Control Approach For Trajectory Tracking Research Articles

A Walking Trajectory Tracking Control Based on Uncertainties Estimation for a Drilling Robot for Rockburst Prevention

A walking trajectory tracking control approach for a walking electrohydraulic control system is developed to reduce the walking trajectory tracking deviation and enhance robustness. The model uncertainties are estimated by a designed state observer. A saturation function is used to attenuate sliding mode chattering in the designed sliding mode controller. Additionally, a walking trajectory tracking control strategy is proposed to improve the walking trajectory tracking performance in terms of response time, tracking precision, and robustness, including walking longitudinal and lateral trajectory tracking controllers. Finally, simulation and experimental results are employed to verify the trajectory tracking performance and observability of the model uncertainties. The results testify that the proposed approach is better than other comparative methods, and the longitudinal and lateral trajectory tracking average absolute errors are controlled in 10.23 mm and 22.34 mm, respectively, thereby improving the walking trajectory tracking performance of the walking electrohydraulic control system for the coal mine drilling robot for rockburst prevention.

A Gaussian-Process-Based Model Predictive Control Approach for Trajectory Tracking and Obstacle Avoidance in Autonomous Underwater Vehicles

To achieve the efficient and precise control of autonomous underwater vehicles (AUVs) in dynamic ocean environments, this paper proposes an innovative Gaussian-Process-based Model Predictive Control (GP-MPC) method. This method combines the advantages of Gaussian process regression in modeling uncertainties in nonlinear systems, and MPC’s constraint optimization and real-time control abilities. To validate the effectiveness of the proposed GP-MPC method, its performance is first evaluated for trajectory tracking control tasks through numerical simulations based on a 6-degrees-of-freedom, fully actuated, AUV dynamics model. Subsequently, for 3D scenarios involving static and dynamic obstacles, an AUV horizontal plane decoupled motion model is constructed to verify the method’s obstacle avoidance capability. Extensive simulation studies demonstrate that the proposed GP-MPC method can effectively manage the nonlinear motion constraints faced by AUVs, significantly enhancing their intelligent obstacle avoidance performance in complex dynamic environments. By effectively handling model uncertainties and satisfying motion constraints, the GP-MPC method provides an innovative and efficient solution for the design of AUV control systems, substantially improving the control performance of AUVs.

Barrier Function-Based Integral Sliding Mode Controller Design for a Single-Link Rotary Flexible Joint Robot

Abstract This paper proposes and evaluates a novel control approach for trajectory tracking, stability enhancement, and vibration reduction of a flexible joint robot (FJR). The FJR is a 2-degree-of-freedom underactuated nonlinear system that is challenging to control due to vibration, underactuation, uncertainties, and external disturbances. The control objectives are high trajectory tracking performance together with suppressing vibration. The proposed control approach uses integral sliding mode control (ISMC) combined with a barrier function based on back-stepping. This ensures robust and smooth performance by eliminating the reaching phase where sliding mode control (SMC) is typically not robust. Robustness is thus guaranteed from the start. The FJR is modeled as a 4th-order system using Lagrangian mechanics and decomposed into two 2nd-order subsystems for control design. Sliding variables are defined for each subsystem. Using these variables, the proposed control achieves robust trajectory tracking, stability, and vibration reduction. Numerical simulations in MATLAB validate the superior performance of the proposed ISMC-barrier function control compared to conventional ISMC for the FJR. This novel control approach addresses the challenges of controlling this FJR.

Nonsingular Hierarchical Approach for Trajectory Tracking Control of Miniature Helicopter with Model Uncertainties

Based on hierarchical inner-outer loop strategy, the tracking control for the helicopter system could be designed individually for the position loop and for the attitude loop, thus simplifying the underactuated control problem. However, due to the nonlinear coupling between the position dynamics and rotation dynamics, the performance of the position control is affected by attitude errors, especially when the attitude control can not tracks the reference attitude instantaneously. This work provides a hierarchical trajectory tracking control design for the helicopter with model uncertainties, ensuring the stability of the overall system considering the perturbation caused by attitude tracking errors and the nonlinear coupling. The attitude of the helicopter is descried by unit-quaternion, for which anti-unwinding control design is presented. Besides, the criteria for avoidance of singularity in generation of the reference attitude is derived. Simulation results demonstrate the effectiveness of the design.

