0
Research Papers

Magnetorheologically Damped Compliant Foot for Legged Robotic Application

[+] Author and Article Information
Esa Kostamo

Aalto University School of Engineering,
Sähkömiehentie 4,
Espoo 02150, Finland
e-mail: esa.kostamo@aalto.fi

Michele Focchi

e-mail: michele.focchi@iit.it

Emanuele Guglielmino

e-mail: emanuele.guglielmino@iit.it
Department of Advanced Robotics,
Istituto Italiano di Tecnologia,
Morego 30,
Genova 16163, Italy

Jari Kostamo

Aalto University School of Engineering,
Sähkömiehentie 4,
Espoo 02150, Finland
e-mail: jari.kostamo@aalto.fi

Claudio Semini

Department of Advanced Robotics,
Istituto Italiano di Tecnologia,
Morego 30,
Genova 16163, Italy
e-mail: claudio.semini@iit.it

Jonas Buchli

Institute of Robotics and Intelligent Systems,
ETH Zurich, Tannenstr. 3,
Zürich 8092, Switzerland
e-mail: buchlij@ethz.ch

Matti Pietola

Aalto University School of Engineering,
Otakaari 4,
Espoo 02150, Finland
e-mail: matti.pietola@aalto.fi

Darwin Caldwell

Department of Advanced Robotics,
Istituto Italiano di Tecnologia,
Morego 30,
Genova 16163, Italy
e-mail: darwin.caldwell@iit.it

Contributed by the Design Innovation and Devices of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 15, 2012; final manuscript received October 17, 2013; published online November 26, 2013. Assoc. Editor: Alexander Slocum.

J. Mech. Des 136(2), 021003 (Nov 26, 2013) (11 pages) Paper No: MD-12-1564; doi: 10.1115/1.4025966 History: Received November 15, 2012; Revised October 17, 2013

