Abstract

The stiffness of robot legs greatly affects legged locomotion performance; tuning that stiffness, however, can be a costly and complex task. In this paper, we directly tune the stiffness of jumping robot legs using an origami-inspired laminate design and fabrication method. In addition to the stiffness coefficient described by Hooke’s law, the nonlinearity of the force-displacement curve can also be tuned by optimizing the geometry of the mechanism. Our method reduces the number of parts needed to realize legs with different stiffness while simplifying manual redesign effort, lowering the cost of legged robots while speeding up the design and optimization process. We have fabricated and tested the leg across six different stiffness profiles that vary both the nonlinearity and coefficient. Through a vertical jumping experiment actuated by a DC motor, we also show that proper tuning of the leg stiffness can result in an 18% improvement in lift-off speed and an increase of 19% in peak power output.

References

1.
Blickhan
,
R.
, and
Full
,
R.
,
1993
, “
Similarity in Multilegged Locomotion: Bouncing Like a Monopode
,”
J. Compar. Physiol. A
,
173
(
5
), pp.
509
517
.
2.
Full
,
R.
, and
Koditschek
,
D.
,
1999
, “
Templates and Anchors: Neuromechanical Hypotheses of Legged Locomotion on Land
,”
J. Exp. Biol.
,
202
(
23
), pp.
3325
3332
.
3.
Roberts
,
T. J.
, and
Azizi
,
E.
,
2011
, “
Flexible Mechanisms: The Diverse Roles of Biological Springs in Vertebrate Movement
,”
J. Exp. Biol.
,
214
(
3
), pp.
353
361
.
4.
Saranli
,
U.
,
Buehler
,
M.
, and
Koditschek
,
D. E.
,
2001
, “
RHex: A Simple and Highly Mobile Hexapod Robot
,”
Int. J. Robot. Res.
,
20
(
7
), pp.
616
631
.
5.
Kim
,
S.
,
Clark
,
J. E.
, and
Cutkosky
,
M. R.
,
2006
, “
iSprawl: Design and Tuning for High-Speed Autonomous Open-Loop Running
,”
Int. J. Robot. Res.
,
25
(
9
), pp.
903
912
.
6.
Birkmeyer
,
P.
,
Peterson
,
K.
, and
Fearing
,
R. S.
,
2009
, “
DASH: A Dynamic 16g Hexapedal Robot
,”
2009
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
St. Louis, MO
,
Oct. 10–15
,
IEEE
, pp.
2683
2689
.
7.
Spröwitz
,
A.
,
Tuleu
,
A.
,
Vespignani
,
M.
,
Ajallooeian
,
M.
,
Badri
,
E.
, and
Ijspeert
,
A. J.
,
2013
, “
Towards Dynamic Trot Gait Locomotion: Design, Control, and Experiments With Cheetah-Cub, A Compliant Quadruped Robot
,”
Int. J. Robot. Res.
,
32
(
8
), pp.
932
950
.
8.
Haldane
,
D. W.
,
Plecnik
,
M. M.
,
Yim
,
J. K.
, and
Fearing
,
R. S.
,
2016
, “
Robotic Vertical Jumping Agility Via Series-Elastic Power Modulation
,”
Sci. Robot.
,
1
(
1
), p.
eaag2048
.
9.
Hubicki
,
C.
,
Grimes
,
J.
,
Jones
,
M.
,
Renjewski
,
D.
,
Spröwitz
,
A.
,
Abate
,
A.
, and
Hurst
,
J.
,
2016
, “
ATRIAS: Design and Validation of a Tether-Free 3D-Capable Spring-Mass Bipedal Robot
,”
Int. J. Robot. Res.
,
35
(
12
), pp.
1497
1521
.
10.
Badri-Spröwitz
,
A.
,
Aghamaleki Sarvestani
,
A.
,
Sitti
,
M.
, and
Daley
,
M. A.
,
2022
, “
BirdBot Achieves Energy-Efficient Gait With Minimal Control Using Avian-Inspired Leg Clutching
,”
Sci. Robot.
,
7
(
64
), p.
eabg4055
.
11.
Galloway
,
K. C.
,
Clark
,
J. E.
,
Yim
,
M.
, and
Koditschek
,
D. E.
,
2011
, “
Experimental Investigations Into the Role of Passive Variable Compliant Legs for Dynamic Robotic Locomotion
,”
2011
IEEE International Conference on Robotics and Automation
,
Shanghai, China
,
May 9–13
,
IEEE
, pp.
1243
1249
.
12.
Sadeghi
,
S.
,
Allison
,
S. R.
,
Bestill
,
B.
, and
Li
,
S.
,
2021
, “
