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2020


Virtual Point Control for Step-down Perturbations and Downhill Slopes in Bipedal Running
Virtual Point Control for Step-down Perturbations and Downhill Slopes in Bipedal Running

Drama, Ö., Badri-Spröwitz, A.

Frontiers in Bioengineering Biotechnology, Bionics and Biomimetics, November 2020 (article) Accepted

Abstract
Bipedal running is a difficult task to realize in robots, since the trunk is underactuated and control is limited by intermittent ground contacts. Stabilizing the trunk becomes even more challenging if the terrain is uneven and causes perturbations. One bio-inspired method to achieve postural stability is the virtual point (VP) control, which is able to generate natural motion. However, so far it has only been studied for level running. In this work, we investigate whether the VP control method can accommodate single step-down perturbations and downhill terrains. We provide guidelines on the model and controller parameterizations for handling varying terrain conditions. Next, we show that the VP method is able to stabilize single step-down perturbations up to 40 cm, and downhill grades up to 20-10° corresponding to running speeds of 2-5 m/s. Our results show that the VP approach leads to asymmetrically bounded ground reaction forces for downhill running, unlike the commonly-used symmetric friction cone constraints. Overall, VP control is a promising candidate for terrain-adaptive running control of bipedal robots.

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link (url) DOI [BibTex]

2020


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

Drama, Ö., Vielemeyer, J., Badri-Spröwitz, A., Müller, R.

Royal Society Open Science, 7, November 2020 (article)

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) DOI [BibTex]

link (url) DOI [BibTex]


A little damping goes a long way: a simulation study of how damping influences task-level stability in running
A little damping goes a long way: a simulation study of how damping influences task-level stability in running

Heim, S., Millard, M., Mouel, C. L., Badri-Spröwitz, A.

Biology Letters, 16(9), September 2020 (article)

Abstract
It is currently unclear if damping plays a functional role in legged locomotion, and simple models often do not include damping terms. We present a new model with a damping term that is isolated from other parameters: that is, the damping term can be adjusted without retuning other model parameters for nominal motion. We systematically compare how increased damping affects stability in the face of unexpected ground-height perturbations. Unlike most studies, we focus on task-level stability: instead of observing whether trajectories converge towards a nominal limit-cycle, we quantify the ability to avoid falls using a recently developed mathematical measure. This measure allows trajectories to be compared quantitatively instead of only being separated into a binary classification of ‘stable' or ‘unstable'. Our simulation study shows that increased damping contributes significantly to task-level stability; however, this benefit quickly plateaus after only a small amount of damping. These results suggest that the low intrinsic damping values observed experimentally may have stability benefits and are not simply minimized for energetic reasons. All Python code and data needed to generate our results are available open source.

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link (url) DOI [BibTex]

link (url) 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.

Frontiers Robots and Ai, 7:110, August 2020 (article)

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) DOI [BibTex]

Youtube link (url) DOI [BibTex]


FootTile: a Rugged Foot Sensor for Force and Center of Pressure Sensing in Soft Terrain
FootTile: a Rugged Foot Sensor for Force and Center of Pressure Sensing in Soft Terrain

Felix Ruppert, , Badri-Spröwitz, A.

In Proceedings of the IEEE International Conference on Robotics and Automation, IEEE, International Conference on Robotics and Automation, May 2020 (inproceedings) Accepted

Abstract
In this paper, we present FootTile, a foot sensor for reaction force and center of pressure sensing in challenging terrain. We compare our sensor design to standard biomechanical devices, force plates and pressure plates. We show that FootTile can accurately estimate force and pressure distribution during legged locomotion. FootTile weighs 0.9g, has a sampling rate of 330 Hz, a footprint of 10×10 mm and can easily be adapted in sensor range to the required load case. In three experiments, we validate: first, the performance of the individual sensor, second an array of FootTiles for center of pressure sensing and third the ground reaction force estimation during locomotion in granular substrate. We then go on to show the accurate sensing capabilities of the waterproof sensor in liquid mud, as a showcase for real world rough terrain use.

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Youtube1 Youtube2 Presentation link (url) [BibTex]

Youtube1 Youtube2 Presentation link (url) [BibTex]


VP above or below? A new perspective on the story of the virtual point
VP above or below? A new perspective on the story of the virtual point

Drama, Ö., Badri-Spröwitz, A.

Dynamic Walking, May 2020 (poster)

Abstract
The spring inverted pendulum model with an extended trunk (TSLIP) is widely used to investigate the postural stability in bipedal locomotion [1, 2]. The challenge of the model is to define a hip torque that generates feasible gait patterns while stabilizing the floating trunk. The virtual point (VP) method is proposed as a simplified solution, where the hip torque is coupled to the passive compliant leg force via a virtual point. This geometric coupling is based on the assumption that the instantaneous ground reaction forces of the stance phase (GRF) intersect at a single virtual point.

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Poster Abstract link (url) [BibTex]

Poster Abstract link (url) [BibTex]


Viscous Damping in Legged Locomotion
Viscous Damping in Legged Locomotion

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

Dynamic Walking, May 2020 (poster)

Abstract
Damping likely plays an essential role in legged animal locomotion, but remains an insufficiently understood mechanism. Intrinsic damping muscle forces can potentially add to the joint torque output during unexpected impacts, stabilise movements, convert the system’s energy, and reject unexpected perturbations.

