Optimal Damping Factor for the Least Squares Inverse Kinematics for the Steam Generator Inspection System

The Steam Generators used in the Prototype Fast Breeder Reactor have sodium on shell side and water/steam on the tube side. Tube inspection and qualification of all 547 tubes, enhances the safety and reduces the operation cost by increasing plant availability. In this work, a two-axis planar reach robotic arm called as Tube Locator Module (TLM) is used for reaching and orienting the Remote Field Eddy Current (RFEC) testing probe at the exact location of individual Steam Generator tube, and the probe is pushed through the entire tube length for inspection and qualification of the same. A conventional method of inverting the Jacobian and using a pseudo inverse will help in running the actuators in joint space to reach the desired position of the end effector. However, as pseudo inverse suffers numerical stability close to singularities of the manipulator, hence it is proposed to use the damped least squares pseudo inverse method by introducing a damping factor to improve the stability. Higher damping factor increases the stability of manipulator, even when the manipulator moves closer to its singular configurations. However, higher damping factors lead to more tracking error in the end-effector trajectory. Hence, in this work, based on the tracking errors and the geometrical constraints, an optimal damping factor is arrived at for the smooth motion of the TLM. This paper also deals with the manipulability study of the TLM to understand the singular configurations, and apply the damping factor to stabilize the joint angular velocities without causing much error in the end-effector trajectory.