Variable stiffness and variable damping can play an important role in robot movement, particularly for legged robots such as bipedal walkers. Variable impedance also introduces new control problems, since there are more degrees of freedom to control, and the resulting robot has more complex dynamics. In this paper, we introduce novel design and fabrication methodologies that are capable of producing cost effective hardware prototypes suitable for investigating the efficacy of impedance modulation. We present two variable impedance bipedal platforms produced using a combination of waterjet cutting and 3D printing, and a novel fused deposition modeling (FDM) 3D printing based method for producing hybrid plastic/metal parts. We evaluate walking trajectories at different speeds and stiffness levels.

References

References
1.
Collins
,
S.
,
Ruina
,
A.
,
Tedrake
,
R.
, and
Wisse
,
M.
,
2005
, “
Efficient Bipedal Robots Based on Passive-Dynamic Walkers
,”
Science
,
307
(
5712
), pp.
1082
1085
.
2.
Pratt
,
J.
,
2000
, “
Exploiting Inherent Robustness and Natural Dynamics in the Control of Bipedal Walking Robots
,” Ph.D. thesis, Computer Science Department, Massachusetts Institute of Technology, Cambridge, MA.
3.
Braun
,
D.
,
Petit
,
F.
,
Huber
,
F.
,
Haddadin
,
S.
,
van der Smagt
,
P.
,
Albu-Schaffer
,
A.
, and
Vijayakumar
,
S.
,
2013
, “
Robots Driven by Compliant Actuators: Optimal Control Under Actuation Constraints
,”
IEEE Trans. Rob.
,
29
(
5
), pp.
1085
1101
.
4.
Howard
,
M.
,
Braun
,
D.
, and
Vijayakumar
,
S.
,
2013
, “
Transferring Human Impedance Behavior to Heterogeneous Variable Impedance Actuators
,”
IEEE Trans. Rob.
,
29
(
4
), pp.
847
862
.
5.
Braun
,
D.
,
Howard
,
M.
, and
Vijayakumar
,
S.
,
2012
, “
Optimal Variable Stiffness Control: Formulation and Application to Explosive Movement Tasks
,”
Auton. Robots
,
33
(
3
), pp.
237
253
.
6.
Radulescu
,
A.
,
Howard
,
M.
,
Braun
,
D.
, and
Vijayakumar
,
S.
,
2012
, “
Exploiting Variable Physical Damping in Rapid Movement Tasks
,”
IEEE/ASME International Conference
on Advanced Intelligent Mechatronics (
AIM 2012
), Kachsiung, Taiwan, July 11–14, pp.
141
148
.
7.
Nakanishi
,
J.
,
Radulescu
,
A.
, and
Vijayakumar
,
S.
,
2013
, “
Spatio-Temporal Optimization of Multi-Phase Movements: Dealing With Contacts and Switching Dynamics
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS 2013
), Tokyo, Nov. 3–7, pp.
5100
5107
.
8.
Vanderborght
,
B.
,
Albu-Schäffer
,
A.
,
Bicchi
,
A.
,
Burdet
,
E.
,
Caldwell
,
D. G.
,
Carloni
,
R.
,
Catalano
,
M.
,
Eiberger
,
O.
,
Friedl
,
W.
,
Ganesh
,
G.
,
Garabini
,
G.
,
Grebenstein
,
M.
,
Grioli
,
G.
,
Haddadin
,
S.
,
Hoppner
,
H.
,
Jafari
,
A.
,
Laffranchi
,
M.
,
Lefeber
,
D.
,
Petit
,
F.
,
Stramigioli
,
S.
,
Tsagarakis
,
N.
,
Van Damme
,
M.
,
Van Ham
,
R.
,
Visser
,
L. C.
, and
Wolf
,
S.
,
2013
, “
Variable Impedance Actuators: A Review
,”
Rob. Auton. Syst.
,
61
(
12
), pp.
1601
1614
.
9.
Enoch
,
A.
,
Sutas
,
A.
,
Nakaoka
,
S.
, and
Vijayakumar
,
S.
,
2012
, “
BLUE: A Bipedal Robot With Variable Stiffness and Damping
,”
12th IEEE-RAS International Conference on Humanoid Robots
(
Humanoids 2012
), Osaka, Japan, Nov. 29–Dec. 1, pp.
487
494
.
10.
Mitrovic
,
D.
,
Klanke
,
S.
,
Howard
,
M.
, and
Vijayakumar
,
S.
,
2010
, “
Exploiting Sensorimotor Stochasticity for Learning Control of Variable Impedance Actuators
,”
10th IEEE-RAS International Conference on Humanoid Robots
(
Humanoids 2010
), Nashville, TN, Dec. 6–8, pp.
536
541
.
11.
Van Ham
,
R.
,
Vanderborght
,
B.
,
Van Damme
,
M.
,
Verrelse
,
B.
, and
Lefeber
,
D.
,
2007
, “
MACCEPA, the Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator: Design and Implementation in a Biped Robot
,”
Rob. Auton. Syst.
,
55
(
10
), pp.
761
768
.
12.
Jafari
,
A.
,
Tsagarakis
,
N. G.
,
Vanderborght
,
B.
