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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]

2018


Oncilla robot: a versatile open-source quadruped research robot with compliant pantograph legs
Oncilla robot: a versatile open-source quadruped research robot with compliant pantograph legs

Sproewitz, A., Tuleu, A., Ajallooeian, M., Vespignani, M., Moeckel, R., Eckert, P., D’Haene, M., Degrave, J., Nordmann, A., Schrauwen, B., Steil, J., Ijspeert, A. J.

Frontiers in Robotics and AI, 5(67), June 2018, arXiv: 1803.06259 (article)

Abstract
We present Oncilla robot, a novel mobile, quadruped legged locomotion machine. This large-cat sized, 5.1 robot is one of a kind of a recent, bioinspired legged robot class designed with the capability of model-free locomotion control. Animal legged locomotion in rough terrain is clearly shaped by sensor feedback systems. Results with Oncilla robot show that agile and versatile locomotion is possible without sensory signals to some extend, and tracking becomes robust when feedback control is added (Ajaoolleian 2015). By incorporating mechanical and control blueprints inspired from animals, and by observing the resulting robot locomotion characteristics, we aim to understand the contribution of individual components. Legged robots have a wide mechanical and control design parameter space, and a unique potential as research tools to investigate principles of biomechanics and legged locomotion control. But the hardware and controller design can be a steep initial hurdle for academic research. To facilitate the easy start and development of legged robots, Oncilla-robot's blueprints are available through open-source. [...]

link (url) DOI Project Page [BibTex]

2018

link (url) DOI Project Page [BibTex]


Learning from Outside the Viability Kernel: Why we Should Build Robots that can Fail with Grace
Learning from Outside the Viability Kernel: Why we Should Build Robots that can Fail with Grace

Heim, S., Sproewitz, A.

Proceedings of SIMPAR 2018, pages: 55-61, IEEE, 2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR), May 2018 (conference)

link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


Impact of Trunk Orientation  for Dynamic Bipedal Locomotion
Impact of Trunk Orientation for Dynamic Bipedal Locomotion

Drama, Ö.

Dynamic Walking Conference, May 2018 (talk)

Abstract
Impact of trunk orientation for dynamic bipedal locomotion My research revolves around investigating the functional demands of bipedal running, with focus on stabilizing trunk orientation. When we think about postural stability, there are two critical questions we need to answer: What are the necessary and sufficient conditions to achieve and maintain trunk stability? I am concentrating on how morphology affects control strategies in achieving trunk stability. In particular, I denote the trunk pitch as the predominant morphology parameter and explore the requirements it imposes on a chosen control strategy. To analyze this, I use a spring loaded inverted pendulum model extended with a rigid trunk, which is actuated by a hip motor. The challenge for the controller design here is to have a single hip actuator to achieve two coupled tasks of moving the legs to generate motion and stabilizing the trunk. I enforce orthograde and pronograde postures and aim to identify the effect of these trunk orientations on the hip torque and ground reaction profiles for different control strategies.

Impact of trunk orientation for dynamic bipedal locomotion [DW 2018] link (url) Project Page [BibTex]


Shaping in Practice: Training Wheels to Learn Fast Hopping Directly in Hardware
Shaping in Practice: Training Wheels to Learn Fast Hopping Directly in Hardware

Heim, S., Ruppert, F., Sarvestani, A., Sproewitz, A.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2018, pages: 5076-5081, IEEE, International Conference on Robotics and Automation, May 2018 (inproceedings)

Abstract
Learning instead of designing robot controllers can greatly reduce engineering effort required, while also emphasizing robustness. Despite considerable progress in simulation, applying learning directly in hardware is still challenging, in part due to the necessity to explore potentially unstable parameters. We explore the of concept shaping the reward landscape with training wheels; temporary modifications of the physical hardware that facilitate learning. We demonstrate the concept with a robot leg mounted on a boom learning to hop fast. This proof of concept embodies typical challenges such as instability and contact, while being simple enough to empirically map out and visualize the reward landscape. Based on our results we propose three criteria for designing effective training wheels for learning in robotics.

Video Youtube link (url) Project Page [BibTex]

Video Youtube link (url) Project Page [BibTex]

2016


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On designing an active tail for legged robots: simplifying control via decoupling of control objectives

Heim, S. W., Ajallooeian, M., Eckert, P., Vespignani, M., Ijspeert, A. J.

Industrial Robot: An International Journal, 43, pages: 338-346, Emerald Group Publishing Limited, 2016 (article)

Preprint [BibTex]

2016

Preprint [BibTex]


ATRIAS: Design and validation of a tether-free 3D-capable spring-mass bipedal robot
ATRIAS: Design and validation of a tether-free 3D-capable spring-mass bipedal robot

Hubicki, C., Grimes, J., Jones, M., Renjewski, D., Spröwitz, A., Abate, A., Hurst, J.

