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2020


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.

link (url) DOI [BibTex]

2020

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.

Youtube link (url) DOI [BibTex]

Youtube link (url) DOI [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.

Youtube Video link (url) DOI [BibTex]

Youtube Video 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.

link (url) [BibTex]

link (url) [BibTex]

2019


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)

Frontiers YouTube link (url) DOI [BibTex]

2019

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.

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]

2010


Roombots: Reconfigurable Robots for Adaptive Furniture
Roombots: Reconfigurable Robots for Adaptive Furniture

Spröwitz, A., Pouya, S., Bonardi, S., van den Kieboom, J., Möckel, R., Billard, A., Dillenbourg, P., Ijspeert, A.

Computational Intelligence Magazine, IEEE, 5(3):20-32, 2010 (article)

Abstract
Imagine a world in which our furniture moves around like legged robots, interacts with us, and changes shape and function during the day according to our needs. This is the long term vision we have in the Roombots project. To work towards this dream, we are developing modular robotic modules that have rotational degrees of freedom for locomotion as well as active connection mechanisms for runtime reconfiguration. A piece of furniture, e.g. a stool, will thus be composed of several modules that activate their rotational joints together to implement locomotor gaits, and will be able to change shape, e.g. transforming into a chair, by sequences of attachments and detachments of modules. In this article, we firstly present the project and the hardware we are currently developing. We explore how reconfiguration from a configuration A to a configuration B can be controlled in a distributed fashion. This is done using metamodules-two Roombots modules connected serially-that use broadcast signals and connections to a structured ground to collectively build desired structures without the need of a centralized planner. We then present how locomotion controllers can be implemented in a distributed system of coupled oscillators-one per degree of freedom-similarly to the concept of central pattern generators (CPGs) found in the spinal cord of vertebrate animals. The CPGs are based on coupled phase oscillators to ensure synchronized behavior and have different output filters to allow switching between oscillations and rotations. A stochastic optimization algorithm is used to explore optimal CPG configurations for different simulated Roombots structures.

DOI [BibTex]

2010

DOI [BibTex]