Bearing-only Formation Control Research Articles

Finite-Time Fault-Tolerant Formation Control for Distributed Multi-Vehicle Networks With Bearing Measurements

This paper addresses a bearing-only formation tracking problem in robotic networks by considering exogenous disturbances and actuator faults. In contrast to traditional position-based coordination strategies, the bearing-only coordinated movements of the unmanned vehicles only rely on the neighboring bearing information. This feature can be utilized to reduce the sensing requirements in the hardware implementation. A gradient-descent protocol is first developed to achieve the desired coordination within a prespecified settling time, where the unknown disturbances are considered in the vehicle dynamics, then the bound of formation tracking error is guaranteed by the Lyapunov approach. In case of damage to the actuators (e.g., motors) in some of the vehicles during the task, fault-tolerant analysis of the proposed controller is provided to ensure the success of the task in extreme environments. Furthermore, the proposed bearing-based method is extended to deal with general linear systems, which can be applied to a wider range of robotic platforms. Finally, numerical simulations and lab-based experiments using unmanned ground vehicles are conducted to validate the effectiveness of the proposed strategy. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The aim of this paper is to develop and design a practical bearing-only formation control approach for multi-vehicle systems. Many real-world complex tasks can be solved by multiple unmanned aerial and ground vehicles being connected by a communication network. This paper has proposed a formation tracking scheme for networked multi-vehicle systems that only relies on the relative bearing information of the neighboring vehicles. Closed-loop stability of the scheme and finite-time convergence of the tracking error have been established using the Lyapunov stability approach. The proposed method ensures the robustness and fault-tolerance of the multi-vehicle system against hardware faults or exogenous disturbances. A systematic set of guidelines on how to apply the proposed strategy in practice is also provided for the control practitioners in the form of an algorithm. In order to demonstrate the feasibility and usefulness of the proposed coordination scheme, numerical simulations and lab-based hardware experiments were conducted. Potential applications of the proposed scheme include search and rescue, security surveillance and cooperative exploration.

Distributed Bearing-Only Formation Control for UAV-UWSV Heterogeneous System

This paper investigates the bearing-only formation control problem of a heterogeneous multi-vehicle system, which includes unmanned aerial vehicles (UAVs) and unmanned surface vehicles (UWSVs). The interactions among vehicles are described by a particular class of directed and acyclic graphs, namely heterogeneous leader-first follower (HLFF) graphs. Under the HLFF structure, a UAV is selected as the leader, moving with the reference dynamics, while the followers, including both UAVs and UWSVs, are responsible for controlling the position with regard to the neighbors in the formation. To solve the problem, we propose a velocity-estimation-based control scheme, which consists of a distributed observer for estimating the reference velocity of each vehicle and a distributed formation control law for achieving the desired formation based on the estimations and bearing measurements. Moreover, it is shown that the translation and scale of the formation can be uniquely determined by the leader UAV. The theoretical analysis demonstrated the finite-time convergence of the velocity estimation and the asymptotic convergence of the formation tracking. Comparative simulation results are provided to substantiate the effectiveness of the proposed method.

Bearing-Only Formation Control With Bounded Disturbances in Agents’ Local Coordinate Frames

Bearing-Only Formation Control With Bounded Disturbances in Agents’ Local Coordinate Frames

Distributed Bearing-Only Formation Control for Heterogeneous Nonlinear Multi-Robot Systems

This paper addresses the bearing-only formation tracking problem for heterogeneous nonlinear multi-robot systems. In contrast to position and distance-based formation algorithms, the robots can only measure the bearing information from their neighbors to achieve cooperation while the state information is unavailable. This characteristic is able to be implemented in the hardware to reduce the requirements of the sensors. We construct a compensation function in the proposed controller to eliminate the effect of the unknown nonlinear terms in the system. This compensation function is also based on bearing measurements, which guarantees that the overall controller is bearing-only. The stability of the proposed formation tracking strategy can be ensured by Lyapunov techniques. Moreover, we analyze the performance of the protocol for moving leaders, where the formation tracking error can be restricted in a bounded set. Finally, the simulation results are presented to validate the feasibility of the proposed algorithm for both fixed and moving leaders.

