Spectral-Based Group Formation Control

Given a pair of keyframe formations for a group consisting of multiple individuals, we present a spectral-based approach to smoothly transforming a source group formation into a target formation while respecting the clusters of the involved individuals. The proposed method provides an effective means for controlling the macroscopic spatiotemporal arrangement of individuals for applications such as expressive formations in mass performances and tactical formations in team sports. Our main idea is to formulate this problem as rotation interpolation of the eigenbases for the Laplacian matrices, each of which represents how the individuals are clustered in a given keyframe formation. A stream of time-varying formations is controlled by editing the underlying adjacency relationships among individuals as well as their spatial positions at each keyframe, and interpolating the keyframe formations while producing plausible collective behaviors over a period of time. An interactive system of editing existing group behaviors in a hierarchical fashion has been implemented to provide flexible formation control of large crowds.     

具有时变时滞耦合的二阶多主体系统的编队控制

多主体系统的编队控制是一类重要的网络协同控制问题.研究了在有向连接拓扑结构下,具有时变时滞耦合的二阶多主体系统的编队控制问题.通过一种多层领导机制的框架建模,得到了时不变编队、时变编队和时变轨迹追踪3种编队问题的充分性条件,并证明了各种预期队列是以指数的收敛速度形成的.数值仿真进一步验证了理论结果的正确性,为该理论在实际中应用起到指导作用.     

非完整性约束的平面多智能体位置时变一致性控制

多智能体的通用一致性协议被广泛用于智能体的编队控制问题中.在实际工程中,多智能体系统为了完成期望的协作控制,智能体之间的位置关系通常是时变的.目前,在多智能体编队控制问题中,尽管已有研究成果能够解决多智能体某些特殊类型的时变编队控制,但对一般性的时变编队还没有成熟的研究成果.本文以受非完整性约束的平面多智能体为研究对象,提出了平面非完整性多智能体的位置时变一致性协议.实验结果表明:本文提出的位置时变一致性协议能够有效解决平面非完整性多智能体系统一般性的时变编队问题.     

Potential-function-based shape formation in swarm simulation

This paper presents a potential-function-based formation shape control scheme for swarm simulation. The potential function is designed to avoid collision among agents, approach a destination, and achieve a certain shape formation around the destination. The agents move in a swarm to the formation position, which is generated from a reference point and the neighboring agents. In the framework, a local minimum case created by combining the potential repulsed from neighboring robots and that attracted from a reference point is presented; herein, a robot escapes from a local minimum using a virtual escape point after recognizing the trapped situation. Similarly, in the proposed framework, for a well-equipped formation shape, potential functions are designed to maintain the same relative distance between neighboring robots on a formation line, which also satisfies scalability for the number of agents. The simulation results show that the proposed approach can effectively construct elliptical, diamond, and heart-shaped formations for swarm agents.     

Attractor dynamics approach to formation control: theory and application

In this paper we show how non-linear attractor dynamics can be used as a framework to control teams of autonomous mobile robots that should navigate according to a predefined geometric formation. The environment does not need to be known a priori and may change over time. Implicit to the control architecture are some important features such as establishing and moving the formation, split and join of formations (when necessary to avoid obstacles). Formations are defined by a formation matrix. By manipulating this formation matrix it is also possible to switch formations at run time. Examples of simulation results and implementations with real robots (teams of Khepera robots and medium size mobile robots), demonstrate formation switch, static and dynamic obstacle avoidance and split and join formations without the need for any explicit coordination scheme. Robustness against environmental perturbations is intrinsically achieved because the behaviour of each robot is generated as a time series of asymptotically stable states, which contribute to the asymptotic stability of the overall control system.     

