Avik Chatterjee, S. Majumder & I. Basak International Journal of Robotics and Automation (IJRA), Volume (4) : Issue (1) : 2013 31 Compensating Joint Configuration through Null Space Control in Composite Weighted Least Norm Solution Avik Chatterjee avik@cmeri.res.in CSIR-CMERI MG Avenue Durgapur, 713209, India S. Majumder sjm@cmeri.res.in CSIR-CMERI MG Avenue Durgapur, 713209, India I. Basak indrajit.basak@me.nitdgp.ac.in Department of Mechanical Engineering NIT MG Avenue Durgapur,713209,India Abstract We have presented a methodology for compensating joint configuration by composite weighting in different sub spaces. It augments the weighted least norm solution by weighted residual of the current joint rate and preferred pose rate in null space, so that we can arrive at a solution which is able to handle both joint limits and preferred joint configuration simultaneously satisfying the primary task. The null space controller is formulated in conjunction with the work space controller to achieve the objective. The contribution of null space has been discussed in the formulation in two different situations including joint limits, workspace and near configuration singularities. Keywords: Null Space Controller, Weighted Least Norm, Joint Limit, Singularity, Joint Configuration. 1. INTRODUCTION A robotic manipulator in general sense or an articulated serial structure in particular is kinematically redundant when the number of operational space variables necessary to specify a given task, is less than the number of joints. Redundancy leads to infinite solutions for the joint space but offers greater flexibility and dexterity in motion as different constraint based or goal based criteria can be formulated as sub tasks in the solution. Two kinds of approaches have been reported in the literature to deal with this situation. One is set to exploit the null space of the Jacobian matrix in the homogeneous solution that infuses self motion of joints without affecting the task space. Typical method of this kind is gradient projection method (GPM) [1][2]. In GPM the anti-gradient of a quadratic cost function, is projected in the null space of the task Jacobian, which is reminiscent of the projected gradient method for constrained minimization. The other approach is weighted least norm (WLN) approach [3][4], which minimizes the weighted norm of joint rate. In both the cases the primary task is to follow the prescribed trajectory and there may be multiple secondary tasks or nested subtasks with priority fixation [5] [6]. GPM has been used in Joint Limit Avoidance (JLA), obstacle avoidance [7], visual servoing [4]. WLN which was introduced in JLA in [3], has been successfully exploited by others with single or multiple criteria and Close Loop Inverse Kinematics (CLIK)[8]. Null space based motion control [9] has been studied with configuration optimization [10], influence of un-weighted and inertia weighted pseudoinverse [11], proportional-integral-derivative (PID) controller considering passivity [12], task priority implementation based on behavioral scheme [13]. An elaborate