Charles A. Klein and Ching-Hsiang Huang

Abstract - Kinematically redundant manipulators have a number of potential advantages over current manipulator designs. For this type of arm, velocity control through pseudoinverses has been suggested. Questions associated with pseudoinverse control are examined in detail and show that in some cases this control leads to undesired arm configurations. A method for distributing joint angles of a redundant arm in a good approximation to a true minimax criterion is described. In addition several numerical considerations are discussed.

**Use of an Extended Jacobian Method to Map Algorithmic Singularities
**

Charles Klein, Caroline Chu-Jenq and Shamim Ahmed

*Proceedings 1993 IEEE Int. Conf. on Robotics and Automation* Vol. 3,
May 2-6 1993, Atlanta, GE. pp. 632-637, IEEE Computer Soc. Press

Abstract - The
extended Jacobian method has been devised to operate a kinematically
redundant manipulator such that a secondary criterion is kept at an
optimal value. This paper describes a formulation of this algorithm
that is better suited numerically for systems with multiple degrees of
redundancy and for more general choices of the secondary criterion.
This formulation is particularly useful for tracing algorithmic
singularities, which mark the bounds of operation for any algorithm
using the same secondary criterion to resolve the redundancy.
Examples of end effector positioning and tracing algorithmic
singularities are presented for both planar and spatial systems.

**
Motion Coordination for Mobile Robots in Unstructured Environments
**

Charles A. Klein, N. Berme and S. Koozekanani

*Advances In Manufacturing Systems Integration and Processes, 15th
Conference on Production, Research and Tech.*, pp. 157-170 Berkeley,
CA. January 13, 1989

Abstract - In order to advance robotics from the traditional factory
setting to a more unstructured environment, mobility needs to be
added.
With this increased functionality, robotics could be applied to
fire-fighting, building construction, and construction in space. In
manufacturing, robotics could be applied to problems like
ship-building where mobility is important to deal with very large
workpieces. The combination of mobility and manipulation systems
forms a kinematically redundant system. Using the methodology of
redundant systems, this project is investigating the coordination of
mobility and manipulation subsystems for the purpose of achieving high
dexterity, obstacle avoidance, and avoiding joint limits.

**Dexterity Measures for the
Design and Control of Kinematically Redundant Manipulators
**

Charles A. Klein and Bruce E. Blaho

*International Journal of Robotics Research*, Summer 1987.
Vol. 6, No. 2, pp. 72-83. 1987.

Abstract
- In this paper, we have proposed a number of measures for the
quantification of dexterity of manipulators. The use of such measures
is especially important for kinematically redundant manipulators since
they can satisfy secondary criteria in addition to satisfying a
specification of end-effector motion. We will compare several
measures for the problems of finding an optimal configuration for a
given end-effector position, finding an optimal workpoint, and
designing the optimal link lengths of an arm.

**Numerical Filtering for the Operation of
Robotic Manipulators through Kinematically Singular Configurations.
**

Anthony A. Maciejewski and Charles A. Klein

*Journal of Robotic Systems*, 5(6), pp. 527-552 (1988)

Abstract - The loss of independent degrees of freedom at singular
configurations is an inherent characteristic of robotic manipulators.
Due to the unavoidable singularity of mechanical wrists, singular
configurations cannot be avoided by simply restricting the bounds of
the workspace. Techniques for operating at singular configurations
without inducing unacceptably high joint velocities or end effector
tracking errors are presented. Extensions to the damped least-squares
formulation which incorporate estimates of the proximity to
singularities and selective filtering of singular components are
illustrated. The generality of the technique presented is
illustrated in a
computer simulation of a commercially available manipulator operating
through singular configurations.

**Obstacle Avoidance for Kinematically Redundant Manipulators in
Dynamically Varying Environments.
**

Anthony A. Maciejewski and Charles A. Klein

*The International Journal of Robotics Research*, Vol. 4, No.3,
pp. 109-117., Fall 1985.

Abstract - The vast majority of
work to date concerned with obstacle avoidance for manipulators has
dealt with task descriptions in the form of pick-and-place movements.
The added flexibility in motion control for manipulators possessing
redundant degrees of freedom permits the consideration of obstacle
avoidance in the context of a specified end-effector trajectory as the
task description. Such a task definition is a more accurate model for
such tasks as spray painting or arc welding. The approach presented
here is to determine the required joint angle rates for the
manipulator under the constraints of multiple goals, the primary goal
described by the specified end-effector trajectory and secondary goals
describing the obstacle avoidance criteria.
The decomposition of the solution into a particular and a homogeneous
component effectively illustrates the priority of the multiple goals
that is exact end-effector control with redundant degrees of freedom
maximizing the distance to obstacles. An efficient numerical
implementation of the technique permits sufficiently fast cycle times
to deal with dynamic environments.

** Use of Redundancy in the Design of Robotic Systems.
**
Charles A. Klein
*Robotics Research: The Second International Symposium*, H. Hanafusa and

H. Inoue, Eds, pp. 207-214, MIT Press, August 1984.

Abstract - Most current industrial robots have no more than the
minimum number of mechanical degrees of freedom necessary for a given
task. By including kinematically redundant links, more flexible
operation can be achieved. To solve these mathematically
underdetermined systems, generalized inverses can be used to determine
unique activator velocities, given end effector motion specifications.
In addition, the set of homogenous solutions, which cause no end
effector motion, can be used to satisfy secondary goals for the arm
motion. One important use of the redundancy is in specifying that the
arm avoid obstacles in the workspace.
A technique will be described which automatically moves the arm away
from obstacles while guiding the hand on the desired trajectory. An
important element of this algorithm is the proper weighting of
multiple constraints. Another use for the redundancy is in keeping
the arm in a configuration which makes it as dexterous as possible.
Several measures for this quantity will be examined.

