31 results
(View BibTeX file of all listed publications)
2023
Virtual pivot point in human walking: always experimentally observed but simulations suggest it may not be necessary for stability
Schreff, L., Haeufle, D. F. B., Badri-Spröwitz, A., Vielemeyer, J., Müller, R.
Journal of Biomechanics, 153, May 2023 (article)
The intersection of ground reaction forces near a point above the center of mass has been observed in computer simulation models and human walking experiments. Observed so ubiquitously, the intersection point (IP) is commonly assumed to provide postural stability for bipedal walking. In this study, we challenge this assumption by questioning if walking without an IP is possible. Deriving gaits with a neuromuscular reflex model through multi-stage optimization, we found stable walking patterns that show no signs of the IP-typical intersection of ground reaction forces. The non-IP gaits found are stable and successfully rejected step-down perturbations, which indicates that an IP is not necessary for locomotion robustness or postural stability. A collision-based analysis shows that non-IP gaits feature center of mass (CoM) dynamics with vectors of the CoM velocity and ground reaction force increasingly opposing each other, indicating an increased mechanical cost of transport. Although our computer simulation results have yet to be confirmed through experimental studies, they already indicate that the role of the IP in postural stability should be further investigated. Moreover, our observations on the CoM dynamics and gait efficiency suggest that the IP may have an alternative or additional function that should be considered.
Muscle prestimulation tunes velocity preflex in simulated perturbed hopping
Izzi, F., Mo, A., Schmitt, S., Badri-Spröwitz, A., Häufle, D.
Scientific Reports, 13, pages: 4559, Nature Publishing Group, March 2023 (article)
Muscle fibres possess unique visco-elastic properties, which generate a stabilising zero-delay response to unexpected perturbations. This instantaneous response—termed “preflex”—mitigates neuro-transmission delays, which are hazardous during fast locomotion due to the short stance duration. While the elastic contribution to preflexes has been studied extensively, the function of fibre viscosity due to the force–velocity relation remains unknown. In this study, we present a novel approach to isolate and quantify the preflex force produced by the force–velocity relation in musculo-skeletal computer simulations. We used our approach to analyse the muscle response to ground-level perturbations in simulated vertical hopping. Our analysis focused on the preflex-phase—the first 30 ms after impact—where neuronal delays render a controlled response impossible. We found that muscle force at impact and dissipated energy increase with perturbation height, helping reject the perturbations. However, the muscle fibres reject only 15% of step-down perturbation energy with constant stimulation. An open-loop rising stimulation, observed in locomotion experiments, amplified the regulatory effects of the muscle fibre’s force–velocity relation, resulting in 68% perturbation energy rejection. We conclude that open-loop neuronal tuning of muscle activity around impact allows for adequate feed-forward tuning of muscle fibre viscous capacity, facilitating energy adjustment to unexpected ground-level perturbations.
Slack-based tunable damping leads to a trade-off between robustness and efficiency in legged locomotion
Mo, A., Izzi, F., Gönen, E. C., Häufle, D., Badri-Spröwitz, A.
Scientific Reports, 13, pages: 3290, Nature Publishing Group, February 2023 (article)
Animals run robustly in diverse terrain. This locomotion robustness is puzzling because axon conduction velocity is limited to a few ten meters per second. If reflex loops deliver sensory information with significant delays, one would expect a destabilizing effect on sensorimotor control. Hence, an alternative explanation describes a hierarchical structure of low-level adaptive mechanics and high-level sensorimotor control to help mitigate the effects of transmission delays. Motivated by the concept of an adaptive mechanism triggering an immediate response, we developed a tunable physical damper system. Our mechanism combines a tendon with adjustable slackness connected to a physical damper. The slack damper allows adjustment of damping force, onset timing, effective stroke, and energy dissipation. We characterize the slack damper mechanism mounted to a legged robot controlled in open-loop mode. The robot hops vertically and planar over varying terrains and perturbations. During forward hopping, slack-based damping improves faster perturbation recovery (up to 170%) at higher energetic cost (27%). The tunable slack mechanism auto-engages the damper during perturbations, leading to a perturbation-trigger damping, improving robustness at minimum energetic cost. With the results from the slack damper mechanism, we propose a new functional interpretation of animals' redundant muscle tendons as tunable dampers.
