Optimal load distribution for two cooperating robot arms using force ellipsoid

The optimal load distribution for two cooperating robots is studied in this paper, and a new solution approach utilizing force ellipsoid is proposed. The load distribution problem is formulated as a nonlinear optimization problem with a quadratic cost function. The limit on instantaneous power is considered in the problem formulation as the joint torque constraints. The optimal solution minimizing energy consumption is obtained using the concept of force ellipsoid and the nonlinear optimization theory. The force ellipsoid provides a useful geometrical insight into the load distribution problem. Despite the presence of the joint torque constraints, the optimal solution is obtained almost as a closed form, in which the joint torques are given in terms of a single scalar parameter that can be obtained numerically by solving a scalar equation.