Gradient-based bearing-only formation control: An elevation angle approach

This paper proposes an elevation angle rigidity theory in both 2D and 3D spaces, and applies it to solve multi-agent formation control with only inter-agent bearing/direction measurements in agents’ local coordinate frames. Motivated by the sensor technology in measuring elevation angle and angular diameter, we develop elevation angle rigidity by attaching each agent in a multi-agent framework with a rod in 2D and a ball in 3D, respectively. By defining the elevation angle rigidity matrix, conditions for infinitesimal elevation angle rigidity are derived. Compared to previously developed angle rigidity-based and bearing rigidity-based formation control laws, the proposed elevation angle rigidity-based control law can maintain the gradient-based control property. Compared to distance-based formation control laws, less sensor measurements are required. The formation maneuvering with desired translation and rotation is also realized by using only local bearing measurements. Simulation examples illustrate the advantages and effectiveness of the proposed approach.

Bearing-only formation control for double integrators in a plane

This paper studies the problem of bearing-only formation control for a group of agents modeled as double integrators. The control for each agent relies only on the relative bearings and relative bearing rates with its neighbors. Although such problems have been studied for undirected sensing graphs or within some leader-first-follower topologies with some additional sensing capabilities, it is still an open problem when the underlying sensing graph is directed and every agent can only sense bearing and bearing rates. In this paper a leader-first-follower (LFF) set up is considered where the leader is completely independent and the follower agents are assigned to control a fixed number of bearings with respect to their neighbors. Due to such assignment a directed sensing topology is obtained and bearing based Henneberg construction is used to realize such graphs. The spectrum of the bearing Laplacian for such underlying graphs with the LFF structure is studied and a bearing-only formation control law is proposed, whose local stability analysis is carried out around the desired equilibrium. Various simulation results are provided to illustrate that the desired formation shape is achieved.

Performance of different Formation control methods between Multiple Spacecraft with local part communications

With the development of network and distributed computing, many applications of multi vehicle system have become possible, and motion transformation can be realized. In multi vehicle coordination, the interaction between information exchange topology and control plays an important role. Different formation control methods have different performance. Thus, in order to figure out which method is suitable for multiple spacecraft, the author simulated the signal unstable environment in space to test the robustness and consensus speed of the following three methods. The author use Bearing-only Formation Control, A leader–follower Formation Control and Affine Formation Control to test their performance with local part communications. The author use matlab and simulink to analog communication process of multiple spacecraft. Finally, the author find Affine Formation Control’s performance is the best. It has the best robustness and the fast consensus speed but more energy and signal paths to communicate.

Bearing-Only Adaptive Formation Control Using Back-Stepping Method

In this paper, the bearing-only formation control problem of a class of second-order system with unknown disturbance is investigated, where the control law merely depends on the relative bearings between neighboring agents. In order to offset the effect of unknown disturbance on the system, adaptive estimation is introduced. In the design of the control law, the back-stepping design method and the negative gradient method are used. The Barbalat’s lemma is used to prove the global stability of the system. The simulation results prove the effectiveness of the proposed formation control algorithm.

Adaptive Formation Control of Networked Robotic Systems With Bearing-Only Measurements.

In this article, we address the bearing-only formation control problem of 3-D networked robotic systems with parametric uncertainties. The contributions of this article are two-fold: 1) the bearing-rigid theory is extended to solve the nonlinear robotic systems with the Euler-Lagrange-like model and 2) a novel almost global stable distributed bearing-only formation control law is proposed for the nonlinear robotic systems. Specifically, the robotic systems subject to nonholonomic constraints and dynamics are first transformed into a Euler-Lagrange-like model. By exploring the bearing-rigid graph theory, a backstepping approach is used to design the distributed formation controller. Simulations for 3-D robotics are given to demonstrate the effectiveness of the proposed control law. Compared to the distance-rigid formation control approach, the bearing-rigid approach guarantees almost global stability while naturally excluding flip ambiguities.

Bearing-Only Formation Control With Prespecified Convergence Time.

This article considers the bearing-only formation control problem, where the control of each agent only relies on relative bearings of their neighbors. A new control law is proposed to achieve target formations in finite time. Different from the existing results, the control law is based on a time-varying scaling gain. Hence, the convergence time can be arbitrarily chosen by users, and the derivative of the control input is continuous. Furthermore, sufficient conditions are given to guarantee almost global convergence and interagent collision avoidance. Then, a leader-follower control structure is proposed to achieve global convergence. By exploring the properties of the bearing Laplacian matrix, the collision avoidance and smooth control input are preserved. A multirobot hardware platform is designed to validate the theoretical results. Both simulation and experimental results demonstrate the effectiveness of our design.

Bearing-Only Formation Control of Multi-Agent System Without Leader’s Velocity Information

This paper studies formation control of multi-agent systems with an underlying network constructed by defined the follower Henneberg construction. We propose a bearing-only formation control law of multi-agent systems, where a leader moves at a constant velocity, and the followers are unaware of the leader’s velocity. We prove that the system can asymptotically reach its desired position and form the target formation. The proposed control law scales the formation to avoid obstacles, where the formation robustness is also analysed. Numerical simulations are provided to further support our findings.

