Data-Driven Identification of the Jacobian Matrix of a 2-DoF Spherical Parallel Manipulator

Modeling is the first step in identification of the behavior of a system. Moreover, the first step in controlling a system consists in identifying its behavior, accurately. In general, analytical methods were used to identify the kinematics behavior of a system. In the kinematic analysis, the most important issue is to find the Jacobian matrix which maps the angular velocities of the end-effector to the angular velocities of the actuated joints. Furthermore, the Jacobian matrix is needed for control purposes. In recent years, several data-driven methods were presented for the identification of linear and nonlinear dynamical systems. The Sparse Identification of Nonlinear Dynamics (SINDy) is one which characterizes the nonlinear equation of the system solely using input/output data. In this study, the foregoing method is applied in order to find the Jacobian matrix of a two Degree-of-Freedom Agile Eye robot which performs spherical motion. The aforementioned robot is an over-constrained mechanism which adds number of difficulties in computing the Jacobian matrix using the analytical method. Finally the nonlinear equations of the Jacobian matrix are acquired using the SINDy method. Comparing the results obtained by the SINDy method with the values obtained by simulation indicates the accuracy of the method. Moreover, the calculation time has been significantly reduced compared to the analytical approaches, which is a definite asset for real-time modeling and control purposes.