Kinematic Model Of Mobile Robot Research Articles

Analysis of the PID Controller Parameters for A Surface Mobility Platform Mobile Robot

Surface mobility control is a fundamental challenge in robotics, and its applications range from autonomous vehicles to industrial automation. The main aim of the paper is to analyze the PID controller parameters for the speed control of a surface mobility platform mobile robot. MATLAB simulation toolbox and mathematical model of the DC motor are used to find the optimal PID controller parameters to complete the DC motor speed control system. For the SMP motion control system, the mobile robot kinematic model is supported as a differential drive system. In this paper, the PID controller parameters for the DC motor control system are analyzed with simulation results using various KP, KI, KD gains. The experimental results of the SMP mobile robot with optimal PID controller parameters are analyzed by driving on the rough, slope and even terrains. According to simulation results and experimental tests, the proposed system effectively controls the speed of the SMP mobile robot, demonstrating satisfactory performance in settling time, rise time, and system overshoot. Among PI and PID controllers, the designed PID controller can quickly control to reach the desired DC motor speed. Using the optimal PID coefficient parameters, all motors reached their desired speed in 0.12 seconds during simulations. In the experimental tests on various terrain (even, slope and rough), all motors achieved their desired speed simultaneously within 25 seconds.Keywords: Differential drive, PID controller, motion trajectory, real-time speed control. skid steering, SMP mobile robot, surface mobility control

Predictive Control of the Mobile Robot under the Deep Long-Short Term Memory Neural Network Model.

At present, there is a phenomenon of network data packet loss in the trajectory tracking control system, which will degrade or even destabilize the system's performance. Therefore, this work first explains the theory of the deep long-short term memory (LSTM) neural network model, the kinematic model of mobile robots, and the trajectory tracking error model. The reasons for data packet loss in the control system are analyzed. Second, a prediction model based on the LSTM network is designed according to the theory mentioned above. Finally, the training effect of the LSTM model and the robot trajectory tracking effect based on the model are tested by setting up simulation experiments. The research results are as follows: (1) The pose test error of the mobile robot will eventually tend to zero through the simulation curve generated by the pose parameters (x, y, θ) of the mobile robot. (2) The trajectory tracking error of the deep LSTM neural network prediction and compensation method with the packet loss rate of 5% is less than that with the packet loss rate of 10%. (3) The linear velocity υ of the mobile robot based on the prediction model of the LSTM network varies greatly but is always in the interval (−2, 2). Its angular velocity ω initially fluctuates greatly but gradually tends to zero after about 13 s. (4) When the prediction model tracks the trajectory of the robot, the horizontal position x, the vertical position y, and the angle θ coincide with the reference trajectory. The exploration is conducted to provide a reference for the research on data packet loss in the networked mobile robot trajectory tracking system.

Globally convergent leaderless formation control for unicycle‐type mobile robots

This study investigates the leaderless formation control problem for unicycle-type mobile robots and designs a formation controller for a two-robot system. The proposed control law is globally effective, namely making mobile robots converge to the formation from all kinds of initial conditions. The kinematic model of mobile robots is directly established on the special Euclidean group, and the mobile robot is merely required to obtain the relative configuration (i.e. position and orientation) in its own body-fixed frame. The approach for the formation problem is to design a virtual system for each mobile robot, which contains the desired formation pattern, so that the formation problem for mobile robots is converted into the consensus problem for virtual systems. Furthermore, the non-holonomic constraint for the virtual systems is derived for the first time, which is explained from the viewpoint of geometric control. In addition, the authors clarify the physical meaning of the multiple control gains, which can guarantee excellent robot behaviour by appropriate selection.

Nonlinear Model Predictive Control for Mobile Robot Using Varying-Parameter Convergent Differential Neural Network

The mobile robot kinematic model is a nonlinear affine system, which is constrained by velocity and acceleration limits. Therefore, the traditional control methods may not solve the tracking problem because of the physical constraint. In this paper, we present the nonlinear model predictive control (NMPC) algorithm to track the desired trajectory based on neural-dynamic optimization. In the proposed algorithm, the NMPC scheme utilizes a new neural network named the varying-parameter convergent differential neural network (VPCDNN) which is a Hopfifield-neural network structure with respect to the differential equation theory to solve the quadratic programming (QP) problem. The new network structure converges to the global optimal solution and it is more efficient than traditional numerical methods. In the simulation, we verify that the proposed method is able to successfully track reference trajectories with a two-wheel mobile robot. The experimental validation has been conducted in simulation and the results show that the proposed method is able to precisely track the trajectory maintaining a high robustness based on the VPCDNN solver.