Muscle Preflex Response to Perturbations in locomotion: In-vitro experiments and simulations with realistic boundary conditions
Araz, M., Weidner, S., Izzi, F., Badri-Spröwitz, A., Siebert, T., Haeufle, D. F. B.
Frontiers in Bioengineering and Biotechnology, 11, 2023 (article)
Neuromuscular control loops feature substantial communication delays, but mammals run robustly even in the most adverse conditions. In-vivo experiments and computer simulation results suggest that muscles’ preflex—an immediate mechanical response to a perturbation—could be the critical contributor. Muscle preflexes act within a few milliseconds, an order of magnitude faster than neural reflexes. Their short-lasting activity makes mechanical preflexes hard to quantify in-vivo. Muscle models, on the other hand, require further improvement of their prediction accuracy during the non-standard conditions of perturbed locomotion. Additionally, muscles mechanically adapt by increased damping force. Our study aims to quantify the mechanical preflex work and test its mechanical force adaptation. We performed in-vitro experiments with biological muscle fibers under physiological boundary conditions, which we determined in computer simulations of perturbed hopping. Our findings show that muscles initially resist impacts with a stereotypical sti↵ness response—identified as short-range sti↵ness—regardless of the exact perturbation condition. We then observe a velocity adaptation to the force related to the amount of perturbation. The main contributor to the preflex work adaptation is not the force di↵erence but the muscle fiber stretch di↵erence. We find that both muscle sti↵ness and damping are activity-dependent properties. These results indicate that neural control could tune the preflex properties of muscles in expectation of ground conditions leading to previously inexplicable neuromuscular adaptation speeds.
2022
Physically Modelling Fluid- and Soft-tissue Mechanics of Lumbosacral Intraspinal Mechanosensing in Avians
Mo, A., Kamska, V., Bribiesca-Contreras, F., Hauptmann, J., Daley, M., Badri-Spröwitz, A.
arxiv, December 2022 (article) Submitted
The lumbosacral organ (LSO) is a lumbosacral spinal canal morphology that is universally and uniquely found in birds. Recent studies suggested an intraspinal mechanosensor function that relies on the compliant motion of soft tissue in the spinal cord fluid. It has not yet been possible to observe LSO soft tissue motion in vivo due to limitations of imaging technologies. As an alternative approach, we developed an artificial biophysical model of the LSO, and characterize the dynamic responses of this model when entrained by external motion. The parametric model incorporates morphological and material properties of the LSO. We varied the model's parameters to study the influence of individual features on the system response. We characterized the system in a locomotion simulator, producing vertical oscillations similar to the trunk motions. We show how morphological and material properties effectively shape the system's oscillation characteristics. We conclude that external oscillations could entrain the soft tissue of the intraspinal lumbosacral organ during locomotion, consistent with recently proposed sensing mechanisms.
Learning plastic matching of robot dynamics in closed-loop central pattern generators
Ruppert, F., Badri-Spröwitz, A.
Nature Machine Intelligence, 4(7):652-660, July 2022 (article)
Animals achieve agile locomotion performance with reduced control effort and energy efficiency by leveraging compliance in their muscles and tendons. However, it is not known how biological locomotion controllers learn to leverage the intelligence embodied in their leg mechanics. Here we present a framework to match control patterns and mechanics based on the concept of short-term elasticity and long-term plasticity. Inspired by animals, we design a robot, Morti, with passive elastic legs. The quadruped robot Morti is controlled by a bioinspired closed-loop central pattern generator that is designed to elastically mitigate short-term perturbations using sparse contact feedback. By minimizing the amount of corrective feedback on the long term, Morti learns to match the controller to its mechanics and learns to walk within 1 h. By leveraging the advantages of its mechanics, Morti improves its energy efficiency by 42% without explicit minimization in the cost function.
BirdBot achieves energy-efficient gait with minimal control using avian-inspired leg clutching
Badri-Spröwitz, A., Sarvestani, A. A., Sitti, M., Daley, M. A.