, and
Caldwell
,
D. G.
,
2010
, “
A Novel Actuator With Adjustable Stiffness (AwAS)
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Taipei, Taiwan, Oct. 18–22, pp.
4201
4206
.
13.
Jafari
,
A.
,
Tsagarakis
,
N. G.
, and
Caldwell
,
D. G.
,
2011
, “
AwAS-II: A New Actuator With Adjustable Stiffness Based on the Novel Principle of Adaptable Pivot Point and Variable Lever Ratio
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Shanghai, May 9–13, pp.
4638
4643
.
14.
Morita
,
T.
, and
Sugano
,
S.
,
1995
, “
Design and Development of a New Robot Joint Using a Mechanical Impedance Adjuster
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Nagoya, Japan, May 21–27, pp.
2469
2475
.
15.
Morita
,
T.
, and
Sugano
,
S.
,
1995
, “
Development of One-DOF Robot Arm Equipped With Mechanical Impedance Adjuster
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Pittsburgh, PA, Aug. 5–9, pp.
407
412
.
16.
Choi
,
J.
,
Park
,
S.
,
Lee
,
W.
, and
Kang
,
S.
,
2008
, “
Design of a Robot Joint With Variable Stiffness
,”
IEEE International Conference on Robotics and Automation
(
ICRA 2008
), Pasadena, CA, May 19–23, pp.
1760
1765
.
17.
Tsagarakis
,
N.
,
Sardellitti
,
I.
, and
Caldwell
,
D.
,
2011
, “
A New Variable Stiffness Actuator (Compact-VSA): Design and Modelling
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS 2011
), San Francisco, CA, Sept. 25–30, pp.
378
383
.
18.
Wolf
,
S.
, and
Hirzinger
,
G.
,
2008
, “
A New Variable Stiffness Design: Matching Requirements of the Next Robot Generation
,”
IEEE International Conference on Robotics and Automation
(
IROS
), San Francisco, CA, Sept. 25–30, pp.
1741
1746
.
19.
Uemura
,
M.
, and
Kawamura
,
S.
,
2010
, “
A New Mechanical Structure for Adjustable Stiffness Devices With Lightweight and Small Size
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS 2010
), Taipei, Taiwan, Oct. 18–22, pp.
2364
2369
.
20.
Choi
,
J.
,
Hong
,
S.
,
Lee
,
W.
,
Kang
,
S.
, and
Kim
,
M.
,
2011
, “
A Robot Joint With Variable Stiffness Using Leaf Springs
,”
IEEE Trans. Rob.
,
27
(
2
), pp.
229
238
.
21.
Petit
,
F.
,
Chalon
,
M.
,
Friedl
,
W.
,
Grebenstein
,
M.
,
Schaffer
,
A.
, and
Hirzinger
,
G.
,
2010
, “
Bidirectional Antagonistic Variable Stiffness Actuation: Analysis, Design & Implementation
,”
IEEE International Conference on Robotics and Automation
(
ICRA 2010
), Anchorage, AK, May 3–7, pp.
4189
4196
.
22.
Laurin-Kovitz
,
K.
,
Colgate
,
J.
, and
Carnes
,
S.
,
1991
, “
Design of Components for Programmable Passive Impedance
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Sacramento, CA, Apr. 9–11, pp.
1476
1481
.
23.
Laffranchi
,
M.
,
Tsagarakis
,
N. G.
,
Caldwell
,
D. G.
, and
Sheffield
,
W. B.
,
2010
, “
A Variable Physical Damping Actuator (VPDA) for Compliant Robotic Joints
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Anchorage, AK, May 3–7, pp.
1668
1674
.
24.
Herr
,
H.
, and
Wilkenfeld
,
A.
,
2003
, “
User-Adaptive Control of a Magnetorheological Prosthetic Knee
,”
Ind. Robot
,
30
(
1
), pp.
42
55
.
25.
Umberger
,
B. R.
, and
Martin
,
P. E.
,
2007
, “
Mechanical Power and Efficiency of Level Walking With Different Stride Rates
,”
J. Exp. Biol.
,
210
(
Pt 18
), pp.
3255
3265
.
26.
Ker
,
R.
,
Bennett
,
M.
,
Bibby
,
S.
, and
Kester
,
R.
,
1987
, “
The Spring in the Arch of the Human Foot
,”
Nature
,
325
(
6100
), pp.
147
149
.
27.
Gefen
,
A.
,
2003
, “
The In Vivo Elastic Properties of the Plantar Fascia During the Contact Phase of Walking
,”
Foot Ankle Int.
,
24
(
3
), pp.
238
244
.
28.
Kappel-Bargas
,
A.
,
Woolf
,
R. D.
,
Cornwall
,
M. W.
, and
McPoil
,
T. G.
,
1998
, “
The Windlass Mechanism During Normal Walking and Passive First Metatarsophalangeal Joint Extension
,”
Clin. Biomech. (Bristol, Avon)
,
13
(
3
), pp.
190
194
.
29.
Coppelia Robotics, 2013, “
V-rep
,” Coppelia Robotics GmbH, Zurich, Switzerland, http://coppeliarobotics.com/
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