Lyapunov-Based Formation Control of Underwater Robots

Robotica ◽  
2019 ◽  
Vol 38 (6) ◽  
pp. 1105-1122 ◽  
Author(s):  
Ali Keymasi Khalaji ◽  
Rasoul Zahedifar
Keyword(s):  
Feedback Linearization ◽  
Formation Control ◽  
Control Algorithm ◽  
Kinematic Model ◽  
Lyapunov Theory ◽  
Control Law ◽  
Underwater Robots ◽  
Oceanographic Research ◽  
Inspection And Maintenance ◽  
Reliability And Robustness

SUMMARYToday, automatic diving robots are used for research, inspection, and maintenance, extensively. Control of autonomous underwater robots (AUVs) is challenging due to their nonlinear dynamics, uncertain models, and the system underactuation. Data collection using underwater robots is increasing within the oceanographic research community. Also, the ability to navigate and cooperate in a group of robots has many advantages compared with individual navigations. Among them, the effectiveness of using resources, the possibility of robots’ collaboration, increasing reliability, and robustness to defects can be pointed out. In this paper, the formation control of underwater robots has been studied. First, the kinematic model of the AUV is presented. Next, a novel Lyapunov-based tracking control algorithm is investigated for the leader robot. Subsequently, a control law is designed using Lyapunov theory and feedback linearization techniques to navigate a group of follower robots in a desired formation associated with the leader and follow it simultaneously. In the obtained results for different reference paths and various formations, the effectiveness of the proposed algorithm is represented.

Stabilization of the Ship Motion by Restricted Control

2020 ◽  
Vol 28 (4) ◽  
pp. 106-123
Author(s):  
G.M. Dovgobrod ◽  
Keyword(s):  
Feedback Linearization ◽  
Control Algorithm ◽  
Linearization Method ◽  
Ship Motion ◽  
Control Law ◽  
Motion Model ◽  
Lateral Deviation ◽  
Bounded Curvature ◽  
Trajectory Attractor ◽  
Singularity Point

. The article presents an algorithm for controlling the motion of an insufficiently controlled ship along a trajectory with a continuous bounded curvature, based on the feedback linearization method. The algorithm allows restricting the control signal, while the state vector of the ship motion model does not approach the singularity point of the control law. The control algorithm returns the ship to the specified trajectory-attractor at any lateral deviation of the ship from the specified trajectory.

scholarly journals Biologically-Inspired Learning and Adaptation of Self-Evolving Control for Networked Mobile Robots

2019 ◽  
Vol 9 (5) ◽  
pp. 1034 ◽  
Author(s):  
Sendren Sheng-Dong Xu ◽  
Hsu-Chih Huang ◽  
Tai-Chun Chiu ◽  
Shao-Kang Lin
Keyword(s):  
Mobile Robots ◽  
Formation Control ◽  
Kinematic Model ◽  
Control Law ◽  
Biologically Inspired ◽  
Modified Genetic Algorithm ◽  
Robot Systems ◽  
Learning And Adaptation ◽  
Self Learning ◽  
Adaptation Method

This paper presents a biologically-inspired learning and adaptation method for self-evolving control of networked mobile robots. A Kalman filter (KF) algorithm is employed to develop a self-learning RBFNN (Radial Basis Function Neural Network), called the KF-RBFNN. The structure of the KF-RBFNN is optimally initialized by means of a modified genetic algorithm (GA) in which a Lévy flight strategy is applied. By using the derived mathematical kinematic model of the mobile robots, the proposed GA-KF-RBFNN is utilized to design a self-evolving motion control law. The control parameters of the mobile robots are self-learned and adapted via the proposed GA-KF-RBFNN. This approach is extended to address the formation control problem of networked mobile robots by using a broadcast leader-follower control strategy. The proposed pragmatic approach circumvents the communication delay problem found in traditional networked mobile robot systems where consensus graph theory and directed topology are applied. The simulation results and numerical analysis are provided to demonstrate the merits and effectiveness of the developed GA-KF-RBFNN to achieve self-evolving formation control of networked mobile robots.

scholarly journals Leader–follower formation with reduction of the off-tracking and velocity estimation under visibility constraints

2021 ◽  
Vol 18 (6) ◽  
pp. 172988142110576
Author(s):  
C. Mauricio Arteaga-Escamilla ◽  
Rafael Castro-Linares ◽  
Jaime Álvarez-Gallegos
Keyword(s):  
Formation Control ◽  
Kinematic Model ◽  
Velocity Estimation ◽  
Lyapunov Theory ◽  
Time Varying ◽  
Absolute Position ◽  
Nonholonomic Mobile Robots ◽  
The Stability ◽  
Time Invariant ◽  
Explicit Communication