Design Interval Type-2 Fuzzy Like (PID) Controller for Trajectory Tracking of Mobile Robot

One of the major problems in the field of mobile robots is the trajectory tracking problem. There are a big number of investigations for different control strategies that have been used to control the motion of the mobile robot when the nonlinear kinematic model of mobile robots was considered. The trajectory tracking control of autonomous wheeled mobile robot in a changing unstructured environment needs to take into account different types of uncertainties. Type-1 fuzzy logic sets present limitations in handling those uncertainties while type-2 fuzzy logic sets can manage these uncertainties to give a superior performance. This paper focuses on the design of interval type-2 fuzzy like proportional-integral-derivative (PID) controller for the kinematic model of mobile robot. The firefly optimization algorithm has been used to find the best values of controller’s parameters. The aim of this controller is trying to force the mobile robot tracking a pre-defined continuous path with minimum tracking error. The Matlab simulation results demonstrate the good performance and robustness of this controller. These were confirmed by the obtained values of the position tracking errors and a very smooth velocity, especially with regards to the presence of external disturbance or change in the initial position of mobile robot. Finally, in comparison with other proposed controllers, the results of nonlinear IT2FLC PID controller outperform the nonlinear PID neural controller in minimizing the MSE for all control variables and in the robustness measure.

Disturbance Observer Based on Biologically Inspired Integral Sliding Mode Control for Trajectory Tracking of Mobile Robots

This paper proposes an integral sliding control system based on the nonlinear disturbance observer, aiming to the trajectory tracking of the mobile robot under the external disturbance. First, a kinematic model of mobile robot was built, besides, the position error signal was gained by the biological membrane potential model, and the problem of velocity oscillation was solved by the design of the backstepping controller. Then, an integral sliding control system was designed in accordance with the kinematic model of the mobile robot, meanwhile, a disturbance observer was designed in consideration of external disturbance to do the real-time observation on the disturbance occurring in the system with an addition of feedforward compensation and the observation error was converged by selecting the design parameters. The Lyapunov function was used to prove the stability of the system. Finally, the simulation of tracking circularity trajectory was utilized, with the comparison of trajectory without the use of jammer, to prove that this method can well overcome the nonlinear and uncertainty originated from external, thereby improving the control performance and increasing the robustness.

Observer-Based Adaptive Tracking Control of Wheeled Mobile Robots With Unknown Slipping Parameters

Based on wheeled mobile robots (WMRs) with unknown longitudinal slipping parameters, an adaptive control strategy for a tracked mobile robot is presented, in which the longitudinal slipping of the left and right wheels are described by two unknown parameters. The kinematic model of mobile robot with wheels’ slipping is derived from the motion model of mobile robot without wheels’ slipping. Employing the Lyapunov direct method, an adaptive nonlinear feedback control law that compensates for the longitudinal slipping is proposed to achieve an objective of tracking a given trajectory. The orientation angle observer is designed to estimate the immeasurable orientation angle of the robot by employing the coordinate information. Asymptotic stability of the closed-loop system is ensured by choosing an appropriate Lyapunov function. Numerical and experimental results show the effectiveness of the proposed control approach.

Leader-Follower Consensus Multi-Robot Formation Control Using Neurodynamic-Optimization-Based Nonlinear Model Predictive Control

This paper investigates a nonlinear-model-predictive-control (NMPC)-strategy-based distributed leader-follower consensus multi-robot formation system. The control objective of this system is to design a group of nonholonomic robots to converge into the desired geometric pattern and to track a designed path. A directed graph that specifies communication topology for the formation is given. A leader-follower consensus formation problem based on the mobile robot kinematic model is obtained, which is further reformulated into a constrained nonlinear minimization problem through the NMPC strategy. A general projection neural network (GPNN) is implemented to efficiently derive the optimal control inputs for the robots. The simulation results verify the effectiveness of the proposed formation algorithm.

