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To solve the problem of trajectory tracking lateral control in autonomous driving technology, a model predictive control (MPC) controller trajectory tracking lateral control method combined with a deep deterministic policy gradient algorithm (DDPG) is proposed in this paper. This method inputs the real-time state of the vehicle into DDPG to achieve real-time automatic optimization of the prediction time domain and control time domain parameters of the MPC controller, and then affects the specific performance of the MPC controller in trajectory tracking lateral control. Specifically, the state space, action space, and reward function of DDPG are defined, and the automatic driving trajectory tracking lateral controller is designed in combination with the vehicle dynamics model. To reduce the exploration space of DDPG and improve the training efficiency of the entire model, the technique of advantage-disadvantage experience separation and extraction is introduced. Finally, the proposed method was trained and verified in various scenarios, and compared with two other lateral control methods for autonomous driving. The results showed that the learning and training time of the trajectory tracking lateral control method based on DDPG-MPC was shorter than that of the DDPG-based method, and the evaluation indicators in the trajectory tracking control process were better than those of the DDPG-based method and original MPC-based method. [ABSTRACT FROM AUTHOR]

For the attitude control system of a quadrotor unmanned aerial vehicle (UAV), an integral backstepping active disturbance rejection control strategy is proposed to solve the tracking and disturbance rejection problems in flight control. To solve the problem of buffeting near the origin of traditional nonlinear functions, this paper designs a function newfal (·) with better smoothness near the origin. Second, to improve the observation performance of the extended state observer and the anti-disturbance performance of the controller, an improved expanded state observer (IESO) based on error is designed according to the working principle of expanded state observer (ESO) and the tracking law of state variables. Then, to improve the tracking accuracy of the controller, the integral term is introduced into the backstepping method and uses the idea of recursion to design the nonlinear backstepping integral control law. Combining the disturbance estimation and compensation functions of active disturbance rejection control (ADRC), an integral backstepping active disturbance rejection control is designed and applied to the attitude angle control channel of quadrotor UAV. Finally, experimental results indicate that the designed control strategy can realize high-precision tracking of the attitude angle of a quadrotor UAV, achieve fast dynamic response, and improve the anti-interference. [ABSTRACT FROM AUTHOR]

To address the nonlinear stabilization problem and improve the tracking control feature of ball on plate system (BPS), this paper puts forward a novel Takagi Sugeno (TS) fuzzy control augmented with the current cycle feedback iterative learning control (CCF-ILC) scheme. According to Bode's sensitivity integral, the performance of linear controllers is always a trade-off between reference tracking and robustness. Hence, to deal with the so-called 'waterbed' effect, this work exploits the capability of TS fuzzy to handle the nonlinear dynamics and synthesizes a learning control scheme based on current iteration error to capitalize the information rich error signal for enhancing the robustness and trajectory tracking features. The global asymptotic stability of the proposed TS fuzzy augmented ILC scheme is proved using the Lyapunov function and linear matrix inequalities (LMIs). Moreover, the monotonic convergence of ILC is presented based on the singular value condition. For identifying the rolling mass from the video stream, a background subtraction algorithm based on thresholding technique is implemented. Finally, the robustness and tracking features of the proposed scheme are evaluated on a two degrees of freedom (DoF) laboratory scale BPS system through hardware in loop (HIL) testing for three realistic test cases. The tracking performance quantified using the root mean square error (RMSE) and power spectral density plot corroborates that the proposed scheme can offer better setpoint tracking and robustness feature compared to state-of-the-art fuzzy and ILC control techniques implemented on BPS. [ABSTRACT FROM AUTHOR]

Robotic manipulators are nowadays widely used in various underwater scenarios, but their motion control remains a challenging task due to hydrodynamic effects. This article proposes a novel adaptive fuzzy sliding mode control (AFSMC) strategy for precise and robust control of underwater manipulators. To simulate the movement of the robotic manipulators in the underwater environment, the Unified Robot Description Format (URDF) file of a custom-designed electric underwater manipulator is imported into the Simscape Multibody and the hydrodynamic disturbance is modeled according to Morison's equation. Furthermore, the proposed control strategy takes advantage of the universal approximation capability of fuzzy systems to avoid chattering and observe disturbances by adjusting the control gains of classical sliding mode control (CSMC). And adaptive laws are designed to update the parameters of the fuzzy systems. The strong friction caused by the seal is also compensated by actual test data. In the simulation experiments, a special environment of water flow and variable loads is considered. The results demonstrate that the AFSMC strategy can achieve high precision and strong robustness against disturbances for trajectory tracking. More importantly, the chattering caused by CSMC can be eliminated and the hydrodynamic disturbance can be estimated with high precision through the proposed control strategy. [ABSTRACT FROM AUTHOR]

