Control Of Nonholonomic Mobile Robot Research Articles

Visual servo optimization stabilization of nonholonomic mobile robots based on control Lyapunov functions

This study considers the visual stabilization problem of nonholonomic mobile robots and proposes a novel optimization stabilization method for visual servo control of nonholonomic mobile robots with monocular cameras fixed onboard. The main idea of the method is to utilize control Lyapunov functions of discrete-time nonlinear systems to design a family of explicit stabilization control laws of the visual servo error system. The parameters of the control laws can indirectly reflect the performance of the visual servo controllers. Then taking account of visibility constraints and actuator limitations, a set of optimal parameters of the control laws is calculated by offline solving a constrained finite horizon optimal control problem. Moreover, the stabilization results on the optimal visual servo controller are established based on the properties of control Lyapunov functions. Finally, some simulation experiments are used to illustrate and evaluate the performance of the visual servo control scheme proposed here.

Event-based tracking control for nonholonomic mobile robots

In this paper, we study the event-triggered control problem for a kind of nonlinear time-varying system. Generally speaking we use the Lyapunov stability theory to solve an event-triggered tracking control problem of non-holonomic mobile robots. Firstly, we propose a continuous tracking control law using nonlinear state feedback. Under some proper assumptions, we use the linearization technique to prove the exponential stability of the tracking system. Then, we propose an event-triggered controller for the robot and prove the uniform boundedness of the solutions by using the Gronwall–Bellman inequality. Moreover, it is shown that the solutions are uniformly ultimately bounded and there is no Zeno behavior in the tracking system. Simulation studies show the effectiveness of the proposed approach.

Leader-Following Formation Control of Nonholonomic Mobile Robots With Velocity Observers

In many existing formation control approaches for nonholonomic mobile robots, the leader velocity is required to be measured and transmitted to the follower for controller design. Though some existing approaches can remove such a requirement, they have their respective shortcomings. For example, some are discontinuous, while others only ensure local closed-loop stability. In this article, we develop novel continuous formation controllers for mobile robots without measurement of the leader velocity such that communication between the mobile robots is not required. To address the unavailability issue of the leader velocity, observers based on adaptive control technique are proposed to obtain estimation of the leader velocity from information of the follower's onboard sensors. The effect of the velocity estimation error on the closed-loop stability is considered in the stability analysis based on Lyapunov stability theory, and it is shown that global stability of the combined observer–controller closed-loop system is ensured by the developed approaches. The effectiveness and performance of the developed approaches is illustrated using experimental results.

Multi-Agent Tracking of Non-Holonomic Mobile Robots via Non-Singular Terminal Sliding Mode Control

SUMMARYThis paper deals with the problem of the formation control of nonholonomic mobile robots in the leader–follower scenario without considering the leader information, as a result of its velocity and position. The kinematic model is reformulated as a formation model by incorporating the model uncertainties and external disturbance. The controller is presented in the two-step process. Firstly, the tracking problem is taken into consideration, which can be used as a platform to design a controller for the multi-agents. The proposed controller is designed based on a non-singular fast terminal sliding mode controller (FTSMC), which drives the tracking error to zero in finite time. It not only ensures the tracking but also handles the problem related to non-singularities. Moreover, the design control scheme is modified using high-gain observer to resolve the undefined fluctuations due to man-made errors in sensors. Secondly, the multi-agent tracking problem is considered; hence, a novel formation control is designed using FTSMC, which ensures the formation pattern as well as tracking. Furthermore, the obstacle avoidance algorithm is incorporated to avoid the collision, inside the region of interest. With the Lyapunov analysis, the stability of the proposed algorithm is verified. As a result, simulated graphs are shown to prove the efficacy of the proposed control scheme.

Leader-follower formation control of nonholonomic mobile robots with bearing-only measurements

This paper investigates the leader-follower formation control problem of nonholonomic vehicles. An estimator is first developed to estimate the relative position in its local coordinate system with bearing measurements, to avoid directly using positions or relative positions in the global reference frame. A control law is then proposed for the follower vehicle to follow the leader based on the estimated relative position. It is shown that the estimation error converges to zero, if some conditions on the relative angular velocity between the leader and the follower are satisfied. It is also shown that the stability of the closed loop system involving both the estimator and the controller is guaranteed if some mild conditions on the trajectory of the leader are satisfied. Extension to the case of multiple followers is also considered. Simulation results of numerical examples verify the effectiveness of the proposed control scheme.

Event-triggered formation tracking control of nonholonomic mobile robots without velocity measurements

This paper investigates an event-triggered formation tracking problem of nonholonomic mobile robots in a leader’s coordinate frame. The proposed control protocol can be implemented in directed sensor networks based on only relative information detected by onboard sensors of mobile robots. A novel observer is proposed, and by virtue of it, neither velocity measurements nor communication among robots is required. Furthermore, by introducing a super-twisting sliding mode differentiator, the convergence of estimation errors is no longer dependent on the convergence of system states, which makes it possible to adopt an event-triggered mechanism, by which the continuous update of control command is avoided and Zeno behavior is excluded. Finally, simulations illustrate the effectiveness of our control protocol.

