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.

A Novel Disturbance Observer Based Fixed-Time Sliding Mode Control for Robotic Manipulators With Global Fast Convergence

This paper proposes a new global fixed-time sliding mode control strategy for the trajectory tracking control of uncertain robotic manipulators.First,a fixed-time disturbance observer(FTDO) is designed to deal with the adverse effects of model uncertainties and external disturbances in the manipulator systems.Then an adaptive scheme is used and the adaptive FTDO(AFTDO) is developed,so that the priori knowledge of the lumped disturbance is not required.Further,a new non-singular fast terminal sliding mode(NFTSM) surface is designed by using an arctan function,which helps to overcome the singularity problem and enhance the robustness of the system.Based on the estimation of the lumped disturbance by the AFTDO,a fixed-time non-singular fast terminal sliding mode controller(FTNFTSMC)is developed to guarantee the trajectory tracking errors converge to zero within a fixed time.The settling time is independent of the initial state of the system.In addition,the stability of the AFTDO and FTNFTSMC is strictly proved by using Lyapunov method.Finally,the fixed-time NFESM(FTNFTSM) algorithm is validated on a 2-link manipulator and comparisons with other existing sliding mode controllers(SMCs) are performed.The comparative results confirm that the FTNFTSMC has superior control performance.

Non-Negative Adaptive Mechanism-Based Sliding Mode Control for Parallel Manipulators with Uncertainties

In this paper,a non-negative adaptive mechanism based on an adaptive nonsingular fast terminal sliding mode control strategy is proposed to have finite time and high-speed trajectory tracking for parallel manipulators with the existence of unknown bounded complex uncertainties and external disturbances.The proposed approach is a hybrid scheme of the online non-negative adaptive mechanism,tracking differentiator,and nonsingular fast terminal sliding mode control(NFTSMC).Based on the online non-negative adaptive mechanism,the proposed control can remove the assumption that the uncertainties and disturbances must be bounded for the NFTSMC controllers.The proposed controller has several advantages such as simple structure,easy implementation,rapid response,chattering-free,high precision,robustness,singularity avoidance,and finite-time convergence.Since all control parameters are online updated via tracking differentiator and non-negative adaptive law,the tracking control performance at high-speed motions can be better in real-time requirement and disturbance rejection ability.Finally,simulation results validate the effectiveness of the proposed method.

Adaptive Backstepping Terminal Sliding Mode Control Method Based on Recurrent Neural Networks for Autonomous Underwater Vehicle

The trajectory tracking control problem is addressed for autonomous underwater vehicle(AUV) in marine environ?ment, with presence of the influence of the uncertain factors including ocean current disturbance, dynamic modeling uncertainty, and thrust model errors. To improve the trajectory tracking accuracy of AUV, an adaptive backstepping terminal sliding mode control based on recurrent neural networks(RNN) is proposed. Firstly, considering the inaccu?rate of thrust model of thruster, a Taylor’s polynomial is used to obtain the thrust model errors. And then, the dynamic modeling uncertainty and thrust model errors are combined into the system model uncertainty(SMU) of AUV; through the RNN, the SMU and ocean current disturbance are classified, approximated online. Finally, the weights of RNN and other control parameters are adjusted online based on the backstepping terminal sliding mode controller. In addition, a chattering?reduction method is proposed based on sigmoid function. In chattering?reduction method, the sigmoid function is used to realize the continuity of the sliding mode switching function, and the sliding mode switching gain is adjusted online based on the exponential form of the sliding mode function. Based on the Lyapu?nov theory and Barbalat’s lemma, it is theoretically proved that the AUV trajectory tracking error can quickly converge to zero in the finite time. This research proposes a trajectory tracking control method of AUV, which can e ectively achieve high?precision trajectory tracking control of AUV under the influence of the uncertain factors. The feasibility and e ectiveness of the proposed method is demonstrated with trajectory tracking simulations and pool?experi?ments of AUV.

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.

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.

Adaptive Terminal Sliding Mode Control for Rigid Robotic Manipulators

In order to apply the terminal sliding mode control to robot manipulators,prior knowledge of the exact upper bound of parameter uncertainties,and external disturbances is necessary.However,this bound will not be easily determined because of the complexity and unpredictability of the structure of uncertainties in the dynamics of the robot.To resolve this problem in robot control,we propose a new robust adaptive terminal sliding mode control for tracking problems in robotic manipulators.By applying this adaptive controller,prior knowledge is not required because the controller is able to estimate the upper bound of uncertainties and disturbances.Also,the proposed controller can eliminate the chattering effect without losing the robustness property.The stability of the control algorithm can be easily verified by using Lyapunov theory.The proposed controller is tested in simulation on a two-degree-of-freedom robot to prove its effectiveness.

