A new analytical method for determining, describing, and visualizing the solution space for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The foot contact forces are first resolved into strategically defined foot contact force components to decouple them, and then the static equilibrium equations are applied. Using the friction cone equation at each foot contact point, the problem is then transformed into a geometrical one. Using geometric properties of the friction cones and by simple manipulation of their conic sections, the entire solution space which satisfies the static equilibrium and friction constraints at each contact point can be found. Two representation schemes, the “force space graph” and the “solution volume representation,” are developed for describing and visualizing the solution space which gives an intuitive visual map of how well the solution space is formed for the given conditions of the system.

1.
Hong
,
D. W.
, 2002, “
Analysis and Visualization of the Contact Force Solution Space for Multi-Limbed Mobile Robots
,” Ph.D. dissertation, Purdue University, West Lafayette, IN.
2.
Hong
,
D. W.
, and
Cipra
,
R. J.
, 2003, “
Choosing the Optimal Contact Force Distribution for Multi-Limbed Mobile Robots with Three Feet Contact
,” in
Proceedings of the ASME 2003 DETC
,
Chicago
, Illinois, September 2–6.
3.
Hong
,
D. W.
, and
Cipra
,
R. J.
, 2003, “
Analysis and Visualization of the Contact Force Solution Space for Multi-Limbed Mobile Robots with Three Feet Contact
,” in
Proceedings of the ASME 2003 DETC
,
Chicago, Illinois
, September 2-6.
4.
Venkataraman
,
S. T.
, and
Iberall
,
T.
, 1990,
Dextrous Robot Hands
,
Springer-Verlag
, New York.
5.
Mason
,
M. T.
, and
Salisbury
,
J. K.
, 1985,
Robot Hands and the Mechanics of Manipulation
,
MIT Press
, Cambridge, MA.
6.
Tao
,
J. M.
, and
Luh
,
J. Y. S.
, 1989, “
Coordination of Two Redundant Robots
,”
IEEE International Conference on Robotics and Automation, v I (of 3)
, Piscataway, NJ, pp.
425
430
.
7.
Klein
,
C. A.
, and
Chung
,
T.
, 1987, “
Force Interaction and Allocation for the Legs of a Walking Vehicle
,”
IEEE J. Rob. Autom.
0882-4967,
RA-3
, pp.
546
555
.
8.
Klein
,
C.
,
Olson
,
K.
, and
Pugh
,
D.
, 1983, “
Use of Force and Attitude Sensors for Locomotion of a Legged Vehicle Over Irregular Terrain
,”
Int. J. Robot. Res.
0278-3649,
2
(
2
), pp.
3
7
.
9.
Salisbury
,
J. K.
, and
Craig
,
J. J.
, 1982, “
Articulated Hands: Force Control and Kinematic Issues
,”
Int. J. Robot. Res.
0278-3649,
1
(
1
), pp.
4
17
.
10.
Kumar
,
V. R.
, and
Waldron
,
K. J.
, 1988, “
Force Distribution in Closed Kinematic Chains
,”
IEEE J. Rob. Autom.
0882-4967,
4
(
6
), pp.
657
664
.
11.
Zuo
,
B.
, and
Qian
,
W.
, 1999, “
On the Equivalence of Internal and Interaction Forces in Multifingered Grasping
,”
IEEE Trans. Rob. Autom.
1042-296X,
15
, pp.
934
941
.
12.
Yoshikawa
,
T.
, and
Nagai
,
K.
, 1991, “
Manipulating and Grasping Forces in Manipulation by Multifingeres Robot Hands
,”
IEEE Trans. Rob. Autom.
1042-296X,
7
(
1
), pp.
67
77
.
13.
Klein
,
C. A.
, and
Kittivatcharapong
,
S.
, 1990, “
Optimal Force Distribution for the Legs of a Walking Machine with Friction Cone Constraints
,”
IEEE Trans. Rob. Autom.
1042-296X,
6
(
1
), pp.
73
85
.
14.
Nahon
,
M.
, and
Angeles
,
J.
, 1992, “
Real-Time Force Optimization in Parallel Kinematic Chains Under Inequality Constraints
,”
IEEE Trans. Rob. Autom.
1042-296X,
8
(
4
), pp.
439
450
.
15.
Chen
,
X.
,
Watanabe
,
K.
,
Kiguchi
,
K.
, and
Izumi
,
K.
, 1999, “
Optimal Force Distribution for the Legs of a Quadruped Robot
,”
Mach. Intell.
0076-2032,
1
(
2
), pp.
87
94
.
16.
Cheng
,
F.
,
Chen
,
T.
, and
Sun
,
Y.
, 1994, “
Resolving Manipulator Redundancy Under Inequality Constraints
,”
IEEE Trans. Rob. Autom.
1042-296X,
10
(
1
), pp.
65
71
.
17.
Chen
,
J.
,
Cheng
,
F.
,
Yang
,
K.
,
Kung
,
F.
, and
Sun
,
Y.
, 1999, “
Optimal Force Distribution in Multilegged Vehicles
,”
Robotica
0263-5747,
17
(
2
), pp.
159
172
.
18.
Kerr
,
J. R.
, and
Roth
,
B.
, 1986, “
Analysis of Multifingered Hands
,”
Int. J. Robot. Res.
0278-3649,
4
(
4
), pp.
3
17
.
19.
Kumar
,
V.
, and
Waldron
,
K. J.
, 1989, “
Suboptimal Algorithms for Force Distribution in Multifingered Grippers
,”
IEEE Trans. Rob. Autom.
1042-296X,
5
(
4
), pp.
491
498
.
20.
Cheng
,
F.
, and
Orin
,
D. E.
, 1990, “
Efficient Algorithm for Optimal Force Distribution—The Compact Dual LP Method
,”
IEEE Trans. Rob. Autom.
1042-296X,
6
(
2
), pp.
178
187
.
21.
Dai
,
J. S.
, and
Kerr
,
D. R.
, 1996, “
Analysis of Force Distribution in Grasps Using Augmentation
,”
J. Mech. Eng. Sci.
0022-2542,
210
(
C1
), pp.
15
22
.
22.
Liu
,
Y. H.
,
Lam
,
M. L.
, and
Ding
,
D.
, 2004, “
A Complete and Efficient Algorithm for Searching 3D Form-Closure Grasps in the Discrete Domain
,”
IEEE Trans. Rob. Autom.
1042-296X,
20
(
5
), pp.
805
816
.
23.
Zhu
,
X.
,
Ding
,
H.
,
Wang
,
M. Y.
, 2004, “
A Numerical Test for the Closure Properties of 3D Grasps
,”
IEEE Trans. Rob. Autom.
1042-296X,
20
(
3
), pp.
543
549
.
24.
Hong
,
D. W.
, and
Cipra
,
R. J.
, 2002, “
Optimal Force Distribution for Tethered Climbing Robots in Unstructured Environments
,” in
Proceedings of the ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Montreal
, Canada, September 29–October 2, 2002.
25.
Ghafoor
,
A.
,
Dai
,
J. S.
, and
Duffy
,
J.
, 2004, “
Stiffness Modeling of the Soft-Finger Contact in Robotic Grasping
,”
J. Mech. Des.
1050-0472,
126
(
4
), pp.
646
656
.
26.
Shah
,
G.
,
Sitti
,
M.
, 2004, “
Modeling and Design of Biomimetic Adhesives Inspired by Gecko Foot-Hairs
,”
IEEE International Conference on Robotics and Biomimetics (ROBIO)
, Shenyang, China.
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