A new analytical method to resolve underspecified systems of algebraic equations is presented. The method is referred to as the full space parameterization (FSP) method and utilizes easily-calculated projected solution vectors to generate the entire space of solutions of the underspecified system. Analytic parameterizations for both the space of solutions and the null space of the system reduce the determination of a task-requirement-based single solution to a m-n dimensional problem, where m-n is the degree of underspecification, or degree of redundancy, of the system. An analytical solution is presented to directly calculate the least-norm solution from the parameterized space and the results are compared to solutions of the standard pseudo-inverse algorithm which embodies the (least-norm) Moore-Penrose generalized inverse. Application of the new solution method to a variety of systems and task requirements are discussed, and sample results using four-link planar manipulators with one or two degrees of redundancy and a seven degree-of-freedom manipulator with one or four degrees of redundancy are presented to illustrate the efficiency of the new FSP method and algorithm.>

An important characteristic of mobile manipulators is their particular kinematic redundancy created by the addition of the degrees of freedom of the platform and those of the manipulator. This kinematic redundancy is very desirable since it allows mobile manipulators to operate under many modes of motion and to perform a wide variety of tasks. On the other hand, it also significantly complicates the problem of planning a series of sequential tasks, in particular for the critical times at which the system needs to "switch" from one task to the other (task commutation), with changes in mode of motion, task requirement, and task constraints. This paper focuses on the problem of planning the positions and configurations in which the system needs to be at task commutation in order to assure that it can properly initiate the next task to be performed. The concept of and need for "commutation configurations" in sequences of mobile manipulator tasks is introduced, and an optimization approach is proposed for their calculation during the task sequence planning phase. A variety of optimization criteria were previously investigated to optimize the task commutation configurations of the system when task requirements involve obstacle avoidance, reach, maneuverability, and optimization of strength. In this paper, the authors show that a "minimax" approach is particularly adapted for most of these requirements. The authors develop the corresponding criteria and discuss solution algorithms to solve the "minimax" optimization problems. An implementation of the algorithms for the authors' HERMIES-III mobile manipulator is then described and sample results are presented and discussed.>

Abstract This paper discusses efforts to develop parallel algorithms that can be used to solve large‐scale assignment problems typical of military battle management systems. Attempts to parallellze the classical Hungarian method are explored. Drawing on experimental data, a regresslon model is derived that relates the Hungarian method's run time to a cubic function of the number of parallel processors used in the solution. Four parallel heuristics for solving the assignment problem are developed and analysed. Two of them perform well in a parallel environment. The first, based on Vagel's approximation, can be used to identify a feasible, near‐optimal assignment. The second algorithm partitions the assignment problem into independent subproblems across the parallel array. The resulting solution, although infeasible in the strict definition of the assignment problem, is seen to be reasonably good and can be obtained very rapidly. Either of these two heuristics are of potential use in the stringent computing environment of a real‐time resource management system.