Science Robotics, 7(64):eabg4055, March 2022 (article)
Designers of legged robots are challenged with creating mechanisms that allow energy-efficient locomotion with robust and minimalistic control. Sources of high energy costs in legged robots include the rapid loading and high forces required to support the robot’s mass during stance and the rapid cycling of the leg’s state between stance and swing phases. Here, we demonstrate an avian-inspired robot leg design, BirdBot, that challenges the reliance on rapid feedback control for joint coordination and replaces active control with intrinsic, mechanical coupling, reminiscent of a self-engaging and disengaging clutch. A spring tendon network rapidly switches the leg’s slack segments into a loadable state at touchdown, distributes load among joints, enables rapid disengagement at toe-off through elastically stored energy, and coordinates swing leg flexion. A bistable joint mediates the spring tendon network’s disengagement at the end of stance, powered by stance phase leg angle progression. We show reduced knee-flexing torque to a 10th of what is required for a nonclutching, parallel-elastic leg design with the same kinematics, whereas spring-based compliance extends the leg in stance phase. These mechanisms enable bipedal locomotion with four robot actuators under feedforward control, with high energy efficiency. The robot offers a physical model demonstration of an avian-inspired, multiarticular elastic coupling mechanism that can achieve self-stable, robust, and economic legged locomotion with simple control and no sensory feedback. The proposed design is scalable, allowing the design of large legged robots. BirdBot demonstrates a mechanism for self-engaging and disengaging parallel elastic legs that are contact-triggered by the foot’s own lever-arm action.
A Novel Spider-Inspired Rotary-Rolling Diaphragm Actuator with Linear Torque Characteristic and High Mechanical Efficiency
Hepp, J., Badri-Spröwitz, A.
Soft Robotics, 19(2):364-375, Mary Ann Liebert, Inc., 2022 (article)
2021
Hybrid Parallel Compliance Allows Robots to Operate With Sensorimotor Delays and Low Control Frequencies
Milad Shafiee Ashtiani, , Alborz Aghamaleki Sarvestani, , Badri-Spröwitz, A.
Frontiers in Robotics and AI, 8(na):645748, (Editors: Dai Owaki, Tohoku University, Japan), June 2021 (article)
Animals locomote robustly and agile, albeit significant sensorimotor delays of their nervous system and the harsh loading conditions resulting from repeated, high-frequent impacts. The engineered sensorimotor control in legged robots is implemented with high control frequencies, often in the kilohertz range. Consequently, robot sensors and actuators can be polled within a few milliseconds. However, especially at harsh impacts with unknown touch-down timing, controllers of legged robots can become unstable, while animals are seemingly not affected. We examine this discrepancy and suggest and implement a hybrid system consisting of a parallel compliant leg joint with varying amounts of passive stiffness and a virtual leg length controller. We present systematic experiments both in computer simulation and robot hardware. Our system shows previously unseen robustness, in the presence of sensorimotor delays up to 60 ms, or control frequencies as low as 20 Hz, for a drop landing task from 1.3 leg lengths high and with a compliance ratio (fraction of physical stiffness of the sum of virtual and physical stiffness) of 0.7. In computer simulations, we report successful drop-landings from 3.8 leg lengths (1.2 m) for a 2 kg quadruped robot with 100 Hz control frequency and a sensorimotor delay of 35 ms.
2020
Virtual Point Control for Step-down Perturbations and Downhill Slopes in Bipedal Running
Drama, Ö., Badri-Spröwitz, A.
Frontiers in Bioengineering and Biotechnology, 8, pages: 586534, Frontiers Media, December 2020 (article)
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.
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(11):200570, November 2020 (article)
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.
3D Anatomy of the Quail Lumbosacral Spinal Canal—Implications for Putative Mechanosensory Function
Kamska, V., Daley, M., Badri-Spröwitz, A.
Integrative Organismal Biology, 2(1):obaa037, Oxford University Press, October 2020 (article)
Birds are diverse and agile vertebrates capable of aerial, terrestrial, aquatic, and arboreal locomotion. Evidence suggests that birds possess a novel balance sensing organ in the lumbosacral spinal canal, a structure referred to as the “lumbosacral organ” (LSO), which may contribute to their locomotor agility and evolutionary success. The mechanosensing mechanism of this organ remains unclear. Here we quantify the 3D anatomy of the lumbosacral region of the common quail, focusing on establishing the geometric and biomechanical properties relevant to potential mechanosensing functions. We combine digital and classic dissection to create a 3D anatomical model of the quail LSO and estimate the capacity for displacement and deformation of the soft tissues. We observe a hammock-like network of denticulate ligaments supporting the lumbosacral spinal cord, with a close association between the accessory lobes and ligamentous intersections. The relatively dense glycogen body has the potential to apply loads sufficient to pre-stress denticulate ligaments, enabling external accelerations to excite tuned oscillations in the LSO soft tissue, leading to strain-based mechanosensing in the accessory lobe neurons. Considering these anatomical features together, the structure of the LSO is reminiscent of a mass-spring-based accelerometer.
