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.