A novel approach for trajectory tracking control of an under-actuated quad-rotor UAV

A novel Udwadia-Kalaba approach for the trajectory tracking control of an under-actuated quad-rotor unmanned aerial vehicle (UAV) is presented. Compared to standard control approaches, the desired trajectories are treated as constraints called trajectory tracking constraints in this approach. Neither making any approximations or linearization of the nonlinear system nor imposing any a priori structure on the nature of the nonlinear controller, this methodology provides closedform nonlinear control. The control inputs satisfying the desired trajectory requirements can be obtained explicitly in compact closed form by solving Udwadia-Kalaba equation. Nonlinear dynamics modeling of a quad-rotor UAV is processed and a desired trajectory is given in this paper to illustrate this approach. The theoretical analysis and MATLAB simulation results verify the validity and efficiency of this approach. The real-time servo constraint forces are obtained conveniently and the quad-rotor UAV's movement meets the designed trajectory precisely.

Intelligent Trajectory Tracking Linear Active Disturbance Rejection Control of a Powered Parafoil Based on Twin Delayed Deep Deterministic Policy Gradient Algorithm Optimization

Powered parafoils, known for their impressive load-bearing capacity and extended endurance, have garnered significant interest. However, the parafoil system is a highly complex nonlinear system. It primarily relies on the steering gear to change flight direction and utilizes a thrust motor for climbing. However, achieving precise trajectory tracking control presents a challenge due to the interdependence of direction and altitude control. Furthermore, underactuation and wind disturbances bring additional difficulties for trajectory tracking control. Consequently, realizing trajectory tracking control for powered parafoils holds immense significance. In this paper, we propose a trajectory tracking method based on Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm-optimized Linear Active Disturbance Rejection Control (LADRC). Our method addresses the underactuation issue by incorporating a guiding law while utilizing two LADRC methods to achieve decoupling and compensate for disturbances. Moreover, we employ the TD3 algorithm to dynamically adjust controller parameters, thus enhancing the controller performance. The simulation results demonstrate the effectiveness of our proposed method as a trajectory tracking control approach. Additionally, since the control process is not reliant on system-specific models, our method can also provide guidance for trajectory tracking control in other aircraft.

A Robust Region Control Approach for Simultaneous Trajectory Tracking and Compliant Physical Human–Robot Interaction

A Robust Region Control Approach for Simultaneous Trajectory Tracking and Compliant Physical Human–Robot Interaction

A Self-Adaptive Double Q-Backstepping Trajectory Tracking Control Approach Based on Reinforcement Learning for Mobile Robots

When a mobile robot inspects tasks with complex requirements indoors, the traditional backstepping method cannot guarantee the accuracy of the trajectory, leading to problems such as the instrument not being inside the image and focus failure when the robot grabs the image with high zoom. In order to solve this problem, this paper proposes an adaptive backstepping method based on double Q-learning for tracking and controlling the trajectory of mobile robots. We design the incremental model-free algorithm of Double-Q learning, which can quickly learn to rectify the trajectory tracking controller gain online. For the controller gain rectification problem in non-uniform state space exploration, we propose an incremental active learning exploration algorithm that incorporates memory playback as well as experience playback mechanisms to achieve online fast learning and controller gain rectification for agents. To verify the feasibility of the algorithm, we perform algorithm verification on different types of trajectories in Gazebo and physical platforms. The results show that the adaptive trajectory tracking control algorithm can be used to rectify the mobile robot trajectory tracking controller’s gain. Compared with the Backstepping-Fractional-Older PID controller and Fuzzy-Backstepping controller, Double Q-backstepping has better robustness, generalization, real-time, and stronger anti-disturbance capability.