Adaptive Leader–Follower Formation Control of Nonholonomic Mobile Robots With Prescribed Transient and Steady-State Performance

In this article, we study the formation tracking control problem for a group of nonholonomic mobile robots under communication constraints. We use a simple leader–follower formation tracking control strategy, in which only the leading robot of the robotic group obtains the given trajectory's information, and each robot only receives information from its immediate leader. Thus, the communication graph forms a static and simple directed spanning tree. We assume that the information exchange among the robots is limited by some given communication radius. Under the limited communication range, the leader–follower distance and bearing angle constraints are considered in the formation control design. To provide the given specifications on the transient and steady-state performances of formation tracking errors, the boundaries of the predefined constraints are enforced by designer-specified performance requirements, which are functions of time. Consequently, we incorporate the barrier Lyapunov function into formation control design to mathematically prove that the formation tracking errors evolve always within the predefined regions and converge asymptotically to zero. The proposed formation control strategy can also guarantee the connectivity maintenance and collision avoidance between the leader and the follower. Simulation results show the performance of the proposed formation tracking control.

Discrete-time predictive trajectory tracking control for nonholonomic mobile robots with obstacle avoidance

This article presents a tracking control approach with obstacle avoidance for a mobile robot. The control law is composed of two parts. The first is a discrete-time model predictive method-based trajectory tracking control law that is derived using an optimal quadratic algorithm. The second part is the obstacle avoidance strategies that switch according to two different designed obstacle avoidance regions. The controllability of the avoidance control law is analyzed. The simulation results validate the effectiveness of the proposed control law considering both trajectory tracking and obstacle avoidance.

Model Predictive Tracking Control of Nonholonomic Mobile Robots With Coupled Input Constraints and Unknown Dynamics

This paper addresses a trajectory-tracking control problem for mobile robots by combining tube-based model predictive control (MPC) in handling kinematic constraints and adaptive control in handling dynamic constraints. In order to handle kinematic constraints, the tube-based MPC scheme is introduced, which includes the state feedback controller to suppress the external disturbance in the velocity level. The tube-based MPC is transformed to a constrained quadratic programming (QP) problem, and then the QP problem can be efficiently solved by a primal-dual neural network over a finite receding horizon so as to obtain the optimal control velocity. Besides, an adaptive controller employing the neural network technology is proposed to acquire the approximation of the uncertain robotic dynamics. Moreover, an auxiliary control is developed in order to deal with actuator saturation, and a disturbance observer is designed to reject the external disturbance online in the dynamic level. Subsequently, through Lyapunov function synthesis, the stability of the closed-loop system have been guaranteed. Finally, in order to verify the effectiveness, the experimental studies are carried out using an actual mobile robot.

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.

Distributed Leader-follower Formation Control of Nonholonomic Mobile Robots

This paper considers the problem of distributed leader-follower formation control for nonholonomic mobile robots only using local interactions among the robots. First, a distributed estimation strategy is presented for each follower robot to estimate the leader’s state. Then the dynamic equations of the formation tracking errors are formulated and a distributed formation control scheme is designed, which yields globally uniformly ultimately bounded stability for the closed-loop systems without requiring persistent excitation conditions. Finally, a simulation example demonstrates the effectiveness of the proposed approach.

Model Predictive Control of Nonholonomic Mobile Robots with Backward Motion

Currently, most of model predictive control (MPC) of moible robots are designed based on forward movements, which is not efficient when the robot in certain initial positions. In this paper, a novel model predictive controller is designed to solve the regulation problem of a nonholonomic wheeled mobile robot with backward motion when its initial position in the first and second quadrants of Cartesian coordinates. System state variables selection and corresponding kinematic models in polar coordinate are defined to characterize backward movements. The terminal state cost function and terminal region together with the local controller are designed to guarantee the stability of the optimization problem (OP). Comparison studies show that the proposed MPC algorithm outperforms conventional ones.

Design of a robust tracking controller for a nonholonomic mobile robot with side slipping based on Lyapunov Redesign and nonlinear H∞ methods

ABSTRACTIn this paper, robust control of nonholonomic mobile robots is considered which is more complex with respect to holonomic types, due to fewer degrees of freedom in their model. In addition, side slipping is considered which disturbs the nonholonomic constraint adversely. In previous researches, the slip is either estimated by an estimator or is measured using additional sensors. In this paper, the Kanayama transformation is modified such that the model of the robot only includes matched disturbances. Then, a robust tracking controller is designed using the Lyapunov redesign method when only the upper bound of the side slip is known. Moreover, in order to compare the performance of the proposed controller, the nonlinear H∞ control is also developed for this robot. Finally, the performance of these two controllers is compared and the simulation results show the appropriate efficiency of the proposed controllers.

