PD-Based Trajectory Tracking Control for Robot Manipulators

1993 ◽  
Vol 115 (3) ◽  
pp. 566-569 ◽  
Author(s):  
Cao Bailin ◽  
Chen Huitang
Keyword(s):  
Trajectory Tracking ◽  
Sliding Mode ◽  
Tracking System ◽  
Coefficient Matrix ◽  
Trajectory Tracking Control ◽  
Control Laws ◽  
Globally Asymptotically Stable ◽  
Control Scheme ◽  
Frictional Forces ◽  
Globally Stable

In this paper, it is proved that a trajectory tracking system of a manipulator is globally stable if the system is controlled under the decentralized PD control law plus a sliding term with a constant coefficient, and the norm of the coefficient matrix of its differential term is no less than that of the centripetal and Coriolis’ force term corresponding to the desired angular velocity, i.e., ∥Kd∥ ≥ ∥C(q, q˙d)∥. Condition ∥Kd∥ ≥ ∥C(q, q˙d)∥ implies that Kd increases only with q˙d instead of q˙. A type of globally asymptotically stable adaptive sliding mode PD-based control scheme is proposed, and the proof of stability of the system is also given. It is easy to implement in real-time compared with other adaptive control laws as no estimation of gravitational and frictional forces is necessary.

Modeling and trajectory tracking control of a two-wheeled mobile robot: Gibbs–Appell and prediction-based approaches

Robotica ◽  
2018 ◽  
Vol 36 (10) ◽  
pp. 1551-1570 ◽  
Author(s):  
Hossein Mirzaeinejad ◽  
Ali Mohammad Shafei
Keyword(s):  
Trajectory Tracking ◽  
Dynamic Models ◽  
Sliding Mode ◽  
Tracking Accuracy ◽  
Wheeled Mobile Robots ◽  
Tracking Errors ◽  
Trajectory Tracking Control ◽  
Control Laws ◽  
Control Approach ◽  
Prediction Time

SUMMARYThis study deals with the problem of trajectory tracking of wheeled mobile robots (WMR's) under non-holonomic constraints and in the presence of model uncertainties. To solve this problem, the kinematic and dynamic models of a WMR are first derived by applying the recursive Gibbs–Appell method. Then, new kinematics- and dynamics-based multivariable controllers are analytically developed by using the predictive control approach. The control laws are optimally derived by minimizing a pointwise quadratic cost function for the predicted tracking errors of the WMR. The main feature of the obtained closed-form control laws is that online optimization is not needed for their implementation. The prediction time, as a free parameter in the control laws, makes it possible to achieve a compromise between tracking accuracy and implementable control inputs. Finally, the performance of the proposed controller is compared with that of a sliding mode controller, reported in the literature, through simulations of some trajectory tracking maneuvers.

Full-state nonlinear trajectory tracking control of underactuated surface vessels

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1286-1296 ◽  
Author(s):  
Karl L Fetzer ◽  
Sergey Nersesov ◽  
Hashem Ashrafiuon
Keyword(s):  
Trajectory Tracking ◽  
Sliding Mode ◽  
Trajectory Tracking Control ◽  
Control Laws ◽  
Control Approach ◽  
Surface Vessels ◽  
Modeling Uncertainties ◽  
Underactuated Surface Vessels ◽  
System States ◽  
Error Dynamics

This article presents the development, implementation, and comparison of two trajectory tracking nonlinear controllers for underactuated surface vessels. A control approach capable of stabilizing all the states of any planar vehicle is specifically adapted to surface vessels. The method relies on transformation of the six position and velocity state dynamics into a four-state error dynamics. The backstepping and sliding mode control laws are then derived for stabilization of the error dynamics and proven to stabilize all system states. Simulations are presented in the absence and presence of modeling uncertainties and unknown disturbances. An experimental setup is then described, followed by successful experimental implementation and comparison of the two controllers.

scholarly journals Fixed-Time Trajectory Tracking Control of Autonomous Surface Vehicle with Model Uncertainties and Disturbances

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jiawen Cui ◽  
Haibin Sun
Keyword(s):  
Trajectory Tracking ◽  
Tracking Control ◽  
Sliding Mode ◽  
Fixed Time ◽  
Convergence Time ◽  
Model Uncertainties ◽  
External Disturbances ◽  
Trajectory Tracking Control ◽  
Integral Sliding Mode ◽  
Control Scheme

The issue of fixed-time trajectory tracking control for the autonomous surface vehicles (ASVs) system with model uncertainties and external disturbances is investigated in this paper. Particularly, convergence time does not depend on initial conditions. The major contributions include the following: (1) An integral sliding mode controller (ISMC) via integral sliding mode surface is first proposed, which can ensure that the system states can follow the desired trajectory within a fixed time. (2) Unknown external disturbances are absolutely estimated by means of designing a fixed-time disturbance observer (FTDO). By combining the FTDO and ISMC techniques, a new control scheme (FTDO-ISMC) is developed, which can achieve both disturbance compensation and chattering-free condition. (3) Aiming at reconstructing the unknown nonlinear dynamics and external disturbances, a fixed-time unknown observer (FTUO) is proposed, thus providing the FTUO-ISMC scheme that finally achieves trajectory tracking of ASVs with unknown parameters. Finally, simulation tests and detailed comparisons indicate the effectiveness of the proposed control scheme.