{The International Journal of Robotics Research}, 35(12):1497-1521, Sage Publications, Inc., Cambridge, MA, 2016 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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On designing an active tail for body-pitch control in legged robots via decoupling of control objectives

Heim, S. W., Ajallooeian, M., Eckert, P., Vespignani, M., Ijspeert, A.

In ASSISTIVE ROBOTICS: Proceedings of the 18th International Conference on CLAWAR 2015, pages: 256-264, 2016 (inproceedings)

[BibTex]

[BibTex]

2013


Benefits of an active spine supported bounding locomotion with a small compliant quadruped robot
Benefits of an active spine supported bounding locomotion with a small compliant quadruped robot

Khoramshahi, M., Spröwitz, A., Tuleu, A., Ahmadabadi, M. N., Ijspeert, A. J.

In Robotics and Automation (ICRA), 2013 IEEE International Conference on, pages: 3329-3334, May 2013 (inproceedings)

Abstract
We studied the effect of the control of an active spine versus a fixed spine, on a quadruped robot running in bound gait. Active spine supported actuation led to faster locomotion, with less foot sliding on the ground, and a higher stability to go straight forward. However, we did no observe an improvement of cost of transport of the spine-actuated, faster robot system compared to the rigid spine.

Youtube DOI Project Page [BibTex]

2013

Youtube DOI Project Page [BibTex]


Central pattern generators augmented with virtual model control for quadruped rough terrain locomotion
Central pattern generators augmented with virtual model control for quadruped rough terrain locomotion

Ajallooeian, M., Pouya, S., Spröwitz, A., Ijspeert, A. J.

In Proceedings of the 2013 IEEE International Conference on Robotics and Automation (ICRA), pages: 3321-3328, IEEE, Karlsruhe, 2013 (inproceedings)

Abstract
We present a modular controller for quadruped locomotion over unperceived rough terrain. Our approach is based on a computational Central Pattern Generator (CPG) model implemented as coupled nonlinear oscillators. Stumbling correction reflex is implemented as a sensory feedback mechanism affecting the CPG. We augment the outputs of the CPG with virtual model control torques responsible for posture control. The control strategy is validated on a 3D forward dynamics simulated quadruped robot platform of about the size and weight of a cat. To demonstrate the capabilities of the proposed approach, we perform locomotion over unperceived uneven terrain and slopes, as well as situations facing external pushes.

DOI [BibTex]

DOI [BibTex]


Motor Control Adaptation to Changes in Robot Body Dynamics for a Compliant Quadruped Robot
Motor Control Adaptation to Changes in Robot Body Dynamics for a Compliant Quadruped Robot

Pouya, S., Eckert, P., Spröwitz, A., Moc̈kel, R., Ijspeert, A. J.

In Biomimetic and Biohybrid Systems, 8064, pages: 434-437, Lecture Notes in Computer Science, Springer, Heidelberg, 2013 (incollection)

Abstract
One of the major deficiencies of current robots in comparison to living beings is the ability to adapt to new conditions either resulting from environmental changes or their own dynamics. In this work we focus on situations where the robot experiences involuntary changes in its body particularly in its limbs’ inertia. Inspired from its biological counterparts we are interested in enabling the robot to adapt its motor control to the new system dynamics. To reach this goal, we propose two different control strategies and compare their performance when handling these modifications. Our results show substantial improvements in adaptivity to body changes when the robot is aware of its new dynamics and can exploit this knowledge in synthesising new motor control.

DOI [BibTex]

DOI [BibTex]


Towards Dynamic Trot Gait Locomotion: Design, Control, and Experiments with Cheetah-cub, a Compliant Quadruped Robot
Towards Dynamic Trot Gait Locomotion: Design, Control, and Experiments with Cheetah-cub, a Compliant Quadruped Robot

Spröwitz, A., Tuleu, A., Vespignani, M., Ajallooeian, M., Badri, E., Ijspeert, A. J.

{The International Journal of Robotics Research}, 32(8):932-950, Sage Publications, Inc., Cambridge, MA, 2013 (article)

Abstract
We present the design of a novel compliant quadruped robot, called Cheetah-cub, and a series of locomotion experiments with fast trotting gaits. The robot’s leg configuration is based on a spring-loaded, pantograph mechanism with multiple segments. A dedicated open-loop locomotion controller was derived and implemented. Experiments were run in simulation and in hardware on flat terrain and with a step down, demonstrating the robot’s self-stabilizing properties. The robot reached a running trot with short flight phases with a maximum Froude number of FR = 1.30, or 6.9 body lengths per second. Morphological parameters such as the leg design also played a role. By adding distal in-series elasticity, self- stability and maximum robot speed improved. Our robot has several advantages, especially when compared with larger and stiffer quadruped robot designs. (1) It is, to the best of the authors’ knowledge, the fastest of all quadruped robots below 30 kg (in terms of Froude number and body lengths per second). (2) It shows self-stabilizing behavior over a large range of speeds with open-loop control. (3) It is lightweight, compact, and electrically powered. (4) It is cheap, easy to reproduce, robust, and safe to handle. This makes it an excellent tool for research of multi-segment legs in quadruped robots.

