A consensus sliding mode control for trajectory tracking of multiple manipulators

<abstract> <bold>Abstract.</bold> For the spraying mobile robot working in greenhouse, due to the inconsistency of drive motors and the rough walking surface, it is easy to track off. For the liquidity of pesticide, the load always changes even the speed jumps. Because of these uncertainties, external disturbances and the difficulty of constructing the system dynamic model, it is hard to implement the trajectory tracking control of the spraying mobile robot steadily, precisely and quickly. In order to solve the problem, a smooth sliding mode trajectory tracking control method is proposed based on the distribute control strategy for each branch. Moreover, its stability is proved using the Lyapunov function. The simulation results show that the proposed method can track the desired trajectories precisely, quickly and steadily under the strong white noise. The chattering phenomenon of the control is restrained compared to the conventional sliding mode control. The trajectory tracking performance is better than that of the fuzzy control. The designed method is easy to realize and doesn't need to construct the precise mathematical model, so, it affords an economical and convenient control method for solving the trajectory tracking problem of the greenhouse spraying mobile robot under various uncertain interferences.

In this paper, an adaptive chattering free neural network‐based sliding mode control (ACFN‐SMC) method is proposed for tracking trajectories of redundant parallel manipulators. ACFN‐SMC combines adaptive chattering free radial basis function neural networks (RBFN), sliding mode control with online updating the robust term parameters, and a nonlinear compensation item for reducing tracking errors. The stability of the closed‐loop system with modeling uncertainties, frictional uncertainties, and external disturbances is ensured by using the Lyapunov method. The proposed controller has a simple structure and little computation time while securing dynamic performance with expected quality in tracking trajectories of redundant parallel manipulators. In addition, the ACFN‐SMC strategy does not need to know the upper bound of any uncertainties. From the simulation results, it is evident that the proposed control strategy not only has significantly higher robustness capability for uncertainties but also can achieve better chattering elimination when compared with those using existing intelligent control schemes.

This paper presents a sliding mode controller for trajectory tracking of robotic manipulators with actuator faults. To achieve finite-time convergence of tracking errors and desirable tracking precision, a fast nonsingular terminal sliding mode controller is designed. The uncertainty caused by actuator faults is transformed into system disturbance which is compensated by introducing the dynamic gain technique. As a result, the prior knowledge about upper bound of system disturbance is not required. Moreover, the sign function is replaced by the saturation function in the control law, so the chattering phenomenon is attenuated. Finally, the designed controller is applied to control a two-link robotic manipulator in simulation, and results validate the effectiveness of the control scheme.

The Delta robot is an over-actuated parallel robot with highly nonlinear kinematics and dynamics. Designing the control for a Delta robot to carry out various operations is a challenging task. Various advanced control algorithms, such as adaptive control, sliding mode control, and model predictive control, have been investigated for trajectory tracking of the Delta robot. However, these control algorithms require a reliable input–output model of the Delta robot. To address this issue, we have created a control-affine neural network model of the Delta robot with stepper motors. This is a completely data-driven model intended for control design consideration and is not derivable from Newton’s law or Lagrange’s equation. The neural networks are trained with randomly sampled data in a sufficiently large workspace. The sliding mode control for trajectory tracking is then designed with the help of the neural network model. Extensive numerical results are obtained to show that the neural network model together with the sliding mode control exhibits outstanding performance, achieving a trajectory tracking error below 5 cm on average for the Delta robot. Future work will include experimental validation of the proposed neural network input–output model for control design for the Delta robot. Furthermore, transfer learnings can be conducted to further refine the neural network input–output model and the sliding mode control when new experimental data become available.

A new sliding mode controller for trajectory tracking of ball and plate system is proposed. In the controller, a nonlinear observer which is independent on plant model is used to observer the uncertainties and disturbance of the system. This paper proved that the nonlinear observer is convergence by properly selecting the parameters of observer. Sliding mode controller based on nonlinear observer is designed for the ball and plate system and it can guarantee stabilization of closed-loop system. The results of simulation and experiments indicate that the proposed nonlinear observer can observer uncertainties and disturbance of system, the proposed sliding mode control method is effectively to solve the problems of trajectory tracking in the nonlinear ,uncertain system.

