Formation control of autonomous robots based on cooperative behavior

This paper investigates an adaptive leader-follower formation control problem of multiple mobile robots in the presence of unknown skidding and slipping. First, we employ the concept of virtual robots to achieve the desired formation and derive the kinematics of the virtual leader and follower robots considering skidding and slipping effects. Then, we design an adaptive formation controller based on a two-dimensional error surface where the adaptive technique is used for compensating the unknown skidding and slipping effects that influence the follower robots. From Lyapunov stability theorem, we show that all errors of the closed-loop system are uniformly ultimately bounded, and thus the desired formation is successfully achieved regardless of the presence of unknown skidding and slipping effects. Simulation results are provided to demonstrate the effectiveness of the proposed formation control scheme.

In this paper, we propose a new nonlinear cooperative steering control to solve the formation control problem for multiple mobile robots with nonholonomic constraints. By using a new contraction mapping method, it is rigorously proved that the proposed cooperative formation control is asymptotically stabilizing under the condition that the sensing/communication network among robots is sequentially complete. Simulation results are included to illustrate the effectiveness of the proposed control.

This paper investigates the distributed formation control problem for multiple nonholonomic wheeled mobile robots. A variable transformation is first proposed to convert the formation control problem into a state consensus problem. Then, when the dynamics of the mobile robots are considered, the distributed kinematic controllers and neural network torque controllers are derived for each robot such that a group of nonholonomic mobile robots asymptotically converge to a desired geometric pattern along the specified reference trajectory. The specified reference trajectory is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers. Also the followers are assumed to have only local interaction. Moreover, the neural network torque controllers proposed in this work can tackle the dynamics of robots with unmodeled bounded disturbances and unstructured unmodeled dynamics. Some sufficient conditions are derived for accomplish the asymptotically stability of the systems based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples illustrate the effectiveness of the proposed controllers.

A novel approach for formation control of differential-drive mobile robots is presented in this paper. The control design is done in the framework of functionally related systems. Functionally related systems are the systems that are ‘virtually’ interconnected. The term ‘virtually’ denotes the situation in which the states or outputs of otherwise separated systems are functionally related to each other. If a formation of mobile robots is analyzed, it can be considered as a group of functionally related systems. Therefore, formation control of the robots can be synthesized in the mentioned framework.

Formation tracking control problem of multiple nonholonomic mobile robots is considered in this paper. Previous tracking control results of single nonholonomic mobile robots are extended to solve the formation tracking control of multiple nonholonomic mobile robots. By using the theory of cascaded systems and cooperative control of linear agents, formation tracking control problem is converted into multi-linear time-varying systems' stabilization problem. Under some persistent excitation condition on the virtual leader, linear cooperative controllers are constructed for the formation tracking control problem. Simulation results using Matlab validates the theoretic results.

Formation control of multiple autonomous robots is an important part of autonomous robot research. And theoretical research should be based on reality. Therefore, thinking of each robot as an agent, this article considers the problems in actual situation of multi-agent formation control, namely energy consumption. The formation is accompanied by energy consumption. If fuel conservation is not considered, it will lead to three problems: 1. Environmental pollution; 2. The formation task cannot be carried out for a long time; 3. Carrying a large amount of fuel will definitely affect the flexibility of autonomous robots. Therefore, how to reduce energy consumption while implementing formation tasks is the focus of this paper. In this paper, the directed graph in graph theory is used to simulate the communication links between multi-agents for continuous systems and discrete systems in general linear systems. According to the linear quadratic method, optimal controllers are designed respectively to realize the control of target formation. At the same time, fuel consumption is reduced as much as possible to achieve the minimum performance index.

Cooperation between multiple autonomous mobile robots is an essential requirement for the successful completion of many tasks that require more resources than a single robot can possibly provide. There are many coordinated missions such as formation control, coordinated exploration etc. The formation control problem consists of designing control inputs for the vehicles so that they form and maintain a predefined geometric shape in space even in the presence of external disturbances. The control is designed in such a way that the vehicles correct their position looking at the position of their neighbours. In this paper a formation control law is proposed for mobile robots while their motion is affected by unknown disturbances. The simulation results illustrates the robustness of the proposed formation control design to the disturbance uncertainties.

This paper presents a decentralized controller design for formation and traction control of multiple robots with collision avoidance. The proposed control design consists of two steps: formation control design with collision avoidance and traction control design for movement of robot formation along the desired trajectory. In the first step, a formation controller is designed based on the formation graph model of multiple robots and potential function approach. Then, the traction control input is derived in the second step by locating the virtual leader at the central position of robot formation which leads mobile robots to follow the assigned trajectory in formation. In this distributed control design, parameter uncertainty in kinematic system model is also accommodated by deriving an adaptive rule for estimation of uncertain system parameters. Together with the stability analysis of the proposed controller, simulation and experiment results verify the feasibility and effectiveness of the distributed controller for multi-robot coordination.

