Obstacle avoidance for redundant manipulators based on a novel gradient projection method with a functional scalar

A new Gradient Projection Method is constructed. The optimization problem with an unequal constraint of joint velocity limit defined by infinity norm is solved, and its analytical form is derived to achieve the best optimization ability within a given joint velocity limit. Based on its optimization ability, and the concern of joint velocity limit, comparison with fixed scalar algorithm is made. A vision-based system is constructed and real time obstacle avoidance experiment is implemented with this new method. The results show that this new method is superior to other methods. It can automatically change the value of scalar k to make the robot obtain the best optimization ability, have no numerical oscillations and meet any specified joint velocity limit in terms of the infinity norm.