A Learnable Safety Measure
Heim, S., Rohr, A. V., Trimpe, S., Badri-Spröwitz, A.
Proceedings of the Conference on Robot Learning, 100, pages: 627-639, Proceedings of Machine Learning Research, (Editors: Kaelbling, Leslie Pack and Kragic, Danica and Sugiura, Komei), PMLR, Conference on Robot Learning, October 2020 (article)
A little damping goes a long way: a simulation study of how damping influences task-level stability in running
Heim, S., Millard, M., Le Mouel, C., Badri-Spröwitz, A.
Biology Letters, 16(9):20200467, September 2020 (article)
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.
Effective Viscous Damping Enables Morphological Computation in Legged Locomotion
Mo, A., Izzi, F., Haeufle, D. F. B., Badri-Spröwitz, A.
Frontiers in Robotics and AI, 7, pages: 110, August 2020 (article)
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.
An Open Torque-Controlled Modular Robot Architecture for Legged Locomotion Research
Grimminger, F., Meduri, A., Khadiv, M., Viereck, J., Wüthrich, M., Naveau, M., Berenz, V., Heim, S., Widmaier, F., Flayols, T., Fiene, J., Badri-Spröwitz, A., Righetti, L.
IEEE Robotics and Automation Letters, 5(2):3650-3657, IEEE, April 2020 (article)
Trunk pitch oscillations for energy trade-offs in bipedal running birds and robots
Drama, Ö., Badri-Spröwitz, A.
Bioinspiration & Biomimetics, 15(3):036013, March 2020 (article)
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.
2019
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)
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)
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.
2018
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)
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. [...]
2017
Spinal joint compliance and actuation in a simulated bounding quadruped robot
Pouya, S., Khodabakhsh, M., Sproewitz, A., Ijspeert, A.
Autonomous Robots, pages: 437–452, Kluwer Academic Publishers, Springer, Dordrecht, New York, NY, February 2017 (article)
2016
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)
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)
2015
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)
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.
2014
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)
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.
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)
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.
2013
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)
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.
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)
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.
2010
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)
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.
2008
Learning to Move in Modular Robots using Central Pattern Generators and Online Optimization
Spröwitz, A., Moeckel, R., Maye, J., Ijspeert, A. J.
The International Journal of Robotics Research, 27(3-4):423-443, 2008 (article)
This article addresses the problem of how modular robotics systems, i.e. systems composed of multiple modules that can be configured into different robotic structures, can learn to locomote. In particular, we tackle the problems of online learning, that is, learning while moving, and the problem of dealing with unknown arbitrary robotic structures. We propose a framework for learning locomotion controllers based on two components: a central pattern generator (CPG) and a gradient-free optimization algorithm referred to as Powell's method. The CPG is implemented as a system of coupled nonlinear oscillators in our YaMoR modular robotic system, with one oscillator per module. The nonlinear oscillators are coupled together across modules using Bluetooth communication to obtain specific gaits, i.e. synchronized patterns of oscillations among modules. Online learning involves running the Powell optimization algorithm in parallel with the CPG model, with the speed of locomotion being the criterion to be optimized. Interesting aspects of the optimization include the fact that it is carried out online, the robots do not require stopping or resetting and it is fast. We present results showing the interesting properties of this framework for a modular robotic system. In particular, our CPG model can readily be implemented in a distributed system, it is computationally cheap, it exhibits limit cycle behavior (temporary perturbations are rapidly forgotten), it produces smooth trajectories even when control parameters are abruptly changed and it is robust against imperfect communication among modules. We also present results of learning to move with three different robot structures. Interesting locomotion modes are obtained after running the optimization for less than 60 minutes.
2006
Passive compliance for a RC servo-controlled bouncing robot
Meyer, F., Spröwitz, A., Berthouze, L.
Advanced Robotics, 20(8):953-961, 2006 (article)
A novel and low-cost passively compliant mechanism is described that can be used with RC servos to actuate legged robots in tasks involving high dynamic loads such as bouncing. Compliance is achieved by combining visco-elastic material and metal parts. Joint response to dynamic loads is evaluated using real-world experiments and force data are obtained from a Lagrangian analysis of the system. The experimental results demonstrate the applicative potential of this mechanism.