Multiple Nonholonomic Wheeled Mobile Robots Research Articles

Formation control for multiple nonholonomic wheeled mobile robots based on integrated sliding mode controller and force function

In this paper, we present a novel method to achieve collision-free formation control for multiple nonholonomic wheeled mobile robots. By utilizing the leader–follower strategy, an integrated controller that combines a sliding mode controller for formation control and a force function for obstacle avoidance is proposed. To address the common chattering issue associated with sliding mode control, a novel depletion model is developed, which constrains the controller input to vary smoothly within a small range and effectively eliminates chattering. Additionally, a dynamic-gain structure is introduced to reconcile the conflicting demands of formation control and obstacle avoidance, providing enhanced coordination between the two tasks. Simulation and experiments’ results are provided to illustrate the effectiveness of the proposed method.

Formation Control and Tracking of Mobile Robots using Distributed Estimators and A Biologically Inspired Approach.

This paper investigates the formation control problem for multiple nonholonomic wheeled mobile robots using distributed estimators and a biologically inspired approach. The formation pattern of the system adopts leader–follower structure and the communication topology among the multi-robot system is modelled by an undirected graph. In our proposed methodology, first, we develop an adaptive trajectory tracking control for the leader robot to follow the desired trajectory. Second, a distributed estimator is designed for each follower mobile robot, which uses its own information to estimate the leader's states, such as position, orientation, and linear velocity. Then, distributed formation tracking control laws are designed based on the distributed estimator. Furthermore, a bioinspired controller is developed to address the impractical velocity jump problem. The closed-loop system stability is analysed with the Lyapunov stability theory showing that tracking errors are asymptotically converge to zero. Finally, simulation results are provided to demonstrate the effectiveness of the proposed methods.

Distributed leader-following formation control for multiple nonholonomic mobile robots via bioinspired neurodynamic approach

This paper investigates the distributed leader-following formation control problem for multiple nonholonomic wheeled mobile robots via a bioinspired neurodynamic approach. To do this, first, we develop a distributed estimator for each follower robot which uses its own information and the information of its neighboring robots to estimate the leader’s states. Second, a formation tracking control law is proposed for each follower robot based on the estimated states of the leader using the backstepping technique. Then, a bioinspired neurodynamics-based backstepping controller is designed to solve the impractical velocity jumps problem. Furthermore, Lyapunov function-based approach is utilized to derive sufficient conditions which guarantee asymptotic stability of the multiple mobile robot system. Finally, simulation results are presented to illustrate the effectiveness of the proposed controllers.

Fixed-time formation tracking for multiple nonholonomic wheeled mobile robots based on distributed observer

This paper studies the distributed fixed-time formation tracking problem of multiple nonholonomic wheeled mobile robots system over directed fixed and switching topologies. Through a classical nonlinear transformation, the formation control problem is transformed into a consensus problem. New control protocols based on a distributed observer are proposed. The directed communication topology between multiple nonholonomic wheeled mobile robots is considered. Some sufficient conditions of multiple robots achieving the desired formation shape are given. All follower robots can form the desired formation shape within a fixed settling time and make the leader in the geometric center of the formation. By adopting graph theory and fixed-time stability theory, an upper bound of settling time that is independent of the system’s initial states is obtained. Finally, two examples are presented to illustrate the correctness of the main results.

Distributed Formation Control of Nonholonomic Wheeled Mobile Robots Subject to Longitudinal Slippage Constraints

This paper investigates the distributed formation control problem of multiple nonholonomic wheeled mobile robots within real environments. The formation pattern of the system adopts leader–follower structure and the communication topology among the multirobot system is modeled by a directed graph. Slippage is hard to avoid due to the possible existence of ice, sand, or muddy roads. To overcome the effect of slippage, an adaptive trajectory tracking controller for leader robot is designed, such that the leader robot can keep up with the virtual reference trajectory and estimate the real value of unknown slipping ratio accurately. In addition, it is difficult for each follower robot to obtain leader’s states in a large formation system, so distributed formation controllers are designed based on distributed observers. It is shown that the proposed controllers can realize formation objective and overcome the slippage constraints at the same time. Finally, the effectiveness of the proposed controllers is verified by simulation results.

