Composite learning adaptive control in Cartesian space for redundant manipulators via least-squares modulation

Abstract This paper presents a Cartesian-space composite learning adaptive controller whose least-squares modulation-based update law tracks the prescribed tasks and identifies the uncertain dynamic parameters of redundant robot manipulators. Unlike joint-space control strategies, the developed method does not require inverse kinematic solutions, an advantage for redundant manipulators with multiple inverse kinematic solutions. The controller ensures exponential convergence of the end-effector tracking error, subtask objectives, and parameter estimation error on a prescribed singularity-free operating region under the interval excitation condition, which is weaker than persistence of excitation. A novel error system is paired with a composite learning update law whose learning term converges at a rate independent of the excitation levels of the regressor channels once the stored data are sufficiently informative, which simplifies the learning-gain tuning. A continuously regularized inverse of the information matrix in the adaptation law ensures convergence of all uncertain parameters to their true values under interval excitation above the regularization threshold. Convergence is established by a Lyapunov-based analysis. Comparative simulations on a three-link revolute manipulator demonstrate improved tracking, subtask, and parameter estimation accuracy over existing methods in the nominal case, and simulations with measurement noise and external disturbances evaluate the robustness of the developed controller.