This article addresses the time-varying leader–follower formation control problem for nonholonomic mobile robots, under communication and visibility constraints. Although the leader–follower formation control under visibility constraints has been studied, the elimination of the off-tracking effect has not been widely addressed yet. In this work, a new method to eliminate the off-tracking effect, considering the time-invariant formation as a tractor–trailer system, for unknown and circular tractor paths, taking into account the visibility constraints, is proposed. For a time-varying formation with not circular tractor’s path, the proposed method significantly reduces the off-tracking. Only the relative position and the relative orientation, provided by the on board monocular camera, are required. Thus, both the leader robot’s absolute position and the leader robot’s velocities are not needed. Furthermore, to avoid explicit communication among the robots, an extended state observer is implemented to estimate both the translational and the rotational leader’s velocity. In this way, the desired tasks are executed and achieved in a decentralized manner. For a time-varying formation, with constant leader robot’s velocities, the proposed control strategy, based on the kinematic model, guarantees that the formation errors asymptotically converge to the origin. Based on the Lyapunov theory, the stability proof of the formation errors dynamics is shown. Simulation results, considering time-varying leader robot’s velocities, show the efficiency of the proposed scheme.

Direct Adaptive Tracking Control of Quadrotor Aerial Vehicles

2006 ◽  
Author(s):  
Yannick Morel ◽  
Alexander Leonessa
Keyword(s):  
Control Algorithm ◽  
Dynamic Surface Control ◽  
Significant Loss ◽  
Lyapunov Theory ◽  
Control Law ◽  
Dynamic Surface ◽  
Adaptive Tracking Control ◽  
Surface Control ◽  
Aerial Vehicles ◽  
Adaptive Control Algorithm

This paper presents a novel adaptive control algorithm solving the trajectory tracking problem for quadrotor aerial vehicles. A model reference approach is used, such that the vehicle tracks the trajectory of a reference system, which itself tracks a specified desired trajectory. The control law is derived using a backstepping procedure. A technique derived from dynamic surface control is used to simplify the expression of the obtained control algorithm, with no significant loss in terms of performance. Proof of stability is obtained using Lyapunov theory. Results from numerical simulations illustrate the performance of the obtained controller.

scholarly journals Bearing-Only Adaptive Formation Control Using Back-Stepping Method

2021 ◽  
Vol 2 ◽  
Author(s):  
Sulong Li ◽  
Qin Wang ◽  
Enci Wang ◽  
Yangyang Chen
Keyword(s):  
Formation Control ◽  
Control Algorithm ◽  
Adaptive Estimation ◽  
Design Method ◽  
Order System ◽  
Control Law ◽  
Barbalat’S Lemma ◽  
Simulation Results ◽  
Unknown Disturbance ◽  
Negative Gradient

In this paper, the bearing-only formation control problem of a class of second-order system with unknown disturbance is investigated, where the control law merely depends on the relative bearings between neighboring agents. In order to offset the effect of unknown disturbance on the system, adaptive estimation is introduced. In the design of the control law, the back-stepping design method and the negative gradient method are used. The Barbalat’s lemma is used to prove the global stability of the system. The simulation results prove the effectiveness of the proposed formation control algorithm.

Distributed Formation Control of UAVs for Circumnavigating a Moving Target in Three-Dimensional Space

2021 ◽  
Vol 01 (03) ◽  
Author(s):  
Yanhong Luo ◽  
Ao Bai ◽  
Huaguang Zhang
Keyword(s):  
Feedback Linearization ◽  
Formation Control ◽  
Control Method ◽  
Dimensional Space ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Moving Target ◽  
Dynamic Feedback ◽  
Space Angle ◽  
Three Dimensional Space

In this paper, a novel formation control strategy is proposed to address the target tracking and circumnavigating problem of multi-UAV formation. First, two sets of definitions, space angle definition and space vector definition, are presented in order to describe the flight state and construct the desired relative velocity. Then, the relative kinematic model between the UAV and the moving target is established. The distributed control law is constructed by using dynamic feedback linearization so as to realize the tracking and circumnavigating control with the desired velocity, circling radius and relative angular spacing. Next, the exponential stability of the closed-loop system is further guaranteed by properly choosing some corresponding parameters based on the Lyapunov method. Finally, the numerical simulation is carried out to verify the effectiveness of the proposed control method.

scholarly journals Adaptive sliding mode formation control of multiple underwater robots

