A reduced-complexity description of arm endpoint stiffness with applications to teleimpedance control

Effective and stable execution of a remote manipulation task in an uncertain environment requires that the task force and position trajectories of the slave robot be appropriately commanded. To achieve this goal, in teleimpedance control, a reference command which consists of the stiffness and position profiles of the master is computed and realized by the compliant slave robot in real-time. This highlights the need for a suitable and computationally efficient tracking of the human limb stiffness profile in real-time. In this direction, based on the observations in human neuromotor control which give evidence on the predominant use of the arm configuration in directional adjustments of the endpoint stiffness profile, and the role of muscular co-activations which contribute to a coordinated regulation of the task stiffness in all directions, we propose a novel and computationally efficient model of the arm endpoint stiffness behaviour. Real-time tracking of the human arm kinematics is achieved using an arm triangle monitored by three markers placed at the shoulder, elbow and wrist level. In addition, a co-contraction index is defined using muscular activities of a dominant antagonistic muscle pair. Calibration and identification of the model parameters are carried out experimentally, using perturbation-based arm endpoint stiffness measurements in different arm configurations and co-contraction levels of the chosen muscles. Results of this study suggest that the proposed model enables the master to naturally execute a remote task by modulating the direction of the major axes of the endpoint stiffness and its volume using arm configuration and the co-activation of the involved muscles, respectively.