This paper suggests a measure constraint locus which gives a global look at the performance of a subtask for a redundant manipulator. The measure constraint locus is the set of configurations satisfying the optimality constraint for a measure in the joint configuration space. The significance of this paper is that the measure constraint locus as well as self-motion manifolds must be considered to uniquely define inverse kinematic solutions. Using the measure constraint locus for manipulability measure, the topological property of the configuration space for finding equilibrium configurations is analyzed and the invertible workspace without singularites is described. Through numerical examples for cyclic tasks, we discuss some limitations of the inverse kinematic algorithms in which the redundancy is resolved through the imposition of optimality constraint. And a promising algorithm which provides a conservative joint trajectory without singularities for almost entire workspace is proposed. Also, by using the measure constraint locus, we evalute the characterization of four dexterity measures for singularity avoidance, and we investigate the global properties for each dexterity measure. And we propose a method for the global optimization of redundancy with an integral-type criterion. The necessary conditions based on the calculus of variations result in a second-order differential equation. For a cyclic task, the boundary conditions for conservative joint motions are discussed. Then, we reformulate a two-point boundary value problem to an initial value adjustment problem and suggest a numerical search method based on the iterative optimization for providing a globally optimal solution using the gradient projection method. Since the initial joint velocity is parameterized with the number of redundancy, we only search parameter values in the parameterized space. Finally, we discuss an algorithm for topological liftings of the paths and demonstrate the generality of the proposed method by considering the dynamics of a manipulator.