2014 ◽  
Vol 24 (4) ◽  
pp. 515-543 ◽  
Author(s):  
Bikramaditya Das ◽  
Bidyadhar Subudhi ◽  
Bibhuti Bhusan Pati
Keyword(s):  
Formation Control ◽  
Sliding Mode ◽  
Autonomous Underwater Vehicles ◽  
The State ◽  
Lyapunov Theory ◽  
Adaptive Sliding Mode Control ◽  
Acoustic Medium ◽  
Underwater Robots ◽  
Adaptive Sliding Mode ◽  
Common Reference

Abstract This paper proposes a new adaptive sliding mode control scheme for achieving coordinated motion control of a group of autonomous underwater vehicles with variable added mass. The control law considers the communication constraints in the acoustic medium. A common reference frame for velocity is assigned to a virtual leader dynamically. The performances of the proposed adaptive SMC were compared with that of a passivity based controller. To save the time and traveling distance for reaching the FRP by the follower AUVs, a sliding mode controller is proposed in this paper that drives the state trajectory of the AUV into a switching surface in the state space. It is observed from the obtained results that the proposed SMC provides improved performance in terms of accurately tracking the desired trajectory within less time compared to the passivity based controller. A communication consensus is designed ensuring the transfer of information among the AUVs so that they move collectively as a group. The stability of the overall closed-loop systems are analysed using Lyapunov theory and simulation results confirmed the robustness and efficiency of proposed controller.

scholarly journals Adaptive Augmented Torque Control of a Quadcopter with an Aerial Manipulator

2021 ◽  
Author(s):  
Vidya Sumathy ◽  
Debasish Ghose
Keyword(s):  
Feedback Linearization ◽  
Estimation Error ◽  
Tracking Error ◽  
Lyapunov Theory ◽  
Torque Control ◽  
Control Law ◽  
Control Input ◽  
Positive Real ◽  
Aerial Robot ◽  
Non Linear

A quadcopter manipulator system is an aerial robot consisting of a quadcopter with a robotic arm attached to it. The system has coupled non-linear dynamics with uncertain time-varying parameters. The work in this paper focuses on designing an adaptive non-linear controller to facilitate the uncertain system’s trajectory tracking and stability. The novelty of the proposed work is the design and implementation of an adaptive feedback linearization controller, called adaptive augmented torque (AAT) control, for the aerial robot. The control law is based on a feedback linearization controller with model reference adaptive controller and a tracking error-based augmented term. Using the input-to-state (ISS) stability concept, a bound on the parameter estimation error is also developed. In the presented methodology, the controller uses estimated values of system parameters obtained from the adaptive mechanism and the tracking error to compute the control input using the AAT control law. An adaptive law for estimating unknown parameters is obtained using the strictly positive real-Lyapunov method. The asymptotic stability of the closed-loop system is analyzed via the Lyapunov theory. Simulations implemented in MATLAB and ROS/Gazebo and preliminary hardware experiments are presented to validate the theoretical results and to corroborate the performance of the AAT control law.

Trajectory Tracking Control of Nonholonomic Wheeled Mobile Robots with Actuator Dynamic Being Considered

2012 ◽  
Vol 433-440 ◽  
pp. 2596-2601 ◽  
Author(s):  
Guang Xin Han ◽  
Yan Hui Zhao
Keyword(s):  
Mobile Robots ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Closed Loop ◽  
Kinematic Model ◽  
Lyapunov Theory ◽  
Control Law ◽  
Wheeled Mobile Robots ◽  
Trajectory Tracking Control ◽  
Actuator Dynamics

In this paper trajectory tracking control problem for nonholonomic wheeled mobile robots with the actuator dynamics being considered is studied. On the basis of rotation error transformation and backstepping technique, tracking control law designed for kinematic model is backstepped into dynamic model and furthermore actuator dynamics is involved. Closed-loop stability is guaranteed by Lyapunov theory and Routh-Hurwitz Criterion. Finally simulation results for tracking typical trajectory are presented.

scholarly journals Formation Control of Multirobot Based on I/O Feedback Linearization and Potential Function

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jie Dong ◽  
Sen Liu ◽  
Kaixiang Peng
Keyword(s):  
Potential Function ◽  
Lyapunov Stability ◽  
Feedback Linearization ◽  
Formation Control ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Multirobot System ◽  
Simulation Results ◽  
Standard Techniques

Standard techniques of I/O linearization are widely applied to leader-follower approach for multirobot formation control. However general leader-follower approach cannot adapt to the environment with obstacles. Concerning that issue, a formation control method of multirobot system based on potential function is proposed in this paper, and a new control law is designed by choosing a proper potential function and employing Lyapunov stability theory, which stabilizes the formation of the multirobot system. We combine the method with a leader-follower approach to solve the problem that the latter cannot avoid obstacles. Simulation results are given to validate the method.

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