This chapter studies the decentralized robot arm cooperation with a hierarchical control topology. We present in this chapter a novel strategy capable of solving the problem even though there exists some robot arms unable to access the command signal directly. The cooperative task execution problem can be formulated as a constrained quadratic programming problem. By replacing the command signal with estimations with neighbor information, the control law becomes to work in the partial command coverage situation. We then prove in theory that the system indeed also globally stabilizes to the optimal solution of the constrained quadratic optimization problem. Simulations demonstrate the effectiveness of the method presented in this chapter.