The idea of modeling first and then finding a control approach might have made sense when systems were changing on a vast scale, but not in today's world where we are in danger of being run over on a highway called the information highway. The feedback phenomenon, which involves a system's future being influenced by its past, presents a rational conflict in this context. However, we can move beyond these challenges by leveraging the system's inherent ability to randomly repeat and re-create parts, allowing new features to emerge and the best repetition to become the standard. To address the mentioned challenges, this paper proposes a new structure based on bilateral long short-term memory (BiLSTM) to provide supervising feedback on the nonlinear components comprising friction, Coriolis, and Centrifugal forces in addition to gravity for adapting uncertain variations in the robotic system dynamics. A key characteristic of the proposed BiLSTM-based controller is the incorporation of memory. A new formulation is developed for determining when to recover old memories and to what extent, ensuring the controller remains both adaptive and efficient. Furthermore, given that for system identification, speed is vital; the proposed approach has dealt with the speed category by introducing a convex combination of BiLSTM layers. The stability of the whole structure has also been analyzed, and the updated learning rules have been derived. The simulation results show improved tracking performance and learning time compared to alternative approaches. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered control mechanism scheme based on dynamic surface control and adaptive dynamic programming (DSC-ETCADP) is proposed for optimal trajectory tracking of the unmanned surface vessel (USV) with input constraints. First, the control structure is designed using dynamic surface control (DSC) as feedforward control and adaptive dynamic programming as feedback control, which not only ensures the tracking of reference trajectory but also improves the control accuracy. Second, due to the data-driven nature of adaptive dynamic programming (ADP) and the ability to adjust parameters online, it can be solved by USV with unknown disturbance. Third, the event-triggered mechanism can save computation and reduce the number of executions of the controller, in addition to avoiding Zeno behavior. Finally, according to the Lyapunov stability theory, all signals in the closed-loop system are globally uniformly and ultimately bounded (UUB). The DSC-ETCADP scheme is compared with DSC method. Simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Considering the problems of unknown external disturbances and parametric uncertainties in trajectory tracking of a quadrotor, a backstepping control method based on time-varying threshold event-triggered extended state observer (TETESO) and a nonlinear differentiator with lead compensation is proposed in this paper. First, to facilitate the controller design, the quadrotor system is divided into the position subsystem and the attitude subsystem, which are transformed into the original cascaded dynamics. Second, a TETESO which can observe the unmeasurable states and the total disturbance as well as reduce the unnecessary communication resources between sensor and observer is proposed. It is proved that the observation errors are bounded, and Zeno behavior is avoided. Third, a new controller synthesized by the proposed TETESO and the backstepping control method is designed for the position subsystem and the attitude subsystem. To address the "differential explosion" problem in the backstepping control method, a nonlinear differentiator with lead compensation is used to compute the derivative of desired attitudes in the controller. Moreover, the stability analysis of the closed-loop system is proved and the proposed controller can ensure the ultimate boundedness of all signals. Finally, the effectiveness and superiority of the proposed control method are verified by simulation. [ABSTRACT FROM AUTHOR]

In this paper, trajectory tracking control of an underwater vehicle in three-dimensional (3D) space has been addressed. The assumed underwater vehicle has 6 degrees of freedom and the aim is to control all system rotations and displacements. In this paper, a finite-time sliding mode controller as a robust control method is proposed for an underwater vehicle with 6 degrees of freedom in 3D space using the method without simplifications or decouplings. Therefore, both system positions and orientations are controlled in the presence of disturbances and uncertainties. In previous research works, control of two-dimensional underwater vehicles is commonly studied. In this paper, a novel stable control algorithm is proposed for an underwater vehicle with 6 degrees of freedom. The stability of the closed-loop system is analyzed using the Lyapunov theory. The designed algorithm can cover 3D complicated tasks. Also, the designed algorithm as a robust control approach can attenuate external disturbances. The performance and stability of this approach are compared with the sliding mode controller. The numerical comparison results show that the proposed approach is effective and applicable in practice. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive sliding mode-based active disturbance rejection control (ASM-ADRC) strategy for the altitude and attitude control of an unmanned quadcopter with disturbances. The quadcopter is an underactuated system subject to parametric perturbations, nonlinearity, unmodeled dynamics, strong coupling, and external disturbances. The proposed algorithm is based on the quadcopter's dynamic model, where the effects of noise and wind are considered additive disturbances. The central concept is to combine the advantages of adaptive sliding mode control (SMC) to accurately track the reference trajectory with the ability of ADRC to reject the parameter uncertainties and external disturbances. The proposed control scheme is verified in simulation studies with sensor noise and external disturbances. The simulation results show that the proposed algorithm can significantly reduce the chattering phenomenon, owing to the estimation capability of the extended state observer (ESO). The proposed method also improves the robustness against modeling errors and disturbances and smoothly tracks the reference trajectory. [ABSTRACT FROM AUTHOR]

