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 underspecified. Therefore, methods for obtaining the wrench distribution in an in-parallel system can be applied to the underconstrained inverse kinematics problem for serial-chain manipulators. In particular, a solution that minimizes a weighted-norm of the joint rates vector is derived in this article. 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. Finally, a geometric interpretation of the solution is provided using screw system theory.
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