Synthesis of Dynamic Responses of Redundant Robot Manipulators

In this paper, we present and validate a novel methodology that synthesizes the dynamic response of robotic manipulators performing Cartesian impedance-related tasks. By leveraging linear system theory and addressing the kinematic redundancies inherent in the system, we derive and directly solve equations to compute the damping parameters based on desired control criteria (damping ratios). The proposed equations correspond to the complex eigenvalues governing the system’s dynamics. Unlike existing approaches, this method bypasses complex optimization or iterative processes, providing direct solutions to damping or stiffness parameters. Our approach applies broadly, irrespective of specific redundancy conditions or Cartesian task coordinates. Using a 7-DoF robot, we demonstrate that multiple solutions can impose similar dynamic responses. We further show that the system’s natural frequencies must align with defined criteria, and while imposing damping ratios may suggest infinite possible frequency values, physically meaningful natural frequencies are calculated based on robot geometry, stiffness, and mass matrices. This ensures that these values are not arbitrary. This methodology contributes significantly to the field by simplifying implementation and improving system stability and predictability.