In this study, an adaptive hierarchical interval type-2 fuzzy control (AHIT2FC) scheme is presented for three-dimensional (3D) trajectory tracking control of an underactuated autonomous underwater vehicle (AUV), which has only three independent control inputs and is subject to partially parametric uncertainty and unknown external disturbances. To decrease reliance on hydrodynamic parameters, an interval type-2 fuzzy logic system (IT2FLS) is utilized, which exhibits superior capabilities in handling high levels of uncertainties prevalent in the underwater environment as compared to a type-1 fuzzy logic system. However, the traditional fuzzy system structure encounters the “curse of dimensionality” issue, which results in high computational complexity and imposes a significant burden on the limited computing resources underwater. The proposed AHIT2FC framework, based on a hierarchical structure, can substantially enhance computational speed while ensuring excellent control performance. Subsequently, Lyapunov’s theory is adopted to guarantee that all the tracking errors in the closed-loop system are semiglobally uniformly bounded (SGUB). Finally, comparative simulation results demonstrate the effectiveness and superiority of the proposed AHIT2FC scheme. [ABSTRACT FROM AUTHOR]

During the operation of an underwater tracked vehicle on a soft substrate, the instantaneous center of rotation (ICR) no longer coincides with the geometric center after the longitudinal offset is accounted for by the external environment. Due to this, designing an underwater trajectory tracking system based on a kinematic model is a challenging task. In order to achieve the high-precision trajectory tracking control of underwater tracked vehicles, this paper proposes a trajectory tracking algorithm based on the kinematic model of tracked vehicles. First, an inverse tangent algorithm is proposed to address the problem that the front viewpoint of the Stanley algorithm may not be on the target path and cause deviation. Second, by using the inverse tangent algorithm to introduce the target bow angle, as well as combining the mechanisms by which biological endocrine hormones are regulated with the advantages of single-neuron proportional–integral–derivative (PID), a composite endocrine intelligent control law is proposed for the design of the lateral control law of an underwater tracked vehicle; a longitudinal control law is designed based on the longitudinal offset of the ICR obtained by the estimation of the unscented Kalman filter as a means of compensating for longitudinal errors. Finally, a kinematic model is used in order to determine the desired drive wheel speed of the underwater tracked vehicle. The method is compared with the method without longitudinal deviation compensation, then with the methods presented in related literature, and finally, a certain degree of experimental validation is carried out. These results validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

When unmanned underwater vehicles (UUVs) navigate on the surface, the UUVs’ speed cannot be accurately measured due to the humid environment. This can lead to a decrease in trajectory tracking control accuracy, and in severe cases, it may lead to controller failure. To solve this problem, a novelty speed observer based on real-time position state is proposed, and the UUV trajectory tracking controller is designed based on this observer. First, a speed observer with position status based on the UUV surface navigation kinematics model is proposed. Considering the impact of environmental disturbances, a disturbance observer is designed to observe surge, sway, and yaw torque disturbances. Next, a virtual control law is designed based on speed observations and reference trajectories to solve control laws. Considering the saturation input problem of the UUV driver, a command filter is introduced to constrain the amplitude and speed of the virtual control law. Then, a trajectory tracking sliding mode controller is designed using the virtual control law and the output of the command filter. Meanwhile, the disturbance of surge torque and heading torque is compensated with the observed value of the disturbance observer. The stability of the entire closed-loop control system is analyzed using Lyapunov’s stability theory. Finally, a series of numerical simulations are added to illustrate the method’s effectiveness. [ABSTRACT FROM AUTHOR]

