Robot Formation Research Articles

A Stable Control Algorithm for Multi Robot Formation

This paper presents the developed trajectory tracking controller for a formation of nonholonomic robots, which combines features from the leader-follower and virtual-structure approaches. The implemented decentralized control strategy allows the robots to be relatively independent and to switch easily between the executed individual tasks and the collective tasks. Convergence is thoroughly analyzed and guarantied using the Lyapunov approach.

Dynamic Leader Allocation in Multi-robot Systems Based on Nonlinear Model Predictive Control

This paper presents an approach to the dynamic leader selection problem in autonomous non-holonomic mobile robot formations when the current leader enters a failure state. Our method is based on a tree structure coupled with a modified version of the Nonlinear Model Predictive Control (NMPC) that allows for behavior change at the controller level. An explanation of the control algorithm, behavior selection, and leader selection structure is given, after which the results of both simulations and experiments using a three robot formation are shown and discussed.

New advances in multiple autonomous aerial robots formation control technology

New advances in multiple autonomous aerial robots formation control technology

Variable formation control of multiple robots via VRc and formation switching to accommodate large heading changes by leader robot

This article describes a novel multi-robot formation control based on a switching technique that allows follower robots to maintain formation when the leader robot’s direction changes rapidly or unexpectedly. The formation pattern is determined using Virtual Robot’s Center of the multi-robot formation. To avoid collision, the formation of robots reformed in optimal size by estimating the distance between the robot and an obstacle in real time. When the leader robot suddenly changes its direction, waypoints of follower robots are switched and the formation is quickly reconstructed. This prevents follower robots from colliding with each other and reduces their radius of movement and allows them to follow the leader robot at higher speed. The proposed method which is inherently a flexible control of multi-robot formation guarantees collision avoidance and prevents sudden changes in waypoints of the system by gradually changing its size. The validity of the proposed method is demonstrated via simulation and experimental results.

Polygon Shape Formation for Multi-Mobile Robots in a Global Knowledge Environment

In coordination of a group of mobile robots in a real environment, the formation is an important task. Multimobile robot formations in global knowledge environments are achieved using small robots with small hardware capabilities. To perform formation, localization, orientation, path planning and obstacle and collision avoidance should be accomplished. Finally, several static and dynamic strategies for polygon shape formation are implemented. For these formations minimizing the energy spent by the robots or the time for achieving the task, have been investigated. These strategies have better efficiency in completing the formation, since they use the cluster matching algorithm instead of the triangulation algorithm.

Trajectory tracking and collision avoidance for the formation of two-wheeled mobile robots

Trajectory tracking and collision avoidance for the formation of two-wheeled mobile robots

Formation Control of Multiple Mobile Robots Incorporating an Extended State Observer and Distributed Model Predictive Approach

This paper studies the extended state observer (ESO)-based distributed model predictive control (DMPC) approach to deal with multiple mobile robot formation with unknown disturbances. The distributed control problem with path parameters synchronization and disturbance rejection is formulated for formation system according to the tracking error dynamic model, where the reference paths are parameterized. A local distributed controller is designed by using DMPC strategy for each mobile robot in the absence of disturbance by including parameter synchronization constraints in the quadratic performance index as coupling terms. The DMPC optimization problem is solved by using Nash-optimization iteration strategy with the maximum number of iteration constraint. To improve the ability of anti-jamming, a feedforward compensation controller is designed by using ESO method, where the ESO is designed by pole assignment. The convergence of the proposed iterative algorithm is given. Furthermore, the input-to-state stability property of the proposed composite controller, combining a feedforward compensation controller and local distributed controller, is analyzed for the closed-loop system. Finally, the validity of the proposed algorithm is verified by two simulation examples.

