In this article we survey some recent developments in optimal robot design, and collect some of the differential geometric approaches into a general mathematical framework for robot design. The geometric framework permits a set of coordinate-free definitions of robot performance that can be optimized for designing both open- and closed-chain robotic mechanisms. In particular, workspace volume is precisely defined by regarding the rigid body motions as a Riemannian manifold, and various features of actuators, as well as inertial characteristics of the robot, can be captured by the suitable selection of a Riemannian metric in configuration space. The integral functional of harmonic mapping theory also provides a simple and elegant global description of dexterity.

Issue Section:
Research Papers
Topics:
Design, Geometry, Robots, Actuators, Chain, Manifolds, Robotics
1.
Asada
H.
,
1983
, “
A Geometrical Representation of Manipulator Dynamics and Its Application to Arm Design
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
105
, No.
3
, pp.
131
–
135
.
2.
Brockett, R. W., “Robotic Manipulators and the Product of Exponentials Formula,” Proc. Symp. Math. Theory Networks and Systems. Beer Sheba, Israel, pp. 120–129.
3.
Brockett
R. W.
,
1989
, “
On the Rectification of Vibratory Motion
,”
Sensors and Actuators
, Vol.
20
, pp.
91
–
96
.
4.
Canny, J., and Goldberg, K., 1994, “RISC Robotics; Recent Results and Open Problems,” Proc. IEEE Int. Conf. Robotics & Autom., San Diego, CA, pp. 1951–1958.
5.
Chiacchio
P.
,
Chiaverini
S.
,
Sciavicco
L.
, and
Sicilliano
B.
,
1991
, “
Global Task Space Manipulability Ellipsoids for Multiple-arm Systems
,”
IEEE Trans. Robotics Autom.
, Vol.
7
, pp.
678
–
685
.
6.
Chiacchio
P.
,
Chiaverini
S.
,
Sciavicco
L.
, and
Siciliano
B.
,
1993
,
Reply to “Comments on ‘Global Task Space Manipulability Ellipsoids for Multiple-arm Systems’ and Further Considerations
,”
IEEE Trans. Robotics Autom.
, Vol.
9
, pp.
235
–
236
.
7.
Curtis, M. L., 1984, Matrix Groups, New York, Springer-Verlag.
8.
Eells
J.
, and
Sampson
J. H.
,
1964
, “
Harmonic Mappings of Riemannian Manifolds
,”
Amer. J. Math.
, Vol.
86
, pp.
109
–
160
.
9.
Eells
J.
, and
Lemaire
L.
,
1997
8
, “
A Report on Harmonic Maps
,”
Bulletin London Math. Sco.
, Vol.
10
, pp.
1
–
68
.
10.
Freudenstein
F.
, and
Primrose
E.
,
1984
, “
On the Analysis and Synthesis of the Workspace of a Three-link, Turning-pair Connected Robot Arm
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
Vol.
106
, pp.
365
–
370
.
11.
Gosselin, C. M., and Angeles, J., 1988, “A New Performance Index for the Kinematic Optimization of Robotic Manipulators,” Proc. 20th ASME Mechanisms Conf., Kissimmee, FL, pp. 441–447.
12.
Gupta
K. C.
,
1986
, “
On the Nature of Robot Workspace
,”
Int. J. Robotics Research
, Vol.
5
, No.
2
, pp.
112
–
121
.
13.
Gupta
K. C.
, and
Roth
B.
,
1982
, “
Design Considerations for Manipulator Workspace
,”
ASME Journal of Mechanical Design
, Vol.
104
, pp.
704
–
711
.
14.
Hollerbach, J. M., 1985, “Optimum Kinematic Design of a Seven Degree of Freedom Manipulator,” in Robotics Research: The Second International Symposium. H. Hanafusa and H. Inoue, eds., Cambridge, MIT Press.
15.
Klein
C. A.
, and
Huang
C. H.
,
1983
, “
Review of Pseudo-inverse Control for Use with Kinematically Redundant Manipulators
,”
IEEE Trans. Sys., Man, Cyber.
, Vol.
13
, No.
2
, pp.
245
–
250
.
16.
Kumar
A.