Bearing-Only Formation Tracking Control of Multiagent Systems

This paper studies the problem of bearing-only formation control of multiagent systems, where the control of each agent merely relies on the relative bearings to its neighbors. Although this problem has received increasing research attention recently, it is still unsolved to a large extent due to its highly nonlinear dynamics. In particular, the existing control approaches are only able to solve the simplest scenario where the target formation is stationary and each agent is modeled as a single integrator. The main contribution of this paper is to propose new bearing-only formation control laws to 1) track moving target formations and 2) handle a variety of agent models including single-integrator, double-integrator, and unicycle models. These control laws are an important step towards the application of bearing-only formation control in practical tasks. Both numerical simulation and real experimental results are presented to verify the effectiveness of the theoretical results.

Bearing-only formation control of multi-agent systems in local reference frames

In this paper, the bearing-only formation control problem of multi-agent systems in local reference frame is studied. By considering that the inter-agent communication topology satisfies the maximal clique graph condition, the formation control can achieve global stability due to the existence of common agents among the maximal cliques. A cost function is proposed based on the target formation. By minimising the cost function under the optimal rotate matrix, a distributed globally stable controller is proposed, which only depends on the local bearing measurement. Then the rotation bias of the final formation and the target formation are analysed. The designed control law can realise the global formation control under the local reference frame. Finally the simulations demonstrate the effectiveness of the proposed controller.

Finite-Time Bearing-Only Formation Control via Distributed Global Orientation Estimation

This paper presents a finite-time bearing-only formation control scheme via finite-time estimation of agents’ global orientations. For the orientation estimation, we propose a distributed estimation law and establish almost global finite-time convergence. We provide analysis for undirected and a class of directed sensing and communication graphs. A distributed bearing-only formation control law is then proposed based on the orientation estimation. We provide a rigorous analysis for almost global stability and finite-time convergence of the system to the desired equilibrium. Particularly, under the proposed bearing-only formation control strategy, the actual formation almost globally exponentially finite-time converges to the desired formation shape. Finally, numerical simulations are provided to support our proposed control method.

Bearing-Only Formation Control with Limited Visual Sensing: Two Agent Case

Abstract This work solves the bearing-only formation control problem for two agents with limited field-of-view sensing. We propose a bearing-only control strategy for both the position and heading of each agent that guarantees the desired formation is obtained from almost all initial conditions, and ensures that the agents always remain inside the field-of-view of the sensor. We support our analysis with simulations and explore an extension for the 3- and 4-agent case.

Bearing Rigidity and Almost Global Bearing-Only Formation Stabilization

A fundamental problem that the bearing rigidity theory studies is to determine when a framework can be uniquely determined up to a translation and a scaling factor by its inter-neighbor bearings. While many previous works focused on the bearing rigidity of two-dimensional frameworks, a first contribution of this paper is to extend these results to arbitrary dimensions. It is shown that a framework in an arbitrary dimension can be uniquely determined up to a translation and a scaling factor by the bearings if and only if the framework is infinitesimally bearing rigid. In this paper, the proposed bearing rigidity theory is further applied to the bearing-only formation stabilization problem where the target formation is defined by inter-neighbor bearings and the feedback control uses only bearing measurements. Nonlinear distributed bearing-only formation control laws are proposed for the cases with and without a global orientation. It is proved that the control laws can almost globally stabilize infinitesimally bearing rigid formations. Numerical simulations are provided to support the analysis.

Distributed control of angle-constrained cyclic formations using bearing-only measurements

This paper studies distributed control of multi-vehicle formations with angle constraints using bearing-only measurements. It is assumed that each vehicle can only measure the local bearings of their neighbors and there are no wireless communications among the vehicles. The desired formation is a cyclic one, whose underlying information flow is described by an undirected cycle graph. We propose a distributed bearing-only formation control law that ensures local exponential or finite-time stability. Collision avoidance between any vehicles can be locally guaranteed in the absence of inter-vehicle distance measurements.

Distributed control of triangular formations with angle-only constraints

This paper considers the coupled, bearing-only formation control of three mobile agents moving in the plane. Each agent has only local inter-agent bearing knowledge and is required to maintain a specified angular separation relative to both neighbor agents. Assuming that the desired angular separation of each agent relative to the group is feasible, a triangle is generated. The control law is distributed and accordingly each agent can determine their own control law using only the locally measured bearings. A convergence result is established in this paper which guarantees global asymptotic convergence of the formation to the desired formation shape.