Grouping efficiency measures and their impact on factory measures for the machine-part cell formation problem: A simulation study

Over the past 25 years, the machine-part cell formation problem has been the subject of numerous studies. Researchers have applied various methodologies to the problem in an effort to determine optimal clusterings of machines and optimal groupings of parts into families. The quality of these machine and part groupings have been evaluated using various objective functions, including grouping efficacy, grouping index, grouping capability index, and doubly weighted grouping efficiency, among others. In this study, we investigate how appropriate these grouping quality measures are in determining cell formations that optimize factory performance. Through the application of a grouping genetic algorithm, we determine machine/part cell formations for several problems from the literature. These cell formations are then simulated to determine their impact on various factory measures, such as flow time, wait time, throughput, and machine utilization, among others. Results indicate that it is not always the case that a “more efficient” machine/part cell formation leads to significant changes or improvements in factory measures over a “less efficient” cell formation. In other words, although researchers are working to optimize cell formations using efficiency measures, cells formed this way do not always demonstrate optimized factory measures.     

Path planning for permutation-invariant multirobot formations

In many multirobot applications, the specific assignment of goal configurations to robots is less important than the overall behavior of the robot formation. In such cases, it is convenient to define a permutation-invariant multirobot formation as a set of robot configurations, without assigning specific configurations to specific robots. For the case of robots that translate in the plane, we can represent such a formation by the coefficients of a complex polynomial whose roots represent the robot configurations. Since these coefficients are invariant with respect to permutation of the roots of the polynomial, they provide an effective representation for permutation-invariant formations. In this paper, we extend this idea to build a full representation of a permutation-invariant formation space. We describe the properties of the representation, and show how it can be used to construct collision-free paths for permutation-invariant formations.     

Robot Navigation Based on Discrimination of Artificial Fields: Application to Robot Formations

In the preceding paper, a method for mobile robot navigation control based on discrimination of multiple artificial fields was introduced. In this second paper, the method is extended to robot formations. Experimental demonstrations are presented taking examples of four types of formations. The experiments cover formation initialization, maneuvering, obstacle avoidance and formation switching.     

Formation control using range-only measurements

This paper proposes algorithms to coordinate a formation of mobile agents when the agents are not able to measure the relative positions of their neighbors, but only the distances to their respective neighbors. In this sense, less information is available to agents than is normally assumed in formation stabilization or station keeping problems. To control the shape of the formation, the solution advanced in the paper involves subsets of non-neighbor agents cyclically localizing the relative positions of their respective neighbor agents while these are held stationary, and then moving to reduce the value of a cost function which is nonnegative and assumes the zero value precisely when the formation has correct distances. The movement schedule is obtained by a novel vertex-coloring algorithm whose computation time is linear in the number of agents when implemented on the graphs of minimally rigid formations. Since in some formations, it may be that an agent is never allowed to be stationary (e.g. it is a fixed-wing aircraft), or because formations may be required to move as a whole in a certain direction, the results are extended to allow for cyclic localization of agents in this case. The tool used is the Cayley–Menger determinant.     

Formation shape control based on bearing rigidity

Distance measurements are not the only geometric quantities that can be used for multi-agent formation shape control. Bearing measurements can be used in conjunction with distances. This article employs bearing rigidity for mobile formations, which was developed for robot and sensor network localisation, so that bearings can be used for shape control in mobile formations. The first part of this article examines graph theoretical models for formation network analysis and control law design that are needed to maintain the shape of a formation in two-dimensional space, while the formation moves as a cohesive whole. Bearing-based shape control for a formation of mobile agents involves the design of distributed control laws that ensure the formation moves, so that bearing constraints maintain some desired values. The second part of this article focuses on the design of a distributed control scheme for nonholonomic agents to solve the bearing-based formation shape control problem. In particular, a control law using feedback linearisation is proposed based on shape variables. We simulate the shape control behaviour on differential drive agents for an exemplary bearing rigid formation using the results obtained in the first and second parts of this article.     

On iterative learning algorithms for the formation control of nonlinear multi-agent systems

This paper deals with formation control problems for multi-agent systems with nonlinear dynamics and switching network topologies. Using the nearest neighbor knowledge, a distributed algorithm is constructed by employing the iterative learning control approach. Sufficient conditions are given to obtain the desired relative formations of agents, which benefits from the strict positiveness of products of stochastic matrices. It is shown that the derived results can effectively work, although the network topologies dynamically change along both time and iteration axes and the corresponding directed graphs may not have spanning trees. Such result is also illustrated via numerical simulations.     

