Constrained operational space control of kinematically redundant manipulators with subtask objectives via adaptive Szász–Mirakyan operators and barrier Lyapunov functions

This paper proposes a constrained adaptive operational space control method for kinematically redundant robot manipulators operating under uncertain nonlinear dynamics and external disturbances. The primary objective is to achieve accurate operational space tracking within predefined error constraints while concurrently regulating a secondary joint space goal through null space projection. To eliminate the necessity of deriving model dependent dynamic regressor matrices, uncertainties are actively captured via an adaptive Szász–Mirakyan operator based approximation structure. Exploiting its positive and linearly parameterized form naturally defined over a semi infinite domain, the proposed mechanism enables online compensation of uncertain nonlinear effects. A barrier Lyapunov function based analysis ensures that operational space tracking errors remain strictly inside the predefined admissible region throughout the entire motion. The null space subtask is embedded within an auxiliary error formulation through a projected component, preserving the primary operational space tracking objective. Rigorous Lyapunov stability analysis proves that all closed loop signals are uniformly ultimately bounded and that operational space error constraints are never violated despite approximation residuals and bounded disturbances. Finally, simulation studies on three and four degree of freedom kinematically redundant manipulators operating on a plane validate the theoretical developments, explicitly demonstrating successful barrier constraint enforcement, accurate online uncertainty approximation, and simultaneous subtask execution, with a comparison against a neural network based control strategy confirming the effectiveness of the proposed control framework.