The method of a designed trajectory tracking for an underactuated unmanned surface vehicle (USV) in the presence of ocean disturbances is addressed in this paper; the differential flatness theory is applied to get the reference inputs and speed states at the reference position trajectory. Second, a transition process is arranged for the reference trajectory to reduce the overshoot of the actuator, which caused by the large deviation in the initial tracking. Third, the nonlinear disturbance observer is designed to obtain the estimated values of unknown disturbances in the ocean. Then, a controller-based model predictive control (MPC) and terminal cost function is designed for the nominal system. The inherent robustness of the controller and estimates of the observer are used to resist and compensate disturbances. Finally, the simulation experiments of linear trajectory and sinusoidal trajectories are carried out to prove the effectiveness and reliability of the control algorithm designed. [ABSTRACT FROM AUTHOR]

The machining robotic manipulators (MRMs) find a broad range of applications due to their high efficiency, wide range of processing, and strong flexibility. High tracking accuracy and strong anti-interference ability are required to trajectory tracking control of machining robot during processing. In view of the above characteristics, this paper proposes a compensation sliding mode control (CSMC) based on nonlinear disturbance observer (NBO-CSMC) for MRM. First, we deduced the dynamic model of MRM considering the uncertainties and disturbances. Then, for improving the trajectory tracking accuracy, a compensation sliding mode controller is designed based on the traditional sliding mode control (TSMC) strategy. Finally, in order to reduce the chattering in sliding mode control, the NBO-CSMC is designed for MRM, NBO is used to estimate the external composite uncertain interference existing in the system, and compensate the system control input in real time. The Lyapunov's theory proved the stability of the proposed algorithm, and simulation experiments verified the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

An auxiliary variable-based output feedback method is constructed in this paper. To obtain the state estimates, an auxiliary variable-based state observer is presented. Instead of calculating the estimates indirectly via the estimation dynamic, the distinguishing characteristic of the proposed observer lies in its ability to directly derive estimates by simply applying a low-pass filter to the observer. Therefore, the proposed observer is similar as a filter, which is more intuitive and concise in terms of structure and parameter tuning. Then, a backstepping-free controller is constructed based on the estimation results, and only one step is required. To facilitate the design procedure, the desired compensation approach is applied both in the observer and the controller. Utilizing the Lyapunov method, the system stability is assured, demonstrating that the presented controller excels in precise tracking tasks despite the presence of time-varying uncertainties. The feasibility of this approach is further corroborated through comparative results. [ABSTRACT FROM AUTHOR]

In this paper, we aim to design the trajectory tracking controller for variable curvature duty-cycled rotation flexible needles with a tube-based model predictive control approach. A non-linear model is adopted according to the kinematic characteristics of the flexible needle and a bicycle method. The modeling error is assumed to be an unknown but bounded disturbance. The non-linear model is transformed to a discrete time form for the benefit of predictive controller design. From the application perspective, the flexible needle system states and control inputs are bounded within a robust invariant set when subject to disturbance. Then, the tube-based model predictive control is designed for the system with bounded state vector and inputs. Finally, the simulation experiments are carried out with tube-based model predictive control and proportional integral derivative controller based on the particle swarm optimisation method. The simulation results show that the tube-based model predictive control method is more robust and it leads to much smaller tracking errors in different scenarios. [ABSTRACT FROM AUTHOR]

This paper investigates concentrates on the trajectory tracking control problem of dynamic positioning (DP) ship, in the presence of the time-varying disturbance and input saturation. Firstly, a simplified mathematical model of three degrees of freedom is established. According to the characteristics of the DP ship, an adaptive backstepping controller which combine the prescribed performance function with disturbance observer is proposed. The control scheme can guarantee the transient and steady state performance of the trajectory tracking and meet the prescribed performance criteria. In addition, an auxiliary dynamic system is introduced into the controller to deal with the input saturation problem of the actuator, so that the DP ship can accomplish the task of trajectory tracking under the condition of actuator constraint. Subsequently, in combination of barrier Lyapunov function (BLF), it is proved that the DP system can stabilize and converge rapidly to the small neighborhood of the equilibrium point, which can achieve the prescribed performance. Finally, the effectiveness of the DP control law is demonstrated by a series of simulation experiments. [ABSTRACT FROM AUTHOR]

This paper studies the fixed-time disturbance estimate and tracking control for two-link manipulators subjected to external disturbance. A fixed-time extended-state disturbance observer (FxTESDO) is proposed by improving the extended state observer. Also, a fixed-time inverse dynamics tracking control (FxTIDTC) scheme based on the FxTESDO is given for two-link manipulators. The fixed-time convergence of the FxTESDO and FxTIDTC is proved by the Lyapunov stability theory and with the aid of the bi-limit homogeneous technique. Numerical simulations are employed to illustrate the effectiveness of the proposed FxTIDTC. [ABSTRACT FROM AUTHOR]