, and
Waldron
K. J.
,
1981
, “
The Workspaces of a Mechanical Manipulator
,”
ASME Journal of Mechanical Design
, Vol.
103
, pp.
665
–
672
.
17.
Liegeois
A.
,
1977
, “
Automatic Supervisory Control for the Configuration and Behavior of Multibody Mechanisms
,”
IEEE Trans. Sys., Man, Cyber.
, Vol.
7
, No.
12
, pp.
842
–
868
.
18.
Lin
C. C.
, and
Freudenstein
F.
,
1986
, “
Optimization of the Workspace of a Three-link Turning-pair Connected Robot Arm
,”
Int. J. Robotics Research
, Vol.
5
, No.
2
, pp.
91
–
103
.
19.
Loncaric, J., 1985, “Geometric Analysis of Compliant Mechanisms in Robotics,” Ph.D. Thesis, Harvard University.
20.
Melchiorri
C.
,
1993
, “
Comments on ‘Global Task Space Manipulability Ellipsoids for Multiple-arm Systems’ and Further Considerations
,”
IEEE Trans. Robotics Autom.
, Vol.
9
, pp.
232
–
235
.
21.
Paden, B., and Sastry, S., 1988, “Optimal Kinematic Design of 6R Manipulators,” Int. J. Robotics Research, Vol. 7, No. 2.
22.
Paredis
C. J.
, and
Khosla
P.
,
1993
, “
Kinematic Design of Serial Link Manipulators from Task Specifications
,”
Int. J. Robotics Res.
, Vol.
12
, No.
3
, pp.
274
–
287
.
23.
Park
F. C.
, and
Brockett
R. W.
,
1994
, “
Kinematic Dexterity of Robotic Mechanisms
,”
Int. J. Robotics Research
, Vol.
13
, No.
2
, pp.
1
–
15
.
24.
Roth, B., 1976, “Performance Evaluation of Manipulators from a Kinematic Viewpoint,” National Bureau of Standards, NBS Special Publication 495, pp. 39–61.
25.
Salisbury
J. K.
, and
Craig
J. J.
,
1982
, “
Articulated Hands: Force Control and Kinematic Issues
,”
Int. J. Robotics Research
, Vol.
1
, No.
1
, pp.
4
–
17
.
26.
Samuel
A. E.
,
McAree
P. R.
, and
Hunt
K. H.
,
1991
, “
Unifying Screw Geometry and Matrix Transformations
,”
Int. J. Robotics Research
, Vol.
10
, No.
5
, pp.
454
–
472
.
27.
Sordalen, O. J., Nakamura, Y., and Chung, W. J., 1994, “Design of a Nonholonomic Manipulator,” Proc. IEEE Int. Conf. Robotics Autom., pp. 8–13.
28.
Spong, M. W., 1992, “Remarks on Robot Dynamics: Canonical Transformations and Riemannian Geometry,” Proc. IEEE Int. Conf. Robotics Autom., pp. 454–472.
29.
Tsai
Y. C.
, and
Soni
A. H.
,
1985
, “
An Algorithm for the Workspace of a General n-R Robot
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
105
, pp.
52
–
57
.
30.
Vijaykumar
R.
,
Waldron
K. J.
, and
Tsai
M. J.
,
1986
, “
Geometric Optimization of Serial Chain Manipulator Structures for Working Volume and Dexterity
,”
Int. J. Robotics Research
, Vol.
5
, No.
2
, pp.
91
–
103
.
31.
Wallace, R., and Selig, J. M., 1994, “Scaling Direct Drive Robots,” Technical Report 669, Dept. Comp. Sci., Courant Inst. Math. Sci., New York Univ.
32.
Yang
D. C. H.
, and
Lee
T. W.
,
1983
, “
On the Workspace of Mechanical Manipulators
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
105
, pp.
62
–
69
.
33.
Yoshikawa
T.
,
1985
, “
Manipulability of Robotic Mechanisms
,”
Int. J. Robotics Research
, Vol.
4
, No.
2
, pp.
3
–
9
.
34.
Yoshkiawa, T., 1985, “Dynamic Manipulability of Robot Manipulators,” Proc. IEEE Int. Conf. Robotics and Autom., pp. 1033–1038.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.