Youtube1 Youtube2 Youtube3 Youtube4 Youtube5 DOI Project Page [BibTex]

Youtube1 Youtube2 Youtube3 Youtube4 Youtube5 DOI Project Page [BibTex]


Gait Optimization for Roombots Modular Robots - Matching Simulation and Reality
Gait Optimization for Roombots Modular Robots - Matching Simulation and Reality

Möckel, R., Yura, N. P., The Nguyen, A., Vespignani, M., Bonardi, S., Pouya, S., Spröwitz, A., van den Kieboom, J., Wilhelm, F., Ijspeert, A. J.

In Proceedings of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 3265-3272, IEEE, Tokyo, 2013 (inproceedings)

Abstract
The design of efficient locomotion gaits for robots with many degrees of freedom is challenging and time consuming even if optimization techniques are applied. Control parameters can be found through optimization in two ways: (i) through online optimization where the performance of a robot is measured while trying different control parameters on the actual hardware and (ii) through offline optimization by simulating the robot’s behavior with the help of models of the robot and its environment. In this paper, we present a hybrid optimization method that combines the best properties of online and offline optimization to efficiently find locomotion gaits for arbitrary structures. In comparison to pure online optimization, both the number of experiments using robotic hardware as well as the total time required for finding efficient locomotion gaits get highly reduced by running the major part of the optimization process in simulation using a cluster of processors. The presented example shows that even for robots with a low number of degrees of freedom the time required for optimization can be reduced by a factor of 2.5 to 30, at least, depending on how extensive the search for optimized control parameters should be. Time for hardware experiments becomes minimal. More importantly, gaits that can possibly damage the robotic hardware can be filtered before being tried in hardware. Yet in contrast to pure offline optimization, we reach well matched behavior that allows a direct transfer of locomotion gaits from simulation to hardware. This is because through a meta-optimization we adapt not only the locomotion parameters but also the parameters for simulation models of the robot and environment allowing for a good matching of the robot behavior in simulation and hardware. We validate the proposed hybrid optimization method on a structure composed of two Roombots modules with a total number of six degrees of freedom. Roombots are self-reconfigurable modular robots that can form arbitrary structures with many degrees of freedom through an integrated active connection mechanism.

DOI [BibTex]

DOI [BibTex]


Modular Control of Limit Cycle Locomotion over Unperceived Rough Terrain
Modular Control of Limit Cycle Locomotion over Unperceived Rough Terrain

Ajallooeian, M., Gay, S., Tuleu, A., Spröwitz, A., Ijspeert, A. J.

In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2013, pages: 3390-3397, Tokyo, 2013 (inproceedings)

Abstract
We present a general approach to design modular controllers for limit cycle locomotion over unperceived rough terrain. The control strategy uses a Central Pattern Generator (CPG) model implemented as coupled nonlinear oscillators as basis. Stumbling correction and leg extension reflexes are implemented as feedbacks for fast corrections, and model-based posture control mechanisms define feedbacks for continuous corrections. The control strategy is validated on a detailed physics-based simulated model of a compliant quadruped robot, the Oncilla robot. We demonstrate dynamic locomotion with a speed of more than 1.5 BodyLength/s over unperceived uneven terrains, steps, and slopes.

DOI [BibTex]

DOI [BibTex]


Horse-Like Walking, Trotting, and Galloping derived from Kinematic Motion Primitives (kMPs) and their Application to Walk/Trot Transitions in a Compliant Quadruped Robot
Horse-Like Walking, Trotting, and Galloping derived from Kinematic Motion Primitives (kMPs) and their Application to Walk/Trot Transitions in a Compliant Quadruped Robot

Moro, F., Spröwitz, A., Tuleu, A., Vespignani, M., Tsagakiris, N. G., Ijspeert, A. J., Caldwell, D. G.

Biological Cybernetics, 107(3):309-320, 2013 (article)

Abstract
This manuscript proposes a method to directly transfer the features of horse walking, trotting, and galloping to a quadruped robot, with the aim of creating a much more natural (horse-like) locomotion profile. A principal component analysis on horse joint trajectories shows that walk, trot, and gallop can be described by a set of four kinematic Motion Primitives (kMPs). These kMPs are used to generate valid, stable gaits that are tested on a compliant quadruped robot. Tests on the effects of gait frequency scaling as follows: results indicate a speed optimal walking frequency around 3.4 Hz, and an optimal trotting frequency around 4 Hz. Following, a criterion to synthesize gait transitions is proposed, and the walk/trot transitions are successfully tested on the robot. The performance of the robot when the transitions are scaled in frequency is evaluated by means of roll and pitch angle phase plots.

DOI [BibTex]

DOI [BibTex]