Adaptive Trajectory Tracking Control for Nonholonomic Wheeled Mobile Robots:A Barrier Function Sliding Mode Approach

The trajectory tracking control performance of nonholonomic wheeled mobile robots(NWMRs)is subject to nonholonomic constraints,system uncertainties,and external disturbances.This paper proposes a barrier function-based adaptive sliding mode control(BFASMC)method to provide high-precision,fast-response performance and robustness for NWMRs.Compared with the conventional adaptive sliding mode control,the proposed control strategy can guarantee that the sliding mode variables converge to a predefined neighborhood of origin with a predefined reaching time independent of the prior knowledge of the uncertainties and disturbances bounds.Another advantage of the proposed algorithm is that the control gains can be adaptively adjusted to follow the disturbances amplitudes thanks to the barrier function.The benefit is that the overestimation of control gain can be eliminated,resulting in chattering reduction.Moreover,a modified barrier function-like control gain is employed to prevent the input saturation problem due to the physical limit of the actuator.The stability analysis and comparative experiments demonstrate that the proposed BFASMC can ensure the prespecified convergence performance of the NWMR system output variables and strong robustness against uncertainties/disturbances.

Adaptive state-constrained/model-free iterative sliding mode control for aerial robot trajectory tracking

This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties.The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller(MFISMC).A position controller is designed based on adaptive sliding mode control(SMC)to safely drive the aerial robot and ensure fast state convergence under external disturbances.Additionally,the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots.Then,the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state.Finally,to demonstrate the performance and robustness of the proposed control strategy,numerical simulations are carried out,which are also compared with other conventional strategies,such as proportional-integralderivative(PID),backstepping(BS),and SMC.The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies.

Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

Adaptive Predefined-Time Attitude Tracking Control for Quadrotor Using a Novel Terminal Sliding Mode Approach

This paper proposes an adaptive predefined-time terminal sliding mode control(APTSMC)scheme for attitude tracking control of a quadrotor.To create this,an adaptive predefined-time stability controller based on a terminal sliding mode is constructed.The upper bound of convergence time in the proposed scheme can be adjusted by the explicit parameters during the design process of the controller.In addition,it is proved that the attitude tracking error will converge within two periods of the preset time.These two periods are set between two ranges:From the initial values to the sliding mode surface and from the sliding mode surface to the region near the origin.Furthermore,an adaptive law is adopted to eliminate unknown external disturbances and the effects of the uncertainties in the quadrotor model,so it is unnecessary to require the prior knowledge of the upper bound of the perturbations.Simulation results are produced and comparative case studies are carried out to demonstrate that the proposed scheme has faster convergence speed and smaller tracking errors.

Time-varying Sliding Mode Controls in Rigid Spacecraft Attitude Tracking

To solve the problem of attitude tracking of a rigid spacecraft with an either known or measurable desired attitude trajectory, three types of time-varying sliding mode controls are introduced under consideration of control input constraints. The sliding surfaces of the three types initially pass arbitrary initial values of the system, and then shift or rotate to reach predetermined ones. This way, the system trajectories are always on the sliding surfaces, and the system work is guaranteed to have robustness against parameter uncertainty and external disturbances all the time. The controller parameters are optimized by means of genetic algorithm to minimize the index consisting of the weighted index of squared error （ISE） of the system and the weighted penalty term of violation of control input constraint. The stability is verified with Lyapunov method. Compared with the conventional sliding mode control, simulation results show the proposed algorithm having better robustness against inertia matrix uncertainty and external disturbance torques.

Adaptive backstepping finite-time sliding mode control of spacecraft attitude tracking

This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con- trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se- cond control law is also designed by combining the second or- der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya- punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers.

Adaptive Robust Motion Trajectory Tracking Control of Pneumatic Cylinders with LuGre Model-based Friction Compensation

Friction compensation is particularly important for motion trajectory tracking control of pneumatic cylinders at low speed movement. However, most of the existing model-based friction compensation schemes use simple classical models, which are not enough to address applications with high-accuracy position requirements. Furthermore, the friction force in the cylinder is time-varying, and there exist rather severe unmodelled dynamics and unknown disturbances in the pneumatic system. To deal with these problems effectively, an adaptive robust controller with LuGre model-based dynamic friction compensation is constructed. The proposed controller employs on-line recursive least squares estimation（RLSE） to reduce the extent of parametric uncertainties, and utilizes the sliding mode control method to attenuate the effects of parameter estimation errors, unmodelled dynamics and disturbances. In addition, in order to realize LuGre model-based friction compensation, the modified dual-observer structure for estimating immeasurable friction internal state is developed. Therefore, a prescribed motion tracking transient performance and final tracking accuracy can be guaranteed. Since the system model uncertainties are unmatched, the recursive backstepping design technology is applied. In order to solve the conflicts between the sliding mode control design and the adaptive control design, the projection mapping is used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Finally, the proposed controller is tested for tracking sinusoidal trajectories and smooth square trajectory under different loads and sudden disturbance. The testing results demonstrate that the achievable performance of the proposed controller is excellent and is much better than most other studies in literature. Especially when a 0.5 Hz sinusoidal trajectory is tracked, the maximum tracking error is 0.96 mm and the average tracking error is 0.45 mm. This paper constructs an adaptive robust controller which can compensate the friction force in the cylinder.