TMP Origami Jumping Mechanism With Nonlinear Stiffness
,”
Smart Mater. Struct.
,
30
(
6
), p.
065002
.
13.
Hawkes
,
E. W.
,
Xiao
,
C.
,
Peloquin
,
R. -A.
,
Keeley
,
C.
,
Begley
,
M. R.
,
Pope
,
M. T.
, and
Niemeyer
,
G.
,
2022
, “
Engineered Jumpers Overcome Biological Limits Via Work Multiplication
,”
Nature
,
604
(
7907
), pp.
657
661
.
14.
Owaki
,
D.
, and
Ishiguro
,
A.
,
2006
, “
Enhancing Stability of a Passive Dynamic Running Biped by Exploiting a Nonlinear Spring
,”
2006
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Beijing, China
,
Oct. 9–15
,
IEEE
, pp.
4923
4928
.
15.
Yu
,
H.
,
Li
,
M.
, and
Cai
,
H.
,
2013
, “
Analysis on the Performance of the SLIP Runner With Nonlinear Spring Leg
,”
Chin. J. Mech. Eng.
,
26
(
5
), pp.
892
899
.
16.
Plecnik
,
M. M.
,
Haldane
,
D. W.
,
Yim
,
J. K.
, and
Fearing
,
R. S.
,
2017
, “
Design Exploration and Kinematic Tuning of a Power Modulating Jumping Monopod
,”
ASME J. Mech. Rob.
,
9
(
1
), p.
011009
.
17.
Galloway
,
K. C.
,
Clark
,
J. E.
, and
Koditschek
,
D. E.
,
2013
, “
Variable Stiffness Legs for Robust, Efficient, and Stable Dynamic Running
,”
ASME J. Mech. Rob.
,
5
(
1
), p.
011009
.
18.
Kalouche
,
S.
,
2017
, “
GOAT: A Legged Robot With 3D Agility and Virtual Compliance
,”
2017
IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Vancouver, BC, Canada
,
Sept. 24–28
,
IEEE
, pp.
4110
4117
.
19.
Grimminger
,
F.
,
Meduri
,
A.
,
Khadiv
,
M.
,
Viereck
,
J.
,
Wuthrich
,
M.
,
Naveau
,
M.
,
Berenz
,
V.
, et al.
2020
, “
An Open Torque-Controlled Modular Robot Architecture for Legged Locomotion Research
,”
IEEE Robot. Autom. Lett.
,
5
(
2
), pp.
3650
3657
.
20.
Zhang
,
M.
,
Fang
,
L.
,
Sun
,
F.
, and
Oka
,
K.
,
2019
, “
A Novel Wire-Driven Variable-Stiffness Joint Based on a Permanent Magnetic Mechanism
,”
ASME J. Mech. Rob.
,
11
(
5
), p.
051001
.
21.
Yu
,
J.
,
Zhao
,
Y.
,
Chen
,
G.
,
Gu
,
Y.
,
Wang
,
C.
, and
Huang
,
S.
,
2019
, “
Realizing Controllable Physical Interaction Based on an Electromagnetic Variable Stiffness Joint
,”
ASME J. Mech. Rob.
,
11
(
5
), p.
054501
.
22.
Basu
,
A.
,
Jujjavarapu
,
S. S.
, and
Esfahani
,
E. T.
,
2020
, “
Design of a Novel Variable Stiffness Active Ankle Foot Orthosis Using Permanent Magnets for Drop Foot Assistance
,”
Volume 10: 44th Mechanisms and Robotics Conference (MR)
,
Virtual, Online
,
Aug. 17–19
,
American Society of Mechanical Engineers
.
23.
Faal
,
S. G.
,
Chen
,
F.
,
Tao
,
W.
,
Agheli
,
M.
,
Tasdighikalat
,
S.
, and
Onal
,
C. D.
,
2016
, “
Hierarchical Kinematic Design of Foldable Hexapedal Locomotion Platforms
,”
ASME J. Mech. Rob.
,
8
(
1
), p.
011005
.
24.
Aukes
,
D. M.
,
Goldberg
,
B.
,
Cutkosky
,
M. R.
, and
Wood
,
R. J.
,
2014
, “
An Analytic Framework for Developing Inherently-Manufacturable Pop-Up Laminate Devices
,”
Smart Mater. Struct.
,
23
(
9
), p.
094013
.
25.
Howell
,
L. L.
, and
Midha
,
A.
,
1995
, “
Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
,
117
(
1
), pp.
156
165
.
26.
Howell
,
L. L.
,
Midha
,
A.
, and
Norton
,
T. W.
,
1996
, “
Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms
,”
ASME J. Mech. Des.
,
118
(
1
), pp.
126
131
.
27.
Storn
,
R.
, and
Price
,
K.
,
1997
, “
Differential Evolution–A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces
,”
J. Global Optim.
,
11
(
4
), pp.
341
359
.
28.
Dormand
,
J.
, and
Prince
,
P.
,
1980
, “
A Family of Embedded Runge-Kutta Formulae
,”
J. Comput. Appl. Math.
,
6
(
1
), pp.
19
26
.
You do not currently have access to this content.