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Dynamic Sliding Mode Controller for Trajectory Tracking Of Nonholonomic Mobile Robots
Abstract
In this paper, a Dynamic Sliding Mode Controller (DSMC) is proposed for trajectory tracking control of a nonholonomic Wheeled Mobile Robot (WMR) in which the centroid doesn't coincide to the connection center of driving wheels. This robust controller is designed based on the developed dynamical model of WMR in Cartesian coordinates, therefore, the application limits in polar coordinates is removed. The asymptotic stability and the convergence of WMR to the desired position, velocity and orientation trajectories are proved according to the Lyapanove's direct method. Simulation results show the superiority of the proposed DSMC to the recent methods.
... However, due to the switching function in SMC structure, the chattering phenomenon is occurred in the control system. In order to best eliminate the chattering, the optimal strategy can be combined with the SMC structure [13][14][15][16]. ...
... Thus, the CLF solves the Hamilton-Jacobi-Bellman equation with respect to the performance index via the Sontag's formula. Consequently in the OSMC, beside the quick stabilization due to the variable structure controller based on SMC, the chattering phenomenon can be rejected successfully because of the optimal system [15][16][17][18][19][20][21]. ...
... To ensure the existence and uniqueness of the optimal control problem, the c i 's must be chosen until L +f 2 ≻ 0 . In order to solve the optimal control problem for finding the optimal v, the control Lyapunov function approach is used [13][14][15][16][17][18][19]. ...
In this wok, chaos analysis along with chaos control is studied in vertical model of the vehicle system. The chaotic behavior has been demonstrated in the suspension system under the specific initial conditions, values of parameters, and profile of road roughness. In order to analyze chaos in the dynamical model, the power spectrum density and Lyapunov exponent methods are used. Moreover, the phase portrait and Poincare’ sections of the simulations verify numerically chaos in uncontrolled system. For the purpose of chaos control, a novel optimal sliding mode control strategy is designed for stabilization of the system’s behavior via the semi-active suspension using MR fluid damper. As results, the optimal sliding mode control eliminates the chattering phenomenon in the responses and suppresses the chaotic oscillations in comparison with ordinary sliding mode control system. Responses of the feedback system depict the far-better performance of the proposed optimal sliding mode control from the viewpoint of reducing the settling time, overshoot, energy, and amortization in the suspension system. © 2019, The Brazilian Society of Mechanical Sciences and Engineering.
... where f (·) denotes a nonlinear function of states and control inputs, representing the twist of the robot. From Eq. (2), we obtain the following discrete-time kinematic model of the robot [43]: ...
... ■ Proving the stability of our proposed NMPC method is challenging, since the method requires solving a finite-horizon optimal control problem at each time step. Most existing NMPC-based approaches for pose stabilization of nonholonomic robots ensure stability by incorporating stabilizing terminal constraints and/or stabilizing terminal costs into the optimization problem [2,43,[48][49][50][51][52][53]. However, constructing suitable stabilizing terminal constraints or costs is a challenging task, and moreover, this approach limits the operating region of the MPC and necessitates a relatively long prediction horizon [54]. ...
In this paper, we present an online nonlinear Model Predictive Control (MPC) method for collision-free, deadlock-free navigation by multiple autonomous nonholonomic Wheeled Mobile Robots (WMRs). Our proposed method solves a nonlinear constrained optimization problem at each time step over a specified horizon to compute a sequence of optimal control inputs that drive the robots to target poses along collision-free trajectories, where the robots’ future states are predicted according to a unicycle kinematic model. To reduce the computational complexity of the optimization problem, we formulate it without stabilizing terminal constraints or terminal costs. We describe a computationally efficient approach to programming and solving the optimization problem, using open-source software tools for fast nonlinear optimization and applying the multiple-shooting method. We also provide rigorous proofs of the feasibility of the optimization problem and the stability of the proposed method. To validate the performance of our MPC method, we implement it in both 3D robot simulations and experiments with real nonholonomic WMRs for different multi-robot navigation scenarios with up to six robots. In all scenarios, the robots successfully navigate to their goal poses without colliding with one another or becoming trapped in a deadlock.
... Sliding mode control (SMC) and super-twisting algorithms (STA) are used for WMR tracking as in [16][17][18][19]. ...
