Visual Trajectory Tracking of Wheeled Mobile Robots With Uncalibrated Camera Extrinsic Parameters

A trajectory tracking design for wheeled mobile robots is presented in this article. The design objective is to develop one nonlinear robust control law for the trajectory tracking problem of wheeled mobile robots in the presence of modeling uncertainties. The main contribution of this investigation is as follows. Under the effects of modeling uncertainties, an effective control design which can quickly converge tracking errors between the controlled wheeled mobile robot and the desired trajectory is derived mathematically. Generally, it is difficult to develop a nonlinear robust control design for the trajectory tracking problem of wheeled mobile robots due to the complexity and nonlinearity of the wheeled mobile robots’ dynamics. Fortunately, based on a series analysis for the tracking error dynamics of the controlled wheeled mobile robot, one promising solution is obtained. For verifying the trajectory tracking performance of this proposed method, two scenarios are utilized in the simulations and the practical tests.

The purpose of this paper is two-fold. First, the smoothness of the distributed consensus control (DCC) protocols of multi-agent systems (MAS) with inherent nonlinear dynamics is investigated. Different from the traditional consensus protocols where variable structure control is considered for robust control, a continuous DCC is presented to achieve consensus tracking without control chattering. Using certain types of exponential functions, it is shown that different smooth DCC schemes can be constructed to achieve asymptotic consensus tracking with smooth control input for MAS with connected directed/undirected and fixed/switched communication topologies. Second, the formation control problem of nonholonomic wheeled mobile robots (WMR) is solved via the continuous DCC. By converting the formation problem into consensus problem using the agents’ kinematics, the formation speed-control problem in planar motion is formulated and solved. The translational and rotational speeds inputs to the WMR are computed using continuous distributed consensus protocols to reduce chattering in the control inputs of mobile robots. The distinctive feature of the proposed consensus and formation algorithms is the high tracking precision with smooth control input to agents’ dynamics. In simulation studies, different numerical examples are illustrated to demonstrate the performance and effectiveness of the proposed DCC.

Velocity and position tracking controllers for wheeled mobile robots

Many researchers have become interested in wheeled mobile robot (WMR) trajectory tracking control in recent years. This is due to the increased application of mobile robots in the industry, the military, the home, and public service. Classically, the movement of WMR is controlled depending on its kinematic model. However, in real-time applications, both the dynamic and kinematic models of robots and external disturbance and uncertainty affect system performance. This paper proposes backstepping combined with a Nonlinear Proportional-Integral-Derivative (NPID) controller to control a two-wheeled mobile robot (TWMR). The kinematic and dynamic models of the WMR are derived. The dynamic modeling is derived using a Lagrangian approach, and stability of the system is achieved using the Lyapunov method. The controller gains are optimized using the Genetic Algorithm optimization technique. The proposed algorithms’ performance is tested using Matlab software. The simulation result shows that the proposed method achieved preferable reference trajectory tracking with a minimum tracking error. The proposed controller outperforms the GA-based backstepping plus PID controller in terms of root-mean-square (RMS) of trajectory tracking error (47.36% in a linear and 60.32% in a nonlinear case). In addition, it shows good unknown disturbance rejection and initial point change in all scenarios.

This article studies a path-following problem for a wheeled mobile robot with nonholonomic constraints. The path-following task is represented by a guidance vector field (GVF), for which an online optimization procedure is adopted to estimate the path error. By exploiting a matrix-measure-based contraction principle, the convergence property of the designed GVF with respect to the task path is theoretically guaranteed. Then, a nonlinear controller is developed to track the defined GVF such that the target path is followed by the controlled mobile robot in the presence of unknown disturbances, including the unmodeled dynamics and the surface friction. Robustness properties of the closed-loop system are analyzed, and it is shown that the path error eventually converges to a residual set, which can be reduced by increasing control gains. Experiments are provided to validate the effectiveness of the desired GVF and the proposed control design.

This paper proposes a hybrid control algorithm with sliding sectors for the control of a wheeled mobile robot (WMR), which is a non-holonomic system. The WMR control system with a set of available or pre-designed control laws is considered as a hybrid system with a set of subsystems. The WMR with one of control laws forms a non-linear subsystem of the hybrid system. The subsystems may be unstable but for each subsystem of the hybrid system, a stable subset called a sliding sector is designed such that a Lyapunov function candidate decreases inside the sliding sector. The hybrid control rule is used to stabilize the WMR control system by switching the hybrid system among its subsystems such that the system is always inside a sliding sector of some subsystem. The proposed hybrid sliding sector control algorithm has been successfully implemented to the real-time control of WMR with good control performance.

This paper investigates the stabilization and trajectory tracking problem of wheeled mobile robot with a ceiling-mounted camera in complex environment. First, an adaptive visual servoing controller is proposed based on the uncalibrated kinematic model due to the complex operation environment. Then, an adaptive controller is derived to provide a solution of uncertain dynamic control for a wheeled mobile robot subject to parametric uncertainties. Furthermore, the proposed controllers can be applied to a more general situation where the parallelism requirement between the image plane and operation plane is no more needed. The overparameterization of regressor matrices is avoided by exploring the structure of the camera-robot system, and thus, the computational complexity of the controller can be simplified. The Lyapunov method is employed to testify the stability of a closed-loop system. Finally, simulation results are presented to demonstrate the performance of the suggested control.

