Distributed fixed-time consensus-based formation tracking for multiple nonholonomic wheeled mobile robots under directed topology

This study aims to explore the tracking control challenge in a swarm of multiple nonholonomic wheeled mobile robots (NWMRs) by utilizing a distributed leader–follower strategy grounded in the cascade system theory. Firstly, the kinematic control law is developed for the leader by constructing a sliding surface based on the error tracking model with a virtual reference trajectory. Secondly, a communication topology with the desired formation pattern is modeled for the multiple robots by using the graph theory. Further, in the leader–follower NWMR system, each follower lacks direct access to the leader’s information. Therefore, a novel distributed-based controller by PD-based controller for the follower is developed, enabling each follower to obtain the leader’s information. Thirdly, for each case, we give a further analysis of the closed-loop system to guarantee uniform global asymptotic stability with the conditions based on the cascade system theory. Finally, the trajectory tracking performance of the proposed controllers for the NWMR system is illustrated through simulation results. The leader robot achieved a low RMSE of 1.6572 (Robot 1), indicating accurate trajectory tracking. Follower robots showed RMSEs of 2.6425 (Robot 2), 3.0132 (Robot 3), and 4.2132 (Robot 3), reflecting minor variations due to the distributed control strategy and local disturbances.

Finite-time tracking control of multiple nonholonomic mobile robots

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.

This paper investigates finite-time tracking control problem of multiple non-holonomic mobile robots via visual servoing. It is assumed that the pinhole camera is fixed to the ceiling, and camera parameters are unknown. The desired reference trajectory is represented by a virtual leader whose states are available to only a subset of the followers, and the followers have only interaction. First, the camera-objective visual kinematic model is introduced by utilising the pinhole camera model for each mobile robot. Second, a unified tracking error system between camera-objective visual servoing model and desired reference trajectory is introduced. Third, based on the neighbour rule and by using finite-time control method, continuous distributed cooperative finite-time tracking control laws are designed for each mobile robot with unknown camera parameters, where the communication topology among the multiple mobile robots is assumed to be a directed graph. Rigorous proof shows that the group of mobile robots converges to the desired reference trajectory in finite time. Simulation example illustrates the effectiveness of our method.

Wheeled mobile robots (WMRs) have been a focus of research for several decades, particularly concerning navigation strategies in static and dynamic environments. This review article carefully examines the extensive academic efforts spanning several decades addressing navigational complexities in the context of WMR route analysis. Several approaches have been explored by various researchers, with a notable emphasis on the inclusion of stability and intelligent capabilities in WMR controllers attracting the attention of the academic community. This study traces historical and contemporary WMR research, including the establishment of kinetic stability and the construction of intelligent WMR controllers. WMRs have gained prominence in various applications, with precise navigation and efficient control forming the basic prerequisites for their effective performance. The review presents a comprehensive overview of stability analysis and navigation techniques tailored for WMRs. Initially, the exposition covers the basic principles of WMR dynamics and kinematics, explaining the different wheel types and their associated constraints. Subsequently, various stability analysis approaches, such as Lyapunov stability analysis and passivation-based control, are discussed in depth in the context of WMRs. Starting an exploration of navigation techniques, the review highlights important aspects including path planning and obstacle avoidance, localization and mapping, and trajectory tracking. These techniques are carefully examined in both indoor and outdoor settings, revealing their benefits and limitations. Finally, the review ends with a comprehensive discussion of the current challenges and possible routes in the field of WMR. The discourse includes the fusion of advanced sensors and state-of-the-art control algorithms, the cultivation of more robust and reliable navigation strategies, and the continued exploration of novel WMR applications. This article also looks at the progress of mobile robotics during the previous three decades. Motion planning and path analysis techniques that work with single and multiple mobile robots have been discussed extensively. One common theme in this research is the use of soft computing methods to give mobile robot controllers cognitive behaviors, such as artificial neural networks (ANNs), fuzzy logic control (FLC), and genetic algorithms (GAs). Nevertheless, there is still a dearth of applications for mobile robot navigation that leverage nature-inspired algorithms, such as firefly and ant colony algorithms. Remarkably, most studies have focused on kinematics analysis, with a small number also addressing dynamics analysis.

This paper proposes an approach to the motion coordination of multiple industrial mobile robots (AGVs). The task of the robots is to cooperatively transport a common object. An ordinary mobile robot has uncertain dynamics, and its motion is constrained by a non-holonomic constraint. Furthermore, multiple robots with a common object form a closed-chain structure which would cause the severe dynamical interactions. The authors' approach overcomes the inherent problems by introducing a robot-mounted coupler with mechanical compliance which provides compliance between each robot and the object. The hierarchical coordinative control scheme is presented to perform accurate object-transportation based on the synchronous motions of the robots. Simulation and fundamental experiment by using a commercially available AGV demonstrate the effectiveness of the authors' approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Application of intelligent Wheeled Mobile Robots (WMR) for material handling in the manufacturing environment has been the topic of research in the past decade. Even though researchers have succeeded in applying mobile robots for material handling purpose in the shop floor environment, transporting heavy objects in the assembly line is still a challenge. The dynamical characteristics of a manufacturing environment impose particular abilities a mobile robot should have if it is to operate on the shop floor efficiently, accurately and successfully. Consequently, a WMR needs to adapt itself to everlasting changes. Under such conditions, the use of multiple WMR in closed defined geometric spatial pattern/ formation can be a solution for such applications. One of the essential problems in guiding multiple mobile robots in such dynamically changing environments is to plan, navigate and coordinate the motion of robots, avoiding obstacles as well as each other while transporting the materials/objects towards the goal. Further it requires the robots to control their relative position and orientation between them on the fly. Hence the control of group of mobile robots performing such tasks requires coordination at different levels starting from navigation to formation (Sugar et al., 2001). A variety of strategies and control approaches for formation control of group of coordinated robots, have been adopted in the literature such as Graph Theory (Desai, 2002), Vector Potential Field (Yamaguchi et al., 2001), Virtual Structure (Belta & Kumar, 2004), Leader Follower (Fierro et al., 2002) and Behaviour Based Approaches (Arkin, 1998; Goldberg & Mataric, 2002). Further, a comprehensive review of robotic formation, control approaches and algorithms, applications and their advantages and disadvantages have also been addressed (Chen & Wang, 2005). Among all the approaches mentioned in the literature, behaviour – based and leader – follower approach has been widely adopted and well recognized by the researchers because of their simplicity and scalability. Even though robots are able to move in a closed defined formation when controlled using the various methods reported in the literature, the major limitation has been the difficulty to achieve a stable formation between the robots in the group in dynamically changing, unknown environments filled with obstacles. Under such circumstances, as the number of robots increases, the control methods such as the virtual structure, leader follower and

