Manipulability ellipsoids and polytopes are well-known tools to graphically represents these capabilities. This paper focuses on the evaluation of force capabilities for redundant manipulators, for which additional constraints must be imposed on the available joint torques in order to satisfy the static assumption. An algorithm to correctly evaluate the task space force polytope is given and a new definition of the force ellipsoid is proposed. The obtained results can be applied also to nonredundant manipulators in singular configurations. Numerical results are provided in the case of a planar redundant arm.

The use of a two-arm robot for assembling two objects, with each being held by one arm, is presented. More precisely, the authors propose some solutions for determining how and where such an assembly task should be performed. For the approach phase (before contact), they define the motion of one end-effector with respect to the other, without reference to any fixed frame. This allows them to take advantage of the two-arm robot redundancy. For the insertion phase, they use a symmetric hybrid control scheme. Real experiments with two PUMA robots have shown that the success of the assembly is highly dependent on the location where the assembly is performed. This is due to the control of contact forces between the objects, which can be done more or less properly. This problem is treated by using the concept of manipulability, represented by ellipsoids.

The authors present solutions for manipulating objects with two robotic arms, when force control is necessary. The applications of interest are the transport and assembly of rigid objects, the deformation, transport, and assembly of flexible objects, and the assembly in space of two objects, each being held by one arm. The authors present a theoretical solution for modeling the tasks and practical solutions implemented for controlling two six-axis arms.>