the leg-mounted, hydraulic damper exhibits the most effective viscous damping. Adjusting the orifice setting did not result in substantial changes of dissipated energy per drop, unlike adjusting damping parameters in the numerical model. Consequently, we also emphasize the importance of characterizing physical dampers during real legged impacts to evaluate their effectiveness for compliant legged locomotion.

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Youtube link (url) [BibTex]


Wearable and Stretchable Strain Sensors: Materials, Sensing Mechanisms, and Applications
Wearable and Stretchable Strain Sensors: Materials, Sensing Mechanisms, and Applications

Souri, H., Banerjee, H., Jusufi, A., Radacsi, N., Stokes, A. A., Park, I., Sitti, M., Amjadi, M.

Advanced Intelligent Systems, 2020 (article)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


Postural Stability in Human Running with Step-down Perturbations: An Experimental and Numerical Study
Postural Stability in Human Running with Step-down Perturbations: An Experimental and Numerical Study

Oezge Drama, , Johanna Vielemeyer, , Alexander Badri-Spröwitz, , Müller, R.

2020 (article) In revision

Abstract
Postural stability is one of the most crucial elements in bipedal locomotion. Bipeds are dynamically unstable and need to maintain their trunk upright against the rotations induced by the ground reaction forces (GRFs), especially when running. Gait studies report that the GRF vectors focus around a virtual point above the center of mass (VPA), while the trunk moves forward in pitch axis during the stance phase of human running. However, a recent simulation study suggests that a virtual point below the center of mass (VPB) might be present in human running, since a VPA yields backward trunk rotation during the stance phase. In this work, we perform a gait analysis to investigate the existence and location of the VP in human running at 5 m s−1, and support our findings numerically using the spring-loaded inverted pendulum model with a trunk (TSLIP). We extend our analysis to include perturbations in terrain height (visible and camouflaged), and investigate the response of the VP mechanism to step-down perturbations both experimentally and numerically. Our experimental results show that the human running gait displays a VPB of ≈ −30 cm and a forward trunk motion during the stance phase. The camouflaged step-down perturbations affect the location of the VPB. Our simulation results suggest that the VPB is able to encounter the step-down perturbations and bring the system back to its initial equilibrium state.

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link (url) [BibTex]

link (url) [BibTex]


Electronics, Software and Analysis of a Bioinspired Sensorized Quadrupedal Robot
Electronics, Software and Analysis of a Bioinspired Sensorized Quadrupedal Robot

Petereit, R.

Technische Universität München, 2020 (mastersthesis)

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[BibTex]


Differentiation of Blackbox Combinatorial Solvers
Differentiation of Blackbox Combinatorial Solvers

Vlastelica, M., Paulus, A., Musil, V., Martius, G., Rolı́nek, M.

In International Conference on Learning Representations, ICLR’20, 2020 (incollection)

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Fish-like aquatic propulsion studied using a pneumatically-actuated soft-robotic model

Wolf, Z., Jusufi, A., Vogt, D. M., Lauder, G. V.

Bioinspiration & Biomimetics, 15(4):046008, Inst. of Physics, London, 2020 (article)

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DOI [BibTex]

DOI [BibTex]

2019


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Dynamics of beneficial epidemics

Berdahl, A., Brelsford, C., De Bacco, C., Dumas, M., Ferdinand, V., Grochow, J. A., nt Hébert-Dufresne, L., Kallus, Y., Kempes, C. P., Kolchinsky, A., Larremore, D. B., Libby, E., Power, E. A., A., S. C., Tracey, B. D.

Scientific Reports, 9, pages: 15093, October 2019 (article)

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DOI [BibTex]

2019


DOI [BibTex]


Series Elastic Behavior of Biarticular Muscle-Tendon Structure in a Robotic Leg
Series Elastic Behavior of Biarticular Muscle-Tendon Structure in a Robotic Leg

Ruppert, F., Badri-Spröwitz, A.

Frontiers in Neurorobotics, 64, pages: 13, 13, August 2019 (article)

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Frontiers YouTube link (url) DOI [BibTex]

Frontiers YouTube link (url) DOI [BibTex]


Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics
Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Steve Heim, , Spröwitz, A.

IEEE Transactions on Robotics (T-RO) , 35(4), pages: 939-952, August 2019 (article)

Abstract
Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. In this paper, we show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low-dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.