Fixed time sliding mode control for disturbed robotic manipulator

In this study, a new fixed-time sliding mode control approach for trajectory tracking control of robotic manipulator systems is devised, which provides fixed-time convergence, robust stabilization, and high precision. A novel fixed-time non-singular fast terminal sliding mode surface (FNFTSMS) with fixed-time convergence is provided, and with settling time independent of the initial condition of the system and can be pre-determined using design parameters. Furthermore, using adaptive disturbance observer and the suggested FNFTSMS, a new composite robust control approach is developed. The adaptive disturbance observer is intended to boost control performance and compensate for unpredictably occurring disturbances. The Lyapunov stability theory is used to establish the fixed-time stability of sliding surface and system states under the suggested composite control strategy. Finally, numerical simulations are carried out using PUMA560 robot in order to demonstrate the effectiveness and efficacy of the proposed control method in terms of accuracy of tracking, fast response, and convergent speed.

A State Observer-Based Fractional-Order Approach for Trajectory Tracking and Attitude Control of A Quadrotor

With the expanding utility base of unmanned aerial vehicles (UAVs), there comes a strong need for dedicated research towards effective control strategies for these aircraft. This paper presents a feedback control scheme for the trajectory tracking and flight control problem for quadrotor-type UAVs. In particular, a robust fractional-order sliding mode control (FOSMC) scheme based on a state observer approach, consisting of position tracking and an attitude control strategy, is proposed. The basic idea behind choosing the state observer technique is to prevent the chattering phenomenon in this highly non-linear and under-actuated dynamic structure, and preserve the robustness and finite time reachability properties of Sliding Mode controllers. The stability of the proposed control law is proved using Lyapunov’s theorem. Furthermore, a detailed performance analysis of the proposed method is presented in comparison to the existing control algorithms from the recent literature. The obtained results are found promising.

A novel trajectory tracking control approach for uncertain 6-DOF manipulators based on fuzzy sliding mode of radial basis function neural network

Due to the influence of uncertain external disturbance and model error, the trajectory tracking of manipulators has some problems such as inaccuracy, low speed and severe chattering. To solve the problems mentioned, a sliding mode control method combined fuzzy controller and Radial Basis Function Neural Network (RBFNN) was proposed. The RBFNN was used to approximate the equivalent system model of manipulators, and the weights of their hidden layers were updated adaptively online. The robust item with the form of sliding mode had been set to compensate the uncertain external disturbances or the approximation errors of the RBFNN. A fuzzy controller was used to adjust the switching gain online adaptively and to solve the chattering of the sliding mode control. The stability and finite time convergence of the closed-loop system had been analyzed by using Lyapunov method. Finally, simulation experiments about trajectory tracking were implemented by MATLAB/SIMULINK, which shows that the proposed method can improve the position-tracking accuracy by more than 40%, the speed-tracking accuracy by more than 70%, and the cumulative-error accuracy by more than 40% compared with the comparison method. Moreover, there is no chattering. The proposed method has been proved to be efficient.

Date-Driven Tracking Control via Fuzzy-State Observer for AUV under Uncertain Disturbance and Time-Delay

This paper focuses on developing a data-driven trajectory tracking control approach for autonomous underwater vehicles (AUV) under uncertain external disturbance and time-delay. A novel model-free adaptive predictive control (MFAPC) approach based on a fuzzy state observer (FSO) was designed to achieve high precision. Concretely, the mathematical model of AUV motion was analyzed, and simplified via model decoupling, thus providing the model basis with an explicit physical explanation for the controller. Second, the MFAPC scheme for a multiple-inputs and multiple-outputs (MIMO) discrete time system was derived, that estimates system external disturbance. The controller can online estimate and predictive time-varying parameter pseudo-Jacobian matrix (PJM) to establish equivalent state space data-model for AUV motion system. Third, the Takagi–Sugeno (T–S) fuzzy model based state observer was designed to combine with the MFAPC scheme for the first time, which was used to online decline the state error generated by system uncertain time-delay. In addition, the stability of the proposed control scheme was analyzed. Finally, two trajectory tracking scenarios were designed to verify the effectiveness and robustness of the proposed FMFAPC scheme, and the simulations are implemented using the realistic parameters of T-SEA AUV.