... A robust SMC is addressed in [16], and stability is proved by Lyapunov direct method. The effectiveness of this controller is illustrated by simulations of circular paths. ...
The kinematic model of a skid-steering mobile robot (SSMR) is manipulated using signed polar transformation which represents a discontinuous state transformation. The influence of relative position between the instantaneous center of rotation (ICR) and SSMR center of mass is considered. Then, adaptive state feedback controller is designed and stability regions are studied. Subsequently, a point-to-point tracking algorithm is introduced to track a trajectory that is defined by a set of way-points, which is the more realistic case of dangerous exploration or landmine detection purposes. The closed-loop system is simulated using MATLAB environment and experimentally validated using a modified TURTLEBOT3 Burger. Results show that the proposed controller reaches almost zero steady state error with smooth paths for point stabilization, moreover, good tracking capabilities are demonstrated. The proposed control system integrates both posture and tracking algorithm, thus achieve trajectory tacking which is defined by a set of way-points.
... As a result, this controller is robust to system uncertainties and less sensitive to modelling errors. It has been applied to different domains in robotics including holonomic [26], [27] and nonholonomic [3], [28] systems and has shown reliable performance in both simulation and experimental studies. Moreover, this controller is compatible with both single-input-single-output and multi-input-multioutput nonlinear systems, and once the controller is designed, the implementation for experimental studies is simple and computationally efficient in comparison with metaheuristic techniques. ...
Compensating for slip and skid is crucial for mobile robots navigating outdoor terrains. In these challenging environments, slipping and skidding introduce uncertainties into trajectory tracking systems, potentially compromising the safety of the vehicle. Despite research in this field, having a real-world feasible online slip and skid compensation remains challenging due to the complexity of wheel-terrain interaction in outdoor environments. This paper proposes a novel trajectory tracking technique featuring real-world feasible online slip and skid compensation at the vehicle level for skid-steering mobile robots operating outdoors. The approach employs sliding-mode control to design a robust trajectory tracking system, accounting for the inherent uncertainties in this type of robot. To estimate the robot's slipping and undesired skidding and compensate for them in real-time, two previously developed deep learning models are integrated into the control-feedback loop. The main advantages of the proposed technique are that is (1) considers two slip-related parameters for the entire robot, as opposed to the conventional approach involving two slip components for each wheel along with the robot's skidding, and (2) has an online real-world feasible slip and skid compensator, reducing the tracking errors in unforeseen environments. Experimental results demonstrate a significant improvement, enhancing the trajectory tracking system's performance by over 27%.
... Chen et al. presented a guidance vector field (GVF) based controller such that the mobile robot could follow the desired path with an admissible error in the presence of uncertainties, including surface friction, unmodeled dynamics, and disturbances [23]. A robust sliding mode control was proposed to follow the circular path, and its stability was proved using the Lyapunov direct method [24]. In [25], the authors designed a state feedback controller for mobile robots based on supertwisting algorithms. ...
Path following is a fundamental problem in skid-steered mobile robots (SSMR). In this study, a Lyapunov stable curved path following controller was designed to generate the steering control command for an SSMR. In contrast to the existing path following controller design methods, where the complete dynamic model of the robot is considered or not, the steering dynamic characteristics approximated by a first-order model are considered in this study. Together with the kinematic model, a steering control law for following a curved path is designed by using the backstepping technique and Lyapunov stability theory. The proposed method was verified on a real SSMR platform to realize following the straight-line, square, and circular paths. Compared with the steering control law that does not consider the steering dynamics, the proposed method can make the robot converge to the predefined path faster with a smaller error overshoot.
... In [13], [14], a first order Sliding Mode Control (SMC) is applied for trajectory tracking control. This controller has good performance and no steady state error. ...
In this paper, Higher-Order Super-Twisting control (HOST) is designed and implemented for trajectory tracking control of four wheels Skid-Steered Mobile Robot (SSMR). The conventional Super-Twisting (ST) Second-Order Sliding Mode Control (SOSMC) is robust, yet it has two main drawbacks for such a system, 1) the chattering phenomena persists on the system inputs and outputs which leads to vibration in the robot motors and 2) the SSMR system has a relative degree equal to two. Therefore, the ST control design requires a sliding variable containing error derivatives, which only permit asymptotic convergence. For that, a higher-order controller is required for this control structure, which is designed for second order sliding variable, in order to obtain a robust controller with finite-time convergence. The HOST control can reduce chattering in steady-state compared with conventional ST-SOSMC and converge the state variables in finite time. The performance of this controller has been validated experimentally on Pioneer P3AT SSMR robot. The experimental results show good performance under parametric uncertainty variations and external disturbance with neglected chattering.
