Rigid Formation Control Research Articles

Distributed multi-robot formation control in switching networks

A rigid formation control problem with switching topology is studied in this paper. Then the nonsmooth analysis and nonlinear theory are employed to analyze the stability of the multi-robot formation system. By use of the navigation function method and the adaptive perturbation method, the proposed formation control law can guarantee the global stabilization of the rigid formation and the collision avoidance between communicating robots regardless of the topology switching, as long as the graph topology remains rigid all the time. The effectiveness of the proposed control strategy is verified by simulation examples.

Rigid formation control of double-integrator systems

ABSTRACTIn this paper, we study rigid formation control systems modelled by double integrators. Two kinds of double-integrator formation systems are considered, namely formation stabilisation systems and flocking control systems. Novel observations on the measurement requirement, the null space and eigenvalues of the system Jacobian matrix will be provided, which reveal important properties of system dynamics and the associated convergence results. We also establish some new links between single-integrator formation systems and double-integrator formation systems via a parameterised Hamiltonian system, which, in addition, provide novel stability criteria for different equilibria in double-integrator formation systems by using available results in single-integrator formation systems.

On the Role and Compensation of Distance Mismatches in Rigid Formation Control for Second-Order Agents

Abstract: This paper presents a robustness analysis of gradient-based formation control law for second-order agents subjected to distance mismatches or constant disturbances. It is shown that, akin to the first-order case, the existence of these mismatches introduces two undesired group behaviors: a distorted final shape and a stationary group motion. We show that such undesired properties can be compensated by combining the gradient-based rigid formation control law and our proposed distributed estimators.

Finite time distributed distance‐constrained shape stabilization and flocking control for d‐dimensional undirected rigid formations

SummaryMost of the existing results on distributed distance‐constrained rigid formation control establish asymptotic or exponential convergence. To further improve the convergence rate, we explain in this paper how to modify existing gradient controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to locally converge to a desired shape with finite settling time. We also show for undirected triangular formation shape control, if all the agents start with non‐collinear positions, then the formation will converge to the desired shape in finite time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control strategies. Copyright © 2015 John Wiley & Sons, Ltd.

Finite Time Distance-based Rigid Formation Stabilization and Flocking

Most of the existing results on distributed distance-based rigid formation control establish asymptotic and often exponentially asymptotic convergence. To further improve the convergence rate, we explain in this paper how to modify existing controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to converge to a desired shape with finite settling time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control.

Distributed rigid formation control algorithm for multi‐agent systems

PurposeRigidity of formation is an important concept in multi‐agent localization and control problems. The purpose of this paper is to design the control laws to enable the group to asymptotically exhibit the flocking motion while preserving the network rigidity at all times.Design/methodology/approachThe novel approach for designing control laws is derived from a smooth artificial potential function based on an undirected infinitesimally rigid formation which specifies the target formation. Then the potential function is used to specify a gradient control law, under which the original system then becomes an orderly infinitesimally rigid formation.FindingsThe strong relationship between the stability of the target formation and the gradient control protocol are utilized to design the control laws which can be proved to make the target formation stable. However, the rigidity matrix is not utilized in the design of control law. Future research will mainly focus on formation control with the relationship of rigidity matrix.Originality/valueThe value of this paper is focused on the control laws design and the control laws could enable the group to asymptotically exhibit the flocking motion while preserving the network rigidity at all times. Also the detailed simulations and experiments are given to prove that the novel approach is available.

A communication-based multirobot rigid formation control system: design and analysis

In this study, a system with cooperative formation control of group of mobile robots is presented to provide a framework to build up complex systems through communication channels. An improved closed-up multirobot rigid formation control algorithm is developed to efficiently implement the systems without markers and other environment constraints under certain complex situations. Furthermore, a fault-tolerance mechanism for multirobot formation is firstly introduced, based on hierarchy graph of formation theory. This study covers the design and analysis for the overall communication-based system. The results have been obtained via a series of virtual robot simulations and experiments by using three mobile robots, which have well demonstrated the efficiency of the proposed procedure.