Survey/review study
The Cooperative Output Regulation by the Distributed Observer Approach

Youfeng Su 1, He Cai 2, and Jie Huang 3,*


1 College of Computer and Data Science, Fuzhou University, Fuzhou 350116, China
2 School of Automation Science and Engineering, South China University of Technology, Guangzhou 510641, China
3 Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China
* Correspondence: jhuang@mae.cuhk.edu.hk
 
 
Received: 7 November 2022
Accepted: 13 November 2022
Published: 22 December 2022
 

Abstract: The cooperative output regulation problem (CORP) is an extension of the leader-following consensus problem of multi-agent systems (MASs), and has been studied by two approaches, namely, the distributed observer (DO) approach and the distributed internal model (DIM) approach. The two approaches are, respectively, the extensions of the classical feedforward control approach and the classical internal model approach (for a single system) to the MASs. This paper overviews the CORP by the DO approach with the emphasis on linear MASs. After formulating the CORP, we present the evolution process of three types of DOs and the corresponding solutions to the CORP. Furthermore, some variants and extensions of the DO approach are also briefly surveyed for completeness.

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The Cooperative Output Regulation by the Distributed Observer Approach

In this paper, the formation obstacle avoidance problem of autonomous underwater vehicles (AUVs) under the disturbances of ocean currents is studied. A variable formation reconfiguration and obstacle avoidance control scheme based on affine transform and the improved artificial potential field (AT-IAPF) is designed, which enable AUVs to avoid both static and dynamic obstacles under external interference, and maintain the desired time-varying formation. Because of the robustness and strong effectiveness of the time-varying control of AT and the obstacle avoidance control law of IAPF. The AT-IAPF algorithm improves the multi-AUV systems’ environmental adaptability and obstacle avoidance performance. Using the Lyapunov function’s stability constraint guarantees stability of a multi-AUV system. A series of simulation results based on MATLAB verify that AUVs can effectively avoid obstacles with different formation shapes. Obstacle avoidance experiments on bionic robotic fish demonstrate the proposed method’s feasibility. Note to Practitioners—This paper was motivated by the problem of formation reconfiguration and obstacle avoidance for AUVs. Still, it also applies to unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs). The existing formation control methods usually solve the problems of formation acquisition and time-invariant maneuvering, and rarely consider the problem of formation obstacle avoidance. This paper presents a new formation obstacle avoidance method using affine transformation (AT) and improved artificial potential field (IAPF) techniques. We use the IAPF method to plan a possible path for the formation in the obstacle environment. At the same time, the appropriate formation shape is selected according to the obstacle information to better adapt to the environment. The preliminary experiments of two bionic robot fish in near-surface positions show that this method is feasible. During the experiment, UWB is used for positioning, and a Zigbee module is used to communicate and transmit data. But it still needs to solve the problem of underwater communication, and it has yet to be tested on multiple bionic robot fish. In future studies, we will conduct multiple actual AUV formation obstacle avoidance experiments or do 3D formation control experiments underwater.

Multi-AUV Formation Reconfiguration Obstacle Avoidance Algorithm Based on Affine Transformation and Improved Artificial Potential Field Under Ocean Currents Disturbance

Enclosing control for nonholonomic mobile agents with a moving target of unknown velocity

The cooperative output regulation problem has been studied by two approaches: the distributed observer (DO) approach and the distributed internal model (DIM) approach, respectively. Each of these two approaches has its own merits and weaknesses. Recently, we presented an overview on the cooperative output regulation problem by the DO approach. This paper further surveys the cooperative output regulation problem by the DIM approach. We first summarize the constructions and the roles of two different versions of the internal models: the distributed p-copy internal model and the distributed canonical internal model. Then, we describe an integrated framework that combines the DO approach and the DIM approach. Extensions and variants of the DIM and their applications will also be highlighted. 

An overview on the distributed internal model approach and its applications

Leader-Following Consensus of Multiple Rigid-Body Systems

Time-varying formation control with attitude synchronization of multiple rigid body systems

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Time-varying formation control with attitude synchronization of multiple rigid body systems