Maneuvering Angle Rigid Formations With Global Convergence Guarantees

Angle rigid multi-agent formations can simultaneously undergo translational, rotational, and scaling maneuvering,therefore combining the maneuvering capabilities of both distance and bearing rigid formations. However, maneuvering angle rigid formations in 2D or 3D with global convergence guarantees is shown to be a challenging problem in the existing literature even when relative position measurements are available. Motivated by angle-induced linear equations in 2D triangles and 3D tetrahedra,th...     

Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence

In this paper, we generalize the notion of persistence, which has been originally introduced for two-dimensional formations, to R^d for d?3, seeking to provide a theoretical framework for real world applications, which often are in three-dimensional space as opposed to the plane. Persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents. We verify that many of the properties of rigid and/or persistent formations established in R² are also valid for higher dimensions. Analysing the closed subgraphs and directed paths in persistent graphs, we derive some further properties of persistent formations. We also provide an easily checkable necessary condition for persistence. We then turn our attention to consider some practical issues raised in multi-agent formation control in three-dimensional space. We display a new phenomenon, not present in R², whereby subsets of agents can behave in a problematic way. When this behaviour is precluded, we say that the graph depicting the multi-agent formation has structural persistence. In real deployment of controlled multi-agent systems, formations with underlying structurally persistent graphs are of interest. We analyse the characteristics of structurally persistent graphs and provide a streamlined test for structural persistence. We study the connections between the allocation of degrees of freedom (DOFs) across agents and the characteristics of persistence and/or structural persistence of a directed graph. We also show how to transfer DOFs among agents, when the formation changes with new agent(s) added, to preserve persistence and/or structural persistence.     

On the robustness to multiple agent losses in 2D and 3D formations

Multi‐agent formations have been recently the subject of many studies. An important operational challenge, largely unaddressed in the literature, is to ensure that functionality of the formation is retained should agents be lost through misadventure, mission reassignment, and so on. In the context of sensor networks, it is also important to allow for the loss of multiple sensors as the low quality of sensor hardware, common unattended implementations, and so on makes it a common issue. In this paper, we address these issues by proposing information structures that are tolerant to the loss of multiple agents. Using graph theory (and more specifically rigidity theory), we characterize several properties of such formations/networks in a unified framework: We characterize the k‐vertex rigidity property of the underling graph of such formations. This is performed by deriving a set of useful conditions that can form a guideline for designing agent‐loss‐tolerant formations. We elaborate the study by characterizing robust formations with the optimal number of control links. We also propose a set of operations preserving the tolerance to multiple agent losses in such formations. These operations provide flexibility in designing the formations in terms of several designing parameters (e.g., geometry, diameter, and max degree). Especially in the case of formations, the ability to handle controller adjustments in a distributed way is important, and the paper addresses this issue for a number of the robustness problems considered. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple UAV Formations for Cooperative Source Seeking and Contour Mapping of a Radiative Signal Field

In this paper, four scenarios are presented for cooperative source seeking and contour mapping of a radiative signal field by multiple UAV formations. A source seeking strategy is adopted with saturation, and then it is modified to achieve contour mapping of the signal field with the moving source situation considered. A formation controller used for consensus problem is simplified and applied in the scenarios to stabilize the multiple UAV formation flight during source detection. The contour mapping strategy and the formation control algorithm are combined to guarantee stable source seeking and contour mapping in both circular flight path and square flight path via multiple UAV formations.     

Minimization of the effect of noisy measurements on localization of multi-agent autonomous formations

This paper considers the problem of reduction of self-localization errors in multi-agent autonomous formations when only distance measurements are available to the agents in a globally rigid formation. It is shown that there is a relationship between different selections of anchors, agents with exactly known positions, and the error induced by measurement error on localization solution. This fact is exploited to develop a mechanism to select anchors in order to minimize the effects of inter-agent distance measurement errors on localization solution. Finally, some simulation results are presented to demonstrate the optimal anchor selection for a particular general class of formations, the globally rigid formations.     

