An application of force ellipsoid to the optimal load distribution for two cooperating robots

The optimal load distribution for two cooperating robots is studied, and a solution approach utilizing a force ellipsoid is presented. The load distribution problem is formulated as a nonlinear optimization problem with a quadratic cost function. The effort exerted by the robots to follow the specified motion is defined to be the joint torque norm square, and the optimal solution minimizing the effort is obtained using the concept of the force ellipsoid and nonlinear optimization theory. Despite the presence of the joint torque constraints, the optimal solution is obtained almost as a closed form which requires small computation time. The proposed solution approach is illustrated and the internal force effect is studied using a numerical example