Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control
In this paper, a generalized nontriangular normal form is presented to facilitate designing a recursive integral backstepping control for the class of underactuated nonholonomic systems, i.e., wheeled mobile robots (WMRs) that perform posture stabilization and trajectory tracking in environments wit...
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doaj-6c7dabed59414d2a8dd66c0b2e7ce1162021-08-26T13:41:47ZengMDPI AGElectronics2079-92922021-08-01101992199210.3390/electronics10161992Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping ControlMuhammad Junaid Rabbani0Attaullah Y. Memon1Department of Electronics and Power Engineering, PN Engineering College, National University of Sciences and Technology, Karachi 75350, PakistanDepartment of Electronics and Power Engineering, PN Engineering College, National University of Sciences and Technology, Karachi 75350, PakistanIn this paper, a generalized nontriangular normal form is presented to facilitate designing a recursive integral backstepping control for the class of underactuated nonholonomic systems, i.e., wheeled mobile robots (WMRs) that perform posture stabilization and trajectory tracking in environments without obstacles. Based on the differential geometry theory, we develop a multiple input multiple output (MINO) generalization of normal form using the input-output feedback linearization technique. Then, the change of variables (diffeomorphism) transform the state-space model of WMR, incorporating both kinematic and dynamic models into nontriangular normal form. As a result, the system dynamics can be represented as internal and external dynamics. The nonlinear internal dynamics of WMR pose serious challenges to design a suitable controller due to its internal dynamics being not minimum phase and non-strict feedback form structure. The proposed backstepping controller is designed in two steps. First, a standard integral backstepping controller is designed to stabilize the robot’s orientation angle. Then, a recursive integral backstepping control technique is applied to achieve asymptotic convergence of position error to zero. Hence, both asymptotic posture stabilization and trajectory tracking are achieved in semi-global regions, except the nonzero initial condition of the orientation angle. The asymptotic stability of the entire closed-loop system is shown using the Lyapunov criteria.https://www.mdpi.com/2079-9292/10/16/1992integral backstepping controlfeedback linearizationnontriangular normal forminternal dynamicstrackingposture stabilization |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Muhammad Junaid Rabbani Attaullah Y. Memon |
spellingShingle |
Muhammad Junaid Rabbani Attaullah Y. Memon Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control Electronics integral backstepping control feedback linearization nontriangular normal form internal dynamics tracking posture stabilization |
author_facet |
Muhammad Junaid Rabbani Attaullah Y. Memon |
author_sort |
Muhammad Junaid Rabbani |
title |
Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control |
title_short |
Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control |
title_full |
Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control |
title_fullStr |
Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control |
title_full_unstemmed |
Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control |
title_sort |
trajectory tracking and stabilization of nonholonomic wheeled mobile robot using recursive integral backstepping control |
publisher |
MDPI AG |
series |
Electronics |
issn |
2079-9292 |
publishDate |
2021-08-01 |
description |
In this paper, a generalized nontriangular normal form is presented to facilitate designing a recursive integral backstepping control for the class of underactuated nonholonomic systems, i.e., wheeled mobile robots (WMRs) that perform posture stabilization and trajectory tracking in environments without obstacles. Based on the differential geometry theory, we develop a multiple input multiple output (MINO) generalization of normal form using the input-output feedback linearization technique. Then, the change of variables (diffeomorphism) transform the state-space model of WMR, incorporating both kinematic and dynamic models into nontriangular normal form. As a result, the system dynamics can be represented as internal and external dynamics. The nonlinear internal dynamics of WMR pose serious challenges to design a suitable controller due to its internal dynamics being not minimum phase and non-strict feedback form structure. The proposed backstepping controller is designed in two steps. First, a standard integral backstepping controller is designed to stabilize the robot’s orientation angle. Then, a recursive integral backstepping control technique is applied to achieve asymptotic convergence of position error to zero. Hence, both asymptotic posture stabilization and trajectory tracking are achieved in semi-global regions, except the nonzero initial condition of the orientation angle. The asymptotic stability of the entire closed-loop system is shown using the Lyapunov criteria. |
topic |
integral backstepping control feedback linearization nontriangular normal form internal dynamics tracking posture stabilization |
url |
https://www.mdpi.com/2079-9292/10/16/1992 |
work_keys_str_mv |
AT muhammadjunaidrabbani trajectorytrackingandstabilizationofnonholonomicwheeledmobilerobotusingrecursiveintegralbacksteppingcontrol AT attaullahymemon trajectorytrackingandstabilizationofnonholonomicwheeledmobilerobotusingrecursiveintegralbacksteppingcontrol |
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1721193916080848896 |