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arXiv preprint arXiv:1806.08081 T-RO link (url) DOI Project Page [BibTex]

arXiv preprint arXiv:1806.08081 T-RO link (url) DOI Project Page [BibTex]


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On the positivity and magnitudes of Bayesian quadrature weights

Karvonen, T., Kanagawa, M., Särkä, S.

Statistics and Computing, 29, pages: 1317-1333, 2019 (article)

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DOI [BibTex]

DOI [BibTex]


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Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective

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

Statistics and Computing, 29(6):1297-1315, 2019 (article)

ei pn

DOI [BibTex]

DOI [BibTex]


Autonomous Identification and Goal-Directed Invocation of Event-Predictive Behavioral Primitives
Autonomous Identification and Goal-Directed Invocation of Event-Predictive Behavioral Primitives

Gumbsch, C., Butz, M. V., Martius, G.

IEEE Transactions on Cognitive and Developmental Systems, 2019 (article)

Abstract
Voluntary behavior of humans appears to be composed of small, elementary building blocks or behavioral primitives. While this modular organization seems crucial for the learning of complex motor skills and the flexible adaption of behavior to new circumstances, the problem of learning meaningful, compositional abstractions from sensorimotor experiences remains an open challenge. Here, we introduce a computational learning architecture, termed surprise-based behavioral modularization into event-predictive structures (SUBMODES), that explores behavior and identifies the underlying behavioral units completely from scratch. The SUBMODES architecture bootstraps sensorimotor exploration using a self-organizing neural controller. While exploring the behavioral capabilities of its own body, the system learns modular structures that predict the sensorimotor dynamics and generate the associated behavior. In line with recent theories of event perception, the system uses unexpected prediction error signals, i.e., surprise, to detect transitions between successive behavioral primitives. We show that, when applied to two robotic systems with completely different body kinematics, the system manages to learn a variety of complex behavioral primitives. Moreover, after initial self-exploration the system can use its learned predictive models progressively more effectively for invoking model predictive planning and goal-directed control in different tasks and environments.

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arXiv PDF video link (url) DOI Project Page [BibTex]


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Even Delta-Matroids and the Complexity of Planar Boolean CSPs

Kazda, A., Kolmogorov, V., Rolinek, M.

ACM Transactions on Algorithms, 15(2, Special Issue on Soda'17 and Regular Papers):Article Number 22, 2019 (article)

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DOI [BibTex]

DOI [BibTex]


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Machine Learning for Haptics: Inferring Multi-Contact Stimulation From Sparse Sensor Configuration

Sun, H., Martius, G.

Frontiers in Neurorobotics, 13, pages: 51, 2019 (article)

Abstract
Robust haptic sensation systems are essential for obtaining dexterous robots. Currently, we have solutions for small surface areas such as fingers, but affordable and robust techniques for covering large areas of an arbitrary 3D surface are still missing. Here, we introduce a general machine learning framework to infer multi-contact haptic forces on a 3D robot’s limb surface from internal deformation measured by only a few physical sensors. The general idea of this framework is to predict first the whole surface deformation pattern from the sparsely placed sensors and then to infer number, locations and force magnitudes of unknown contact points. We show how this can be done even if training data can only be obtained for single-contact points using transfer learning at the example of a modified limb of the Poppy robot. With only 10 strain-gauge sensors we obtain a high accuracy also for multiple-contact points. The method can be applied to arbitrarily shaped surfaces and physical sensor types, as long as training data can be obtained.

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link (url) DOI [BibTex]


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Co-Contraction facilitates Body Stiffness Modulation during Swimming with Sensory Feedback in a Soft Biorobotic Physical Model

Jusufi, A., Vogt, D., Wood, R. J.

Integrative and Comparative Biology, 59(Supplement 1):E116-E116, Society of Integrative and Comparative Biology, McLean, VA, 2019 (article)

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DOI [BibTex]

DOI [BibTex]


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Dense connectomic reconstruction in layer 4 of the somatosensory cortex

Motta, A., Berning, M., Boergens, K. M., Staffler, B., Beining, M., Loomba, S., Hennig, P., Wissler, H., Helmstaedter, M.

Science, 366(6469):eaay3134, American Association for the Advancement of Science, 2019 (article)

ei pn

DOI [BibTex]

DOI [BibTex]


Das Tier als Modell für Roboter, und Roboter als Modell für Tiere
Das Tier als Modell für Roboter, und Roboter als Modell für Tiere

Badri-Spröwitz, A.