**Spatial Robotic Isotropy
**

Charles A. Klein and Todd A. Miklos

*The International Journal of Robotics Research*. Vol. 10,
No. 4. August 1991., pp. 426-437.

Abstract - Previous work on posture
optimization for robots has examined the condition number as a measure
of kinematic dexterity.
When the condition number equals an optimal value of one, the robot
is described as isotropic. Isotropic configurations have a number of
advantages, including good servo accuracy, noise rejection, and
singularity avoidance. This article introduces a definition for
spatial isotropy of a robot, which is combined isotropy for both
positioning and orienting the end effector.
Generally isotropy may be used either as a robotic design criterion
or as a posture optimization function for redundant manipulators.
This work demonstrates design techniques using positional,
orientational, or spatial isotropy and presents some algorithms for
locating isotropic designs without explicit evaluation of singular
values. Several representative robot designs illustrate these
concepts for both nonredundant and redundant manipulators.

**The Singular Value Decomposition: Computation and
Applications to Robotics.
**

Anthony A. Maciejewski and Charles A. Klein

*The International Journal of Robotics Research*, Vol. 8, No. 6,
pp. 63-79. December 1989.

Abstract - The singular value decomposition
has been extensively used for the analysis of the kinematic and
dynamic characteristics of robotic manipulators. Due to a reputation
for being numerically expensive to compute, however, it has not been
used for real-time applications. This work illustrates a formulation
for the singular value decomposition that takes advantage of the
nature of robotics matrix calculations to obtain a computationally
feasible algorithm.
Several applications, including the control of redundant manipulators
and the optimization of dexterity, are discussed. A detailed
illustration of the use of the singular value decomposition to deal
with the general problem of singularities is also presented.

**The Nature of
Drift in Pseudoinverse Control of Kinematically Redundant
Manipulators.
**

Charles A. Klein and Koh-Boon Kee

*IEEE Transactions on Robotics and Automation*. Vol. 5, No. 2, April
1989, pp. 231-234

Abstract - Control of kinematically redundant
manipulators using only pseudoinverse control is known to produce
drift in joint space when a cyclic task is performed in rectilinear
space. The purpose of this communication is to examine properties of
this drift by performing numerical experiments. This drift has
predictable properties including a numerically stable limit in some
situations. At this limit the arc length of the path in joint space
appears to be near a minimum.

**Dynamic Simulation of a Kinematically Redundant
Manipulator System.
**

Charles A. Klein and
Antonio I. Chirco

*Journal of Robotic Systems*, 4(1), pp. 5-23 (1987)

Abstract - A number of methods have been proposed
for the control of kinematically redundant manipulators, that is,
those with more than the minimum number of degrees of freedom. This
article uses a dynamic simulation to test whether proposed schemes
should, in fact, work well when the dynamics of the actual system are
considered. In order to perform a realistic simulation, a
nine-degree-of-freedom arm has been designed using commercially
available motors. The simulation shows the effects that specifying a
secondary goal has on the satisfaction of the primary goal. Also
shown is the dependence of servo performance on modeling the load.

**The Lie Bracket Condition as a Test of Stable,
Drift-Free Pseudoinverse Trajectories.
**

Charles A. Klein

*IEEE Transactions on Robotics and Automation*, Vol. 9, No. 3,
p 334, June 1993.

Abstract - Stable trajectories described earlier by Klein and Huang
are not surfaces determined by the Lie Bracket Condition being zero.

**Testing Iterative Robotic Algorithms by
Their Rate of Convergence
**

Charles A. Klein, Caroline Chu-Jenq and
Sakon Kittivatcharapong.

*IEEE Transactions on Robotics and Automation*, Vol. 7, No. 5,
pp. 686-687. October 1991.

Abstract - A common problem is verifying the
correctness of robotic computer programs based on iterative
methods. This work presents a number of principles that the authors
have found to be useful in testing such programs.

**A New Formulation of the Extended Jacobian Method and
its Use in Mapping Algorithmic Singularities for Kinematically
Redundant Manipulators.
**

Charles A. Klein, Caroline Chu-Jenq and
Shamim Ahmed.

*IEEE Transactions on Robotics and Automation.* Vol. 11, No. 1,
pp. 50-55, February 1995.

Abstract - The extended Jacobian method
resolves the redundancy of a kinematically redundant manipulator such
that a secondary criterion is kept at an optimal value. This paper
describes a new formulation of this algorithm that is well suited
numerically for systems with multiple degrees of redundancy and for
more general choices of the secondary criterion. This formulation is
used here for tracing algorithmic singularities, which mark a boundary
of operation for any algorithm using the same secondary criterion to
resolve the redundancy. Examples of tracing algorithmic singularities
are presented for both planar and spatial systems.

**Repeatable Pseudoinverse Control for Planar Kinematically Redundant
Manipulators.
**

Charles A. Klein and Shamim Ahmed

*IEEE Transaction on System, Man, and Cybernetics*, Vol. 25, No. 12,
pp. 1657-1662, December 1995.

Abstract - the necessary and sufficient conditions for
repeatable pseudoinverse control are now well known. A very simple
example of a configuration for planar manipulators that is
conservative is also known. It is also known there is no conservative
configuration for the most common definition of joint angles. The
question remains whether there exists any other conservative case
using other definitions of joint angles, or equivalently, for
pseudoinverse control using different, but constant, joint norms.
This paper addresses this question using a combination of analytical
and numerical methods. Such cases have been found, however, the
resulting configurations are the same as previously known.