Global task space manipulability ellipsoids for multiple-arm systems

Abstract

New definitions of force and velocity manipulability ellipsoids for multiple-arm systems are given in this paper. A suitable kinetostatic formulation for multiple cooperating arms is adopted that allows a global task space description of external and internal forces as well as absolute and relative velocities at the object level. The well-known concept of a force manipulability ellipsoid for a single arm is formally extended to the multiarm case by regarding the whole system as a mechanical transformer from the extended joint space to the global task space. Kinetostatic duality properties are then conveniently exploited to derive velocity manipulability ellipsoids for the multiple-arm system. The proposed method is compared with other approaches via numerical examples.

Kinematic manipulability of general constrained rigid multibody systems

“…For the specific cases of multifinger grasp, the development here is similar to that in [12] and [13] and the more recent work in [18].…”

“…Characterization for both velocity and force ellipsoids is presented. When applied to multiple cooperative arms employing a rigid grasp or to multiple finger grasping, this work is closely related to the work by [10] and [11] and is also closely related to the past work by [12] and [13]. We also extend the important concepts of grasp stability and manipulability.…”

“…Due to the constraint (1), only a certain slice of the ball (resp., ellipsoid) is feasible. It is reasonable to define the constrained ellipsoid as the set of spatial task velocities generated by a unit ball in the active joint velocity space: (20) The general kinematic equation (1) can be used to solve for . Partition and according to the dimension of and (active and passive joints):…”

“…We obtain explicit characterization for both properties and present their physical interpretation. As illustrations, we include a planar Gough-Stewart platform, a full 6-DOF Gough-Stewart platform, and a planar two-finger grasping example from [12] and [13].…”

Positioning Two Redundant Arms for Cooperative Manipulation of Objects

“…When performing cooperative tasks, or grasping an object with multiple arms, there are approaches to obtain a combined manipulability [16,17]. However, combined manipulability computation for multiple arms holding an object relies on the arms poses, which are unknown for our workspace representation, as we use the average of many IK computations with different orientations and the redundancy of the robot gives us infinite solutions.…”