In pages: 167-175, Springer, 2019 (incollection)

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DOI [BibTex]

DOI [BibTex]


Probabilistic Linear Solvers: A Unifying View
Probabilistic Linear Solvers: A Unifying View

Bartels, S., Cockayne, J., Ipsen, I., Hennig, P.

Statistics and Computing, 29(6):1249-1263, 2019 (article)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2017


Probabilistic Line Searches for Stochastic Optimization
Probabilistic Line Searches for Stochastic Optimization

Mahsereci, M., Hennig, P.

Journal of Machine Learning Research, 18(119):1-59, November 2017 (article)

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link (url) Project Page [BibTex]

2017


link (url) Project Page [BibTex]


Spinal joint compliance and actuation in a simulated bounding quadruped robot
Spinal joint compliance and actuation in a simulated bounding quadruped robot

Pouya, S., Khodabakhsh, M., Sproewitz, A., Ijspeert, A.

{Autonomous Robots}, pages: 437–452, Kluwer Academic Publishers, Springer, Dordrecht, New York, NY, Febuary 2017 (article)

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link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings

Kanagawa, M., Sriperumbudur, B. K., Fukumizu, K.

Arxiv e-prints, arXiv:1709.00147v1 [math.NA], 2017 (article)

Abstract
This paper presents convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We provide convergence guarantees based on two different assumptions on a quadrature rule: one on quadrature weights, and the other on design points. More precisely, we show that convergence rates can be derived (i) if the sum of absolute weights remains constant (or does not increase quickly), or (ii) if the minimum distance between distance design points does not decrease very quickly. As a consequence of the latter result, we derive a rate of convergence for Bayesian quadrature in misspecified settings. We reveal a condition on design points to make Bayesian quadrature robust to misspecification, and show that, under this condition, it may adaptively achieve the optimal rate of convergence in the Sobolev space of a lesser order (i.e., of the unknown smoothness of a test integrand), under a slightly stronger regularity condition on the integrand.

pn

arXiv [BibTex]

arXiv [BibTex]


Early Stopping Without a Validation Set
Early Stopping Without a Validation Set

Mahsereci, M., Balles, L., Lassner, C., Hennig, P.

arXiv preprint arXiv:1703.09580, 2017 (article)

Abstract
Early stopping is a widely used technique to prevent poor generalization performance when training an over-expressive model by means of gradient-based optimization. To find a good point to halt the optimizer, a common practice is to split the dataset into a training and a smaller validation set to obtain an ongoing estimate of the generalization performance. In this paper we propose a novel early stopping criterion which is based on fast-to-compute, local statistics of the computed gradients and entirely removes the need for a held-out validation set. Our experiments show that this is a viable approach in the setting of least-squares and logistic regression as well as neural networks.

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link (url) Project Page Project Page [BibTex]


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Krylov Subspace Recycling for Fast Iterative Least-Squares in Machine Learning

Roos, F. D., Hennig, P.

arXiv preprint arXiv:1706.00241, 2017 (article)

Abstract
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time approximations, such as spectral and inducing-point methods, have been suggested and are now in wide use. These are low-rank approximations that choose the low-rank space a priori and do not refine it over time. While this allows linear cost in the data-set size, it also causes a finite, uncorrected approximation error. Authors from numerical linear algebra have explored ways to iteratively refine such low-rank approximations, at a cost of a small number of matrix-vector multiplications. This idea is particularly interesting in the many situations in machine learning where one has to solve a sequence of related symmetric positive definite linear problems. From the machine learning perspective, such deflation methods can be interpreted as transfer learning of a low-rank approximation across a time-series of numerical tasks. We study the use of such methods for our field. Our empirical results show that, on regression and classification problems of intermediate size, this approach can interpolate between low computational cost and numerical precision.

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link (url) Project Page [BibTex]


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Self-Organized Behavior Generation for Musculoskeletal Robots

Der, R., Martius, G.

Frontiers in Neurorobotics, 11, pages: 8, 2017 (article)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Efficiency of analytical and sampling-based uncertainty propagation in intensity-modulated proton therapy

Wahl, N., Hennig, P., Wieser, H. P., Bangert, M.