ABSTRACTThis paper presents a trajectory tracking approach based on terminal sliding mode control (TSMC) technique for wheeled mobile robot where the wheel-soil friction can be measured and the estimated errors will converge to their stable values within finite-time, by which the control system is able to be designed in accordance with the prescribed performance. Three kinds of friction effects and their acting mechanisms, at the first place, are argued by exploring the disturbance-like friction behaviors, and then two updated laws, i.e., taking uncertain friction as an entire term or as a parametric form for varied effects, are proposed. In addition, the adoption of TSMC enables the tracking error estimation being faster and more reliable, and the stability and reliability of closed-loop control system are guaranteed by means of Lyapunov stability theorem. Subsequently, the numerical simulation validates the feasibility and effectiveness of the proposed controllers by which the terrain adaptability, movement precision, and maneuvering capability will be improved significantly.

Unmanned Aerial Vehicles are among the most widely attracting interest, especially in the applications of transportation, inspection, and surveillance. The great mechanisms for motion control are set to become a vital factor in performing the robust and accurate stabilized flight relied on perturbations and disturbances. This paper presents modified adaptive sliding mode control for trajectory tracking of mini-drone quadcopter unmanned aerial vehicles, which aims at demonstrating the effectiveness of nonlinear adaptive control strategy for achieving the desired performance of the mini-drone quadcopter system. Besides providing mathematical modeling and nonlinear dynamic characteristic details of mini-drone quadcopter actuated system, the modified adaptive sliding mode algorithm is developed using adaptation law based on Lyapunov stability approach then applied on the attitude loop and the altitude loop control system so that the nonlinear adaptive behavior of the controller enables the compensation of disturbances and parameter perturbations. The effectiveness validations of the proposed control technique compared with the traditional approach are performed through the Matlab simulation. The results have been illustrated that the modified adaptive sliding mode control can decrease the error performance indexes to the minimum ISE at 1.041 m 2 and the zero percentage of overshoot while enables excellent stability and robustness even in the presence of parameter perturbations and disturbance.

An Adaptive Optimal Backstepping &amp; Sliding Mode Control for Trajectory Tracking of a Differential Drive Autonomous Mobile Robot Using Cross-Entropy and Neural Network

Fuzzy sliding mode control for trajectory tracking of an electric powered wheelchair

Achieving precise trajectory tracking with practical applicability for underactuated autonomous underwater vehicles (AUVs) is challenging due to uncertainties and inherent underactuation. This paper presents a finite-time control framework with continuous inputs to address this issue. By incorporating a sliding mode observer, the framework estimates lumped disturbances – including mismatched lateral velocity disturbances – to facilitate effective control law design. A key feature is the direct dependence of the control input on the sliding manifold, which avoids chattering and yields a continuous dynamical control law. Furthermore, the controller utilises an integral form to obtain the equivalent sign-function of sliding variables, eliminating the need for saturation function approximations. This design guarantees finite-time convergence and reduces the reliance on high-order state derivatives. Simulation on the REMUS AUV verifies that the proposed controller achieves favorable performance in the convergence of both position and velocity tracking errors. These results robustly validate the practical value of the proposed controller for real-world AUV applications.

Robotic manipulator is a multi-input multi-output (MIMO), highly nonlinear and coupled system. Controlling this system always has been a challenging task for control engineers. In this paper, sliding mode control (SMC) technique utilizing Proportional and Derivative (PD) surface with different reaching laws has been applied on a two-link planar rigid robotic manipulator. Performance of PD sliding surface has been investigated with three different control laws namely, constant rate, exponential and power rate reaching law. Stability of the studied controller configurations have been demonstrated using Lyapunov theory. One of the major problems in SMC, “chattering” is reduced by introducing boundary layer in the controller. Genetic Algorithm optimization technique is used for tuning of parameters of SMC and boundary layer in all the cases for minimum Integral Absolute Error and chattering. Simulation results revealed that all the investigated laws performed equally for set-point tracking and the constant rate reaching law outperforms the other two laws for noise suppression. Also, all three reaching control laws of SMC offered significantly enhanced trajectory tracking and chattering performance as compared to recent literature.