Human-Machine Cooperative Trajectory Planning and Tracking for Safe Automated Driving

This paper investigates a human-machine cooperative trajectory planning and tracking control approach for automated vehicles. The proposed method is developed based on a novel algorithm of cooperative human-machine rapidly-exploring random (HM-RRT) for path planning, together with the risk assessment of driver behavior. First, the driver’s behaviour is assessed according to the information of the predicted vehicle trajectory, the identified safe driving area and the driving risks evaluated in both lateral and longitudinal directions. Based on the driver’s expected driving task, when driving risks are identified by real-time assessment, then the human-machine cooperation is activated during trajectory planning. By HM-RRT, the newly developed safety assurance mechanism for path planning, the cooperative trajectory is then generated, which incorporates the driver’s desire and actions and automation’s corrective actions, to ensure the safety, stability and smoothness of the human-vehicle system. The simulation and experimental results show that the proposed HM-RRT algorithm can effectively improve the convergence rate and reduce the computation load, comparing to the conventional method. Beyond this, the proposed human-machine cooperation approach is able to simultaneously ensure the safety, stability and smoothness of the vehicle and largely reduce human-machine conflicts in real-time applications, demonstrating its feasibility and effectiveness.

Trajectory Tracking Control of Rowing Pectoral Fin-Actuated Robotic Fish

Robotic fish has received increasing attention in the last few decades, as they hold strong promise in a myriad of applications. Efficient and precise control of these robots, particularly accurate trajectory control, has become essential in many of these applications. This article proposes a dual-loop backstepping-based trajectory tracking control approach for a robotic fish actuated by rowing pectoral fins. While rowing pectoral fin-based locomotion is important for maneuvering, the range constraints of fin movement pose significant challenges in the control of robotic fish, including potentially preventing the robot from generating the thrust needed to maneuver in a desired direction. To overcome these challenges, we propose a dual-loop controller, designed based on an averaged dynamic model of the robot. In particular, an outer-loop backstepping-based controller finds the needed force and moment inputs for the robot to track the desired trajectory, while the inner loop determines the optimal fin-beat parameters such that the resulting fin-generated forces and moment are close to their desired values. Experimental results are presented to show the efficacy of the proposed control scheme, where the robot is commanded to track a trajectory with variable linear and angular velocities. Comparing to a well-tuned proportional–integral–derivative controller, the proposed control scheme shows a distinct advantage in tracking desired orientations in addition to tracking desired positions.

Capture and detumble of a non-cooperative target without a specific gripping point by a dual-arm space robot

This paper focuses on the control strategy of a dual-arm space robot to capture and detumble a non-cooperative satellite without a specific gripping point. First, an elastic hemispherical claw was designed to reduce the collision impacts and adjust the capture position, and its contact dynamics and capture ability were verified by ground experiments. Analysis of the position constraints led to the proposal of a compliant control scheme to achieve stable capture without a contact-force sensor. Subsequently, a modified adaptive sliding mode based prescribed trajectory tracking control (PTTC) and null space intersection approach was proposed to achieve target detumbling under the actuator constraints. The control system stability was analyzed via the Lyapunov method. Finally, numerical simulations were employed to validate the effectiveness and correctness of the strategy. Results showed that, a large inertia target could be steadily captured and detumbled within 80 s.

