Fixed‐time cooperative control for robotic manipulators with motion constraints using unified transformation function

Abstract

This article investigates the fixed‐time consensus tracking control problem for multiagent systems composed of uncertain l‐link robotic manipulators with position and velocity constraints. Fuzzy logic systems are employed to model the uncertain dynamic of the robotic manipulators. In order to cope with the asymmetric yet time‐varying constraints, a nonlinear transformation function is introduced. With the help of the nonlinear transformation function, the original constrained manipulator systems are converted into the equivalent systems without constraint. As long as the boundedness of the state variables in the transformed systems is ensured, the constraint conditions of the original systems are not violated. Then, a fixed‐time adaptive fuzzy control scheme is developed. Under the proposed control method, the consensus tracking error can converge into a small neighborhood of origin in fixed‐time, and all the signals in the closed‐loop systems are bounded. Meanwhile, the motion constraints are not violated all the time. Specially, in view of the property of nonlinear transformation function, it is not necessary to change the control structure when the systems are subjected to no state constraint. Finally, a simulation is presented to illustrate the feasibility and effectiveness of implementing the proposed control algorithms.

Fixed-time Output Feedback Stabilization and Settling Time Analysis for High-Order Integrator Systems

“…Lemma 2.4. [28] The system (1) is practically fixed-time stable if ∀δ > 0 there exist a positive definite function V δ (t, x) and parameters…”

“…At the same time, the existing fixed-time controls established for state constrained systems fail in the cases with both constrained and unconstrained states. Although reference [28] designed a unified fixed-time controller for robotic systems with state constraints, it was only applicable to second-order systems.…”

Fixed-time safe tracking control of uncertain high-order nonlinear pure-feedback systems via unified transformation functions

“…At the same time, the existing fixed-time controls established for state constrained systems fail in the cases with both constrained and unconstrained states. Although reference [22] designed a unified fixed-time controller for robotic systems with state constraints, it was only applicable to second-order systems.…”

Adaptive task‐space cooperative tracking control for manipulators with a desired trajectory estimator and a velocity observer

“…To date, considering the theoretical and practical significance of cooperative problems, scholars and experts have made great progress in the cooperative control of first-order and second-order multi-agent systems. [3][4][5][6] Different from the cooperative problems of first-order and second-order networked systems, the cooperative problem is more complicated for multiple robotic manipulators [7][8][9][10] because of kinematic and dynamic uncertainties and high nonlinearity. Due to the wide range of practical applications, cooperation for robotic manipulators has become a research hotspot in the past few years.…”

“…Different from the cooperative problems of first‐order and second‐order networked systems, the cooperative problem is more complicated for multiple robotic manipulators 7‐10 because of kinematic and dynamic uncertainties and high nonlinearity. Due to the wide range of practical applications, cooperation for robotic manipulators has become a research hotspot in the past few years.…”