In the transportation process of a three-dimensional double-pendulum overhead crane, the system is significantly influenced by the pronounced coupling introduced by the double-pendulum effect, posing a considerable challenge for the development of effective anti-swing control strategies. Moreover, uncertainties in certain system parameters and errors in trolley positioning contribute to the complexity of anti-swing control strategy design. To address these practical issues, a control strategy is proposed: First, an S-shaped transport trajectory with minimal positioning error is introduced, incorporating more system parameters into the coupling signal design to enhance system coupling. Based on this, an error-coupled trajectory signal is introduced. Second, the error-coupled trajectory signal is integrated into the energy function, and leveraging adaptive principles, an adaptive coupled trajectory tracking anti-swing control strategy is proposed to estimate uncertain system parameters online. Subsequently, the asymptotic stability of the equilibrium point of the closed-loop system is verified using the Lyapunov techniques and the Barbalat lemma. Finally, through simulations and experiments, it is demonstrated that the proposed control strategy not only ensures precise positioning of the trolley and bridge but also effectively suppresses oscillations of the hook and load, exhibiting excellent control performance. Even in scenarios where system parameters undergo changes or external disturbances are introduced, the proposed control strategy exhibits strong robustness and holds significant practical potential. [ABSTRACT FROM AUTHOR]

This paper proposes a non-singular fast terminal sliding mode control method for a binocular active vision platform of a picking robot with unknown dynamics. The method uses radial basis function (RBF) neural networks to achieve trajectory tracking accuracy and enhance robustness against external interference. A non-singular fast terminal sliding mode controller is designed for the system’s convergence within a limited time. An adaptive neural network approximates the unknown nonlinear function of the dynamic model. Stability and finite-time convergence of the closed-loop system are established using Lyapunov theory. Experimental verification on the binocular vision platform demonstrates position and speed errors converging to the desired trajectory within 2 and 1 second, respectively. Moreover, when subjected to external interference, the position and velocity errors converge within 0.1 seconds. Simulation experiments confirm the method’s effectiveness in improving convergence speed, trajectory tracking accuracy, and robustness against external interference, while reducing system chattering. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time trajectory tracking control for a group of nonholonomic mobile robots, where the desired trajectory is generated by a virtual leader, the leader's information is available to only a subset of the followers, and the followers are assumed to have only local interaction. According to fixed-time control theory and adding a power integrator technique, distributed fixed-time tracking controllers are developed for each robot such that all states of each robot can reach the desired value in a fixed time. Moreover, the settling time is independent of the system initial conditions and only determined by the controller parameters. Simulation results illustrate and verify the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

Due to the serious drift phenomenon of underactuated air cushion vehicle, the actual trajectory is determined by the total speed and course angle. In this paper, the course angle and total speed model are derived from the general four degrees of freedom air cushion vehicle model and named nonlinear vector model. Nonlinear vector model can be used to directly design the course and total speed controllers for underactuated air cushion vehicle. Adaptive radial basis function neural network is introduced to deal with the strong nonlinearity and uncertainty of air cushion vehicle's complex dynamics. However, the adaptive weights to be calculated and updated may be too many in each sampling period. For the relief of the burden caused by the online computing, parameter reduction algorithm is designed in this paper. It gives us a power to choose the number of online update parameters freely. Then the new trajectory tracking control method with independent total speed and course controller is designed based on nonlinear vector model and parameter reduction algorithm. The designed controller ensures that the tracking errors are uniformly ultimately bounded. Also, only a few weights need to be updated online. The effectiveness and superiority of the designed controller is verified by simulation results. [ABSTRACT FROM AUTHOR]