In this paper, two knowledge based controllers are proposed to overcome the difficulties of a computed torque nonlinear controller (NC) in perfect trajectory tracking of nonholonomic wheeled mobile robots (WMRs). First, the effects of different dynamic models developed in angular andCartesian coordinate systems are fully examined on the persistent excitation condition and consequently on the trajectory tracking performance of WMRs. Using the dynamic model coordinated in theCartesian frame as the base of theNCresults in perfect compensation of large position off‐tracks and unbiased estimation of the plant's unknown parameters. However, using theWMR's dynamic model with rotation angles of driving wheels as the base of nonlinear and fuzzy controllers leads to accurate orientation tracking. Through replacing the proportional and differential terms of theNCby fuzzy functions, a fuzzy nonlinear controller (FNC) is generated. Due to the complicated dynamics of the WMR in which the center of mass does not coincide with the center of rotation, the expert knowledge of fuzzy controllers is extracted considering the rotation angles and rates of driving wheels as input variables. Fuzzy tuning of theNCresults in a superior tracking performance against measurement noises, though the control torques are decreased and smoothed significantly. Second, a complete fuzzy controller (FC) is generated to make perfect tracking of theWMR's position and orientation. The local stability analysis of fuzzy controllers is examined considering the corresponding analytical structures as nonlinear controllers. The superior performances of the proposed fuzzy controllers compared to those of theNCs are evaluated through simulations.

Nonholonomic systems have been the object of research for control theorists for many years [24]. The key difficulty in controlling this class of systems, like wheeled mobile robots and wheeled vehicles [24], is tied to the fact that nonholonomic systems do not satisfy Brockett’s necessary smooth feedback stabilization condition [8] as shown in [29]. The control problem is further complicated whenever uncertainties of various nature affect the nonholonomic system model.

Several research studies are conducted based on the control of wheeled mobile robots. Nonholonomy constraints associated with wheeled mobile robots have encouraged the development of highly nonlinear control techniques. Nonholonomic wheeled mobile robot systems might be exposed to numerous payloads as per the application requirements. This can affect statically or dynamically the complete system mass, inertia, the location of the center of mass, and additional hardware constraints. Due to the nonholonomic and motion limited properties of wheeled mobile robots, the precision of trajectory tracking control is poor. The nonholonomic wheeled mobile robot tracking system is therefore being explored. The kinematic model and sliding mode control model are analyzed, and the trajectory tracking control of the robot is carried out using an enhanced variable structure based on sliding mode. The shear and sliding mode controls are designed, and the control stability is reviewed to control the trajectory of a nonholonomic wheeled mobile robot. The simulation outcomes show that the projected trajectory track control technique is able to improve the mobile robot’s control, the error of a pose is small, and the linear velocity and angular speed can be controlled. Take the linear and angular velocity as the predicted trajectory.

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.

This study deals with a nonlinear constrained control system for the trajectory tracking of wheeled mobile robots (WMR) with constraints. To this aim, a new constrained controller is developed for WMR based on a predictive approach with input limitations for trajectory tracking. The proposed method leads to an optimization problem that is solved by the Karush Kuhn Tucker conditions (KKT) which employ a continuous nonlinear model of WMR. Finally, the performance of the proposed control method is evaluated by realistic motion models within a virtual robot experimentation platform (V-Rep). The results indicate that the proposed control method not only decreases the trajectory tracking error in the presence of input constraints but also it is suitable for online implementation compared with conventional nonlinear model predictive control (NMPC).

SummaryIn this paper, a homography‐based visual servo controller is developed for a rigid body to track a moving object in three‐dimensional space with a fixed relative pose. Specifically, a monocular camera is mounted on the rigid body, and the desired relative pose is expressed by a pre‐recorded reference image. Homography is exploited to obtain the orientation and scaled position for controller design. Considering the unknown moving object's velocities and distance information, a continuous nonlinear visual controller is developed using the robust integral of the signum of the error methodology. To facilitate the stability analysis, the system uncertainties regarding the moving object's velocities and distance information are divided into the error‐unrelated system uncertainties and the error‐related system uncertainties. After that, the upper bounds of the error‐related system uncertainties are derived with composited system errors. An asymptotic tracking of the leading object is proved based on the Lyapunov methods and the derived upper bounds. In addition, the proposed controller is extended to address the trajectory tracking problem. Simulation results validate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.

This paper presents a novel visual tracking model in image plane for autonomous mobile robots. Based on this control model, a single visual tracking controller is proposed for both static and moving objects in a two-dimensional plane. In this design, the mobile robot is equipped with a fixed camera for environment detection. The visual feedback is used to control the robot pose for tracking a moving object of interest. A novel state space representation of the camera-object visual interaction model fully defined in the image plane is first derived, a closed-loop stabilizing control law is then designed. The visual tracking control scheme achieves exponential convergence of the closed-loop visual tracking system through pole-placement method. Simulation results verify the effectiveness of the proposed control scheme, both in terms of tracking performance and system convergence

A visual servo controller is developed for a monocular camera system mounted on a wheeled mobile robot (WMR), which simultaneously solves the tracking and regulation control problems. A prerecorded image sequence (e.g., a video) or single image of four target points is used to define a desired trajectory or desired fixed position and orientation for the WMR. By comparing the target points from a stationary reference image with the corresponding target points in the live image and the prerecorded sequence of images, projective geometric relationships are exploited to construct Euclidean homographies. The information obtained by decomposing the Euclidean homographies is then used to derive a standard WMR form. The proposed result is the first visual servo control result that solves the unified tracking and regulation problem.