A Survey of Multi-mobile Robot Formation Control

A Survey of Multi-mobile Robot Formation Control

Adaptation Mechanism of Asymmetrical Potential Field Improving Precision of Position Tracking in the Case of Nonholonomic UAVs

SummaryPosition-tracking problems in the structures of rigid formations of nonholonomic mobile robots, such as fixed-wing unmanned aerial vehicle (UAVs), must reconcile tracking precision and flight stability, which usually exclude each other due to nonholonomic motion constraints. Therefore, a position-tracking control that is based on distance and position displacement, defined as inputs of control loops, requires the application of dead zones around target positions, which are the points of instability. For this reason, the control becomes sensitive to any external disturbance causing oscillations of control signals and so it becomes difficult to maintain a zero value of position displacement over a long time horizon. Thus, we propose an approach based on the adaptive mechanism of an asymmetrical local artificial potential field, which is defined by a local frame of reference whose origin is located in the tracked position of a UAV in the formation frame. It couples controls of both airspeed and heading angle into a nonlinear potential function of relative position and orientation with respect to the tracked position and adapts it according to heading rate of the leader. The function splits the area around the tracked position longitudinally into two zones of acceleration and deceleration; therefore, velocity vectors are longer (higher airspeed) only when a UAV is behind the tracked position and shorter (lower airspeed) when it is ahead. The area is laterally symmetrical, and orientations of velocity vectors align asymptotically to the longitudinal direction accordingly with the decrease in the lateral error. Finally, velocity vectors are rotated proportionally to the heading rate of the leader, which improves the tracking precision during turns. If we assumed that a UAV’s tracked position is in motion, it could easily be proven that the position control based on the adaptive asymmetrical potential function becomes asymptotically stable in the tracked position. Numerical simulation verifies this thesis and presents more precise and stable position tracking due to the adaptation mechanism.

Search and Localization of a Weak Source with a Multi-robot Formation

This paper proposes an algorithm to guide a formation of mobile robots, subject to communication constraints, from an arbitrary position to the location of the source of a physical signal in a planar environment. The information on the signal is only based on noisy measurements of its strength collected during the mission and the signal is considered to be weak and indistinguishable from the noise in a large portion of the environment. The goal of the team is thus to search for a reliable signal and finally converge to the source location. An accurate estimation of the signal gradient is obtained by fusing the data gathered by the robots while moving in a circular formation. The algorithm proposed to steer the formation, called Gradient-biased Correlated Random Walk (GCRW), exploits the gradient estimation to bias a correlated random walk, which ensures an efficient non-oriented search motion when far from the source. The resulting strategy is so able to obtain a suitable trade-off between exploration and exploitation. Results obtained in simulated experiments, including comparisons with possible alternatives, are presented to analyze and evaluate the performance of the proposed approach.

Formation Control and Distributed Goal Assignment for Multi-Agent Non-Holonomic Systems

This paper presents control algorithms for multiple non-holonomic mobile robots moving in formation. Trajectory tracking based on linear feedback control is combined with inter-agent collision avoidance. Artificial potential functions (APF) are used to generate a repulsive component of the control. Stability analysis is based on a Lyapunov-like function. Then the presented method is extended to include a goal exchange algorithm that makes the convergence of the formation much more rapid and, in addition, reduces the number of collision avoidance interactions. The extended method is theoretically justified using a Lyapunov-like function. The controller is discontinuous but the set of discontinuity points is of zero measure. The novelty of the proposed method lies in integration of the closed-loop control for non-holonomic mobile robots with the distributed goal assignment, which is usually regarded in the literature as part of trajectory planning problem. A Lyapunov-like function joins both trajectory tracking and goal assignment analyses. It is shown that distributed goal exchange supports stability of the closed-loop control system. Moreover, robots are equipped with a reactive collision avoidance mechanism, which often does not exist in the known algorithms. The effectiveness of the presented method is illustrated by numerical simulations carried out on the large formation of robots.