This work presents a novel control strategy for the trajectory tracking control of the quadrotor unmanned aerial vehicle (UAV) with parameter uncertainties and external unknown disturbances. As a stepping stone, two fixed-time extended state observers (ESOs) are proposed to estimate the external disturbances and/or the parameter uncertainties for the position and attitude subsystems, respectively. Then, the fast terminal sliding mode-based improved dynamic surface control (DSC) approaches are developed. To eliminate the problem of "explosion of complexity" inherent in backstepping method-based controllers, the finite-time command filters and an error compensation signals are used in the design of the dynamic surface controllers. Subsequently, the practically finite-time stability of the closed-loop tracking system is guaranteed by utilizing the proposed control scheme. The simulation results are obtained to demonstrate the effectiveness and fine performance of the proposed trajectory tracking control approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic surface active disturbance rejection control (ADRC) strategy to deal with trajectory tracking problems for a quadrotor unmanned aerial vehicle (UAV). Compared with backstepping control, the design process of the dynamic controller is more simple; the dynamic surface control introduces a first-order filter to obtain the derivative of the virtual control, the purpose is to avoid the virtual control derivation, and to simplify the control law of the whole system. The ADRC technique is mainly used to reject the disturbances and stabilize the quadrotor UAV system. Parametric uncertainties and external disturbances have been considered for the whole system, the control strategy that proposed in this paper has been simulated by MATLAB and the advantages and effectiveness of the control strategy that proposed in the paper are shown by comparing with the classical ADRC. [ABSTRACT FROM AUTHOR]

In this paper, a new swarm intelligent-based backstepping control scheme is proposed for quadrotor trajectory tracking and obstacle avoidance. First, the sliding mode extended state observer (SMESO) is used to estimate different disturbances, and the tracking differentiator (TD) is integrated to enhance the performance of backstepping control scheme. Then, the chaotic grey wolf optimization (CGWO) is developed with chaotic initialization and chaotic search to optimize the parameters of attitude and position controllers. Further, the virtual target guidance approach is proposed for quadrotor trajectory tracking and obstacle avoidance. Comparative simulations and Monte Carlo tests are carried out to demonstrate the effectiveness and robustness of the CGWO-based backstepping control scheme and virtual target guidance approach. [ABSTRACT FROM AUTHOR]

This paper presents a longitudinal trajectory tracking scheme with L 1 adaptive control for hypersonic reentry vehicles (HRVs). A linear time-varying (LTV) multiple input multiple output (MIMO) model, in which influences of lateral states, earth rotation, and linearization are considered as model uncertainties, is derived based on state and input errors of longitudinal model. The normalization of error model is used to reduce differences of magnitude orders in state and input matrix elements which may affect the stability of L 1 adaptive controller. In order to achieve an accurate tracking performance, a linear quadratic regulator (LQR) controller is employed as the baseline controller, augmented with an L 1 adaptive controller to attenuate the matched and unmatched uncertainties. Based on the augmented controller, the optimization process is executed with the estimate of uncertainties at the same time. The simulation results of LQR controller, L 1 augmentation controller and robust H ∞ controller show that the L 1 adaptive control method can reduce the terminal and integral of squared state errors validly. Terminal state errors in all simulation scenarios are less than 2.5m/s, 1e-3 and 10m, respectively, which reflects its effectiveness in increasing robustness of baseline controller. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid centralized control architecture for formation control of N -homogeneous mobile robots. The addressed problem is maintaining an equilateral triangular formation using three mobile robots while moving towards a desired target avoiding any collision. The proposed architecture is divided into four main subsystems; a main path-planner, a nonlinear Lyapunov-based controller, a Secure Shell (SSH) communication module and an image processing algorithm. The main path-planner subsystem itself is subdivided into three algorithms; brain-like algorithm, sub-path-planner and an information center algorithm. The brain-like algorithm is responsible for all the decision making. On the other hand, the sub-path-planner works on translating the decisions of the brain into more precise decisions to the individual robots. Meanwhile, the information center acts as the memory for the brain to access saved information previously shared between the robots. It is shown that the control algorithm allows any initial allocation of the three robots to converge to a triangle formation in an optimal manner while avoiding collisions. Finally, the potential use of this formation as a platform acting as an autonomous mobile helipad is introduced as a practical application for the proposed architecture. [ABSTRACT FROM AUTHOR]

The payload mass and the cable length are always different/uncertain for various transportation tasks and external disturbances that accompany industrial overhead crane systems. In addition, existing control methods can obtain merely asymptotic results. To solve the aforementioned problems, an accurate model-free trajectory tracking controller subject to finite time convergence for overhead crane systems is proposed based on the suitably defined non-singular terminal sliding vector. Moreover, the proposed controller is absolutely continuous, addressing the limitations and shortcomings of the traditional sliding mode control. Lyapunov techniques are used to prove that the proposed controller guarantees finite-time tracking result and the finite time T is calculated. Simulation and experimental results are included to demonstrate the robustness of the proposed controller with respect to model uncertainties, parameter variations and external disturbances. [ABSTRACT FROM AUTHOR]