This article, concerned with a part of the research on distributed coordination work by multiple robots, discusses an algorithm for creating maps of unknown environments which are searched for and observed by multiple mobile robots, and on the results of a simulation experiment using this algorithm. This algorithm comprises a moving method, an observation method, and a task planning method which are intended to help the multiple mobile robots carry out an efficient search of unknown environments.

Practical time‐varying formation tracking analysis and design problems for multiple non‐holonomic mobile robot systems with directed interaction topologies are investigated by using the distributed extended state observers, where the practical time‐varying formation tracking error is controlled within an arbitrary small bound. Different from the previous work, the dynamics of each robot is non‐holonomic and the followers are required to form the practical time‐varying formation with respect to the leader of unknown control inputs. Besides, the disturbances and the uncertainties are considered in the dynamic model of the follower. Distributed extended state observers are constructed by using only the neighbouring relative information to estimate both the state and the unknown control inputs of the leader simultaneously. A practical time‐varying formation tracking protocol is presented based on the distributed extended state observers. The gain matrices of the observers in the practical time‐varying formation tracking protocol can be obtained by solving three linear matrix inequalities. Moreover, the stability of the multiple non‐holonomic mobile robot system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, two numerical simulation examples are given to illustrate the effectiveness of the obtained theoretical results.

This paper considers formation control of a group of wheeled mobile robots with uncertainty. Decentralized cooperative robust controllers are proposed in two steps. In the first step, cooperative control laws are proposed for multiple kinematic systems with the aid of results from graph theory such that a group of robots comes into a desired formation. In the second step, cooperative robust control laws for multiple uncertain dynamic systems are proposed with the aid of backstepping techniques and the passivity properties of the dynamic systems such that multiple robots comes into a desired formation. Since communication delay is inevitable in cooperative control, its effect on the proposed controllers is analyzed. Simulation results show the effectiveness of the proposed controllers.

This paper deals with a framework of decentralized approach to division of labor by multiple mobile robots. An iterative-transportation task by multiple robots with multiple sets of starts (pick-up place of the object) and goals (put down place) is considered as the task. On each route between a start and a goal, the efficiency of transportation improves when the number of robots increases. Due to jams, however, excessive number of robots on the same route causes inefficiency. We propose a control law of each robot to choose an appropriate route so as to optimize the total efficiency of the transportation, where each robot utilizes information which can be obtained only by local observation (without any explicit communication among robots). The proposed control is based on the estimation of the number of robots on the routes in the future. In simulation, it was verified that the proposed control law realized 96% efficiency of the fully centralized control by appropriately choosing the route, compared with the case where global information can be utilized.

Consensus problems of multiple nonholonomic mobile robots are considered in this paper. These problems are simplified into consensus problems of two subsystems based on structure of nonholonomic mobile robots. Linear distributed controllers are constructed respectively for these two subsystems thanks to the theory of nonautonomous cascaded systems. Consensus of multiple nonholonomic mobile robots has been realized using the methodology proposed in this paper no matter whether the group reference signal is persistent excitation or not. Different from previous research on cooperative control of nonholonomic mobile robots where the consensus problem under persistent exciting reference has received a lot of attention, this paper reports the first consensus result for multiple nonholonomic mobile robots whose group reference converges to zero. Simulation results using Matlab illustrate the effectiveness of the proposed controllers in this paper.

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.

The paper is concerned with the region tracking control problem of multiple nonholonomic mobile robot systems with collision avoidance. The peculiar characteristic of the proposed scheme is that a class of potential energy functions is chosen to form the desired target region constraining the robots for aggregation, and some local potential energy functions are selected to maintain collision avoidance among robots. Such that each mobile robot only needs to interact with their neighbors to realize the region tracking control task. Moreover, this paper provides a new analytical framework of region tracking control for a network of wheeled mobile robots, in which the integration of the system decomposition and sliding mode control method enables to convert the nonholonomic constraint problem of the controlled mobile robot system into a holonomic constraint problem. This provides a new approach to solving the mobile robot control problem. Theoretical analysis and numerical simulation results are given to validate the effectiveness of the proposed control scheme.

This paper deals with multi-objective behavior coordination and sensory networks based on fuzzy control for multiple mobile robots. In multi-objective behavior coordination, weights are assigned to basic behaviors and updated gradually according to the time series of sensory inputs. A robot with our behavior coordination can take a smooth action. The sensory network is the self-update mechanism of a sensory range in order to realize flexible control with a small number of control rules. Both methods have been successfully applied to a single mobile robot. In this paper, we focus on an environment including multiple mobile robots. We examine the effects of the values for updating behavior weights and sensory ranges on the performance of multiple mobile robots. From the experimental results, we show the effectiveness of the multi-objective behavior coordination and sensory networks in the environment including multiple mobile robots.