The Impact of Parametric Uncertainties on Mobile Robots Velocities and Pose Estimation

This paper analyses the impact of parametric uncertainties of a mobile robot kinematic model on velocity and pose estimation, providing models and quantifiable knowledge about them. Most works neglect how the uncertainty regarding the robot's construction aspects (such as wheels radii, the distance between them, and the robot's center of mass) affects both velocities and pose estimation. To help readers understand the influence of such parametric uncertainties, we performed experiments in a simulator and used the collected data on the proposed models. The paper also analyses how the magnitude of velocities considered by the controllers and the followed path can decrease or increase the impact of the parametric uncertainties. The proposed models and presented analysis help understanding the influence (isolated or simultaneous) of different sources of uncertainty in the robot's velocities and pose estimation. This knowledge can be applied to estimate uncertainties for localization methods based on data fusion, complementing or even avoiding the experimental procedures. Also, the development of controllers, robot simulators and new methodologies for parameters' calibration and the design and construction of new robots can also profit from the results presented in this paper.

Multi-robot Cooperation Strategy Based on Wireless Sensor Network

To realize the design of multi-robot cooperative control based on wireless sensor networks, a large number of local control research experiments are carried out on a specific model of mobile robots. Combined with the kinematic model of mobile robot, the motion characteristics of this kind of mobile robot are grasped. On the basis of realizing the multi-target tracking and positioning of wireless sensor network, a multi mobile robot cooperative control system based on the feedback of wireless sensor network is developed, and the synchronous motion between the master and the robot is maintained through the feedback control of the network. Finally, a cooperative trajectory tracking control algorithm for mobile robot is introduced, and the principle of the controller design is mastered. A multi mobile robot cooperative trajectory tracking LQG controller is designed for mobile robot in wireless sensor network. The simulation results show that the algorithm can reach the cooperative control target.

English

In this paper, a trajectory tracking control for a non-holonomic differential wheeled mobile robot (WMR) system is presented. A big number of investigations have been used the kinematic model of mobile robot which is a nonlinear model in nature, thus a hard task to control it. This work focuses on the design of fuzzy PID controller tuned with a firefly optimization algorithm for the kinematic model of mobile robot. The firefly optimization algorithm has been used to find the best values of controller's parameters. The aim of this controller is trying to force the mobile robot tracking a pre-defined continuous path with the least possible value of error. Matlab Simulation results show that a good performance and robustness of the controller. This is confirmed by the value of minimized tracking error and the smooth velocity especially concerning presence of external disturbance or change in initial position of mobile robot.

Design a Fuzzy PID Controller for Trajectory Tracking of Mobile Robot

In this paper, a trajectory tracking control for a non-holonomic differential wheeled mobile robot (WMR) system is presented. A big number of investigations have been used the kinematic model of mobile robot which is a nonlinear model in nature, thus a hard task to control it. This work focuses on the design of fuzzy PID controller tuned with a firefly optimization algorithm for the kinematic model of mobile robot. The firefly optimization algorithm has been used to find the best values of controller's parameters. The aim of this controller is trying to force the mobile robot tracking a pre-defined continuous path with the least possible value of error. Matlab Simulation results show that a good performance and robustness of the controller. This is confirmed by the value of minimized tracking error and the smooth velocity especially concerning presence of external disturbance or change in initial position of mobile robot.

Control Design for Mobile Robot Based on Step-by-step Point Stabilization

In this paper the control object is non-holonomic mobile robot and the control problem focus on point stabilization which is one of the most important issues on non-holonomic mobile robot motion control in view of both theory and application. The integrity of mobile robot kinematic model and the position error formula is established under the polar coordinates for point stabilization problem. Then the step-by-step point stabilization control problem is studied where the method of kinematic control design is given. By successively changing the state variables, the mobile robot will get the expecting position and will be step-by-step convergence. On the basis of this point stabilization control law the simulation is carried on by MATLAB. The results prove the feasibility of the controller.

Global Finite-Time Partial Stabilization for a Class of Nonholonomic Mobile Robots Subject to Input Saturation

In this paper, the global finite-time partial stabilization problem is discussed for a class of nonholonomic mobile wheeled robots with continuous pure state feedback and subject to input saturation. Firstly, for the mobile robot kinematic model, a “3 inputs, 2 chains, 1 generator” nonholonomic chained form systems can be obtained by using a state and input transformation. The continuous, saturated pure state feedback control law is proposed such that the special chained form systems can be stabilized to zero (except an angle variable) in a finite time, i.e., finite-time partial stabilization. Secondly, the rigorous stability analysis of the corresponding closed-loop system is presented by applying Lyapunov theorem combined with the finite-time control theory, and the angle variable can be proved to converge to a constant, moreover, its convergent limit may be accurately estimated in advance. Finally, the simulation results show the correctness and the validity of the proposed controller not only for the chained system but also for the original mobile robots system.