... The simplest model of a nonholonomic WMR is that of the unicycle, which corresponds to a single upright wheel rolling on the plane ([4],[5],[6],[7]). A kinematic model is thus: ...
In this paper, trajectory tracking for nonholonomic mobile robots is addressed. Two strategies are proposed: the first is based on Lyapunov stability theory, while the second adopts sliding mode control. The main difference between the two proposed strategies is that the time required for the error to converge towards zero is not a constraint in the first strategy while it is limited in the second strategy. The results of simulations and of the validation on a real system are presented. Comparison between the two strategies is based on the performance and on the efficiency of the tracking.
This paper presents design and implementation of adaptive Second Order Sliding Mode Control (SOSMC) for a four wheels Skid-Steered Mobile Robot (SSMR). The control objective is to follow a predefined trajectory by regulating the linear and angular velocities, and in presence of external disturbance and parametric uncertainty. Adaptive Super Twisting (AST) algorithm is designed in order to build a robust controller with neglected chattering in steady state. The proposed controller is validated experimentally. The results show that the proposed controller guarantees the performance of the conventional SOSMC under external disturbance and parametric uncertainty with less chattering.
Stoichiometric air-to-fuel ratio (lambda) control plays a significant role on the performance of three way catalysts in the reduction of exhaust pollutants of Internal Combustion Engines (ICEs). The classic controllers, such as PI systems, could not result in robust control of lambda against exogenous disturbances and modeling uncertainties. Therefore, a Model Predictive Control (MPC) system is designed for robust control of lambda. As an accurate and control oriented model, a mean value model of a Spark Ignition (SI) engine is developed to generate simulation data of the engine's subsystems. Based on the simulation data, two neural networks models of the engine are generated. The identified Multi-Layer Perceptron (MLP) neural network model yields small verification error compared with that of the adaptive Radial Base Function (RBF) neural network model. Consequently, based on the MLP engine's model, the MPC system is performed through a nonlinear constrained optimization within gradient descent algorithm. The performance of the MPC system is compared with that of a first order Sliding Mode Control (SMC) system. According to simulation results, the tracking accuracy of lambda by the MPC system is close to that of the SMC system. However, the MPC system results in considerably smoother injected fuel signal.
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 and Cartesian 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 the Cartesian frame as the base of the NC results in perfect compensation of large position off-tracks and unbiased estimation of the plant's unknown parameters. However, using the WMR'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 the NC by 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 the NC results 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 the WMR'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 the NCs are evaluated through simulations.
Purpose
– The purpose of this paper is to focus on perfect trajectory tracking control of 2 DOF non‐holonomic mobile robots in which the guidance and control commands are imposed through independent driver wheels. Model‐based nonlinear controllers for these robots with unknown parameters require estimation of a specified set of the robot parameters. The effects of the proposed model dynamics in both local and global coordinate systems are fully examined on the parameter estimation and tracking performance.
Design/methodology/approach
– Design of suitable feedback linearization (FL) controllers for trajectory tracking control of wheeled mobile robots (WMRs) is first reviewed. A FL controller whose parameters are tuned using fuzzy computations (fuzzy if‐then rules) is then developed. In the line of the other contributions of the paper, a pure fuzzy controller that is merely based on fuzzy if‐then rules is proposed to trajectory tracking control of the mobile robots.
Findings
– Use of global dynamics for designing a suitable FL control system leads to a perfect compensation for initial off‐tracks. Furthermore, the estimated parameters are unbiased because the corresponding regressor/signal matrix indicates a high rank of persistent excitation. Fuzzy tuning of the controller instead of keeping the gains fixed makes the overall system more robust against measurement noises while upper bounds and fluctuations of the input torques are both remarkably reduced. The pure fuzzy controller is naturally independent of the robot dynamics and therefore, the necessity of parameter estimation algorithm is removed.