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Adaptive robust motion trajectory tracking control of pneumatic cylinders

High-accuracy motion trajectory tracking control of a pneumatic cylinder driven by a proportional directional control valve was considered. A mathematical model of the system was developed firstly. Due to the time-varying friction force in the cylinder, unmodeled dynamics, and unknown disturbances, there exist large extent of parametric uncertainties and rather severe uncertain nonlinearities in the pneumatic system. To deal with these uncertainties effectively, an adaptive robust controller was constructed in this work. 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, unmodeled dynamics and disturbances. 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 was applied. In order to solve the conflicts between the sliding mode control design and the adaptive control design, the projection mapping was used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Extensive experimental results were presented to illustrate the excellent achievable performance of the proposed controller and performance robustness to the load variation and sudden disturbance.

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.

Adaptive Sliding-Mode Control of an Automotive Electronic Throttle in the Presence of Input Saturation Constraint

In modern vehicles, electronic throttle(ET) has been widely utilized to control the airflow into gasoline engine. To solve the control difficulties with an ET, such as strong nonlinearity,unknown model parameters and input saturation constraints,an adaptive sliding-mode tracking control strategy for an ET is presented. Compared with the existing control strategies for an ET, input saturation constraints and parameter uncertainties are adequately considered in the proposed control strategy. At first, the nonlinear dynamic model for control of an ET is described. According to the dynamical model, the nonlinear adaptive sliding-mode tracking control method is presented,where parameter adaptive laws and auxiliary design system are employed. Parameter adaptive law is given to estimate the unknown parameter with an ET. An auxiliary system is designed,and its state is utilized in the tracking control method to handle the input saturation. Stability proof and analysis of the adaptive sliding-mode control method is performed by using Lyapunov stability theory. Finally, the reliability and feasibility of the proposed control strategy are evaluated by computer simulation.Simulation research shows that the proposed sliding-mode control strategy can provide good control performance for an ET.

Precise trajectory tracking of mecanum-wheeled omnidirectional mobile robots via a novel fixed-time sliding mode control approach

This paper proposes a novel fixed-time sliding mode control approach for trajectory-tracking tasks of a mecanum-wheeled omnidirectional mobile robot.First,the idea of two-phase attractors is introduced into the domain of sliding mode control,and a new fixed-time sliding surface is proposed.Then,according to this sliding surface,a new type of nonsingular fast terminal sliding mode control algorithm is designed for the omnidirectional mobile robot,which can realize a fast fixed-time convergence property.The stability of the control system is proven scrupulously,and a guideline for control-parameter tuning is expounded.Finally,experiments are implemented to test the trajectory-tracking performance of the robot.Experimental results demonstrate the superiority of the proposed sliding surface and the corresponding control scheme in comparison with benchmark controllers.

Adaptive Backstepping Slide Mode Control of Pneumatic Position Servo System

With the price decreasing of the pneumatic proportional valve and the high performance micro controller, the simple structure and high tracking performance pneumatic servo system demonstrates more application potential in many fields. However, most existing control methods with high tracking performance need to know the model information and to use pressure sensor. This limits the application of the pneumatic servo system. An adaptive backstepping slide mode control method is proposed for pneumatic position servo system. The proposed method designs adaptive slide mode controller using backstepping design technique. The controller parameter adaptive law is derived from Lyapunov analysis to guarantee the stability of the system. A theorem is testified to show that the state of closed-loop system is uniformly bounded, and the closed-loop system is stable. The advantages of the proposed method include that system dynamic model parameters are not required for the controller design, uncertain parameters bounds are not need, and the bulk and expensive pressure sensor is not needed as well. Experimental performance, as compared with some existing methods. results show that the designed controller can achieve better tracking

Trajectory tracking control for underactuated unmanned surface vehicles with dynamic uncertainties

The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturbance, etc. By introducing the reference, trajectory was generated by a virtual USV, and the error equation of trajectory tracking for USV was obtained, which transformed the tracking problem of underactuated USV into the stabilization problem of the trajectory tracking error equation. A backstepping adaptive sliding mode controller was proposed based on backstepping technology and method of dynamic slide model control. By means of theoretical analysis, it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property. Simulation results are presented to illustrate the effectiveness of the proposed controller.