Energy Saving Control Approach for Trajectory Tracking of Autonomous Mobile Robots

This research presents an adaptive energy-saving H2 closed-form control approach to solve the nonlinear trajectory tracking problem of autonomous mobile robots (AMRs). The main contributions of this proposed design are as follows: closed-form approach, simple structure of the control law, easy implementation, and energy savings through trajectory tracking design of the controlled AMRs. It is difficult to mathematically obtained this adaptive H2 closed-form solution of AMRs. Therefore, through a series of mathematical analyses of the trajectory tracking error dynamics of the controlled AMRs, the trajectory tracking problem of AMRs can be transformed directly into a solvable problem, and an adaptive nonlinear optimal controller, which has an extremely simple form and energy-saving properties, can be found. Finally, two test trajectories, namely circular and S-shaped reference trajectories, are adopted to verify the control performance of the proposed adaptive H2 closed-form control approach with respect to an investigated H2 closed-form control design.

Improved Performance in Quadrotor Trajectory Tracking Using MIMO PIλ-D Control

This paper aims to develop a fractional control approach for quadrotor trajectory tracking. A fractional-order integrator (PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> ) with a feedback derivative scheme is designed to control each state of the MIMO system. The designed feedback controller stabilizes the initially unstable decoupled states and widens the stability, while PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> provides precise trajectory tracking capabilities. After a successful simulation study, the new PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> -D controller is implemented in the hardware environment. The various performance and load disturbance analyses reveal the effectiveness of the proposed scheme compared with the classical PD/PID controllers. The real-time study also shows that this scheme is a simple yet robust solution.

Robust adaptive fractional-order nonsingular terminal sliding mode stabilization of three-axis gimbal platforms

This paper proposes an adaptive fractional-order nonsingular terminal sliding mode (AFNTSMC) control scheme combined with the independent joint control approach for trajectory tracking of three-axis gimbal platforms (GPs) mounted on a moving vehicle subjected to external disturbances. To achieve accurate images taken by the camera mounted on the GP, the motions and vibrations of the vehicle must be isolated from the camera. Thus, precise mathematical modeling of a three-axis GP with considering the external disturbances is studied, such that the GP tracks the target accurately and holds the line of sight stationary. Various tests with different vehicle conditions are performed to collect the movement data to be considered as the desired input for the GP. Thanks to the utilization of AFNTSMC, fast convergence together with simultaneous accurate trajectory tracking and strong robustness can be ensured. Corresponding comparative simulation results validate the effectiveness of the theoretical design results and superiorities of the proposed method over the existing methods.

A hierarchical constraint approach for dynamic modeling and trajectory tracking control of a mobile robot

The dynamic modeling and trajectory tracking control of a mobile robot is handled by a hierarchical constraint approach in this study. When the wheeled mobile robot with complex generalized coordinates has structural constraints and motion constraints, the number of constraints is large and the properties of them are different. Therefore, it is difficult to get the dynamic model and trajectory tracking control force of the wheeled mobile robot at the same time. To solve the aforementioned problem, a creative hierarchical constraint approach based on the Udwadia–Kalaba theory is proposed. In this approach, constraints are classified into two levels, structural constraints are the first level and motion constraints are the second level. In the second level constraint, arbitrary initial conditions may cause the trajectory to diverge. Thus, we propose the asymptotic convergence criterion to deal with it. Then, the analytical dynamic equation and trajectory tracking control force of the wheeled mobile robot can be obtained simultaneously. To verify the effectiveness and accuracy of this methodology, a numerical simulation of a three-wheeled mobile robot is carried out.

Observer-based adaptive neural sliding mode trajectory tracking control for remotely operated vehicles with thruster constraints

For a class of remotely operated vehicle (ROV) systems with thruster constraints, immeasurable states, and unknown nonlinearities, the trajectory tracking control problem was discussed in this paper. The unknown nonlinear functions were approximated by radial basis function (RBF) neural networks. An adaptive state observer based on neural networks was designed and the immeasurable states were estimated. Considering the problem of thruster saturation constraints, an auxiliary system for saturation compensation was designed and a saturation factor was constructed by the auxiliary system state. By applying the backstepping design method, an adaptive neural sliding mode trajectory tracking controller was developed, in which the saturation factor is contained in adaptive laws. It was proved that the uniformly ultimately bounded (UUB) of trajectory tracking errors can be obtained. Finally, the effectiveness of the proposed trajectory tracking control approach was checked by simulations.