In this article, stable local solutions with global characteristics are developed for the weighted joint torque optimization in redundant manipulator. Conditions for these symmetric weight matrices are found that can guarantee that the local optimization of joint torque weighted by these matrices will have the same stability and optimality as the local optimization for the inertia inverse weighted joint torque. The symbolic results of the weighted projection operator of Jacobian matrix are also derived. It is also proposed that the weight matrix plays an important role in avoiding instabilities by relating the null space of the Jacobian matrix to what the authors termed an effective null space of J.>

The nonlinear and cross-coupled dynamics of motor-manipulator systems is studied, and a control strategy is developed for achieving ease of controller design and high control performance. By using the algorithm developed in this paper, not only can the highly complicated motor-manipulator dynamics be effectively controlled, but the motors are also made "sensible" for sensing and compensating for the uncertain dynamics acting at manipulator joints. Furthermore, as a significant result, the modeling difficulty and control complexity of the manipulator dynamics can be significantly reduced.