Data-Driven Kinematic Model for the End-Effector Pose Control of a Manipulator Robot

This paper presents a data-driven kinematic model for the end-effector pose control applied to a variety of manipulator robots, focusing on the entire end-effector’s pose (position and orientation). The measured signals of the full pose and their computed derivatives, along with a linear combination of an estimated Jacobian matrix and a vector of joint velocities, generate a model estimation error. The Jacobian matrix is estimated using the Pseudo Jacobian Matrix (PJM) algorithm, which requires tuning only the step and weight parameters that scale the convergence of the model estimation error. The proposed control law is derived in two stages: the first one is part of an objective function minimization, and the second one is a constraint in a quasi-Lagrangian function. The control design parameters guarantee the control error convergence in a closed-loop configuration with adaptive behavior in terms of the dynamics of the estimated Jacobian matrix. The novelty of the approach lies in its ability to achieve superior tracking performance across different manipulator robots, validated through simulations. Quantitative results show that, compared to a classical inverse-kinematics approach, the proposed method achieves rapid convergence of performance indices (e.g., Root Mean Square Error (RMSE) reduced to near-zero in two cycles vs. a steady-state RMSE of 20 in the classical approach). Additionally, the proposed method minimizes joint drift, maintaining an RMSE of approximately 0.3 compared to 1.5 under the classical scheme. The control was validated by means of simulations featuring an UR5e manipulator with six Degrees of Freedom (DOF), a KUKA Youbot with eight DOF, and a KUKA Youbot Dual with thirteen DOF. The stability analysis of the closed-loop controller is demonstrated by means of the Lyapunov stability conditions.