Abstract
At the outset, a nonlinear dynamic system for the generalized robots with input constraint is given to design an adaptive fixed-time fault-tolerant constraint control (AFTFTCC) for trajectory tracking. The proposed AFTFTCC includes a nonlinear filtering tracking error, which can shape the system response. As the operating point is in the neighborhood of the zero nonlinear filtering tracking error, nonlinear filtering gains are increasing to accelerate its tracking ability. The skew-symmetric matrix's condition for the time-derivative of the inertia matrix and Coriolis and centrifugal force matrix is not required. The upper bound of uncertainties is learned to improve system performance. The stabilities of the closed-loop system are verified by the Lyapunov stability theory. Without true force feedback, the cooperative task of multiple robots with multiple arms is also addressed by the proposed AFTFTCC. Finally, two examples, including the trajectory tracking control of planar three-link robot arm and the cooperative control of dual planar three-link robot arms, are employed to validate the effectiveness and robustness of the proposed control.
Highlights
Cooperative control has been extensively studied in many practical applications [1]–[14]
In the cooperative control for robotic manipulators, multiple arms need to handle a common payload, and a closed kinematic chain mechanism is formed, which imposes a series of constraints on the position and velocity, especially for the humanoid robots
Fig. 1): (i) The proposed adaptive fixed-time fault-tolerant constraint control is designed with nonlinear filtering gains such that the VOLUME 8, 2020
Summary
Cooperative (or formation) control has been extensively studied in many practical applications [1]–[14]. The proposed adaptive finite-time fault-tolerant constrained control (AFTTFTCC) for the tracking control of robot manipulator and the cooperative control of multiple robots with grasped object includes the following advantageous features: (i) without the condition of skew-symmetric matrix (cf., Properties P2 and P3) as compared with some previous studies [3], [4], [21]; (ii) without an extra addition of persistent signal [26] to accelerate the parameter convergence and without the true force feedback [2] to design the cooperative control of multiple robots (see Remark 6); (iii) possessing nonlinear filtering tracking error to shape the system frequency response [34] together with the fault and constrained control torque [13]. The proposed adaptive finite-time fault-tolerant constrained control (AFTTFTCC) for the tracking control of robot manipulator and the cooperative control of multiple robots with grasped object includes the following advantageous features: (i) without the condition of skew-symmetric matrix (cf., Properties P2 and P3) as compared with some previous studies [3], [4], [21]; (ii) without an extra addition of persistent signal [26] to accelerate the parameter convergence and without the true force feedback [2] to design the cooperative control of multiple robots (see Remark 6); (iii) possessing nonlinear filtering tracking error to shape the system frequency response [34] together with the fault and constrained control torque [13]. (iv) a simplified on-line learning uncertainty compensation (see (15) and Lemma 2) as compared with fuzzy neural approximation [2]–[5], [10], [28] (see Lemma 3 for computational complexity); (v) possessing nonlinear filtering gains increasing to accelerate its tracking ability and to obtain a better noise-endured characteristic [9], [10], [31]–[34] as the operating point is in the vicinity of the zero nonlinear filtering tracking error; (vi) no requirement of state estimator [10], [12] or disturbance observer [14] to simplify the control scheme
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