Finite-Time Switching Control of Nonholonomic Mobile Robots for Moving Target Tracking Based on Polar Coordinates

In this paper, finite-time tracking problem of nonholonomic mobile robots for a moving target is considered. First of all, polar coordinates are used to characterize the distance and azimuth between the moving target and the robot. Then, based on the distance and azimuth transported from the sensor installed on the robot, a finite-time tracking control law is designed for the nonholonomic mobile robot by the switching control method. Rigorous proof shows that the tracking error converges to zero in a finite time. Numerical simulation demonstrates the effectiveness of the proposed control method.

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.

Image-Based Position Control of Mobile Robots With a Completely Unknown Fixed Camera

In this paper, we consider the position control problem of nonholonomic mobile robots, i.e., the regulation of mobile robots to a desired position specified by the image position of a feature point onboard the mobile robot, by using visual feedback information from an overhead fixed camera. Many vision-based control approaches have been proposed for motion control of nonholonomic mobile robots, however, they usually assume that exact or approximate knowledge of full/partial intrinsic and/or extrinsic parameters of the camera can be available, and large or even very small errors in these parameters can deteriorate the control performance, reduce the control accuracy, and even affect the system stability. Hence, it is interesting and highly desirable to develop vision-based controllers without depending on the camera parameters, from both control performance and controller implementation perspectives. With this in mind, we propose novel image-based position control schemes for nonholonomic mobile robots completely without knowing the camera parameters. In the proposed schemes, neither accurate nor approximate knowledge about the camera intrinsic and extrinsic parameters is required, and the totally unknown camera can be mounted on the ceiling with an arbitrary pose, which can make the controller implementation very simple and flexible. Experimental results are provided to show the feasibility and effectiveness of the proposed schemes.

Robust and adaptive chatter free formation control of wheeled mobile robots with uncertainties

This paper addresses the robust formation control of non-holonomic mobile robots with homogeneous system architecture and decentralized control structure. Therefore, it was necessary the mathematical modeling of mobile robots, from which, the Separation-Bearing variant of Leader-Following control strategy was implemented. The stability proof were based on the Lyapunov theory. The sliding mode control (SMC) strategy was used in the controller design to make the control robust to the incidence of uncertainties and disturbances. The Fuzzy Adaptive Formation Control is designed to eliminate the previous bounding knowledge of these uncertainties and disturbances. The proposed control effectiveness is demonstrated by results obtained with simulations in Matlab/Simulink. The pure kinematic and kinematic with disturbances is also analyzed. The results shows the controllers effectiveness to formation of multi-robots systems to the eight-shaped trajectory.

Formation Control of Nonholonomic Mobile Robots Without Position and Velocity Measurements

Most existing formation control approaches are based on the assumption that the global/relative position and/or velocity measurements of mobile robots are directly available. To extend the application domain and to improve the formation control performance, it is extremely necessary to avoid the use of position and velocity measurements in the design of formation controllers. In this paper, we propose new leader-following formation tracking control schemes for nonholonomic mobile robots with onboard perspective cameras, without using both position and velocity measurements. To address the unavailability issue of position measurements, the leader–follower kinematics model in the image space is developed, which can facilitate the complete elimination of measurement/estimation of the position information. Furthermore, feedback information from the perspective camera of the follower robot is used to design adaptive observers to estimate the leader linear velocity for feedforward compensation, which can handle the absence of velocity measurements such that the proposed schemes can be applied to control formations of mobile robots without mutual communication abilities. By using the Lyapunov stability theory, a rigorous stability analysis based on the nonlinear formation dynamics is provided to show that the global stability of the combined observer–controller closed-loop system can be guaranteed. Both simulation and experimental results are also given to demonstrate the performance of the proposed formation tracking control schemes.

Nonlinear model predictive control for trajectory tracking of nonholonomic mobile robots

Trajectory tracking for autonomous vehicles is usually solved by designing control laws that make the vehicles track predetermined feasible trajectories based on the trajectory error. This type of approach suffers from the drawback that usually the vehicle dynamics exhibits complex nonlinear terms and significant uncertainties. Toward solving this problem, this work proposes a novel approach in trajectory tracking control for nonholonomic mobile robots. We use a nonlinear model predictive controller to track a given trajectory. The novelty is introduced by using a set of modifications in the robot model, cost function, and optimizer aiming to minimize the steady-state error rapidly. Results of simulations and experiments with real robots are presented and discussed verifying and validating the applicability of the proposed approach in nonholonomic mobile robots.

A Guiding Vector-Field Algorithm for Path-Following Control of Nonholonomic Mobile Robots

In this paper, we propose an algorithm for path-following control of the nonholonomic mobile robot based on the idea of the guiding vector field (GVF). The desired path may be an arbitrary smooth curve in its implicit form, that is, a level set of a predefined smooth function. Using this function and the robot's kinematic model, we design a GVF, whose integral curves converge to the trajectory. A nonlinear motion controller is then proposed, which steers the robot along such an integral curve, bringing it to the desired path. We establish global convergence conditions for our algorithm and demonstrate its applicability and performance by experiments with wheeled robots.