Coordinated Planar Path-Following Control for Multiple Nonholonomic Wheeled Mobile Robots.

This article is concerned with both consensus and coordinated path-following control for multiple nonholonomic wheeled mobile robots. In the design, the path-following control is decoupled into the longitudinal control (speed control) and the lateral control (heading control) for the convenience of implementation. Different from coordinated trajectory tracking control schemes, the proposed control scheme removes the temporal constraint, which greatly improves the coordination robustness. In particular, two new coordinated error variables describing a chasing-and-waiting strategy are introduced in the proposed coordinated path-following control for injective paths and circular paths, respectively. All the closed-loop signals have proved to be asymptotically stable in the Lyapunov sense. Finally, simulation results under three typical paths are presented to verify the proposed coordination controllers.

Distributed formation control for multiple non-holonomic wheeled mobile robots with velocity constraint by using improved data-driven iterative learning

In this paper, a distributed proportional-integral data-driven iterative learning control (PI-DDILC) algorithm is developed to achieve the formation problem for non-holonomic and velocity constrained wheeled mobile robots (WMRs) under repeatable operation environment. Firstly, the formation problem is transformed into a tracking problem with a certain deviation from the reference trajectory. And a distributed kinematics control algorithm is designed by using leader-follower strategy and graph theory. Then, to solve the problem of unknown dynamic model, the relationship between WMR’s output and input is first derived by utilizing the iteration-domain dynamical linearization technique. After that, the improved data-driven iterative learning dynamics control algorithm is provided, which includes both proportional and integral terms along the iteration axis. This algorithm can ensure a group of WMRs to realize formation and only use I/O data of each WMR. Compared with DDILC, PI-DDILC can significantly enhance the response speed and transient performance of WMR system formation. The excellence of the improved algorithm is certified by simulation, and a performance index is designed to quantify the results of the two on formation performance.

Adaptive practical leader‐following formation control of multiple nonholonomic wheeled mobile robots

SummaryThis article investigates the leader‐following formation control of multiple uncertain nonholonomic wheeled mobile robots. The leader trajectory can be any sufficiently smooth signal, either feasible or nonfeasible. This includes but not limited to a fixed point, a trimming trajectory, and the one that does not satisfy the nonholonomic constraint as robots in question do. To compensate for the effects that only a subset of follower robots has connected to the leader, we develop a distributed observer to estimate the leader's position and velocities. Using leader's estimated states, we convert formation errors into an augmented system with external oscillator states, which introduce an additional control variable and overcome the difficulties caused by underactuation. Subsequently, an adaptive tracking control law dealing with model uncertainties and stabilizing the augmented system is proposed, ensuring that formation errors are globally uniformly ultimately convergent to arbitrarily small balls near the origin. Simulation results are performed to validate the proposed control design.

Distributed regular polygon formation control and obstacle avoidance for non‐holonomic wheeled mobile robots with directed communication topology

This study investigates distributed regular polygon formation control and obstacle avoidance problem for multi-robot systems with the leader–follower structure. The communication topology of the networked multi-robot system is modelled by a directed graph. Firstly, a distributed state observer is designed such that only part of the follower robots need to know the desired distance between the leader and followers. Based on the state observer, distributed obstacle avoidance can be realised. Then, an improved state transformation is designed such that the formation control of multiple non-holonomic wheeled mobile robots with observed states can be converted into a consensus-like problem. Based on the state transformation, novel controllers are proposed to achieve the formation control objectives. Finally, the effectiveness of the proposed control laws is verified by simulations.

