Local optimization of weighted joint torques for redundant robotic manipulators

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