Nonlinear trajectory tracking control of a new autonomous underwater vehicle in complex sea conditions

Autonomous underwater vehicles (AUVs) navigating in complex sea conditions usually require a strong control system to keep the fastness and stability. The nonlinear trajectory tracking control system of a new AUV in complex sea conditions was presented. According to the theory of submarines,the six-DOF kinematic and dynamic models were decomposed into two mutually non-coupled vertical and horizontal plane subsystems. Then,different sliding mode control algorithms were used to study the trajectory tracking control. Because the yaw angle and yaw angle rate rather than the displacement of the new AUV can be measured directly on the horizontal plane,the sliding mode control algorithm combining cross track error method and line of sight method was used to fulfill its high-precision trajectory tracking control in the complex sea conditions. As the vertical displacement of the new AUV can be measured,in order to achieve the tracking of time-varying depth signal,a stable sliding mode controller was designed based on the single-input multi-state system,which took into account the characteristic of the hydroplane and the amplitude and rate constraints of the hydroplane angle. Moreover,the application of dynamic boundary layer can improve the robustness and control accuracy of the system. The computational results show that the designed sliding mode control systems of the horizontal and vertical planes can ensure the trajectory tracking performance and accuracy of the new AUV in complex sea conditions. The impacts of currents and waves on the sliding mode controller of the new AUV were analyzed qualitatively and quantitatively by comparing the trajectory tracking performance of the new AUV in different sea conditions,which provides an effective theoretical guidance and technical support for the control system design of the new AUV in real complex environment.

Control of trajectory tracking of two-wheeled differential spherical mobile robot

This paper presents a two-wheeled differential spherical mobile robot in view of the problems that the motion of spherical robot is difficult to control and the sensor is limited by the spherical shell.The robot is simple in structure,flexible in motion and easy to control.The kinematics and dynamics model of spherical mobile robot is established according to the structure of spherical mobile robot.On the basis of the adaptive neural sliding mode control,the trajectory tracking controller of the system is designed.During the simulation of the s-trajectory and circular trajectory tracking control of the spherical mobile robot,it is concluded that the spherical mobile robot is flexible in motion and easy to control.In addition,the simulation results show that the adaptive neural sliding mode control can effectively track the trajectory of the spherical robot.The adaptive control eliminates the influence of unknown parameters and disturbances,and avoids the jitter of left and right wheels during the torque output.

Feedback Attitude Sliding Mode Regulation Control of Spacecraft Using Arm Motion

The problem of spacecraft attitude regulation based on the reaction of arm motion has attracted extensive attentions from both engineering and academic fields.Most of the solutions of the manipulator’s motion tracking problem just achieve asymptotical stabilization performance,so that these controllers cannot realize precise attitude regulation because of the existence of non-holonomic constraints.Thus,sliding mode control algorithms are adopted to stabilize the tracking error with zero transient process.Due to the switching effects of the variable structure controller,once the tracking error reaches the designed hyper-plane,it will be restricted to this plane permanently even with the existence of external disturbances.Thus,precise attitude regulation can be achieved.Furthermore,taking the non-zero initial tracking errors and chattering phenomenon into consideration,saturation functions are used to replace sign functions to smooth the control torques.The relations between the upper bounds of tracking errors and the controller parameters are derived to reveal physical characteristic of the controller.Mathematical models of free-floating space manipulator are established and simulations are conducted in the end.The results show that the spacecraft’s attitude can be regulated to the position as desired by using the proposed algorithm,the steady state error is 0.000 2 rad.In addition,the joint tracking trajectory is smooth,the joint tracking errors converges to zero quickly with a satisfactory continuous joint control input.The proposed research provides a feasible solution for spacecraft attitude regulation by using arm motion,and improves the precision of the spacecraft attitude regulation.

Robust BELBIC-Extension for Trajectory Tracking Control

In real-life trajectory tracking applications of robotic manipulators uncertain robot dynamics, external disturbances and switching constraints which cannot be accommodated for by a conventional controller affect the system performance. We suggested an additional control element combining sliding mode and bio-mimetic, neurologically-inspired BELBIC （brain emotional learning-based intelligent control）. The former is invariant to internal and external uncertainties and guarantees robust behavior. The latter is based on an interplay of inputs relating to environmental information through error-signals of position and sliding surfaces and of emotional signals regulating the learning rate and adapting the future behaviour based on prior experiences and with the goal to maximize a reward function. We proofed the stability and the performance of the suggested control scheme through Lyapunov theory and numerical simulations, respectively.