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Abstract
New approaches are developed for the solution of inverse instantaneous kinematic problems for manipulators, and for the solution of contact forces required for multiple contact grasping.
A screw decomposition is introduced for resolving screw quantities which are sequentially reciprocal to screws representing the joint axes of a manipulator. Based on the results of this screw decomposition, an approach is developed for the identification of joint displacement configurations leading to the degeneration of the end effector motion capability. The screw decomposition also identifies a particular joint rate solution and a null-space basis for the matrix of joint axes screws, allowing a general joint rate solution to be found.
Using the general joint rate solution form described above, optimal joint rate solutions for several manipulation objectives are derived for manipulators having redundant joints. These optimal solutions require only the inverse of a matrix having a dimension equal to the number of redundant joints. Further, an approach is developed for finding joint rate solutions for kinematically coupled multiple-arm manipulators. This approach is based upon assembling general joint rate solutions for the individual arms, and allows most of the required computations to be performed at the individual arm level.
A technique is introduced for resolving acceptable joint rates for manipulators incapable of producing desired end effector velocities. The method is based upon finding feasible alternative end effector motions, using reciprocal screw quantities and optimization techniques. Application to manipulators operating near degenerate configurations is considered.
Approaches are developed for the examination of the feasibility, and for the optimization, of the contact forces required for multiple contact grasping. These approaches are based upon consideration of the internal forces of grasps. Analytical bases are derived using screw decomposition, for the possible internal forces of grasps formed from point contacts with friction. These bases are used to examine the feasibility of specific grasps. A method is introduced for determining internal force directions having minimal friction dependence, for grasps formed from three point contacts with friction. This method is novel in its consideration of arbitrary contact surface normal directions.
The developed approaches are demonstrated through application to several practical manipulation systems.
