Stabilised Koopman Kinematic Modelling and Tracking Control of a Manipulator

Abstract

This paper presents a Koopman-based data-driven kinematic modelling and tracking control framework for a 7-DOF manipulator. State and squared-state lifting functions map the nonlinear forward kinematics into a linear lifted space, where system matrices are identified via ordinary least squares and stabilised by scaling eigenvalues to a spectral radius below unity, ensuring asymptotic stability. Combined with a linear quadratic regulator, the stabilised model is evaluated on real robot data. Single-step prediction yields joint angle errors within ±0.005 rad and end-effector position errors predominantly below 0.005 m with a concentrated distribution. In closed-loop tracking of an unseen circular trajectory, the stabilised model converges within approximately 2 s and maintains millimetre-level periodic accuracy, whereas the unstabilised model diverges immediately. The results confirm that eigenvalue stabilisation is essential for reliable kinematic control and that the proposed framework captures the intrinsic kinematic structure of the manipulator with strong generalisation from limited data.