This paper presents an innovative solution for bounce reduction between a robotic leg and the ground by means of a semi-active compliant foot. The aim of this work is to enhance the controllability and the balance of a legged robot by improving the traction between the foot tip and the ground. The compliant foot is custom-designed for quadruped walking robots and it consists of a linear spring and a magnetorheological (MR) damper. By utilizing magnetorheological technology in the damper element, the damping coefficient of the compliant foot can be altered across a wide range without any additional moving parts. The content of this paper is twofold. In the first part the design, a prototype and a model of the semi-active compliant foot are presented, and the performance of the magnetorheological damper is experimentally studied in quasi-static and dynamic cases. Based on the quasi-static measurements, the damping force can be controlled in a range from 15 N to 310 N. From the frequency response measurements, it can be shown that the controllable damping force has a bandwidth higher than 100 Hz. The second part of this paper presents an online stiffness identification algorithm and a mathematical model of the robotic leg. A critical damping control law is proposed and implemented in order to demonstrate the effectiveness of the device that makes use of smart materials. Further on, drop tests have been carried out to assess the performance of the proposed control law in terms of bounce reduction and settling time. The results demonstrate that by real-time control of the damping force 98% bounce reduction with settling time of 170 ms can be achieved.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Robinson, D. W., Pratt, J. E., Paluska, D. J., and Pratt, G. A., 1999, “Series Elastic Actuator Development for a Biomimetic Walking Robot,” Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Atlanta, pp. 561–568
Buchli, J., Kalakrishnan, M., Mistry, M., Pastor, P., and Schaal, S., 2009, “Compliant Quadruped Locomotion Over Rough Terrain,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), St. Louis, pp. 814–820.
Focchi, M., 2013, “Strategies to Improve the Impedance Control Performance of a Quadruped Robot,” Ph.D thesis, Istituto Italiano di Tecnologia, Genoa, Italy.
Pratt, G. A., and Williamson, M. M., 1995, “Series Elastic Actuators,” Proceedings of IEEE—Int. Workshop on Intelligent Robots and Systems (IROS'95), Pittsburgh, PA., pp. 399–406.
Tonietti, G., Schiavi, R., and Bicchi, A., 2005, “Design and Control of a Variable Stiffness Actuator for Safe and Fast Physical Human/Robot Interaction,” Proceedings of IEEE—International Conference Robotics and Automation (ICRA’05), Barcelona, Spain, pp. 526–531.
Hurst, J. W., Chestnutt, J., and Rizzi, A., 2004, “An Actuator With Mechanically Adjustable Series Compliance,” Carnegie Mellon Robotics Institute, Technical Report No. CMU-RI-TR-24. (Available at http://www.ri.cmu.edu/pub_files/pub4/hurst_jonathan_w_2004_1/hurst_jonathan_w_2004_1.pdf)
Chou, C.-P., and Hannaford, B., 1996, “Measurement and Modeling of McKibben Pneumatic Artificial Muscles,” IEEE Trans. Rob. Autom., 12(1), pp. 90–102. [CrossRef]
Verrelst, B., Van Ham, R., Vanderborght, B., Daerden, F., and Lefeber, D., 2005, “The Pneumatic Biped LUCY Actuated With Pleated Pneumatic Artificial Muscles,” Auton. Rob., 18(2), pp. 201–213. [CrossRef]
Klute, G. K., Czerniecki, J. M., and Hannaford, B., 2002, “Artificial Muscles: Actuators for Biorobotic Systems,” Int. J. Rob. Res., 21(4), pp. 295–309. [CrossRef]
Chee–Meng, C., Geok–Soon, H., and Wei, Z., 2004, “Series Damper Actuator: A Novel Force/Torque Control Actuator,” 4th IEEE/RAS International Conference on Humanoid Robots, Santa Monica, pp. 533–546.
Laffranchi, M., Tsagarakis, N., and Caldwell, D., 2010, “A Variable Physical Damping Actuator (VDPA) for Compliant Robotic Joints,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, Alaska, pp. 1668–1674.
Semini, C., Tsagarakis, N. G., Guglielmino, E., Focchi, M., Cannella, F., and Caldwell, D. G., 2011, “Design of HyQ—A Hydraulically and Electrically Actuated Quadruped Robot,” J. Syst. Control Eng., 225(6), pp. 831–849. [CrossRef]
Semini, C., 2010, “HyQ—Design and Development of a Hydraulically Actuated Quadruped Robot,” Ph.D. thesis, Italian Institute of Technology and University of Genoa, Italy.
Jalili, N., 2002, “A Comparative Study and Analysis of Semi-Active Vibration-Control Systems,” J. Vib. Acoust., 124(4), pp. 593–605. [CrossRef]
Bossis, G., Lacis, S., Meunier, A., and Volkova, O., 2002, “Magnetorheological Fluids,” J. Magn. Magn. Mater., 252, pp. 224–228. [CrossRef]
Goncalves, F. D., Ahmadian, M., and Carlson, J. D., 2006, “Investigating the Magnetorheological Effect at High Flow Velocities,” Smart Mater. Struct., 15(1), pp. 75–85. [CrossRef]
Kostamo, J., Kostamo, E., Kajaste, J., and Pietola, M., 2008, “Magnetorheological (MR) Damper With a Fast Response Time,” Proceedings of FPMC 2008, Bath, UK, pp. 169–182.
Lord Corporation, 2009, “Magnetorheological Fluid MRF132DG,” Product specification.
Wilkinson, W. L., 1960, “Non-Newtonian Fluids: Fluid Mechanics, Mixing and Heat Transfer,” London Pergamon, pp. 50–54.
Mao, M., Young-Tai, W. H., and Wereley, N. M., 2007, “A Magnetorheological Damper With Bifold Valves for Shock and Vibration Mitigation,” J. Intell. Mater. Syst. Struct., 18, pp. 1227–1232. [CrossRef]
Bass, B. J., and Christenson, R. E., 2007, “System Identification of a 200 kN Magneto-Rheological Fluid Damper for Structural Control in Large-Scale Smart Structures,” Proceedings of American Control Conference, pp. 2690–2695.
Nguyen, Q.-H., and Choi, S.-B., 2009, “Optimal Design of a Vehicle Magnetorheological Damper Considering the Damping Force and Dynamic Range,” J. Smart Mater. Struct., 18(1), pp. 1–10. [CrossRef]
Siciliano, B., Sciavicco, L., Villani, L., and Oriolo, G., 2009, Robotics Modelling, Planning and Control, Springer, New York.
Franklin, G. F., Powell, J. D., and Emami-Naeini, A., 1993, Feedback Control of Dynamic Systems, Addison-Wesley Longman Publishing, Boston, MA.