Event-Triggered Sliding Mode Control for Trajectory Tracking of Nonlinear Systems

In this paper, an event-triggered sliding mode control approach for trajectory tracking problem of nonlinear input affine system with disturbance has been proposed. A second order robotic manipulator system has been modeled into a general nonlinear input affine system. Initially, the global asymptotic stability is ensured with conventional periodic sampling approach for reference trajectory tracking. Then the proposed approach of event-triggered sliding mode control is discussed which guarantees semi-global uniform ultimate boundedness. The proposed control approach guarantees non-accumulation of control updates ensuring lower bounds on inter-event triggering instants avoiding Zeno behavior in presence of the disturbance. The system shows better performance in terms of reduced control updates, ensures system stability which further guarantees optimization of resource usage and cost. The simulation results are provided for validation of proposed methodology for tracking problem by a robotic manipulator. The number of aperiodic control updates is found to be approximately 44% and 61% in the presence of constant and time-varying disturbances respectively.

Maximum Power Point Tracking in Variable Speed Wind Turbine Based on Permanent Magnet Synchronous Generator Using Maximum Torque Sliding Mode Control Strategy

The present study was carried out in order to track the maximum power point in a variable speed turbine by minimizing electromechanical torque changes using a sliding mode control strategy. In this strategy, first, the rotor speed is set at an optimal point for different wind speeds. As a result of which, the tip speed ratio reaches an optimal point, mechanical power coefficient is maximized, and wind turbine produces its maximum power and mechanical torque. Then, the maximum mechanical torque is tracked using electromechanical torque. In this technique, tracking error integral of maximum mechanical torque, the error, and the derivative of error are used as state variables. During changes in wind speed, sliding mode control is designed to absorb the maximum energy from the wind and minimize the response time of maximum power point tracking(MPPT). In this method, the actual control input signal is formed from a second order integral operation of the original sliding mode control input signal. The result of the second order integral in this model includes control signal integrity, full chattering attenuation, and prevention from large fluctuations in the power generator output. The simulation results, calculated by using MATLAB/m-file software, have shown the effectiveness of the proposed control strategy for wind energy systems based on the permanent magnet synchronous generator(PMSG).

High-speed tracked vehicle model order reduction for static and dynamic simulations

In this paper, a model order reduction strategy is adopted for the static and dynamic behaviour simulation of a high-speed tracked vehicle. The total number of degree of freedom of the structure is condensed through a selection of interface degrees of freedom and significant global mode shapes, for an approximated description of vehicle dynamic behaviour. The methodology is implemented in a customised open-source software to reduce the computational efforts. The modelled tracked vehicle includes the sprung mass, the unsprung masses, connected by means of torsional bars, and all the track assemblies, composing the track chain. The proposed research activity presents a comprehensive investigation of the influence of the track chain, combined with longitudinal vehicle speed, on statics and vehicle dynamics, focusing on vertical dynamics. The vehicle response has been investigated both in frequency and time domain. In this last case road-wheel displacements are assumed as inputs for the model, under different working conditions, hence considering several road profiles with different amplitudes and characteristic excitation frequencies. Simulation results have proven a high fidelity in model order reduction approach and a significant contribution of the track chain in the global dynamic behaviour of the tracked vehicle.

Tracking consensus for nonlinear heterogeneous multi-agent systems subject to unknown disturbances via sliding mode control

We investigate the tracking control for a class of nonlinear heterogeneous leader-follower multi-agent systems（MAS）with unknown external disturbances. Firstly, the neighbor-based distributed finite-time observers are proposed for the followers to estimate the position and velocity of the leader. Then, two novel distributed adaptive control laws are designed by means of linear sliding mode（LSM） as well as nonsingular terminal sliding mode（NTSM）, respectively. One can prove that the tracking consensus can be achieved asymptotically under LSM and the tracking error can converge to a quite small neighborhood of the origin in finite time by NTSM in spite of uncertainties and disturbances. Finally, a simulation example is given to verify the effectiveness of the obtained theoretical results.

Sliding-Mode-Based Attitude Tracking Control of Spacecraft Under Reaction Wheel Uncertainties

The attitude tracking operations of an on-orbit spacecraft with degraded performance exhibited by potential actuator uncertainties(including failures and misalignments) can be extraordinarily challenging. Thus, the control law development for the attitude tracking task of spacecraft subject to actuator(namely reaction wheel) uncertainties is addressed in this paper. More specially, the attitude dynamics model of the spacecraft is firstly established under actuator failures and misalignment(without a small angle approximation operation). Then, a new non-singular sliding manifold with fixed time convergence and anti-unwinding properties is proposed, and an adaptive sliding mode control(SMC) strategy is introduced to handle actuator uncertainties, model uncertainties and external disturbances simultaneously. Among this, an explicit misalignment angles range that could be treated herein is offered. Lyapunov-based stability analyses are employed to verify that the reaching phase of the sliding manifold is completed in finite time, and the attitude tracking errors are ensured to converge to a small region of the closest equilibrium point in fixed time once the sliding manifold enters the reaching phase. Finally, the beneficial features of the designed controller are manifested via detailed numerical simulation tests.

