Load Distribution between Two Coordinating Robots by Nonlinear Programming

Coordinating two industrial robots to perform tasks is essential for those tasks that cannot be accomplished by using only one robot [1-5]. When the two robots make a direct or indirect contact, they form a closed kinematic chain. The combined degrees of freedom of the chain is usually larger than six so that the redundancy occurs [6]. Thus the joint solution for a given task is not unique unless realistic constraints and conditions are added to the problem. Among these additional requirements, the bounds on the magnitudes of joint torques and the least energy consumed at the joints are practical choices. These conditions yield a set of linear inequality constraints and a nonlinear objective function. They form an optimization problem which can naturally be solved by the technique of nonlinear programming. Since only the objective function is nonlinear, it is feasible to apply the method of approximate programming which is developed by Griffith and Stewart [71]. In the following sections, this problem will be defined and discussed in details.