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Abstract Poster link (url) [BibTex]

Abstract Poster link (url) [BibTex]


How Quadrupeds Benefit from Lower Leg Passive Elasticity
How Quadrupeds Benefit from Lower Leg Passive Elasticity

Ruppert, F., Badri-Spröwitz, A.

Dynamic Walking, May 2020 (poster)

Abstract
Recently developed and fully actuated, legged robots start showing exciting locomotion capabilities, but rely heavily on high-power actuators, high-frequency sensors, and complex locomotion controllers. The engineering solutions implemented in these legged robots are much different compared to animals. Vertebrate animals share magnitudes slower neurocontrol signal velocities [1] compared to their robot counterparts. Also, animals feature a plethora of cascaded and underactuated passive elastic structures [2].

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Abstract Poster link (url) [BibTex]


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]


Potential for elastic soft tissue deformation and mechanosensory function within the lumbosacral spinal canal of birds
Potential for elastic soft tissue deformation and mechanosensory function within the lumbosacral spinal canal of birds

Kamska, V., Daley, M., Badri-Spröwitz, A.

Society of Integrative & Comparative Biology Annual Meeting, January 2020 (poster)

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[BibTex]

[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]

2012


Quasi-Newton Methods: A New Direction
Quasi-Newton Methods: A New Direction

Hennig, P., Kiefel, M.

In Proceedings of the 29th International Conference on Machine Learning, pages: 25-32, ICML ’12, (Editors: John Langford and Joelle Pineau), Omnipress, New York, NY, USA, ICML, July 2012 (inproceedings)

Abstract
Four decades after their invention, quasi- Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newton methods can be interpreted as approximations of Bayesian linear regression under varying prior assumptions. This new notion elucidates some shortcomings of classical algorithms, and lights the way to a novel nonparametric quasi-Newton method, which is able to make more efficient use of available information at computational cost similar to its predecessors.

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website+code pdf link (url) [BibTex]

2012


website+code pdf link (url) [BibTex]


Entropy Search for Information-Efficient Global Optimization
Entropy Search for Information-Efficient Global Optimization

Hennig, P., Schuler, C.

Journal of Machine Learning Research, 13, pages: 1809-1837, -, June 2012 (article)

Abstract
Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum. The reason for the absence of probabilistic global optimizers is that the corresponding inference problem is intractable in several ways. This paper develops desiderata for probabilistic optimization algorithms, then presents a concrete algorithm which addresses each of the computational intractabilities with a sequence of approximations and explicitly adresses the decision problem of maximizing information gain from each evaluation.

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PDF Web Project Page [BibTex]

PDF Web Project Page [BibTex]


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Learning Tracking Control with Forward Models

Bócsi, B., Hennig, P., Csató, L., Peters, J.

In pages: 259 -264, IEEE International Conference on Robotics and Automation (ICRA), May 2012 (inproceedings)

Abstract
Performing task-space tracking control on redundant robot manipulators is a difficult problem. When the physical model of the robot is too complex or not available, standard methods fail and machine learning algorithms can have advantages. We propose an adaptive learning algorithm for tracking control of underactuated or non-rigid robots where the physical model of the robot is unavailable. The control method is based on the fact that forward models are relatively straightforward to learn and local inversions can be obtained via local optimization. We use sparse online Gaussian process inference to obtain a flexible probabilistic forward model and second order optimization to find the inverse mapping. Physical experiments indicate that this approach can outperform state-of-the-art tracking control algorithms in this context.

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PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Approximate Gaussian Integration using Expectation Propagation

Cunningham, J., Hennig, P., Lacoste-Julien, S.

In pages: 1-11, -, January 2012 (inproceedings) Submitted

Abstract
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We offer here an empirical study of the utility of Expectation Propagation (EP) as an approximate integration method for this problem. For rectangular integration regions, the approximation is highly accurate. We also extend the derivations to the more general case of polyhedral integration regions. However, we find that in this polyhedral case, EP's answer, though often accurate, can be almost arbitrarily wrong. These unexpected results elucidate an interesting and non-obvious feature of EP not yet studied in detail, both for the problem of Gaussian probabilities and for EP more generally.

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Web [BibTex]

Web [BibTex]


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Kernel Topic Models

Hennig, P., Stern, D., Herbrich, R., Graepel, T.

In Fifteenth International Conference on Artificial Intelligence and Statistics, 22, pages: 511-519, JMLR Proceedings, (Editors: Lawrence, N. D. and Girolami, M.), JMLR.org, AISTATS , 2012 (inproceedings)

Abstract
Latent Dirichlet Allocation models discrete data as a mixture of discrete distributions, using Dirichlet beliefs over the mixture weights. We study a variation of this concept, in which the documents' mixture weight beliefs are replaced with squashed Gaussian distributions. This allows documents to be associated with elements of a Hilbert space, admitting kernel topic models (KTM), modelling temporal, spatial, hierarchical, social and other structure between documents. The main challenge is efficient approximate inference on the latent Gaussian. We present an approximate algorithm cast around a Laplace approximation in a transformed basis. The KTM can also be interpreted as a type of Gaussian process latent variable model, or as a topic model conditional on document features, uncovering links between earlier work in these areas.

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PDF Web [BibTex]

PDF Web [BibTex]