High‐precision formation control of nonlinear multi‐agent systems with switching topologies: A learning approach

Arbitrary high precision is considered one of the most desirable control objectives in the relative formation for many networked industrial applications, such as flying spacecrafts and mobile robots. The main purpose of this paper is to present design guidelines of applying the iterative schemes to develop distributed formation algorithms in order to achieve this control objective. If certain conditions are met, then the control input signals can be learned by the developed algorithms to accomplish the desired formations with arbitrary high precision. The systems under consideration are a class of multi‐agent systems under directed networks with switching topologies. The agents have discrete‐time affine nonlinear dynamics, but their state functions do not need to be identical. It is shown that the learning processes resulting from the relative output formation of multi‐agent systems can converge exponentially fast with the increase of the iteration number. In particular, this work induces a distributed algorithm that can simultaneously achieve the desired relative output formation between agents and regulate the movement of multi‐agent formations as desired along the time axis. The illustrative numerical simulations are finally performed to demonstrate the effectiveness and performance of the proposed distributed formation algorithms. Copyright © 2014 John Wiley & Sons, Ltd.     

Formation control of mobile agents based on inter-agent distance dynamics

We propose a novel formation control strategy based on inter-agent distances for single-integrator modeled agents in the plane. Attempting to directly control the inter-agent distances, we derive a control law from the distance dynamics. The proposed control law achieves the local asymptotic stability of infinitesimally rigid formations. Triangular infinitesimally rigid formations are globally asymptotically stable under the proposed control law, with all squared distance errors exponentially and monotonically converging to zero. As an extension of existing results, the stability analysis in this paper reveals that any control laws related with the gradient law by multiplication of a positive matrix ensure the local asymptotic stability of infinitesimally rigid formations.     

Formation optimization for a fleet of wheeled mobile robots — A geometric approach

Tight formation-based operations are critical in several emerging applications for robot collectives — ranging from cooperative payload transport to synchronized distributed data-collection. In this paper, we investigate the optimal relative layout for members of a team of Differentially-Driven Wheeled Mobile Robots (DD-WMRs) moving in formation for ultimate deployment in cooperative payload transport tasks.Our particular focus is on modeling such formations, developing the motion plans and determining the “best formation” in a differential-geometric setting. Specifically, a preferred team-fixed frame serves as a virtual leader inducing motion plans for the individual DD-WMRs which form the vertices of a virtual structure. The resulting motion plans for the DD-WMRs as well as overall team-performance depend both on the specifiedteam-frame motions as well as their relative-layout within the formation.Emphasis is placed on developing suitable invariant (yet quantitative) measures of formation quality and a systematic optimization-based selection of the formation-layout. The use of relative formation-parameterization with respect to a team-frame serves to decouple the team-level optimal layout selection process. The optimal location of each DD-WMR can now be found with respect to the team-frame individually and the feasibility of distributed implementation facilitates scaling to larger-sized formations. Analytical and numerical results, from case studies of formation optimization of three DD-WMRs maneuvering along certain desired planar paths, are presented to highlight the salient features and benefits.     

Coordinated formation control of multiple nonlinear systems

A general method of controller design is developed for the purpose of formation keeping and reconfiguration of nonlinear systems with multiple subsystems, such as the formation of multiple aircraft, ground vehicles, or robot arms. The model consists of multiple nonlinear systems. Controllers are designed to keep the subsystems in a required formation and to coordinate the subsystems in the presence of environmental changes. A step-by-step algorithm of controller design is developed. Sufficient conditions for the stability of formation tracking are proved. Simulations and experiments are conducted to demonstrate some useful coordination strategies such as movement with a leader, simultaneous movement, series connection of formatiom, and human-machine interaction.