Originality/value
– The paper provides some new nonlinear controllers for WMRs, in order to make perfect trajectory tracking and initial off‐tracks compensation.
A variable structure controller (VSC) for a nonholonomic wheeled
mobile robot is proposed for tracking desired trajectories. Although the
matching condition for VSC is not satisfied due to nonholonomic property
of the robot having two drive wheels, the proposed algorithm guarantees
bounded tracking errors by choosing the sliding surface gain properly.
Yet the robot tracks its given trajectory without error if there is no
initial posture and velocity errors. Simulation results show the
effectiveness of the proposed controller
This paper is concerned with trajectory tracking control of mobile robots. In order to overcome the local stability resulting from linearization design methods, a tracking controller with global asymptotical stability (GAS) is designed using backstepping method. This method breaks down nonlinear systems into low dimensional systems and simplifies the controller design using virtual control inputs and partial Lyapunov functions. The stability of the system is easily proven via the Lyapunov function. Simulation results have verified effectiveness of the theoretical analysis.
We consider the loca1 behavior of control problems described by (* = dx/dr)
Based on differential geometry theory, applying the dynamic extension approach of relative degree, the exact feedback linearization on the kinematic error model of mobile robot is realized. The trajectory-tracking controllers are designed by pole-assignment approach. When angle speed of mobile robot is permanently nonzero, the local asymptotically stable controller is designed. When angle speed of mobile robot is not permanently nonzero, the trajectory-tracking control strategy with globally tracking bound is given. The algorithm is simple and applied easily. Simulation results show their effectiveness.
In this paper, an improved sliding mode algorithm with global asymptotic stability is presented for tracking control of nonholonomic mobile robot. Centroid offset parameters are used in the design of the controller, which can drive the position error to zero quickly in the premise of guaranteeing stability of the whole system. The Kinematics mathematical model and the position and posture error model of the mobile robot are presented. Switch function of variable structure control is designed based on the backstepping method. Comparative experiments are given and simulation results show that the proposed control method is effective and has better control performances.
The purpose of the paper is to propose a neural network-based
sliding mode control law for solving the trajectory tracking problem of
mobile robots. Artificial neural networks (ANN) help us choose a proper
sliding surface, which is time-varying. The weights of the ANN are
changed according to an adaptive algorithm to control the system state
to hit a user-defined sliding surface and then slide along it. The input
parameters to the ANN are chosen as delayed outputs of the sliding mode
controller and delayed output of the plant. The sliding surface is
adapted such that convergence towards the path to be followed is
guaranteed. A non-holonomic mobile robot as a practical example for the
application of this control system is considered
Nonholonomic mobile robots have constraints imposed on the motion
that are not integrable, i.e., the constraints cannot be written as time
derivatives of some function of the generalized coordinates. The
position control of nonholonomic mobile robots has been an important
class of control problems. In this paper, we propose a robust tracking
control of nonholonomic wheeled mobile robots using sliding mode. The
posture of a mobile robot is represented by polar coordinates and the
dynamic equation of the robot is feedback-linearized by the
computed-torque method. A novel sliding mode control law is proposed for
asymptotically stabilizing the mobile robot to a desired trajectory. It
is shown that the proposed scheme is robust to bounded external
disturbances. Experimental results demonstrate the effectiveness of
accurate tracking capability and the robust performance of the proposed
scheme
The author describes neural network controllers for robot
manipulators in a variety of applications, including position control,
force control, parallel-link mechanisms, and digital neural network
control. These “model-free” controllers offer a powerful and
robust alternative to adaptive control
Provides a summary of recent developments in control of
nonholonomic systems. The published literature has grown enormously
during the last six years, and it is now possible to give a tutorial
presentation of many of these developments. The objective of this
article is to provide a unified and accessible presentation, placing the
various models, problem formulations, approaches, and results into a
proper context. It is hoped that this overview will provide a good
introduction to the subject for nonspecialists in the field, while
perhaps providing specialists with a better perspective of the field as
a whole. The paper is organized as follows: introduction to nonholonomic
control systems and where they arise in applications, classification of
models of nonholonomic control systems, control problem formulations,
motion planning results, stabilization results, and current and future
research topics
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