A new mapping method for joint and Cartesian stiffness, damping and mass matrices for large displacement in impedance control

This paper investigates mapping of stiffness, damping and mass matrices for joint and Cartesian space in robot impedance control. The stiffness mapping is studied more than others for serial and parallel robots by lots of researchers. But all the mapping methods are considered for small displacement or static problems. In fact there is no formulation for large displacement or dynamic problems. So in the presented paper, impedance mapping is studied by considering old methods against new one. The new proposed method is called Large Displacement Mapping Method. Two main methods are presented in researchers’ works and are studied beside the new proposed one in this paper. A test is designed and simulated by Simulink/MATLAB in order to analyze different methods clearly. Then the proposed test is applied on a SCARA robot practically. According to simulation and experimental results, only the proposed method can map the stiffness, damping and mass matrices in large displacement case. The results show, as robot is getting away from the initial position, more deviation is happened. Considering impedance control mapping results, two main differences are seen in stiffness and damping matrices while mass matrix mapping result is the same in all three methods.