Multi-circular formation control with reinforced transient profiles for nonholonomic vehicles:A path-following framework

This article investigates a multi-circular path-following formation control with reinforced transient profiles for nonholonomic vehicles connected by a digraph.A multi-circular formation controller endowed with the feature of spatial-temporal decoupling is devised for a group of vehicles guided by a virtual leader evolving along an implicit path,which allows for a circumnavigation on multiple circles with an anticipant angular spacing.In addition,notice that it typically imposes a stringent time constraint on time-sensitive enclosing scenarios,hence an improved prescribed performance control(IPPC)using novel tighter behavior boundaries is presented to enhance transient capabilities with an ensured appointed-time convergence free from any overshoots.The significant merits are that coordinated circumnavigation along different circles can be realized via executing geometric and dynamic assignments independently with modified transient profiles.Furthermore,all variables existing in the entire system are analyzed to be convergent.Simulation and experimental results are provided to validate the utility of suggested solution.

Adaptive Trajectory Tracking Control for Nonholonomic Wheeled Mobile Robots:A Barrier Function Sliding Mode Approach

The trajectory tracking control performance of nonholonomic wheeled mobile robots(NWMRs)is subject to nonholonomic constraints,system uncertainties,and external disturbances.This paper proposes a barrier function-based adaptive sliding mode control(BFASMC)method to provide high-precision,fast-response performance and robustness for NWMRs.Compared with the conventional adaptive sliding mode control,the proposed control strategy can guarantee that the sliding mode variables converge to a predefined neighborhood of origin with a predefined reaching time independent of the prior knowledge of the uncertainties and disturbances bounds.Another advantage of the proposed algorithm is that the control gains can be adaptively adjusted to follow the disturbances amplitudes thanks to the barrier function.The benefit is that the overestimation of control gain can be eliminated,resulting in chattering reduction.Moreover,a modified barrier function-like control gain is employed to prevent the input saturation problem due to the physical limit of the actuator.The stability analysis and comparative experiments demonstrate that the proposed BFASMC can ensure the prespecified convergence performance of the NWMR system output variables and strong robustness against uncertainties/disturbances.

Dynamic event-triggered formation control of second-order nonholonomic systems

In this paper,the formation control problem of secondorder nonholonomic mobile robot systems is investigated in a dynamic event-triggered scheme.Event-triggered control protocols combined with persistent excitation(PE)conditions are presented.In event-detecting processes,an inactive time is introduced after each sampling instant,which can ensure a positive minimum sampling interval.To increase the flexibility of the event-triggered scheme,internal dynamic variables are included in event-triggering conditions.Moreover,the dynamic event-triggered scheme plays an important role in increasing the lengths of time intervals between any two consecutive events.In addition,event-triggered control protocols without forward and angular velocities are also presented based on approximate-differentiation(low-pass)filters.The asymptotic convergence results are given based on a nested Matrosov theorem and artificial sampling methods.

Relay-Switching-Based Fixed-Time Tracking Controller for Nonholonomic State-Constrained Systems:Design and Experiment

Dear Editor,This letter investigates the fixed-time trajectory tracking controller design for nonholonomic chained systems with static state constraints.Firstly,a fixed-time tracking control law is given to carry out relay switching,which divides the controller development process into two stages.

Lagrangian Formulation of Fractional Nonholonomic Constrained Damping Systems

Fractional Euler Lagrange equations for fractional nonholonomic constrained damping systems have been presented. The equations of motion are obtained using fractional Euler Lagrange equations in a similar manner to the usual technique. The results of fractional method reduce to those obtained from classical method when μ →0 and α,β →1 are equal unity only. This work is discussed using illustrative example.

Cost-effective distributed FTFC for uncertain nonholonomic mobile robot fleet with collision avoidance and connectivity preservation

In this paper,the fault-tolerant formation control(FTFC)problem is investigated for a group of uncertain nonholonomic mobile robots with limited communication ranges and unpredicted actuator faults,where the communication between the robots is in a directed one-to-one way.In order to guarantee the connectivity preservation and collision avoidance among the robots,some properly chosen performance functions are incorporated into the controller to per-assign the asymmetrical bounds for relative distance and bearing angle between each pair of adjacent mobile robots.Particularly,the resultant control scheme remains at a costeffective level because its design does not use any velocity information from neighbors,any prior knowledge of system nonlinearities or any nonlinear approximator to account for them despite the presence of modeling uncertainties,unknown external disturbances,and unexpected actuator faults.Meanwhile,each follower is derived to track the leader with the tracking errors regarding relative distance and bearing angle subject to prescribed transient and steady-state performance guarantees,respectively.Moreover,all the closed-loop signals are ensured to be ultimately uniformly bounded.Finally,a numerical example is simulated to verify the effectiveness of this methodology.

