Viscous Damping in Legged Locomotionposa/DynamicWalking2020/636...Viscous Damping in Legged...
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Viscous Damping in Legged Locomotion An Mo 1 , Fabio Izzi 1,2 , Daniel F. B. Haeufle 2 and Alexander Badri-Spr¨ owitz 1 1 Dynamic Locomotion Group, Max Planck Institute for Intelligent Systems, Stuttgart, Germany 2 Hertie-Institute for Clinical Brain Research, University of T¨ ubingen, T¨ ubingen, Germany Email: [email protected], [email protected], daniel.haeufl[email protected], [email protected] Damping likely plays an essential role in legged animal locomotion, but remains an insufficiently understood mech- anism. 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 [1, 2]. Recent legged robots exploit virtual damping as part of a virtual compliance controller [3]: actively produced and sensor-controlled negative actuator work. Virtual damping requires high-frequency force control loops, and precise timing to identify loading conditions during touch-down and take- off events. Virtual damping systems must feature high-power actuators mechanically and electrically capable of producing negative power, and absorbing negative power peaks. Mechan- ical damper leg configurations can act instantaneously and without the need for sensing and control feedback, similar to springs [4] (Fig. 1A). Dampers can also share impact loads with leg designs featuring parallel actuator and spring configurations [5]. However, only a few implementations of mechanical damped-systems exist in robotic legged locomo- tion [6]. The requirements for mechanical dampers are not yet defined, and it remains unknown how the expected benefits from mechanical damping transfer into practice. Real-world effects such as unsprung mass impact dynamics and nonlinear effects of segmented leg designs shape the stance-phase loco- motion dynamics and might interfere with mechanical damper implementations. We want to understand how physical damping can be exploited for locomotion tasks [7]. We study the effect of mechanical damping on the total energy of the leg-system and quantify the dissipated energy within one drop cycle— from touch-down to lift-off—for different drop heights and at different damping rates. The simplified drop experiment cap- tures the core aspects of the more complex legged locomotion task: negotiating ground contact, including uncertainties. With a wide parameter space to explore, we combine insights both from numerical simulations and hardware experiments. In a numerical simulation, we implemented a 2-segment leg model with a passive spring-damper element at the knee-joint (Fig.1A). We characterised this system under different drop conditions: drop height, damping rate, and damping strategy. The simulation results indicate that an adjustable and viscous damper is desired to reject perturbations of the system’s total energy due to variations in the drop height. We examined how our predictions from the numerical simulation relate to hardware experiments (Fig. 1C). We sep- Fig. 1: (A) 2-segment leg model with parallel spring-damper element mounted at the knee joint. (B) Example of work loop for different damping settings – data from hardware experiments. (C) High-speed snapshots of the hardware set-up, dropped onto force sensor. arated the measured dissipated energy into its components by experimental design. The recorded work loops (Fig. 1B) allowed us to characterise the dissipation from the early impact (unsprung-mass effects), viscous damping, Coulomb damping, and damping adjustments individually, and qualita- tively. We also observed that the damping characteristics of mechanical dampers are complex and mostly dependent on the impact’s loading conditions, and mechanical configura- tion. Hence we emphasise the importance of characterising mechanical dampers during real legged impacts to evaluate their effectiveness for compliant legged locomotion. REFERENCES [1] Z. Shen and J. Seipel, “A fundamental mechanism of legged locomotion with hip torque and leg damping,” Bioinspiration & biomimetics, vol. 7, no. 4, p. 046 010, 2012. [2] K. T. Kalveram, D. F. B. Haeufle, A. Seyfarth, and S. Grimmer, “Energy management that generates terrain following versus apex-preserving hopping in man and machine.,” Biological Cybernetics, vol. 106, no. 1, pp. 1–13, 2012. [3] F. Grimminger, A. Meduri, M. Khadiv, et al., “An Open Force-Controlled Modular Robot Architecture for Legged Locomotion Research,” RA-L, accepted in, 2020. [4] A. Spr¨ owitz, A. Tuleu, M. Vespignani, et al., “Towards dynamic trot gait locomotion: Design, control, and experiments with cheetah-cub, a compliant quadruped robot,” The International Journal of Robotics Research, vol. 32, no. 8, pp. 932–950, 2013. [5] F. Ruppert and A. Badri-Spr¨ owitz, “Series Elastic Behavior of Biarticular Muscle- Tendon Structure in a Robotic Leg,” Frontiers in Neurorobotics, vol. 13, p. 64, Aug. 2019. [6] E. Garcia, J. C. Arevalo, G. Munoz, and P. Gonzalez-de-Santos, “Combining series elastic actuation and magneto-rheological damping for the control of agile locomotion,” Robotics and Autonomous Systems, vol. 59, no. 10, pp. 827–839, 2011. [7] A. Mo, F. Izzi, D. F. B. Haeufle, and A. Badri-Spr¨ owitz, “Effective viscous damping enables morphological computation in legged locomotion,” Submitted.
Transcript of Viscous Damping in Legged Locomotionposa/DynamicWalking2020/636...Viscous Damping in Legged...
