This paper investigates the use of an infinity norm in formulating the optimization measures for computing the inverse kinematics of redundant arms. The infinity norm of a vector is its maximum absolute value component and hence its minimization implies the determination of a minimum effort solution as opposed to the minimum-energy criterion associated with the Euclidean norm. In applications where individual magnitudes of the vector components are of concern, this norm represents the physical requirements more closely than does the Euclidean norm. We first study the minimization of the infinity-norm of the joint velocity vector itself, and discuss its physical interpretation. Next, a new method of optimizing a subtask criterion, defined using the infinity-norm, to perform additional tasks such as obstacle avoidance or joint limit avoidance is introduced. Simulations illustrating these methods and comparing the results with the Euclidean norm solutions are presented.

In this paper, the authors present a new control algorithm for multiple cooperating mechanisms manipulating a common object, with rolling contact between the end-effectors and the object. The algorithm is based on a new dynamic formulation, in which the rolling degrees of freedom between the end-effector and the object are modeled as one or more unactuated joints of the manipulator. Such an augmentation of the rolling contacts imparts each manipulator with additional degrees of freedom and could also make it kinematically redundant. This can be exploited for the satisfaction of a secondary subtask criterion such as collision avoidance. In addition, a control law can be specified that enables simultaneous control of the object trajectory, the internal forces in the object and the trajectories of the contact points on the object or the end-effecters.

The authors introduce a novel formulation of subtask performance for redundant manipulators. This formulation uses the singularity robust inverse (SRI), which is effective in yielding feasible joint motions in single regions, in conjunction with a homogeneous-like joint velocity component to perform an additional subtask such as obstacle avoidance. This novel inverse kinematic scheme enables the manipulator to overcome singularities (or, more accurately, avoid infeasible joint motions at or near singular configurations) and avoid obstacles in addition to the main motion task. The attractive aspect of this scheme is that it results in the satisfaction of two subtasks without requiring two explicit subtask criteria. This is because one of the subtasks, i.e., feasible joint motion, is implicitly incorporated in the particular solution in the form of the SRI. As depicted in simulations, the proposed formulation proves to be an effective inverse kinematic solution in singular regions of the manipulator workspace.>