Autonomous underwater vehicles (AUVs) are highly nonlinear underactuated systems with uncertain dynamics and a challenging control problem. The main focus of this paper is to present a control law that shows desirable performance in the presence of modeling uncertainties. In this study, uncertainties are considered to be bounded and the AUV mathematical model is obtained in the presence of such uncertainties. Forces and torques applied to the AUV are also designed using a nonlinear dynamic controller. Appropriate adaptive rules are also presented to overcome system uncertainties and external disturbances. The adaptive nonlinear dynamic controller is designed based on upper bounds of system uncertainties and its stability is proven using the Lyapunov theory. In this article, the performance of the proposed control algorithm for tracking reference trajectories in an obstacle-rich environment is investigated. Therefore, the control algorithm is combined with potential fields for obstacle avoidance. Obtained results show the efficiency of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fault tolerant controller based on L 1 control is developed and applied to the trajectory tracking for a quadrotor helicopter. Both multiplicative and additive actuator faults are considered. The proposed design is based on nonlinear feed-forward compensations and a typical nonlinear quadrotor model with uncertain inertial parameters and external disturbances. The L 1 adaptive control design is slightly modified to adapt with the position and the attitude error dynamics. The proposed adaptive controller yields uniformly verifiable bounds on the transient and the steady-state tracking error for any designated bounded reference trajectory. In the presence of fast adaptation, the adaptive controller compensates for actuator fault and disturbances in a particular frequency range. Finally, simulation results are included to validate the effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]

To overcome the low operation efficiency, high labour-intensiveness and high risk in the artificial live-line replacement of insulator strings, a robot for overhead transmission line maintenance was developed. In order to suppress effectively the influences of disturbance signals and uncertainties on tracking precision and stability of the robot mechanical arm motion under high voltage and strong electromagnetic interference, this paper proposed a H∞ control theory-based robust trajectory tracking control method for the robot mechanical arm. Through layering robot control architecture, a dynamic model of mechanical arm basic motion was established by the Lagrange method combined with an armature voltage equation of the joint motor, and the unified dynamic model of mechanical arm different motion was obtained. On this basis, the state-space model of mechanical arm motion error was deduced under disturbances and uncertainties, and thus an H∞ control model for mechanical arm motion was constructed. Subsequently, the H∞ controller for the mechanical arm trajectory tracking control system was solved by linear matrix inequality (LMI) based on the established model, and the asymptotic stability of the mechanical arm motion control system was verified by selecting the appropriate Lyapunov function. The proposed method for such a controller was proved to be of good versatility, strong adaptability and sound expansibility. Finally, simulation results verified the effectiveness of the H∞ controller and field operation tests further validated the engineering practicability of such a control method in macro and micro aspects. [ABSTRACT FROM AUTHOR]

Human-robot interaction is inherently available and used actively in ankle rehabilitation robots. This interaction causes disturbances to be counteracted on the rehabilitation robots in order to reduce the side effects. This paper presents a fractional order proportional-integral-derivative controller to improve the trajectory tracking ability of a developed 2-degree of freedom parallel ankle rehabilitation robot subject to external disturbances. The parameters of the controller are optimally tuned by using both the cuckoo search algorithm and the particle swarm optimization algorithm. A traditional proportional-integral-derivative controller, which is also tuned using both of the algorithms, is designed to test the performance of the fractional order proportional-integral-derivative controller. The experimental results show that the optimally tuned FOPID controller improves the tracking performance of the ankle rehabilitation robot subject to external disturbances significantly and decreases the steady-state tracking errors compared to the optimally tuned PID controller. [ABSTRACT FROM AUTHOR]

This research presents a nonlinear adaptive trajectory tracking controller for quadrotor unmanned aircraft. When external disturbances and model uncertainty are present, traditional control algorithms may not be able to provide enough control accuracy. An adaptive nonlinear controller is a remedy for this unsatisfactory performance caused by disturbances and parameter fluctuations. This work proposes a nonlinear adaptive controller based on the Lyapunov method. The technique used here for achieving the adaptive nonlinear control is to adaptively determine the optimal controller gain values. To fine-tune the controller gains, the proposed method suggests the use of either trial and error or the adaptive particle swarm optimization. Simulations with the MATLAB/Simulink software show that the proposed method works superior as compared to traditional control algorithms such as proportional–integral–derivative (PID) and sliding mode controllers even under the influence of parameter variations, external disturbances and communication noises. [ABSTRACT FROM AUTHOR]

