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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.

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References

Figures

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Fig. 1

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

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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.

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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.

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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.

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Fig. 4

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

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Fig. 6

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

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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

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Fig. 8

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

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Fig. 9

Frequency response measurements of the damping force of the magnetorheological damper

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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

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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.

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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.

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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

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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

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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

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Fig. 7

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

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