Rigid Formation Control Research Articles

Rigid Formation Control on a Sphere: A Heterogeneous System Approach.

We consider a heterogeneous multiagent system for tracking multiple targets with a rigid formation on a unit sphere, where the targets and chasing agents are governed by single- and double-integrator models, respectively. To make asymptotic rendezvous between agents and their corresponding targets, we use an autonomous system consisting of attraction forces and velocity alignments. If the target's position, velocity, and acceleration information are available, we derive a multiagent system for complete rendezvous and obtain its exponential convergence result. If we have only the location and velocity information of the targets, we provide an autonomous system for practical rendezvous and the corresponding mathematical analysis. To prove the main results, we employ frame-rotation-structure decomposition for the double-integrator model and the geometric properties of a rigid formation on a sphere. We also provide numerical simulations to confirm our mathematical results and apply them to multiagent dynamics with a rigid formation that patrols the boundary line for a certain area on the sphere.

An adaptive neural design for planar rigid formation of three coleaders in unknown flowfields

AbstractThis article deals with the robust planar rigid formation control problem of three second‐order coleaders with unknown flowfields acting on the velocity and acceleration respectively. To yield the uniform boundedness property of the resulting system, an adaptive projection is introduced to design the novel adaptive neural control law. To avoid the derivatives of Gaussian functions of neural networks, dynamic surface is used. Simulation results are provided to illustrate the effectiveness of the proposed control law.

Optimal Rigid Graph-Based Cooperative Formation Control of AUVs in Anchor-Free Environments

Optimal Rigid Graph-Based Cooperative Formation Control of AUVs in Anchor-Free Environments

Image-Based Visual Relative Information for Distributed Rigid Formation Control in 3D Space

Image-Based Visual Relative Information for Distributed Rigid Formation Control in 3D Space

An adaptive bearing rigid formation control of multi-agent systems with nonlinear dead-zone inputs

In this paper, an adaptive bearing rigid formation control strategy for a class of nonlinear system with unknown dead-zone inputs and external disturbance is proposed. Firstly, the I-Type fuzzy system is used to approximate the unknown nonlinear dynamics of the formation model, and the approximation errors and unknown external disturbance are eliminated by the parameter adaptive estimation. Furthermore, the adaptive dynamic estimation algorithm is utilized to estimate and compensate the unknown dead-zone parameters, effectively suppressing the impact of dead-zone on formation system performance. Finally, the stability of the formation system is proved based on LaSalle’s invariance principle, and the effectiveness of the algorithm is verified by simulation results.

Application of Rigid Formation Control to marine vessels

This paper presents experimental results from controlling a formation of three Uncrewed Surface Vessels (USVs) using Rigid Formation Control (RFC). RFC algorithm output commands are then modified for use on marine vessels as they are inherently different from other multi-agent systems, both in design and environmental factors. The RFC algorithm assumes that formation agents are located at a graph’s vertices and the inter-agent spacing is the length of a graph’s edges. Each agent is assumed to have dynamics represented by a single integrator. While this control approach benefits from its simplicity, the RFC algorithm’s fixed frame velocity command must be modified in such a manner that the vessel’s low level controller can achieve formation convergence and maneuvering. Both simulated and experimental results are presented, demonstrating both formation acquisition and maneuvering.

Event-based rigid formation system with cooperative finite-time control

Abstract We note that most of the rigid formation control based on distance-constrained theory only guarantees exponential or asymptotic convergence of the system. In this paper, we proposed a finite-time event-based control scheme applied in rigid formation control system. Centralized finite-time event-based formation control system is designed where the next trigger time is determined by a central event-based controller, which broadcasts and updates the control input signal to all agents. Then, we build a distributed finite-time event-based control strategy, different from the above system where each agent only uses its own local information. For the above two protocols, we discussed the trigger situation, which ensures that the formation system converges in a finite time. Finally, simulation results proved the performance and effectiveness of the proposed finite-time event-based scheme.