Decentralized leader-following formation control of nonholonomic mobile robots by local measurement: A small-gain approach

This article investigates the circular formation control problem of multiple unicycle-type mobile robots under a directed sensor graph. The topology of the sensor graph among all robots is described by a directed graph containing a spanning tree, and the node denoting the center is only required to be globally reachable in the sensor graph. A dynamic control law is developed such that the multi-robot systems with speed constraint are able to globally converge to a circular formation prescribed by a stationary center, a radius, and a spacing configuration. Remarkably, the proposed control law does not rely on any communication, and only requires each robot to use local measurements with respect to its neighbors based on its local coordinate frame, which makes it feasible to implement this control law in a decentralized manner. The global asymptotic stability of the closed-loop multi-robot system is established by small-gain theorem of which the small-gain condition is guaranteed by a low gain parameter in the designed observer.

In his pioneering paper on matroids in 1935, Whitney obtained a characterization for binary matroids and left a comment at end of the paper that the problem of characterizing graphic matroids is the same as that of characterizing matroids which correspond to matrices (mod 2) with exactly two ones in each column. Later on Tutte obtained a characterization of graphic matroids in terms of forbidden minors in 1959. It is clear that Whitney indicated about incidence matrices of simple undirected graphs. Here we introduce the concept of a segment binary matroid which corresponds to matrices over $\mathbb{Z}_2$ which has the consecutive $1$'s property (i.e., $1$'s are consecutive) for columns and obtained a characterization of graphic matroids in terms of this. In fact, we introduce a new representation of simple undirected graphs in terms of some vectors of finite dimensional vector spaces over $\mathbb{Z}_2$ which satisfy consecutive $1$'s property. The set of such vectors is called a coding sequence of a graph $G$. Among all such coding sequences we identify the one which is unique for a class of isomorphic graphs. We call it the code of the graph. We characterize several classes of graphs in terms of coding sequences. It is shown that a graph $G$ with $n$ vertices is a tree if and only if any coding sequence of $G$ is a basis of the vector space $\mathbb{Z}_2^{n-1}$ over $\mathbb{Z}_2$. Moreover considering coding sequences as binary matroids, we obtain a characterization for simple graphic matroids and found a necessary and sufficient condition for graph isomorphism in terms of a special matroid isomorphism between their corresponding coding sequences. For this, we introduce the concept of strong isomorphisms of segment binary matroids and show that two simple (undirected) graphs are isomorphic if and only if their canonical sequences are strongly isomorphic segment binary matroids.

In this article, formation control of networked mobile robots is studied. Two control strategies for the leaderless case and the leader‐following case are developed from the Udwadia–Kalaba approach, respectively. Differing from the existing results about formation control, which focus on kinematic models of robots, this article considers dynamic models and obtained a lower‐cost control force. To improve the robustness of the communication network, two distributed formation controllers are designed by establishing distributed estimators. Different from the centralized controllers, the distributed controllers established here only require local information, thus save communication resources and improve system robustness. Finally, some numerical simulations are provided to demonstrate the proposed methods are effective and have lower control cost.

Formation control of nonholonomic mobile robots is considered in this paper and decentralized linear controllers based on cascade design are proposed for a group of nonholonomic mobile robots. By using the theory of cascaded systems and cooperative control of linear agents, multiple nonholonomic robots' formation control problem is converted into multi-linear time-varying systems' stabilization problem. Linear decentralized cooperative controllers are brought out for the formation control problem when the reference targets satisfy the condition of persistent excitation which has relaxed the requirements on reference trajectory than those given in previous papers.

The coordinated formation control of wheeled mobile robots (WMRs) with directed and switching communication topologies is studied. In particular, together with the non‐holonomic constraint, physical constraints on the velocity, acceleration and angular velocity are taken into account. Through dynamic feedback linearisation, the kinematic model of each robot is transformed into a double‐integrator subject to the physical constraints. Then, coordinated controllers with successive loops are developed for the formation control. The problem caused by the physical constraints is solved by introducing saturations to the control loops. It is proved that each controlled WMR admits an invariant set property, and the formation control objective is achievable as long as a mild joint connectivity condition is satisfied by the communication topology.

This paper studies distributed formation and orientation control of multiple robots using relative measurements in local coordinate frames. The control objective is to achieve a desired formation with all robots facing a target for monitoring. It is assumed that each robot can only measure neighbors’ relative positions to the target and relative orientations to their neighbors, and that communication among robots is unavailable. To address this issue, we introduce a unified framework of formation and orientation control, and proposed a distributed and relative control law to ensure achieving the control objective. Not only formation but also orientation control is successful because a clique-based method is employed, instead of conventional edge-based ones. Here, the cliques are complete subgraphs. Besides, the effectiveness of the proposed method is illustrated through a simulation, and the stability of the system is analyzed. Because this method is applicable regardless of the dimension of the space, the proposed method can be applied to both UGV and UAV, as well as the coordination of heterogeneous multi-robot systems in the case of cooperative monitoring and transport.