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.

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A novel immersion and invariance (I&I) angular velocity observer is presented for the attitude tracking control of a rigid body with the lack of angular rate. Global exponential convergence of angular velocity estimate errors are guaranteed by an innovative filter design for the estimates' Euclidean norm. The proposed method requires fewer filter states compared with existing I&I angular velocity observer designs, which achieves a simpler closed-loop structure (dynamic reduction). The observer synthesis and convergence are independent of the control torque, which leads to much convenience in establishing "separation property" when combining a proportional-derivative attitude tracking controller driven by angular velocity estimates. A rigorous stability analysis is provided to ensure the (almost) global asymptotic convergence of the overall closed-loop tracking errors, and several numerical simulations are carried out to demonstrate the effectiveness of the combined implementation of proposed angular velocity observer and full-state feedback attitude tracking controller.

A modular dynamic scaling-based immersion and invariance (I&I) adaptive control framework for a class of nonlinear system with parametric uncertainties is presented in this paper. The framework is based on an invariant manifold approach which allows for predefined target dynamics to be assigned to the closed-loop systems. The integrability obstacle typically inherent to I&I methodology is overcome by the matrix reconstruction and dynamic scaling technique.The prominent feature is that this methodology can be implemented without scaling factor, and hence the introduction of the scaling factor is just to prove the additive disturbance brought by the matrix reconstruction can be eliminated by constant feedback gains. Moreover, the bounded robustness against three different types of disturbance is verified. As an application, Euler-Lagrange systems with unknown inertia parameters are applied to illustrate the effectiveness of the proposed method.

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