In this paper, we present a thorough kinematics analysis of a humanoid two degrees-of-freedom (DoF) ankle module based on a parallel kinematics mechanism. Compared with the conventional serial configuration, the parallel kinematics ankle permits the distribution of the torque/power of the actuators to the two DoF of the ankle taking full advantage of available power/torque capacity of the two actuators. However, it complicates the kinematics study in return. In this work, a complete study of a parallel ankle mechanism is performed that permits the full characterization of the ankle module for the purpose of its design study, control, and performance evaluation. Screw theory is employed for mobility analysis to first determine the number and properties of the mechanism's DoFs. Then the inverse kinematics is solved analytically and the Jacobian matrix for describing the velocity relation between the ankle joints and motors is found. Based on these results, the forward kinematics of the parallel mechanism can be numerically computed using the Newton–Raphson method. The workspace of the ankle is also analyzed and the motor limits are decided accordingly. Finally, an experimental demonstration consisting of four tests is carried out to evaluate the proposed methods and ankle module.

References

References
1.
Lenarcic
,
J.
, and
Stanisic
,
M.
,
2003
, “
A Humanoid Shoulder Complex and the Humeral Pointing Kinematics
,”
IEEE Trans. Rob. Autom.
,
19
(
3
), pp.
499
506
.
2.
Carricato
,
M.
, and
Parenti-Castelli
,
V.
,
2004
, “
A Novel Fully Decoupled 2-DOF Parallel Wrist
,”
Int. J. Rob. Res.
,
23
(
6
), pp.
661
667
.
3.
Morisawa
,
M.
,
Yakoh
,
T.
,
Murakami
,
T.
, and
Ohnishi
,
K.
,
2000
, “
An Approach to Biped Robot With Parallel Mechanism
,”
International Workshop on Advanced Motion Control
, Nagoya, Japan, Mar. 30–Apr. 1, pp.
537
541
.
4.
Sugahara, Y.
,
Endo, T.
,
Lim, H.
, and
Takanishi, A.
, 2002, “
Design of a Battery-Powered Multi-Purpose Bipedal Locomotor with Parallel Mechanism
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
3
, pp. 2658–2663.
5.
Saglia
,
J. A.
,
Tsagarakis
,
N. G.
,
Dai
,
J. S.
, and
Caldwell
,
D. G.
,
2009
, “
A High-Performance Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation
,”
Int. J. Rob. Res.
,
28
(
9
), pp.
1216
1227
.
6.
Roy
,
A.
,
Krebs
,
H. I.
,
Williams
,
D. J.
,
Bever
,
C. T.
,
Forrester
,
L. W.
,
Macko
,
R. M.
, and
Hogan
,
N.
,
2009
, “
Robot-Aided Neurorehabilitation: A Novel Robot for Ankle Rehabilitation
,”
IEEE Trans. Rob.
,
25
(
3
), pp.
569
582
.
7.
Lohmeier
,
S.
,
Buschmann
,
T.
,
Schwienbacher
,
M.
,
Ulbrich
,
H.
, and
Pfeiffer
,
F.
,
2006
,“
Leg Design for a Humanoid Walking Robot
,”
IEEE-RAS International Conference on Humanoid Robots
, Genova, Italy, Dec. 4–6, pp.
536
541
.
8.
Hyon
,
S.-H.
,
Suewaka
,
D.
,
Torii
,
Y.
, and
Oku
,
N.
,
2017
, “
Design and Experimental Evaluation of a Fast Torque-Controlled Hydraulic Humanoid Robot
,”
IEEE/ASME Trans. Mechatronics
,
22
(
2
), pp.
623
634
.
9.
Feng
,
S.
,
Xinjilefu
,
X.
,
Atkeson
,
C. G.
, and
Kim
,
J.
,
2015
, “
Optimization Based Controller Design and Implementation for the Atlas Robot in the Darpa Robotics Challenge Finals
,”
IEEE-RAS International Conference on Humanoid Robots
, Seoul, South Korea, Nov. 3–5, pp. 1028–1035, pp.
1028
1035
.
10.
Kaminaga
,
H.
,
Ko
,
T.
,
Masumura
,
R.
,
Komagata
,
M.
,
Sato
,
S.
,
Yorita
,
S.
, and
Nakamura
,
Y.
,
2016
, “
Mechanism and Control of Whole-Body Electro-Hydrostatic Actuator Driven Humanoid Robot Hydra
,”
International Symposium on Experimental Robotics
, Tokyo, Japan, Oct. 3–6, pp.
656
665
.
11.
Knabe
,
C.
,
Griffin
,
R.
,
Burton
,
J.
,
Cantor-Cooke
,
G.
,
Dantanarayana
,
L.
,
Day
,
G.