Practical consensus tracking control of multiple nonholonomic wheeled mobile robots in polar coordinates

SummaryThis paper proposes a sliding‐mode control (SMC) method to achieve practical cooperative consensus tracking for a network of multiple nonholonomic wheeled mobile robots (MNWMRs) with input disturbances. A novel SMC surface under the nonholonomic constraints is first formulated to characterize the network communication interactions among the networked robots under the framework of polar coordinates. A unified distributed consensus tracking strategy is then proposed by systematically combining a position controller and a direction controller. Furthermore, a simple yet general criterion is derived to achieve the desired practical consensus of trajectory tracking and posture stabilization for MNWMRs. In particular, for a specific common consensus trajectory, the complete asymptotic tracking in heading direction can be fully guaranteed when the perfect asymptotic position‐tracking errors are realized. Accordingly, the developed consensus tracking strategy for MNWMRs demonstrates some advantages of control performance including stability, robustness, and effectiveness over the existing control method proposed for their single‐robot counterparts. Some comparative simulation results are given to confirm the effectiveness of the proposed cooperative consensus control method.

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

This paper investigates the distributed fixed-time consensus-based formation tracking problems for multiple nonholonomic wheeled mobile robots under a directed interaction topology. The distributed fixed-time consensus-based controllers under the directed interaction topology are proposed for the multiple wheeled mobile robots with nonholonomic constraints, which can guarantee the group of robots converge to a predefined formation pattern with its centroid moving along the predefined reference trajectory in a fixed time. The fixed-time formation tracking can be achieved within a fixed settling time, which is independent of the initial states of the whole system. Moreover, the conditions of formation stability control are analysed by utilising graph and Lyapunov stability theories. Finally, the feasibility of the proposed distributed controllers is verified by numerical simulation.

Energy-optimal problem of multiple nonholonomic wheeled mobile robots via distributed event-triggered optimization algorithm**Project supported by the National Natural Science Foundation of China (Grant No. 11701138) and the Natural Science Foundation of Hebei Province, China (Grant Nos. F2017202009 and F2018202075).

The distributed event-triggered optimization problem for multiple nonholonomic robots has been studied to minimize the global battery energy consumption. Each robot possesses its own cost function which depends on the state of the hand position and represents battery energy consumption. By coordinate transformation, the dynamics of the hand positions can be formulated into two groups of first-order integrators. Then the distributed event-triggered optimization algorithm is designed such that the states of robots’ hand positions exponentially converge to the optimizer of the global cost function. Meanwhile, the velocity and orientation of each robot are ensured to reach zero and a certain constant, respectively. Moreover, the inter-execution time is lower bounded and the Zeno behavior is therefore naturally avoided. Numerical simulations show the effectiveness of the proposed algorithm.

Robust finite‐time consensus formation control for multiple nonholonomic wheeled mobile robots via output feedback

SummaryThe finite‐time formation control for multiple nonholonomic wheeled mobile robots with a leader‐following structure is studied. Different from the existing results, the considered mobile robot has the following features: (i) a higher‐order dynamic model, (ii) the robot's velocities cannot be measured, and (iii) there are external disturbances. To solve the problem, a finite‐time consensus formation control algorithm via output feedback is explicitly given. At the first step, some finite‐time convergent observers are skillfully constructed to estimate both the unknown velocity information and the disturbance in finite time by imposing certain assumptions on the disturbances. Then, on the basis of the integral sliding‐mode control method, a disturbance observer‐based finite‐time output feedback controller is developed. Rigorous proof shows that the finite‐time formation can be achieved in finite time. An example is finally given to verify the efficiency of the proposed method.

Performance comparison of consensus protocol and l-&phi approach for formation control of multiple nonholonomic wheeled mobile robots

This paper investigates formation control of multiple nonholonomic differential drive wheeled mobile robots (WMRs). Assume the communication between the mobile robots is possible where the leader mobile robot can share its state values to the follower mobile robots using the leader-follower notion. Two approaches are discussed for controlling a formation of nonholonomic WMRs. The first approach is consensus tracking based on graph theory concept, where the linear and angular velocity input of each follower are formulated using first order consensus protocol, such that the heading angle and velocity of the followers are synchronized to the corresponding values of the leader mobile robot. The second is l-φ approach (distance angle) that is developed based on Lyapunov analysis, where the linear and angular velocity inputs of each follower mobile robot are adjusted such that the followers keep a desired separation distance and deviation angle with respect to the leader robot, and the overall system is asymptotically stable.The aim of this paper is to compare the performances of the presented methods for controlling a formation of wheeled mobile robots with matlab simulations.