Physics in Medicine & Biology, 62(14):5790-5807, 2017 (article)

Abstract
The sensitivity of intensity-modulated proton therapy (IMPT) treatment plans to uncertainties can be quantified and mitigated with robust/min-max and stochastic/probabilistic treatment analysis and optimization techniques. Those methods usually rely on sparse random, importance, or worst-case sampling. Inevitably, this imposes a trade-off between computational speed and accuracy of the uncertainty propagation. Here, we investigate analytical probabilistic modeling (APM) as an alternative for uncertainty propagation and minimization in IMPT that does not rely on scenario sampling. APM propagates probability distributions over range and setup uncertainties via a Gaussian pencil-beam approximation into moments of the probability distributions over the resulting dose in closed form. It supports arbitrary correlation models and allows for efficient incorporation of fractionation effects regarding random and systematic errors. We evaluate the trade-off between run-time and accuracy of APM uncertainty computations on three patient datasets. Results are compared against reference computations facilitating importance and random sampling. Two approximation techniques to accelerate uncertainty propagation and minimization based on probabilistic treatment plan optimization are presented. Runtimes are measured on CPU and GPU platforms, dosimetric accuracy is quantified in comparison to a sampling-based benchmark (5000 random samples). APM accurately propagates range and setup uncertainties into dose uncertainties at competitive run-times (GPU ##IMG## [http://ej.iop.org/images/0031-9155/62/14/5790/pmbaa6ec5ieqn001.gif] {$\leqslant {5}$} min). The resulting standard deviation (expectation value) of dose show average global ##IMG## [http://ej.iop.org/images/0031-9155/62/14/5790/pmbaa6ec5ieqn002.gif] {$\gamma_{{3}\% / {3}~{\rm mm}}$} pass rates between 94.2% and 99.9% (98.4% and 100.0%). All investigated importance sampling strategies provided less accuracy at higher run-times considering only a single fraction. Considering fractionation, APM uncertainty propagation and treatment plan optimization was proven to be possible at constant time complexity, while run-times of sampling-based computations are linear in the number of fractions. Using sum sampling within APM, uncertainty propagation can only be accelerated at the cost of reduced accuracy in variance calculations. For probabilistic plan optimization, we were able to approximate the necessary pre-computations within seconds, yielding treatment plans of similar quality as gained from exact uncertainty propagation. APM is suited to enhance the trade-off between speed and accuracy in uncertainty propagation and probabilistic treatment plan optimization, especially in the context of fractionation. This brings fully-fledged APM computations within reach of clinical application.

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link (url) [BibTex]

link (url) [BibTex]


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Analytical probabilistic modeling of RBE-weighted dose for ion therapy

Wieser, H., Hennig, P., Wahl, N., Bangert, M.

Physics in Medicine and Biology (PMB), 62(23):8959-8982, 2017 (article)

pn

link (url) [BibTex]

link (url) [BibTex]


Evaluation of the passive dynamics of compliant legs with inertia
Evaluation of the passive dynamics of compliant legs with inertia

Györfi, B.

University of Applied Science Pforzheim, Germany, 2017 (mastersthesis)

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[BibTex]

[BibTex]

2015


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Probabilistic Interpretation of Linear Solvers

Hennig, P.

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

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Web PDF link (url) DOI [BibTex]

2015


Web PDF link (url) DOI [BibTex]


Exciting Engineered Passive Dynamics in a Bipedal Robot
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.

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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.

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PDF DOI [BibTex]

PDF DOI [BibTex]


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Novel plasticity rule can explain the development of sensorimotor intelligence

Der, R., Martius, G.

Proceedings of the National Academy of Sciences, 112(45):E6224-E6232, 2015 (article)

Abstract
Grounding autonomous behavior in the nervous system is a fundamental challenge for neuroscience. In particular, self-organized behavioral development provides more questions than answers. Are there special functional units for curiosity, motivation, and creativity? This paper argues that these features can be grounded in synaptic plasticity itself, without requiring any higher-level constructs. We propose differential extrinsic plasticity (DEP) as a new synaptic rule for self-learning systems and apply it to a number of complex robotic systems as a test case. Without specifying any purpose or goal, seemingly purposeful and adaptive rhythmic behavior is developed, displaying a certain level of sensorimotor intelligence. These surprising results require no system-specific modifications of the DEP rule. They rather arise from the underlying mechanism of spontaneous symmetry breaking, which is due to the tight brain body environment coupling. The new synaptic rule is biologically plausible and would be an interesting target for neurobiological investigation. We also argue that this neuronal mechanism may have been a catalyst in natural evolution.

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link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Quantifying Emergent Behavior of Autonomous Robots

Martius, G., Olbrich, E.

Entropy, 17(10):7266, 2015 (article)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]