Viscous Damping in Legged LocomotionAn Mo1, Fabio Izzi1,2, Daniel F. B. Haeufle 2 and Alexander Badri-Sprowitz1
1Dynamic Locomotion Group, Max Planck Institute for Intelligent Systems, Stuttgart, Germany2Hertie-Institute for Clinical Brain Research, University of Tubingen, Tubingen, Germany
Email: [email protected], [email protected], [email protected], [email protected]
Damping likely plays an essential role in legged animallocomotion, but remains an insufficiently understood mech-anism. Intrinsic damping muscle forces can potentially addto the joint torque output during unexpected impacts, stabilisemovements, convert the system’s energy, and reject unexpectedperturbations [1, 2].
Recent legged robots exploit virtual damping as part ofa virtual compliance controller [3]: actively produced andsensor-controlled negative actuator work. Virtual dampingrequires high-frequency force control loops, and precise timingto identify loading conditions during touch-down and take-off events. Virtual damping systems must feature high-poweractuators mechanically and electrically capable of producingnegative power, and absorbing negative power peaks. Mechan-ical damper leg configurations can act instantaneously andwithout the need for sensing and control feedback, similarto springs [4] (Fig. 1A). Dampers can also share impactloads with leg designs featuring parallel actuator and springconfigurations [5]. However, only a few implementations ofmechanical damped-systems exist in robotic legged locomo-tion [6]. The requirements for mechanical dampers are not yetdefined, and it remains unknown how the expected benefitsfrom mechanical damping transfer into practice. Real-worldeffects such as unsprung mass impact dynamics and nonlineareffects of segmented leg designs shape the stance-phase loco-motion dynamics and might interfere with mechanical damperimplementations.
We want to understand how physical damping can beexploited for locomotion tasks [7]. We study the effect ofmechanical damping on the total energy of the leg-systemand quantify the dissipated energy within one drop cycle—from touch-down to lift-off—for different drop heights and atdifferent damping rates. The simplified drop experiment cap-tures the core aspects of the more complex legged locomotiontask: negotiating ground contact, including uncertainties. Witha wide parameter space to explore, we combine insights bothfrom numerical simulations and hardware experiments.
In a numerical simulation, we implemented a 2-segment legmodel with a passive spring-damper element at the knee-joint(Fig. 1A). We characterised this system under different dropconditions: drop height, damping rate, and damping strategy.The simulation results indicate that an adjustable and viscousdamper is desired to reject perturbations of the system’s totalenergy due to variations in the drop height.
We examined how our predictions from the numericalsimulation relate to hardware experiments (Fig. 1C). We sep-
Fig. 1: (A) 2-segment leg model with parallel spring-damper element mountedat the knee joint. (B) Example of work loop for different damping settings –data from hardware experiments. (C) High-speed snapshots of the hardwareset-up, dropped onto force sensor.
arated the measured dissipated energy into its componentsby experimental design. The recorded work loops (Fig. 1B)allowed us to characterise the dissipation from the earlyimpact (unsprung-mass effects), viscous damping, Coulombdamping, and damping adjustments individually, and qualita-tively. We also observed that the damping characteristics ofmechanical dampers are complex and mostly dependent onthe impact’s loading conditions, and mechanical configura-tion. Hence we emphasise the importance of characterisingmechanical dampers during real legged impacts to evaluatetheir effectiveness for compliant legged locomotion.
REFERENCES[1] Z. Shen and J. Seipel, “A fundamental mechanism of legged locomotion with hip
torque and leg damping,” Bioinspiration & biomimetics, vol. 7, no. 4, p. 046 010,2012.
[2] K. T. Kalveram, D. F. B. Haeufle, A. Seyfarth, and S. Grimmer, “Energymanagement that generates terrain following versus apex-preserving hopping inman and machine.,” Biological Cybernetics, vol. 106, no. 1, pp. 1–13, 2012.
[3] F. Grimminger, A. Meduri, M. Khadiv, et al., “An Open Force-Controlled ModularRobot Architecture for Legged Locomotion Research,” RA-L, accepted in, 2020.
[4] A. Sprowitz, A. Tuleu, M. Vespignani, et al., “Towards dynamic trot gaitlocomotion: Design, control, and experiments with cheetah-cub, a compliantquadruped robot,” The International Journal of Robotics Research, vol. 32, no. 8,pp. 932–950, 2013.
[5] F. Ruppert and A. Badri-Sprowitz, “Series Elastic Behavior of Biarticular Muscle-Tendon Structure in a Robotic Leg,” Frontiers in Neurorobotics, vol. 13, p. 64,Aug. 2019.
[6] E. Garcia, J. C. Arevalo, G. Munoz, and P. Gonzalez-de-Santos, “Combiningseries elastic actuation and magneto-rheological damping for the control of agilelocomotion,” Robotics and Autonomous Systems, vol. 59, no. 10, pp. 827–839,2011.
[7] A. Mo, F. Izzi, D. F. B. Haeufle, and A. Badri-Sprowitz, “Effective viscousdamping enables morphological computation in legged locomotion,” Submitted.