Figures

Grahic Jump Location
Fig. 1

MRF-132DG magnetization characteristic curve [18] and yield stress as a function of magnetic field strength

Grahic Jump Location
Fig. 2

CAD cross-section view of the MR foot. Numbered components: (1) rubber coated foot tip, (2) spring, (3) piston shaft, (4) lower end cap, (5) seal, (6) sliding bushing, (7) MR fluid, (8) MR fluid gap, (9) solenoid, (10) piston, (11) cylinder, (12) upper end cap, (13) spring precompression adjustment nut, (14) spring precompression locking nut, (15) mounting component to the robotic leg.

Grahic Jump Location
Fig. 3

Solved FEMM model of the core parts of the magnetorheological damper at an electric current of 2 A. Numbered details: (3) piston shaft, (7) MR fluid, (8) MR fluid gap, (9) solenoid, (10) piston, (11) cylinder, (16) an illustration of the element that has been used to analyze the magnetic field strength distribution over the both MR fluid gaps. The numbering is equivalent with Fig. 2.

Grahic Jump Location
Fig. 4

Simulated magnetic field strengths on the dashed line (16) in Fig. 4. Simulations are calculated with four different electric currents.

Grahic Jump Location
Fig. 5

The balance of forces on a symmetrically locating rectangular fluid element with total height of 2 r, length of L, and width of b. In this illustration, h is the total height of the fluid gap, ΔP is the pressure difference over the fluid element, σr is the shear stress at the surface of the fluid element and σw is the shear stress at the wall of the fluid gap.

Grahic Jump Location
Fig. 6

Stress–strain machine setup to analyze quasi-static and dynamic properties of the MR damper

Grahic Jump Location
Fig. 7

Comparison of measured and simulated quasi-static force-velocity characteristics of MR damper for different electric current inputs (0–2 A)

Grahic Jump Location
Fig. 8

Measured and simulated damping force responses of the magnetorheological damper of the compliant foot as a function of the electric current

Grahic Jump Location
Fig. 9

Frequency response measurements of the damping force of the magnetorheological damper

Grahic Jump Location
Fig. 10

Picture of the HyQ robotic leg with the magnetorheological compliant foot attached to a vertically sliding test setup: (1) slider position encoder, (2) hip support, (3) knee support, (4) slider guide, (5) magnetorheological compliant foot, and (6) foot compression sensor

Grahic Jump Location
Fig. 11

(a) Spring-mass-damper equivalent of the robotic leg and (b) joint and task space coordinates of the degrees of freedom and forces

Grahic Jump Location
Fig. 12

Damped response of a second order spring-mass-damper system (solid), compression of the spring after the impact (dashed). Once the spring has recovered its rest length a mechanical end-stop prevents further extension.

Grahic Jump Location
Fig. 13

Drop test (0.3 m) for identification of kyy and dyy. Simulation with the identified parameters is illustrated with dashdot line and measured response with solid line.

Grahic Jump Location
Fig. 14

Critical damping law for the 0.1 m drop test with kratio = 10 (solid), 30 (dashed–dotted), 50 (dotted): first plot slider displacement, second plot damper force

Grahic Jump Location
Fig. 15

Critical damping law for the 0.2 m drop test with kratio = 10 (solid), 30 (dashed–dotted), 50 (dotted): first plot slider displacement, second plot damper force

Grahic Jump Location
Fig. 16

Critical damping law for the 0.3 m drop test with kratio = 10 (solid), 30 (dashed–dotted), 50 (dotted): first plot slider displacement, second plot damper force

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In