A Novel Smooth Design for Globally Three-agent Rigid Formation

This paper solves a rigid formation control problem of three-agent system in the plane motion. A novel global stable formation method is proposed, where some additional items are constructed by a rotation matrix and used to design a control law combined with the negative gradient method. For any desired formation and different initial state, the proposed control law achieves globally stability, and at the same time the collision among the agents is effectively avoided via using a potential function. The simulation results verify the effectiveness of the proposed scheme.

A Rigid Formation Control Approach for Multi-Agent Systems With Curvature Constraints

A coordinated control law to achieve rigid formation based on directed graph constructed by the Henneberg insertion for multi-agent systems subject to nonholonomic constraints and curvature constraints is proposed. The stability of the multi-agent system is established by the control law, and the control law can be applied to some practical scenarios, such as the possible sideslip problem or the formation of agents with a minimum turning radius of motion. Finally, the effectiveness of the control approach is illustrated by some numerical simulations.

Cooperative Multi-Robot Object Transportation System Based on Hierarchical Quadratic Programming

Formation control gains significant attention in the multi-robot system field as it contributes to a vast range of applications, such as transportation. This letter presents a constrained optimization-based control law for cooperative logistics mission, which consists of rigid shape formation control, group navigation, individual and team obstacle avoidance tasks. These tasks are defined as equality and inequality constraints with different levels of priority. Hierarchical quadratic programming (HQP) approach is used to solve for the optimal solution with an inclusion of velocity limits as inequality constraints to ensure implementation feasibility. Experiment using actual industrial robots is demonstrated in order to validate the theory.

Cooperative Event-Based Rigid Formation Control

This article discusses cooperative stabilization control of rigid formations via an event-based approach. We first design a centralized event-based formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the triggering condition, event function, and triggering behavior are discussed in detail, and the exponential convergence of the event-based formation system is guaranteed.

Control of Directed Formations Using Interconnected Systems Stability

This paper deals with the problem of rigid formation control using directed graphs in both two-dimensional (2D) and three-dimensional (3D) spaces. Directed graphs reduce the number of communication, sensing, and/or control channels of the multi-agent system. We show that the directed version of the gradient descent control law asymptotically stabilizes the interagent distance error dynamics of minimally persistent formation graphs. The control analysis begins with a (possibly cyclic) primitive formation that is grown consecutively by Henneberg-type insertions, resulting at each step in two interconnected nonlinear systems, which are recursively analyzed using the stability of interconnected systems. Simulation and experimental results are presented for the directed formation controller in comparison to the standard undirected controller.

Quantization effects and convergence properties of rigid formation control systems with quantized distance measurements

SummaryIn this paper, we discuss quantization effects in rigid formation control systems when target formations are described by interagent distances. Because of practical sensing and measurement constraints, we consider in this paper distance measurements in their quantized forms. We show that under gradient‐based formation control, in the case of uniform quantization, the distance errors converge locally to a bounded set whose size depends on the quantization error, while in the case of logarithmic quantization, all distance errors converge locally to zero. A special quantizer involving the signum function is then considered with which all agents can only measure coarse distances in terms of binary information. In this case, the formation converges locally to a target formation within a finite time. Lastly, we discuss the effect of asymmetric uniform quantization on rigid formation control.

Globally rigid formation of [formula omitted]-link doubly nonholonomic mobile manipulators

This paper provides a new framework for the collective motion control of a team of n-link doubly nonholonomic mobile manipulators in a constrained environment. A continuous decentralized motion planner is proposed. It guarantees the establishment and strict maintenance of a team formation using the Lyapunov-based control scheme (LbCS), which takes into account all the practical limitations, and the constraints due to fixed obstacles, nonholonomy and globally rigid formation requirements. The control scheme inherently utilizes artificial potential fields within an overarching leader–follower framework to mobilize the prescribed globally rigid formation. The designated leader of the team is modeled as a moving reference point, referred to as the virtual leader. With its protective polygonal region, it directs the motion of the team and manipulate the geometry of the formation. It is the authors’ belief that this navigation and globally rigid formation control problem of n-link doubly nonholonomic mobile manipulators is treated for the first time with the use of continuous time-invariant control laws within the framework of LbCS and a variant of the leader–follower scheme. The effectiveness of the motion planner and the resulting acceleration-based control laws are demonstrated via computer simulations.

