Iterative estimation of the end-effector apparent gravity force for 3DoF impedance haptic devices

The position-dependent apparent gravity acting on the end-effector of impedance haptic devices may represent a loss of transparency, and generally requires to be actively compensated. To that purpose, a new approach to the problem of gravity compensation was introduced in our previous work [1]. The apparent gravity is preliminarily estimated in a given set of positions inside the workspace, then the acquired data are used to set up a suitable gravity compensation control law. At each position of the aforementioned set, the estimation is performed via an iterative method based on a nonlinear model subject to a feedback-linearizing PD controller. This paper, which builds upon our previous contribution, improves the mathematical formulation of the problem and addresses the analysis of stability and convergence properties of the iterative estimation method. Finally guidelines for performance-based parameter design are discussed. Validation experiments have been performed, and results are in good agreement with theoretical findings.