Trajectory tracking and obstacle avoidance method for robots based on fast terminal sliding mode

For accurate trajectory tracking and obstacle avoidance in finite time of a nonholonomic mobile robot,a trajectory tracking controller based on global fast terminal sliding mode method is proposed,which has the advantages of chattering-free and adjustable convergence time.First of all,the kinematics model of the robot is established in mobile carrier coordinates.Secondly,the global structure including terminal attractor and exponential convergence of the fast terminal sliding mode trajectory tracking controller is proved by Lyapunov stability theory,ensuring that the trajectory and heading angle tracking error converges to a smaller zero range in finite time.Finally,the artificial potential field obstacle avoidance method is introduced to make the robot not only track the reference trajectory strictly,but also avoid the obstacles.The simulation results show that the proposed method can achieve a stable tracking control in finite time for a given reference trajectory.

Fractional order nonsingular terminal sliding mode control for flexible spacecraft attitude tracking

This paper investigates a fractional terminal sliding mode control for flexible spacecraft attitude tracking in the presence of inertia uncertainties and external disturbances. The controller is based on the fractional calculus and nonsingular terminal sliding mode control technique,and it guarantees the convergence of attitude tracking error in finite time rather than in the asymptotic sense. With respect to the controller,a fractional order sliding surface is given,the corresponding control scheme is proposed based on Lyapunov stability theory to guarantee the sliding condition,and the finite time stability of the whole close loop system is also proven. Finally,numerical simulations are presented to illustrate the performance of the proposed scheme.

Adaptive Tracking Control for Diffractive Film Based on Nonlinear Sliding Mode

A nonlinear sliding mode adaptive controller for a thin-film diffractive imaging system is designed to achieve accurate pointing direction over the attitude of subarrays in large-diameter mirror arrays.The kinematics and dynamics equations based on error quaternion and angular velocity are derived,and a diffractive thin-film sub-mirror array controller is designed to point precisely.Moreover,the global stability of the controller is proved by the Lyapunov method.Since the controller can adaptively identify the inertia matrix of each sub-mirror system,it is robust to bounded disturbances and changes in inertia parameters.At the same time,the continuous arctangent function is introduced,which is effectively anti-chattering.The simulation results show that the designed controller can ensure the accurate tracking of the diffractive film in each sub-mirror in the presence of rotational inertia matrix uncertainty and various disturbances.

Robust Region Tracking for Swarms via a Novel Utilization of Sliding Mode Control

Control of multi-agent autonomous swarms is studied for targeted flocking exercises. The desired decentralized control takes into account robustness against modeling uncertainties as well as bounded unknown forces. In this analysis, we consider the task of driving multiple agents to a moving “target region”, as inter-agent repulsive forces help spread out the agents within the region. An unconventional form of sliding mode control is implemented to provide the robust attraction towards the region’s center. For robustness a finite “boundary layer” is conceived, which corresponds to the desired target region. The flocking control forces are intentionally softened inside this target region, allowing agents to create a uniformly spaced formation guided by the inter-agent repulsion forces. Examples are given for moving circular and elliptical regions which illustrate the effectiveness of the proposed strategy.

Robust Tracking Control for Self-balancing Mobile Robots Using Disturbance Observer

In this paper,a robust tracking control scheme based on nonlinear disturbance observer is developed for the self-balancing mobile robot with external unknown disturbances.A desired velocity control law is firstly designed using the Lyapunov analysis method and the arctan function.To improve the tracking control performance,a nonlinear disturbance observer is developed to estimate the unknown disturbance of the self-balancing mobile robot.Using the output of the designed disturbance observer,the robust tracking control scheme is presented employing the sliding mode method for the selfbalancing mobile robot.Numerical simulation results further demonstrate the effectiveness of the proposed robust tracking control scheme for the self-balancing mobile robot subject to external unknown disturbances.

Consecutive tracking for ballistic missile based on bearings-only during boost phase

This paper proposes a modified centralized shifted Rayleigh filter（MCSRF） algorithm for tracking boost phase of ballistic missile（BM） trajectory with a highly nonlinear dynamical model based on bearings-only.This paper contributes three folds.Firstly,the mathematical model of an MCSRF for multiple passive sensors is derived.Then,minimum entropy based onedimensional optimization search to adaptively adjust the probability of the different filters for real time state estimation is deployed.Finally,the unscented transform（UT） is introduced to resolve the asymmetric state estimation problem.Simulation results show that the proposed algorithm can consecutively track the BM precisely during the boost phase.In comparison with the unscented Kalman filter（UKF） algorithm,the proposed algorithm effectively reduces the tracking position and velocity root mean square（RMS） errors,which will make more sense for early precision interception.

Attitude tracking control of flexible spacecraft with large amplitude slosh

This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli–Euler beam, and the assumed modal method is employed.A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics,liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking.