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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.

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.

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.

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.

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]

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]


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)

DOI [BibTex]

DOI [BibTex]

2015


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.

link (url) DOI Project Page [BibTex]

2015

link (url) DOI Project Page [BibTex]