Consensus Algorithms Based Multi-Robot Formation Control under Noise and Time Delay Conditions

In recent years, the formation control of multi-mobile robots has been widely investigated by researchers. With increasing numbers of robots in the formation, distributed formation control has become the development trend of multi-mobile robot formation control, and the consensus problem is the most basic problem in the distributed multi-mobile robot control algorithm. Therefore, it is very important to analyze the consensus of multi-mobile robot systems. There are already mature and sophisticated strategies solving the consensus problem in ideal environments. However, in practical applications, uncertain factors like communication noise, communication delay and measurement errors will still lead to many problems in multi-robot formation control. In this paper, the consensus problem of second-order multi-robot systems with multiple time delays and noises is analyzed. The characteristic equation of the system is transformed into a quadratic polynomial of pure imaginary eigenvalues using the frequency domain analysis method, and then the critical stability state of the maximum time delay under noisy conditions is obtained. When all robot delays are less than the maximum time delay, the system can be stabilized and achieve consensus. Compared with the traditional Lyapunov method, this algorithm has lower conservativeness, and it is easier to extend the results to higher-order multi-robot systems. Finally, the results are verified by numerical simulation using MATLAB/Simulink. At the same time, a multi-mobile robot platform is built, and the proposed algorithm is applied to an actual multi-robot system. The experimental results show that the proposed algorithm is finally able to achieve the consensus of the second-order multi-robot system under delay and noise interference.

Polygon Shape Formation for Multi-Mobile Robots in a Local Knowledge Environment

The formation is an important task in multi-mobile robots coordination in a defined environment. In a local knowledge environment the multi-mobile robot formations are realized using small robots with minor hardware requirements. The localization, path planning and obstacle avoidance processes are required to perform formation. In this paper a static strategy for polygon shape formation is implemented using a several number of mobile robots. This strategy has a better efficiency, since it use the cluster matching algorithm instead of the triangulation algorithm in completing the formation. Also, the visibility binary tree algorithm and the reciprocal orientation algorithm are used in this paper. This strategy has better performance in the multi-robot formation, since it use the cluster matching algorithm instead of the triangulation algorithm.

Design Guarantees for Resilient Robot Formations on Lattices

This letter presents guarantees to satisfy resilience on the communication network of robot formations. In these resilient networks, cooperative robots can achieve consensus in the presence of faulty or malicious robots. We propose a design framework on triangular and square lattices, providing an underlying structure for proximity-based robot networks. We present sufficient conditions on the robot communication range to guarantee resilient consensus. Our results can be used to design robot formations considering obstacles, number of robots, and energy usage. Additionally, robot networks with homogeneous and heterogeneous communication range are studied. We support our theoretical analysis with simulations on selected scenarios.

Optimal Control Method for Robot-Tracking Based on Control-Lyapunov-Function

A control Lyapunov function (CLF)-based optimal control method is proposed to solve an affine nonlinear system with input limitation for the wheeled robot. Motivated by Lyapunov stability theory, viability theory, and exact linearization and sliding mode control, the construction of the CLF uses the information of the multi-order derivatives of the system outputs. The result shows the stability depends on the controller coefficients and the input limitation. Thus, the sufficient conditions are given and proved for stable controller design. The proposed control method provides a new robust regulation map to an affine nonlinear system for high-dimensional trajectory tracking. A simulation of multi-agent wheeled robot formation is designed to illustrate the application of the proposed controller. Meanwhile, the validation and feasibility of the controller are also verified by the simulation.

Group control of autonomous robots motion in uncertain environment via unstable modes

The paper is devoted to the methods and algorithms of group control, providing a consistent movement of a moving objects group in a partially uncertain three-dimensional environment with obstacles. The uncertainty of the environment is a priori unknown moving obstacles. Mobile robots of the group should create a formation in a given rectangular area in the plane. The robots formation must move in the given direction. The problem solution is carried out by using algorithms based on unstable modes. The unstable modes allow to transform obstacles into repellers. The proposed algorithms can be implemented decentralized. Two algorithms options for group control are analyzed in the paper. Also a numerical simulation of a hexacopters group in an uncertain environment with obstacles is performed. The developed algorithms are used in the control system of mobile robots in their group locomotion in an uncertain 3-d environment. A group of mobile robots should be self-organized into a structure that does not require a preliminary assignment of the place of each robot. The group of robots can adjust the formation at occurrence of obstacles.

