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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]


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.

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.

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.

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].

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.

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)

[BibTex]

[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]

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]


Comparing the effect of different spine and leg designs for a small bounding quadruped robot
Comparing the effect of different spine and leg designs for a small bounding quadruped robot

Eckert, P., Spröwitz, A., Witte, H., Ijspeert, A. J.

In Proceedings of ICRA, pages: 3128-3133, Seattle, Washington, USA, 2015 (inproceedings)

Abstract
We present Lynx-robot, a quadruped, modular, compliant machine. It alternately features a directly actuated, single-joint spine design, or an actively supported, passive compliant, multi-joint spine configuration. Both spine con- figurations bend in the sagittal plane. This study aims at characterizing these two, largely different spine concepts, for a bounding gait of a robot with a three segmented, pantograph leg design. An earlier, similar-sized, bounding, quadruped robot named Bobcat with a two-segment leg design and a directly actuated, single-joint spine design serves as a comparison robot, to study and compare the effect of the leg design on speed, while keeping the spine design fixed. Both proposed spine designs (single rotatory and active and multi-joint compliant) reach moderate, self-stable speeds.

link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]

2014


Roombots: A hardware perspective on 3D self-reconfiguration and locomotion with a homogeneous modular robot
Roombots: A hardware perspective on 3D self-reconfiguration and locomotion with a homogeneous modular robot

Spröwitz, A., Moeckel, R., Vespignani, M., Bonardi, S., Ijspeert, A. J.

{Robotics and Autonomous Systems}, 62(7):1016-1033, Elsevier, Amsterdam, 2014 (article)

Abstract
In this work we provide hands-on experience on designing and testing a self-reconfiguring modular robotic system, Roombots (RB), to be used among others for adaptive furniture. In the long term, we envision that RB can be used to create sets of furniture, such as stools, chairs and tables that can move in their environment and that change shape and functionality during the day. In this article, we present the first, incremental results towards that long term vision. We demonstrate locomotion and reconfiguration of single and metamodule RB over 3D surfaces, in a structured environment equipped with embedded connection ports. RB assemblies can move around in non-structured environments, by using rotational or wheel-like locomotion. We show a proof of concept for transferring a Roombots metamodule (two in-series coupled RB modules) from the non-structured environment back into the structured grid, by aligning the RB metamodule in an entrapment mechanism. Finally, we analyze the remaining challenges to master the full Roombots scenario, and discuss the impact on future Roombots hardware.

DOI [BibTex]

2014

DOI [BibTex]


Automatic Generation of Reduced CPG Control Networks for Locomotion of Arbitrary Modular Robot Structures
Automatic Generation of Reduced CPG Control Networks for Locomotion of Arbitrary Modular Robot Structures

Bonardi, S., Vespignani, M., Möckel, R., Van den Kieboom, J., Pouya, S., Spröwitz, A., Ijspeert, A.

In Proceedings of Robotics: Science and Systems, University of California, Barkeley, 2014 (inproceedings)

Abstract
The design of efficient locomotion controllers for arbitrary structures of reconfigurable modular robots is challenging because the morphology of the structure can change dynamically during the completion of a task. In this paper, we propose a new method to automatically generate reduced Central Pattern Generator (CPG) networks for locomotion control based on the detection of bio-inspired sub-structures, like body and limbs, and articulation joints inside the robotic structure. We demonstrate how that information, coupled with the potential symmetries in the structure, can be used to speed up the optimization of the gaits and investigate its impact on the solution quality (i.e. the velocity of the robotic structure and the potential internal collisions between robotic modules). We tested our approach on three simulated structures and observed that the reduced network topologies in the first iterations of the optimization process performed significantly better than the fully open ones.

DOI [BibTex]

DOI [BibTex]


Kinematic primitives for walking and trotting gaits of a quadruped robot with compliant legs
Kinematic primitives for walking and trotting gaits of a quadruped robot with compliant legs

Spröwitz, A. T., Ajallooeian, M., Tuleu, A., Ijspeert, A. J.

Frontiers in Computational Neuroscience, 8(27):1-13, 2014 (article)

Abstract
In this work we research the role of body dynamics in the complexity of kinematic patterns in a quadruped robot with compliant legs. Two gait patterns, lateral sequence walk and trot, along with leg length control patterns of different complexity were implemented in a modular, feed-forward locomotion controller. The controller was tested on a small, quadruped robot with compliant, segmented leg design, and led to self-stable and self-stabilizing robot locomotion. In-air stepping and on-ground locomotion leg kinematics were recorded, and the number and shapes of motion primitives accounting for 95\% of the variance of kinematic leg data were extracted. This revealed that kinematic patterns resulting from feed-forward control had a lower complexity (in-air stepping, 2–3 primitives) than kinematic patterns from on-ground locomotion (νm4 primitives), although both experiments applied identical motor patterns. The complexity of on-ground kinematic patterns had increased, through ground contact and mechanical entrainment. The complexity of observed kinematic on-ground data matches those reported from level-ground locomotion data of legged animals. Results indicate that a very low complexity of modular, rhythmic, feed-forward motor control is sufficient for level-ground locomotion in combination with passive compliant legged hardware.

link (url) DOI [BibTex]

link (url) DOI [BibTex]