Periodic event‐triggered cooperative control of multiple non‐holonomic wheeled mobile robots

This study investigates the periodic event-triggered control for the hand position centroid consensus/formation problems of multiple non-holonomic wheeled mobile robots. By constructing invertible input transformation, the dynamics of the hand positions are formulated as two groups of first-order integrators. Then, the event-triggered control laws and the event conditions are proposed. On the basis of Lyapunov theory and the algebraic graph theory, permissible value ranges of the sampling period and the event condition parameters are established, guaranteeing that all the hand positions asymptotically tend to the common initial centroid location or the desired formation shape centred at the initial centroid. In addition, the orientations and the velocity inputs of each robot are ensured to reach some constants and zeros, respectively. Finally, simulations illustrate the efficiency of the proposed theoretical results.

Distributed consensus-based formation control for nonholonomic wheeled mobile robots using adaptive neural network

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.

Adaptive distributed formation control for multiple nonholonomic wheeled mobile robots

This paper investigates the adaptive distributed formation control problem for multiple nonholonomic wheeled mobile robots. First, the formation control problem is converted into a state consensus problem by the aid of a variable transformation. Then, distributed kinematic controllers and adaptive dynamic controllers are developed for each robot such that a group of nonholonomic mobile robots asymptotically converge to a desired geometric pattern with its centroid moving 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. Some sufficient conditions are derived for accomplishing 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.

Multirobot rendezvous with bearing-only or range-only measurements

This paper studies distributed rendezvous strategies for multiple nonholonomic wheeled mobile robots with the aim of testing their practicality on real robots. We investigate control strategies which use just bearing-only or range-only measurements and do not need inter-robot radio communication to share the measurements. For the bearing-only case, two control laws proposed in our previous study are recalled and adapted. For the range-only case, rendezvous control laws for a two-robot system are proposed first and it is shown analytically a two-robot system achieves rendezvous globally under these control laws. Then the range-only-based control laws are extended to multirobot systems. Monte Carlo simulations indicate that a multirobot system achieves practical convergence under the range-only-based control laws. Experimental results illustrate the applicability and performance of the proposed control strategies for multiple wheeled-robot systems.

Finite-time tracking control of multiple nonholonomic mobile robots

This paper investigates finite-time tracking control problem of multiple nonholonomic wheeled mobile robots in dynamic model. First of all, the resulting tracking error dynamic is transformed into two subsystems, i.e., a third-order subsystem and a second-order subsystem for each mobile robot. Then, the two subsystems are discussed respectively, continuous distributed finite-time tracking control laws are designed for each mobile robot. Rigorous proof shows that the group of mobile robots can track the desired trajectory in finite time. Simulation example illustrates the effectiveness of our method.

Multiple Nonholonomic Wheeled Mobile Robots Trajectory Tracking While Maintaining Time-Varying Formation via Synchronous Controller

A new synchronization control method is developed for multiple nonholonomic wheeled mobile robot path tracking while maintaining time-varying formations. Every robot is controlled to track its desired path while its movement is synchronized with nearby robots to maintain the desired time-varying formation. A new derivation for dynamic model of the nonholonomic wheeled mobile robot (WMR) is proposed based on the Lagrange methods. The robot model is divided into translational and rotational models, such that, each model will be controlled individually. Furthermore, synchronous controller for each robot's translation is developed to guarantee the asymptotic stability of both position and synchronization errors. In addition, an orientation controller is proposed to ensure that the robot is always oriented towards its desired position. The simulation results validate the effectiveness of the proposed synchronous controller in the formation control tasks.