Distributed Estimation and Control for Leader-Following Formations of Nonholonomic Mobile Robots

The problem of the leader-following formation control of nonholonomic mobile robots is addressed in this paper. A distributed formation control strategy using explicitly the coordination errors among robots is proposed without assuming that each follower robot knows the full state of the leader. First, a distributed estimation law is proposed for each follower robot to estimate the states, including the position, orientation, and linear velocity of the leader. The distributed formation control law is then designed based on the estimated states of the leader, and the neighborhood formation tracking error. Under some mild assumptions on the interaction graph among the leader and the follower robots, and the velocity of the leader, asymptotic convergence of formation tracking errors to zero can be achieved. Finally, some numerical simulations and experiments on a group of nonholonomic mobile robots are presented to demonstrate the effectiveness of the proposed strategy. Note to Practitioners —The motivation of this paper is to investigate a practical control strategy for the leader-following formation of multiple autonomous mobile robots subjected to nonholonomic constraints. In most of the existing leader-following formation control schemes for nonholonomic mobile robots, having access to the full state of the leader is a requirement. However, due to limitations in communication bandwidth and range, it is reasonable to assume that the information of the leader is available only to a subset of followers. Hence, this paper suggests a new distributed leader-following formation control strategy based on the distributed estimation of the leader’s states. Moreover, the coordination error between a pair of interacting robots is explicitly used in the control design to weaken the dependence on the estimated state of the leader, and enhance the decentralized nature of the proposed control scheme. The stability and convergence of the system are analyzed mathematically and the experiment using unicycles provides promising results. In ongoing research, we are addressing the issues of collision avoidance and communication delays to provide more realistic setup for the industrial applications of multivehicle systems.

Controlling robot formations by means of spatial reasoning based on rough mereology

This research focuses on controlling robots and their formations using rough mereology as a means for spatial reasoning. The authors present the state of the art theory behind path planning, robot cooperation domains and ways of creating robot formations. Furthermore, the theory behind Rough Mereology as a way of implementing mereological potential field based path creation and navigation for single and multiple robots is described. An implementation of the algorithm is shown in simulation using RoboSim simulator. Five formations are tested (Line, Rhomboid, Snake, Circle, Cross) along with three decision systems (First In, Leader First, Horde Mode) as compared to other methods.

Formation Control of Teleoperating Cyber-Physical System With Time Delay and Actuator Saturation

Teleoperating cyber-physical system (TCPS) is referred to as a promising technology to extend human actions and intelligences to remote locations. Many applications of TCPS demand operator and slaves to keep a desired formation. However, the cyber- and physical-constrained characteristics on TCPS make it challenging to achieve such a formation task. This brief is concerned with a formation control problem for multislave TCPS, subject to time-varying delays in cyber channels and actuator saturation in physical channels. We design a decentralized controller to enforce the formation of master and slave robots. Sufficient conditions for stability are provided to show that the formation controller can stabilize the master-slave TCPS. In order to estimate the domain of attraction, the stability conditions are rearranged into a form of linear matrix inequalities (LMIs), and then, the required initial stability conditions for master and salves are developed. The transparent interaction between human operator and environment is also provided. Finally, simulations and experiments are performed for illustration and validation purposes.

Weighted Bearing-Compass Dynamics: Edge and Leader Selection

This paper considers the design and effective interfaces of a distributed robotic formation running planar weighted bearing-compass dynamics. We present results that support methodologies to construct formation topologies using submodular optimization techniques. Further, a convex optimization framework is developed for the selection of edge weights which increase performance. We explore a method to select leader agents that can translate and scale the formation, and a corresponding controller that promotes the formation keeping its overall shape intact during manipulation. The results are supported with examples that illustrate the approach and their differing levels of performance.