Robust Adaptive Stabilization of Nonholonomic Mobile Robots with Bounded Disturbances

The stabilization problem of nonholonomic mobile robots with unknown system parameters and environmental disturbances is investigated in this paper. Considering the dynamic model and the kinematic model of mobile robots, the transverse function approach is adopted to construct an additional control parameter, so that the closed-loop system is not underactuated. Then the adaptive backstepping method and the parameter projection technique are applied to design the controller to stabilize the system. At last, simulation results demonstrate the effectiveness of our proposed controller schemes.

Adaptive Tracking and Obstacle Avoidance Control for Mobile Robots with Unknown Sliding

An adaptive control approach is proposed for trajectory tracking and obstacle avoidance for mobile robots with consideration given to unknown sliding. A kinematic model of mobile robots is established in this paper, in which both longitudinal and lateral sliding are considered and processed as three time-varying parameters. A sliding model observer is introduced to estimate the sliding parameters online. A stable tracking control law for this nonholonomic system is proposed to compensate the unknown sliding effect. From Lyapunov-stability analysis, it is proved, regardless of unknown sliding, that tracking errors of the controlled closed-loop system are asymptotically stable, the tracking errors converge to zero outside the obstacle detection region and obstacle avoidance is guaranteed inside the obstacle detection region. The efficiency and robustness of the proposed control system are verified by simulation results.

Cooperative behavior of nano-robots as an analogous of the quantum harmonic oscillator

A multi-robot system that consists of N nano-robots is studied. It is assumed that the robots correspond to diffusing particles, and interact to each other as the theory of Brownian motion predicts. Brownian motion is the analogous of the quantum harmonic oscillator (Q.H.O.), i.e., of Schrodinger's equation under harmonic (parabolic) potential. It is shown that the motion of the robots can be described by Langevin's equation which is a stochastic linear differential equation. It is proved that Langevin's equation is a generalization of conventional gradient algorithms. Therefore the kinematic models of mobile robots which follow conventional gradient algorithms can be considered as a subcase of the kinematic models which are derived from the diffusion analogous of the Q.H.O model.

Design of dead reckoning system for mobile robot

A dead reckoning system for a wheeled mobile robot was designed, and the method for robot’s pose estimation in the 3D environments was presented on the basis of its rigid-body kinematic equations. After analyzing the locomotion architecture of mobile robot and the principle of proprioceptive sensors, the kinematics model of mobile robot was built to realize the relative localization. Considering that the research on dead reckoning of mobile robot was confined to the 2 dimensional planes, the locomotion of mobile robot in the 3 coordinate axis direction was thought over in order to estimate its pose on uneven terrain. Because the computing method in a plane is rather mature, the calculation in height direction is emphatically represented as a key issue. With experimental results obtained by simulation program and robot platform, the position of mobile robot can be reliably estimated and the localization precision can be effectively improved, so the effectiveness of this dead reckoning system is demonstrated.

Kinematic modeling of mobile robots by transfer method of augmented generalized coordinates

AbstractA kinematic modeling method, which is directly applicable to any type of planar mobile robots, is proposed in this work. Since holonomic constraints have the same differential form as nonholonomic constraints, the instantaneous motion of the mobile robot at current configuration can be modeled as that of a parallel manipulator. A pseudo joint model denoting the interface between the wheel and the ground (i.e., the position of base of the mobile robot) enables the derivation of this equivalent kinematic model. The instantaneous kinematic structures of four different wheels are modeled as multiple pseudo joints. Then, the transfer method of augmented generalized coordinates, which has been popularly employed in modeling of parallel manipulators, is applied to obtain the instantaneous kinematic models of mobile robots. The kinematic models of six different types of planar mobile robots are derived to show the effectiveness of the proposed modeling method. Lastly, for the mobile robot equipped with four conventional wheels, an algorithm estimating a sensed forward solution for the given information of the rotational velocities of the four wheels is discussed. © 2004 Wiley Periodicals, Inc.

Path tracking and a practical point stabilization of mobile robot

Based on differential geometry theory, applying the dynamic extension approach of relative degree, the path tracking controller of mobile robot is designed by the input/output feedback linearization. And on the foundation, the exact feedback linearization on the kinematic model of mobile robot is realized. Its proof is different from and simpler than the literature (Robotics Comput Integ Manuf 16 (2000) 353). A practical point stabilization controller is proposed, and a fault in the literature (Robotics Comput Integ Manuf 16 (2000) 353) is indicated. Hence, the path tracking and point stabilization problems are solved in a unified approach. The designed controllers have the local asymptotic stability. Simulation results show their effectiveness.