,
Ebeling-Koning
,
O.
,
Hahn
,
E.
,
Hopkins
,
M.
,
Neal
,
J.
,
Jackson
,
N.
,
Chris
,
N.
,
Viktor
,
O.
,
John
,
P.
,
Michael
,
R.
,
John
,
S.
,
Yoonchang
,
S.
,
Jacob
,
W.
,
Nikolaus
,
W.
,
Jason
,
Z.
,
Alexander
,
L.
,
Brian
,
L.
, and
Tomonari
,
F.
,
2017
, “
Team VALOR's ESCHER: A Novel Electromechanical Biped for the DARPA Robotics Challenge
,”
J. Field Rob.
,
34
(
5
), pp.
912
939
.
12.
Kakiuchi
,
Y.
,
Kamon
,
M.
,
Shimomura
,
N.
,
Yukizaki
,
S.
,
Takasugi
,
N.
,
Nozawa
,
S.
,
Okada
,
K.
, and
Inaba
,
M.
,
2017
, “
Development of Life-Sized Humanoid Robot Platform With Robustness for Falling Down, Long Time Working and Error Occurrence
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Vancouver, BC, Canada, Sept 24–28, pp.
689
696
.
13.
Reher
,
J.
,
Cousineau
,
E. A.
,
Hereid
,
A.
,
Hubicki
,
C. M.
, and
Ames
,
A. D.
,
2016
, “
Realizing Dynamic and Efficient Bipedal Locomotion on the Humanoid Robot DURUS
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Stockholm, Sweden, May 16–21, pp.
1794
1801
.
14.
Mazumdar
,
A.
,
Spencer
,
S. J.
,
Hobart
,
C.
,
Salton
,
J.
,
Quigley
,
M.
,
Wu
,
T.
,
Bertrand
,
S.
,
Pratt
,
J.
, and
Buerger
,
S. P.
,
2017
, “
Parallel Elastic Elements Improve Energy Efficiency on the STEPPR Bipedal Walking Robot
,”
IEEE/ASME Trans. Mechatronics
,
22
(
2
), pp.
898
908
.
15.
Han
,
S.
,
Um
,
S.
, and
Kim
,
S.
,
2016
, “
Mechanical Design of Robot Lower Body Based on Four-Bar Linkage Structure for Energy Efficient Bipedal Walking
,”
IEEE International Symposium on Safety, Security, and Rescue Robotics
(
SSRR
), Lausanne, Switzerland, Oct. 23–27, pp.
402
407
.
16.
Alfayad
,
S.
,
Ouezdou
,
F. B.
, and
Namoun
,
F.
,
2009
, “
New Three DoF Ankle Mechanism for Humanoid Robotic Application: Modeling, Design and Realization
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
, pp.
4969
4976
.
17.
Huang
,
Z.
, and
Li
,
Q.
,
2003
, “
Type Synthesis of Symmetrical Lower-Mobility Parallel Mechanisms Using the Constraint-Synthesis Method
,”
Int. J. Rob. Res.
,
22
(
1
), pp.
59
79
.
18.
Hunt
,
K. H.
,
1978
,
Kinematic Geometry of Mechanisms
,
Oxford University Press
, Oxford, UK.
19.
Murray
,
R. M.
,
Li
,
Z.
,
Sastry
,
S. S.
, and
Sastry
,
S. S.
,
1994
,
A Mathematical Introduction to Robotic Manipulation
,
CRC Press
, Boca Raton, FL.
20.
Dai
,
J. S.
,
Huang
,
Z.
, and
Lipkin
,
H.
,
2006
, “
Mobility of Overconstrained Parallel Mechanisms
,”
ASME J. Mech. Des.
,
128
(
1
), pp.
220
229
.
21.
Zhou
,
C.
,
Wang
,
X.
,
Li
,
Z.
, and
Tsagarakis
,
N.
,
2017
, “
Overview of Gait Synthesis for the Humanoid COMAN
,”
J. Bionic Eng.
,
14
(
1
), pp.
15
25
.
22.
Zhou
,
C.
,
Fang
,
C.
,
Wang
,
X.
,
Li
,
Z.
, and
Tsagarakis
,
N.
,
2016
, “
A Generic Optimization-Based Framework for Reactive Collision Avoidance in Bipedal Locomotion
,” IEEE Conference on Automation Science and Engineering (
CASE
), Fort Worth, TX, Aug. 21–25, pp.
1026
1033
.
23.
Tsai
,
M.-S.
,
Shiau
,
T.-N.
,
Tsai
,
Y.-J.
, and
Chang
,
T.-H.
,
2003
, “
Direct Kinematic Analysis of a 3-PRS Parallel Mechanism
,”
Mech. Mach. Theory
,
38
(
1
), pp.
71
83
.
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