Motion Coordination for Redundant Robots by Tracking 
Position-Level Equality Constraints

Abstract - This paper describes a novel motion coordination method  for redundant robots. The method combines closed-form  reverse position analysis and multi-criteria optimization to form a powerful and efficient algorithm. This method of redundancy resolution has been tested (either in simulation or experimentation) on robots with 7, 8, 9, 10, 17, and 21 DOF. This paper presents results for a dual-arm robot with 17 DOF designed and implemented at Oak Ridge National Lab.

Introduction - 
Motion coordination for redundant robots enjoys a rich history as a part of the inverse kinematics problem. Dimentberg in the 1950’s and Freudenstein in the 1960’s and 1970’s were seminal authors. With the realization in the late 1960’s that a serial robot could be modelled as a spatial mechanism, the disciplined and analytical theory of mechanisms was applied to the exciting new field of robotics. This work dominated inverse kinematics research during the 1970’s as the search for a general closed-form solution for robots with six Degrees Of Freedom (DOF) became the “Mount Everest” of kinematics problems (Freudenstein, 1972). Duffy, Pieper, and Roth were at the forefront of inverse kinematics research during this time. 

Within the context of redundant robots, the focus shifted towards optimization and linear algebra during the 1980’s. Much of this work derives from Whitney’s (1969) resolved motion rate control that suggests the use of the pseudo-inverse to resolve redundancy. Liegeois (1977) showed the extension of this method to include self-motions via the null-space. Since then, a large number of researchers have implemented pseudo-inverse based methods. Notable approaches include: Seraji’s (1992) configuration control, Baillieul’s (1986) extended Jacobian, and the Jacobian transpose (Das, Slotine, and Sheridan, 1988). Dubey and Luh (1988) include task-based performance measures in the redundancy resolution. Maciejewski (1989) discusses the kinetic limitations of redundant robots. 

This paper discusses a motion coordination method that has shown great promise in both simulation and application. Essentially, the method uses closed-form reverse position analysis to satisfy the placement constraints on the robot’s hand and numerical optimization to resolve the redundancy. The numerical 
optimization generates configuration options and, based on a six DOF substructure of the robot’s geometry, closed-form reverse position analysis ensures the options satisfy the placement constraints. This process explicitly identifies configuration options within the robot’s null space. A decision making process based on multiple performance criteria chooses one option as the next set-point for the robot’s servo controllers. Crane, Duffy, and Carnahan (1991) have also shown the use of closed-form reverse position analysis to solve 6 DOF substructures within a redundant robot, though they leave the decision making to a human operator.  Next Page ->