Global κ-exponential Tracking Control of Nonholonomic Systems in Chained-form by Output Feedback

追踪 nonholonomic 的控制问题的输出锁住形式系统在这份报纸被学习，没有坚持的刺激，全球指数的输出追踪者被介绍或对零不收敛在参考书轨道上。首先，变化时间的并列转变被介绍避免操作指数地收敛的信号。在串联系统和线性使不安的系统的理论的帮助下，然后，全球指数的产量追踪者成功地被获得。没有坚持的刺激的流行条件，建议控制器的新特征是追踪 nonholonomic 的控制问题的输出锁住形式系统的 A 也是可溶解的在以前的工作在引用信号上收敛到零。建议方法与一辆大蓬车借助于 nonholonomic 被示威并且讨论活动机器人和汽车。

Dynamic feedback robust stabilization of nonholonomic mobile robots based on visual servoing

This paper investigates the visual servoing robust stabilization of nonholonomic mobile robots. The calibration of visual parameters is not only complicated, but also needs great consumption of calculated time so that the accurate calibration is impossible in some situations for high requirement of real timing. Hence, it is interesting and important to consider the design of stabilizing controllers for nonholonomic kinematic systems with uncalibrated visual parameters. A novel uncertain model of these nonholonomic kinematic systems is proposed. Based on this model, a stabilizing controller is discussed by using dynamic feedback and two-step techniques. The proposed robust controller makes the mobile robot image pose and the orientation converge to the desired configuration despite the lack of depth information and the lack of precise visual parameters. The stability of the closed loop system is rigorously proved. The simulation is given to show the effectiveness of the presented controllers.

Adaptive Trajectory Tracking Control for a Nonholonomic Mobile Robot

As one of the core issues of the mobile robot motion control, trajectory tracking has received extensive attention. At present, the solution of the problem only takes kinematic or dynamic model into account separately, so that the presented strategy is difficult to realize satisfactory tracking quality in practical application. Considering the unknown parameters of two models, this paper presents an adaptive controller for solving the trajectory tracking problem of a mobile robot. Firstly, an adaptive kinematic controller utilized to generate the command of velocity is designed based on Backstepping method. Then, in order to make the real velocity of mobile robot reach the desired velocity asymptotically, a dynamic adaptive controller is proposed adopting reference model and Lyapunov stability theory. Finally, through simulating typical trajectories including circular trajectory, fold line and parabola trajectory in normal and perturbed cases, the results illustrate that the control scheme can solve the tracking problem effectively. The proposed control law, which can tune the kinematic and dynamic model parameters online and overcome external disturbances, provides a novel method for improving trajectory tracking performance of the mobile robot.

PARAMETRIC EQUATIONS OF NONHOLONOMIC NONCONSERVATIVE SYSTEMS IN THE EVENT SPACE AND THE METHOD OF THEIR INTEGRATION

In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then the field method for integrating these equations is given.Finally,an example illustrating the appli- cation of the integration method is given.

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.

Unified symmetry of nonholonomic mechanical systems with variable mass

Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained, An example is given to illustrate the application of the results.

A FIELD METHOD FOR SOLVING THE EQUATIONS OF MOTION OF NONHOLONOMIC SYSTEMS

In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrate its application.

Symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type

This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.

Lagrange equations of nonholonomic systems with fractional derivatives

This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton＇s principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d＇Alembert-Lagrange principle with fractional derivatives is presented, and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.

Generalized Chaplygin equations for nonholonomic systems on time scales

The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamil- ton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equa- tions are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results.

Robust adaptive control for a nonholonomic mobile robot with unknown parameters

A robust adaptive controller for a nonholonomic mobile robot with unknown kinematic and dynamic parameters is proposed. A kinematic controller whose output is the input of the relevant dynamic controller is provided by using the concept of backstepping. An adaptive algorithm is developed in the kinematic controller to approximate the unknown kinematic parameters, and a simple single-layer neural network is used to express the highly nonlinear robot dynamics in terms of the known and unknown parameters. In order to attenuate the effects of the uncertainties and disturbances on tracking performance, a sliding mode control term is added to the dynamic controller. In the deterministic design of feedback controllers for the uncertain dynamic systems, upper bounds on the norm of the uncertainties are an important clue to guarantee the stability of the closed-loop system. However, sometimes these upper bounds may not be easily obtained because of the complexity of the structure of the uncertainties. Thereby, simple adaptation laws are proposed to approximate upper bounds on the norm of the uncertainties to address this problem. The stability of the proposed control system is shown through the Lyapunov method. Lastly, a design example for a mobile robot with two actuated wheels is provided and the feasibility of the controller is demonstrated by numerical simulations.

Exact invariants and adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system

The exact invariants and the adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher-order adiabatic invariant of a mechanical system under the action of a small perturbation, the forms of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.

Vision-based Stabilization of Nonholonomic Mobile Robots by Integrating Sliding-mode Control and Adaptive Approach

Vision-based pose stabilization of nonholonomic mobile robots has received extensive attention. At present, most of the solutions of the problem do not take the robot dynamics into account in the controller design, so that these controllers are difficult to realize satisfactory control in practical application. Besides, many of the approaches suffer from the initial speed and torque jump which are not practical in the real world. Considering the kinematics and dynamics, a two-stage visual controller for solving the stabilization problem of a mobile robot is presented, applying the integration of adaptive control, sliding-mode control, and neural dynamics. In the first stage, an adaptive kinematic stabilization controller utilized to generate the command of velocity is developed based on Lyapunov theory. In the second stage, adopting the sliding-mode control approach, a dynamic controller with a variable speed function used to reduce the chattering is designed, which is utilized to generate the command of torque to make the actual velocity of the mobile robot asymptotically reach the desired velocity. Furthermore, to handle the speed and torque jump problems, the neural dynamics model is integrated into the above mentioned controllers. The stability of the proposed control system is analyzed by using Lyapunov theory. Finally, the simulation of the control law is implemented in perturbed case, and the results show that the control scheme can solve the stabilization problem effectively. The proposed control law can solve the speed and torque jump problems, overcome external disturbances, and provide a new solution for the vision-based stabilization of the mobile robot.

Lie-form invariance of nonholonomic mechanical systems

The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is givea to illustrate the application of the results.