Kinematic solution and singularity analysis for 7-DOF redundant manipulators with offsets at the elbow

Redundant manipulators can accomplish much more challenging tasks than traditional industrial manipulators. However, it is tedious to compute the analytical inverse kinematic solution and analyze it's singularity configurations with Jacobian matrix. No general closed-form techniques have been developed so far. This paper uses the joint parameterization method to derive a closed-form analytical inverse kinematic solution of a 7-DOF manipulator with offset at the elbow which is made by Kinova Robotics. Then vector product method is proposed to calculate the Jacobian matrix and the complex singularity problem is decoupled into quite simple position singularity problem and orientation singularity problem. Moreover, the approach of damped least-squares is proposed to avoid the singularity. The simulation of the joints' movement of this manipulator is implemented by MATLAB and the simulation results validate the reliability and high-efficiency of the proposed algorithm in this paper, which is suitable for application in industrial robot control.