Random contact strategy using the Kalman filter to solve the robotic contact uncertainty problem

This paper addresses the problem of finding the uncertainties present in a robotic contact. There are two kinds of uncertainties: grasping uncertainties and contact uncertainties. The grasping uncertainty vector contains errors (angles and displacements) associated with improper grasping. The contact uncertainty vector contains errors in angles and positions of nominal contact. A force sensor is used together with Kalman filters to solve the uncertainties. The straightforward use of Kalman filters is found to be effective in finding only some of the uncertainties. The quantities that form dependencies cannot be estimated in this manner. This dependency brings about the problem of observability. The unobservable quantities can be determined using a sequence of contacts. The error covariance matrix of the Kalman filter can indicate the directions of dependency and accuracy of the values estimated. A new contact in any of the dependent directions can be randomly chosen as the next contact to try. The relational transformations between contacts are used to eventually obtain the complete solution. A two dimensional contact situation will be used to demonstrate the effectiveness of the method. Experimental data are also presented to prove the validity of the procedure. Due to the non-linear relationship between the uncertainties and the forces, an extended Kalman filter (EKF) has been used.