Taming Mismatches in Inter-agent Distances for the Formation-Motion Control of Second-Order Agents

This paper presents the analysis on the influence of distance mismatches on the standard gradient-based rigid formation control for second-order agents. It is shown that, similar to the first-order case as recently discussed in the literature, these mismatches introduce two undesired group behaviors: A distorted final shape and a steady-state motion of the group formation. We show that such undesired behaviors can be eliminated by combining the standard formation control law with distributed estimators. Finally, we show how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation.

Leader-Follower Based Locally Rigid Formation Control

This paper addresses motion control of a cooperative intelligent transport system (C-ITS) of nonholonomic mobile robots navigating a dynamic environment while maintaining a locally rigid formation. We consider the design of acceleration-based control inputs that govern the motion of cooperative intelligent transport system (C-ITS) using the artificial potential fields method for the avoidance of obstacles and attraction to designated targets. The control scheme utilizes a new leader-follower strategy using Cartesian coordinates to accomplish a collision-free locally rigid formation of an autonomous and intelligent transportation system. The concepts of virtual parking bays and minimum distance technique (MDT) are utilized to attain prescribed orientations of the formation at the final destination. The robustness of the control scheme is established by considering the effect noise on the formation, while the effectiveness of the proposed nonlinear control laws is demonstrated through computer simulations.

A decentralized cooperative control scheme for a distributed space transportation system

In this paper, a new concept for a distributed space transportation system is proposed and a corresponding decentralized cooperative control scheme is investigated. First, for a leaderless team of homogeneous space robots transporting a large object in orbit, a systematic control architecture that includes information flow is developed. Second, based on relative orbit dynamics, a rendezvous guidance law and a rigid formation control law are designed, and the necessary communication topology for the space robot team is discussed. Third, to guarantee the consensus of the motion of the large object with the robot team, both orbital maneuver control and attitude control for the large object are studied Emphasis is placed not on the attitude control law but on the force distribution problem, for which an algorithm exploiting a special property of trigonometric functions is proposed to transfer the necessary attitude control torque to the distributed forces. To support the above control method, an estimation of the motion of the formation center contributed by each robot in a decentralized manner is developed using a Kalman filter. Fourth, the robustness of the system to the failure of one robot is analyzed, and four effective typical fault response modes are proposed. Finally, numerical simulations validated the performance, robustness and practicability of the developed control scheme.

Multi-agent formation control in switching networks using backstepping design

A rigid formation control problem of n agents described by double integrators is proposed in this paper. At the same time, the arbitrary switching topology with no dwell time between consecutive switches is considered. Then the nonsmooth analysis, the backstepping technique and the adaptive perturbation method are employed to design the globally stable rigid formation control strategy. The main result is that regardless of the topology switching, the global stabilization of the rigid formation, the convergence to a common velocity vector and the collision avoidance between communicating agents are still guaranteed as long as the graph topology remains rigid all the time. Simulations are given to demonstrate the effectiveness of the proposed control algorithm.

Distributed algorithm for controlling scale-free polygonal formations

This paper presents a distributed algorithm for controlling the deployment of a team of mobile agents in formations whose shapes can be characterized by a broad class of polygons, including regular ones, where each agent occupies a corner of the polygon. The algorithm shares the appealing properties of the popular distance-based rigid formation control, but with the additional advantage of requiring the control of fewer pairs of neighboring agents. Furthermore, the scale of the polygon can be controlled by only one pair of neighboring agents. We also exploit the exponential stability of the controlled formation in order to steer the formation as a whole with translations and rotations in a prescribed way. We provide both theoretical analysis and illustrative simulations.

Robustness issues in double-integrator undirected rigid formation systems

In this paper we consider rigid formation control systems modelled by double integrators (including formation stabilization systems and flocking control systems), with a focus on their robustness property in the presence of distance mismatch. By introducing additional state variables we show the augmented double-integrator distance error system is self-contained, and we prove the exponential stability of the distance error systems via linearization analysis. As a consequence of the exponential stability, the distance error still converges in the presence of small and constant distance mismatches, while additional motions of the resulted formation will occur. We further analyze the rigid motions induced by constant mismatches for both double-integrator formation stabilisation systems and flocking control systems.