scholarly journals Design and Implementation of Integral Backstepping Sliding Mode Control for Quadrotor Trajectory Tracking

Processes ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1951
Author(s):  
Shun-Hung Tsai ◽  
Yi-Ping Chang ◽  
Hung-Yi Lin ◽  
Luh-Maan Chang
Keyword(s):  
Trajectory Tracking ◽  
Sliding Mode ◽  
Unmanned Aircraft ◽  
Trajectory Tracking Control ◽  
Attitude Tracking ◽  
Control Scheme ◽  
Tracking Controller ◽  
Backstepping Sliding Mode Control ◽  
Trajectory Tracking Controller ◽  
The Stability

A robust trajectory tracking control scheme for quadrotor unmanned aircraft vehicles under uncertainties is proposed herein. A tracking controller combined with the sliding mode and integral backstepping is performed for position and attitude tracking. The stability of the trajectory tracking controller of the quadrotor is investigated via Lyapunov stability analysis. By incorporating force and torque disturbances into numerical simulations, the results demonstrate the effectiveness of the proposed quadrotor trajectory controller. Finally, the experiments validate the feasibility of the proposed controller.

scholarly journals Trajectory tracking control of a quadrotor UAV based on sliding mode active disturbance rejection control

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Yong Zhang ◽  
Zengqiang Chen ◽  
Mingwei Sun ◽  
Xinghui Zhang
Keyword(s):  
Trajectory Tracking ◽  
Disturbance Rejection ◽  
Tracking Control ◽  
Sliding Mode ◽  
Reference Trajectory ◽  
Active Disturbance Rejection Control ◽  
Trajectory Tracking Control ◽  
Active Disturbance Rejection ◽  
Disturbance Rejection Control ◽  
Control Scheme

This paper proposes a sliding mode active disturbance rejection control scheme to deal with trajectory tracking control problems for the quadrotor unmanned aerial vehicle (UAV). Firstly, the differential signal of the reference trajectory can be obtained directly by using the tracking differentiator (TD), then the design processes of the controller can be simplified. Secondly, the estimated values of the UAV's velocities, angular velocities, total disturbance can be acquired by using extended state observer (ESO), and the total disturbance of the system can be compensated in the controller in real time, then the robustness and anti-interference capability of the system can be improved. Finally, the sliding mode controller based on TD and ESO is designed, the stability of the closed-loop system is proved by Lyapunov method. Simulation results show that the control scheme proposed in this paper can make the quadrotor track the desired trajectory quickly and accurately.

scholarly journals Robust trajectory tracking control for an underactuated autonomous underwater vehicle based on bioinspired neurodynamics

2018 ◽  
Vol 15 (5) ◽  
pp. 172988141880674 ◽  
Author(s):  
Yunbiao Jiang ◽  
Chen Guo ◽  
Haomiao Yu
Keyword(s):  
Sliding Mode Control ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Autonomous Underwater Vehicle ◽  
Sliding Mode ◽  
Underwater Vehicle ◽  
External Disturbances ◽  
Trajectory Tracking Control ◽  
Control Laws ◽  
Parameter Perturbations

This article investigates the three-dimensional trajectory tracking control problem for an underactuated autonomous underwater vehicle in the presence of parameter perturbations and external disturbances. An adaptive robust controller is proposed based on the velocity control strategy and adaptive integral sliding mode control algorithm. First, the desired velocities are developed using coordinate transformation and the backstepping method, which is the necessary velocities for autonomous underwater vehicle to track the time-varying desired trajectory. The bioinspired neurodynamics is used to smooth the desired velocities, which effectively avoids the jump problem of the velocity and simplifies the derivative calculation. Then, the dynamic control laws are designed based on the adaptive integral sliding mode control to drive the underactuated autonomous underwater vehicle to sail at the desired velocities. At the same time, the auxiliary control laws and the adaptive laws are introduced to eliminate the influence of parameter perturbations and external disturbances, respectively. The stability of the control system is guaranteed by the Lyapunov theorem, which shows that the system is asymptotically stable and all tracking errors are asymptotically convergent. At the end, numerical simulations are carried out to demonstrate the effectiveness and robustness of the proposed controller.

A Study of the Ball-and-Plate System Driven by Pneumatic Direct Cylinders

2013 ◽  
Vol 310 ◽  
pp. 294-303
Author(s):  
Wei Zhao
Keyword(s):  
Trajectory Tracking ◽  
Feedback Loop ◽  
Sliding Mode ◽  
Tracking System ◽  
Fast Response ◽  
Pneumatic Actuators ◽  
Loop Control ◽  
Control Scheme ◽  
Hardware In Loop ◽  
Plate System

The ball-and-plate system actuated by pneumatic direct cylinders is a typical nonlinear control system, which can be used to display the performance of pneumatic components and offer a test platform for the study of control theory. A control scheme of double-feedback-loop structure is utilized in this ball and plate system. A fuzzy-sliding mode controller is proposed according to the robust and fast response requirements of ball-and-plate pneumatic driven subsystem in the inner loop. A hardware-in-loop simulation system is established to test the trajectory tracking system. The experiment results show that the fuzzy-sliding model controller suits the robust and fast response requirements of pneumatic actuators. The trajectory tracking curves shows that the double-feedback-loop control scheme is suitable for the pneumatic ball-and-plate system.

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