The paper addresses a significant challenge in on-orbit robotics servicing and assembly, which is to overcome the saturation setback of force/torque on robot joint and spacecraft actuators during the post-capture stage while controlling a target spacecraft with uncontrolled large angular and linear momentums. The authors propose a novel solution based on two robust and efficient control algorithms: Optimal Control Allocation (OCA) and Non-linear Model Predictive Control (NMPC). Both algorithms aim to minimize joint torques, spacecraft actuator moments, contact forces, and moments of a compound redundant system that includes a common payload (target spacecraft) grasped by dual n-degree space robotics manipulators mounted on a chaser spacecraft. The OCA algorithm minimizes a quadratic cost function using only the current states and the system dynamics, but the NMPC also considers the future state estimates and the control inputs over a specified prediction horizon. It is computationally more involved but provides superior results in reducing joint torques. The literature to date in application of MPC to robotics mainly focuses on linear models but the dual arm coordination is highly non-linear and there is no MPC application on dual arm coordination. The proposed discretized technique offers exact realizations (of a non-linear model) with elegance and simplicity and yet considers the full non-linear model of the dual arm coordinating system. It is computationally very efficient. The computer simulation results show that the proposed algorithms work efficiently, and the minimum torques, contact forces, and moments are realized. The developed algorithm also is very efficient in tracking problems.