A Novel Nonlinear Control Law with Trajectory Tracking Capability for Nonholonomic Mobile Robots: Closed-Form Solution Design

A closed-form H2 approach of a nonlinear trajectory tracking design and practical implementation of a swarm of wheeled mobile robots (WMRs) is presented in this paper. For the nonlinear trajectory tracking problem of a swarm of WMRs, the design purpose is to point out a closed-form H2 nonlinear control method that analytically fulfills the H2 control performance index. The key and primary contribution of this research is a closed-form solution with a simple control structure for the trajectory tracking design of a swarm of WMRs is an absolute achievement and practical implementation. Generally, it is challenging to solve and find out the closed-form solution for this nonlinear trajectory tracking problem of a swarm of WMRs. Fortunately, through a sequence of mathematical operations for the trajectory tracking error dynamics between the control of a swarm of WMRs and desired trajectories, this H2 trajectory tracking problem is equal to solve the nonlinear time-varying Riccati-like equation. Additionally, the closed-form solution of this nonlinear time-varying Riccati-like equation will be acquired with a straightforward form. Finally, for simulation-controlled performance of this H2 proposed method, two testing scenarios, circular and S type reference trajectories, were applied to performance verification.

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Nonlinear Optimal Control Law of Autonomous Unmanned Surface Vessels

Applied Sciences ◽

10.3390/app10051686 ◽

2020 ◽

Vol 10 (5) ◽

pp. 1686

Author(s):

Yung-Yue Chen ◽

Chun-Yen Lee ◽

Shao-Han Tseng ◽

Wei-Min Hu

Keyword(s):

Optimal Control ◽

Closed Form ◽

Closed Form Solution ◽

Nonlinear Optimal Control ◽

Form Solution ◽

Control Law ◽

Tracking Problem ◽

Optimal Tracking ◽

Surface Vessels ◽

Marine Surface

For energy conservation, nonlinear-optimal-control-law design for marine surface vessels has become a crucial ocean technology for the current ship industry. A well-controlled marine surface vessel with optimal properties must possess accurate tracking capability for accomplishing sailing missions. To achieve this design target, a closed-form nonlinear optimal control law for the trajectory- and waypoint-tracking problem of autonomous marine surface vessels (AUSVs) is presented in this investigation. The proposed approach, based on the optimal control concept, can be effectively applied to generate control commands on marine surface vessels operating in sailing scenarios where ocean environmental disturbances are random and unpredictable. In general, it is difficult to directly obtain a closed-form solution from this optimal tracking problem. Fortunately, by having the adequate choice of state-variable transformation, the nonlinear optimal tracking problem of autonomous marine surface vessels can be converted into a solvable nonlinear time-varying differential equation. The solved closed-form solution can also be acquired with an easy-to-implement control structure for energy-saving purposes.

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Synthetic Jet Actuator-Based Aircraft Tracking Using a Continuous Robust Nonlinear Control Strategy

International Journal of Aerospace Engineering ◽

10.1155/2017/4934281 ◽

2017 ◽

Vol 2017 ◽

pp. 1-13

Author(s):

N. Ramos-Pedroza ◽

W. MacKunis ◽

M. Reyhanoglu

Keyword(s):

Nonlinear Control ◽

Trajectory Tracking ◽

Parameter Uncertainty ◽

Tracking Error ◽

Synthetic Jet ◽

Parameter Estimates ◽

Control Law ◽

Robust Nonlinear Control ◽

Trajectory Tracking Control ◽

Nonlinear Control Law

A robust nonlinear control law that achieves trajectory tracking control for unmanned aerial vehicles (UAVs) equipped with synthetic jet actuators (SJAs) is presented in this paper. A key challenge in the control design is that the dynamic characteristics of SJAs are nonlinear and contain parametric uncertainty. The challenge resulting from the uncertain SJA actuator parameters is mitigated via innovative algebraic manipulation in the tracking error system derivation along with a robust nonlinear control law employing constant SJA parameter estimates. A key contribution of the paper is a rigorous analysis of the range of SJA actuator parameter uncertainty within which asymptotic UAV trajectory tracking can be achieved. A rigorous stability analysis is carried out to prove semiglobal asymptotic trajectory tracking. Detailed simulation results are included to illustrate the effectiveness of the proposed control law in the presence of wind gusts and varying levels of SJA actuator parameter uncertainty.

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A PRACTICAL TRAJECTORY TRACKING APPROACH FOR AUTONOMOUS MOBILE ROBOTS: NONLINEAR ADAPTIVE H2 DESIGN

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-2013-0028 ◽

2013 ◽

Vol 37 (3) ◽

pp. 385-394 ◽

Cited By ~ 2

Author(s):

Yung Hsiang Chen ◽

Tzuu Hseng S. Li ◽

Yung Yue Chen

Keyword(s):

Mobile Robot ◽

Closed Form ◽

Trajectory Tracking ◽

Tracking Error ◽

Closed Form Solution ◽

Form Solution ◽

Practical Implementation ◽

Autonomous Mobile Robot ◽

Nonlinear Controller ◽

Trajectory Tracking Control

A nonlinear adaptive trajectory tracking design for autonomous mobile robot and its practical implementation are presented in this paper. This approach can be applied to generate trajectory tracking control commands for autonomous mobile robot tracking predefined trajectories. The design objective is to specify one nonlinear controller with a parameter adaptive law that satisfies the adaptive H2 optimal performance. In general, it is hard to obtain the closed-form solution from this nonlinear trajectory tracking problem. Fortunately, based on the property of the trajectory tracking error dynamic system of the autonomous mobile robot, one closed-form solution to this problem can be obtained with a very simple form for the preceding control design.

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An Adaptive Nonlinear Trajectory Tracking Design for Mobile Robots and it’s Practical Implementation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.284-287.1744 ◽

2013 ◽

Vol 284-287 ◽

pp. 1744-1748

Author(s):

Yung Hsiang Chen ◽

Tzuu Hseng S. Li ◽

Yung Yue Chen

Keyword(s):

Mobile Robot ◽

Closed Form ◽

Trajectory Tracking ◽

Tracking System ◽

Closed Form Solution ◽

Form Solution ◽

Practical Implementation ◽

Time Varying ◽

Nonlinear Controller ◽

Reference Trajectories

An adaptive nonlinear trajectory tracking design for mobile robot and its practical implementation are presented in this paper. The design objective is to specify one nonlinear controller with a parameter adaptive law that satisfies the adaptive H2 optimal performance. In general, it is hard to obtain the closed-form solution from this nonlinear trajectory-tracking problem. Fortunately, based on the property of the trajectory tracking system of the nonholonomic mobile robot, the adaptive H2 trajectory tracking problems can be reduced to solving one nonlinear time varying Riccati-like equations. Furthermore, one closed-form solution to this nonlinear time varying Riccati-like equation can be obtained with very simple forms for the preceding control design. Finally, there are two practical testing conditions: circular and S type reference trajectories are used for performance verification.

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