This study investigates the design of a trajectory tracking constraint control method for hovercraft non-affine formulations via neural network approximation. The tracking scheme comprises an outer closed-loop of attitude and an inner closed-loop of velocity (double-loop). First, a performance function is devised to constrain the attitude errors and then a transformed error function is introduced to simplify it into an equivalent unconstrained control system. Next, an improved asymmetric integral barrier Lyapunov function is designed to address asymmetric velocity constraint problems, which can guarantee the safe turning motion or performance required at high speed. Furthermore, neural networks are employed to estimate the unknown terms of each subsystem, which solve system uncertainties and non-affine dynamics problems. The double closed-loop control system is ultimately uniformly bounded by utilizing the Lyapunov stability principle. Finally, simulation results are presented to verify the tracking performance and effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

A quadrotor is a kind of vertical takeoff and landing unmanned aerial rotorcraft which has been attracting wide interest around the world. However, small-scale quadrotors usually suffer from modeling error and external disturbance which are severe challenges for the control system design. To this end, the disturbance-observer-based (DOB) control strategy is applied to reject the performance degradation caused by the above negative factors. To further improve the trajectory tracking precision for an indoor quadrotor suffering from modeling error and external disturbance, a linear dual DOB (LDDOB) trajectory tracking control scheme is developed in this paper. Considering the practical implementation in engineering, the LDDOB position control approach is developed based on the linear quadrotor model. In addition, regarding to the non-minimum phase characteristic of the translational motion model, a modified version of a PID position controller is utilized to attenuate the undershoot of the closed-loop system in the initial response. Extensive numerical simulations show the effectiveness of the proposed trajectory tracking control scheme. [ABSTRACT FROM AUTHOR]

An iterative learning control based on Automatic Train Operation is proposed for repetitively running train to deal with trajectory tracking problem under iteration-varying operation condition and certain speed constrains. Iteration-varying operation condition considered in this paper focuses on the air resistance coefficient of the train, which may be completely different at any two consecutive operation processes due to different weather conditions. To eliminate the influence of the resistance coefficient caused by the different weather conditions, data measured by the temperature sensors is used. In order to meet the speed constrains, the Barrier Composite Energy Function scheme is used to guarantee that the speed constraints are not violated. The effectiveness of the proposed method is verified by theoretical analysis and numerical simulation. [ABSTRACT FROM PUBLISHER]

This paper presents the development, stability analysis and validation of an intelligent proportional integral (iPI) controller for the tip position control of a flexible-link manipulator. A stability analysis included in the paper shows that the iPI controller is equivalent to the proportional integral-squared controller. In order to verify the performance of the iPI controller, several experiments were conducted. In these experiments, step and square-wave inputs and two other trajectories were applied to the flexible-link manipulator. Also, the performance of the iPI controller was compared with those of classical PI and PID controllers. The results obtained from the comparison experiments showed that, the PI and PID controllers produced better performance in step and square-wave inputs, but the iPI controller yielded better trajectory tracking performance. All of the controllers were tested for disturbance and noise rejection capability. The iPI controller eliminated disturbance and noise better than the classical controllers. Considering all of the results, the iPI controller has great potential in trajectory tracking control of flexible-link manipulators. [ABSTRACT FROM AUTHOR]

A 3-DOF (degree of freedom) planar motion motor using multiple linear motors as actuators is widely implemented in ultra-precision positioning systems. It is a multi-input multi-output (MIMO) system and requires an accurate decoupled model for controller design. In practice, there are modelling errors between the nominal model and the actual model, such as the force ripple, inhomogeneous air-gap thickness, measurement noise and uncertain disturbances. Due to the modelling errors, this MIMO system cannot be decoupled and the desired tracking performance specifications will not be achieved. In order to improve the servo performance of the planar motor with uncertainties, a non-linear composite controller consisting of u1 and u2 terms is proposed. u1 is designed to compensate for the modelling errors; therefore the coupling effects between multi-degrees of freedom are reduced and the robustness is improved. In order to reduce the large servo error amplitudes, which are caused by the low-frequency disturbances and high-frequency noise, an amplitude-based variable-gain function is applied in u2; thus the control action benefits from this operation by suppressing the low-frequency contribution and no extra control effect, to avoid the high-frequency noise. The convergence and stability of the control law are guaranteed by Lyapunov stability theory. The trajectory tracking experimental results show that the proposed control method has superior tracking performance and positioning ability compared with the well-known inverse dynamics controller. This indicates that the non-linear composite controller is an attractive approach to improve the servo performance of a system with uncertainties. [ABSTRACT FROM AUTHOR]