This contribution deals with an adaptive sliding mode control for a hybrid actuator consisting of a piezo, a mechanicacal and a hydraulic part that can be used for camless engine motor applications. The control structure comprises a feedforward controller and a sliding mode controller. The general approach of this actuator is to use the advantages of both systems, the high precision of the piezoelectric actuator and the force of the hydraulic part. In fact, piezoelectric actuators (PEAs) are commonly used for precise positioning, despite PEAs present nonlinearities, such as hysteresis, saturations, and creep. A sliding mode control is proposed and for deriving the structure of such a controller a Lyapunov approach is used. An adaptive self-tuning algorithm is realised. The conceived sliding mode control takes the hydraulic actuator in a resonance operating point which corresponds to the rotational speed of the engine. When the engine speed changes, the sliding mode controller adapts its parameter in a way that the resonance frequency of the controlled hydraulic part of the actuator changes and corresponds to the working frequency of the engine. The resulting controller is therefor totally self-tuning and robust with respect to the model parameter variation. Asymptotic tracking is shown using Lyapunov approach. Moreover, the proposed technique avoids a switching function for the calculation of the equivalent signal of the sliding mode controller. In this way the chattering problem is completely avoided. Simulations with real data of a camless engine are presented.

This paper provides a comparative study of three Sliding Mode Control (SMC)-based fault tolerant controllers for trajectory tracking of a quadrotor UAV subject to actuator faults. Conventional SMC, Integral (ISMC) and Integral Terminal SMC (ITSMC) designs are designed and implemented to a quadrator UAV. The controllers' performance along with their respective robustness was assessed using various faulty conditions. Stability analysis was carried over using the Lyapunov approach. A thorough discussion of the controllers' respective performance in light of the obtained results was also performed and presented in the paper.

An effective method, adaptive fuzzy sliding-mode (SM) PI Control to design full-bridge inverter is proposed in this paper. For practical applications, sliding mode control (SMC) with chattering phenomenon is a large hindrance. The modified model of the PI controller is built by the plant extension scheme, in order to relieve the chattering. Also, the fuzzy logic is applied to find the appropriate parameter values of the PI controller, and can adapt to plant parameter variations and external load disturbances. The proposed method has been realized for the actual full-bridge inverters controlled by DSP and CPLD. Simulation and experimental results of the closed-loop system show that the proposed method yields system performance improvement, such as low total harmonic distortion (THD), fast dynamic response, reduced steady-state error, and reduced chattering.

Variable structure control with sliding mode, which is commonly known as sliding mode control (SMC), is a nonlinear control strategy that is well known for its robust characteristics (Utkin, 1977). The main feature of SMC is that it can switch the control law very fast to drive the system states from any initial state onto a user-specified sliding surface, and to maintain the states on the surface for all subsequent time (Utkin, 1977), (Phuah et al., 2005 a). The conventional SMC has two disadvantages (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), which are the chattering phenomenon (Slotine & Sastry, 1983), (Young et al., 1999) and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), (Hussain & Ho, 2004). Many methods of SMC using neural networks (NN) have been proposed (Phuah et al., 2005 a), (Ertugrul & Kaynak, 2000), (Hussain & Ho, 2004), (Phuah et al., 2005 b), (Yasser et al., 2007), (Topalov et al., 2007). In this paper, sliding mode controls using NN are proposed to deal with the problem of eliminating the chattering effect and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant. The first method of this method applies a method using a simplified form of the distance function proposed in (Phuah et al., 2005 a), (Phuah et al., 2005 b). Furthermore, the simplified distance function of our method uses a sliding surface in the space of the output error and its derivations, as proposed in (Yasser et al., 2006 a), (Yasser et al., 2006 c), instead of the space of the states error to construct a corrective control input. Thus, no observer is required in the proposed method. Moreover, we also propose the application of an NN to construct the equivalent control input of SMC. The weights of the NN are adjusted using a backpropagation algorithm as in (Yasser et al., 2006 b). Hence, a thorough knowledge of the parameters and dynamics of the nominal controlled plant is not required for calculating the equivalent control law. Finally, a stability analysis is carried out, and the effectiveness of this first control method is confirmed through computer simulations. This first method has been previously discussed in (Yasser et al., 2007). The second method of this paper applies an NN to produce the gain of the corrective control of SMC. Furthermore, the output of the switching function the corrective control of SMC is applied for the learning and training of the NN. There is no equivalent control of SMC is used in this second method. As in the first method, this second method applies a method using a sliding surface in the space of the output error and its derivations, as proposed in