Immersion and invariance adaptive tracking control for robot manipulators with a novel modified scaling factor design

Abstract

SummaryThe robot manipulators' tracking control problem in the presence of inertia uncertainties is addressed in this paper, and a novel dynamic scaling–based immersion and invariance (I&I) adaptive tracking controller is utilized to stabilize the proposed system. By virtue of the reconstruction method of the parameter regression matrix, this paper provides a new perspective on how to overcome the integrability obstacle typically arising in the I&I controller design through dynamic scaling and presents a new controller design method. What is more, a novel modified scaling factor is proposed as well so that the controller can be implemented without the prior knowledge of the inertia matrix's lower bound, and only the saturation function involving the scaling factor is included in the feedback gains. Finally, the numerical simulations show the validity of the proposed controller.

Output feedback tracking control for rigid body attitude via immersion and invariance angular velocity observers

“…By applying Young inequality similarly, the Equations (25) and (33) can be further derived in the followinġ…”

“…Recent years, References 22-24 shed light on the immersion and invariance (I&I) observer design method aided by dynamic scaling technique, which effectively overcame the "integrability obstacle" typically emerging in the I&I methodology. 22,25 On account of the existence of gyroscopic term in the governing dynamics of the rigid-body motion, the main difficulties in the I&I angular velocity observer design are the elimination of the additional disturbance resulting from the nonlinear gyroscopic compensation term including the observer states in the observer dynamics. The solutions to the problem in References 15,18 are to redesign a three-dimensional filter for observer states, and then the additive disturbance is removed by dynamic scaling skills and high gain injection.…”

Dynamic scaling‐based adaptive control without scaling factor: With application to Euler–Lagrange systems

“…From a practical standpoint of view, the closed-loop performance the model-based controller guarantees does relatively rely on how precisely the mathematical formulation you build matches with actual physical system. 1,2 However, it is inevitable the mathematical model exists more or less uncertain plant parameters because the system parameter identification cannot always be ideally achieved in practice. 3,4 To handle this problem, a considerable amount of researches has concentrated on pursuing nonlinear adaptive control methodologies due to the robustness against parametric uncertainties.…”

“…Thus, the large scaling factor appeared in the feedback gains with a quadratic form could result in "high-gain" control action and undesired transient behavior of the closed-loop systems. 2,14,29 In this paper, the dynamic scaling based I&I adaptive control approach is further improved. First, a new regressor matrix reconstruction method to overcome the integrability obstacle is presented, which is easier to tune.…”

Immersion and Invariance Adaptive Control for Spacecraft Pose Tracking via Dual Quaternions

“…As a novel noncertainty equivalent (NCE) method for adaptive control of nonlinear systems with uncertain parameters [38][39][40][41], immersion and invariance (I&I) adaptive control has great potential to overcome many limitations resulting from the CE-based methods. It has been effectively utilized in the attitude [36,[42][43][44][45] and/or orbit control [46][47][48][49] with unknown inertial or mass parameters and has shown significant improvements in both closed-loop performance and adjustability of the estimation convergence process. However, little attention has been paid to its application in tackling unknown disturbances in the six-DOF motion control.…”