A compact inverse velocity solution for redundant robots

A compact inverse rate kinematics solution for serial-chain redundant n-jointed robots is presented. The serial-chain inverse rate kinematics problem is dual to the inverse statics problem in in-parallel systems such as cooperating robots, in which the task of distributing the load wrench between multiple subsystems is typically under-specified. Therefore, the method proposed earlier in J.H. Kim and V. Kumar (1991) and V. Kumar (1990) for obtaining the wrench distribution in multirobot systems can be applied to redundant serial-chain manipulators. The solution thus obtained is one in which a weighted-norm of the joint rates vector is minimized. The advantages of this method are the ability to accommodate any type of joint and the availability of analytical, closed-form solutions for the joint rates. A geometric interpretation of the solution is provided using screw system theory