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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]

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]

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]