Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control
Abstract
:1. Introduction
- We have proposed a novel generalized nontriangular normal form by a suitable change of coordinates (diffeomorphism) transformation. During the formulation of generalized nontriangular normal form, the output vector is selected in such a way that the decoupling matrix would be nonsingular, even when the look-ahead distance (coordinates of virtual reference point in front of the mobile robot) or linear velocity is zero, as compared with previous work [5,6,8,16,17,18,19]. The proposed internal dynamics of WMR is one dimension, where nonholonomic constraints of WMR has been sensibly exploited to reduce the complexity of nonlinear internal dynamics, with structural properties that provide ease to the design controller. In contrast to the previous research [16,18], internal dynamics were two-dimension coupling with the derivative of output functions.
- We have proposed a systematic method of ensuring asymptotic stabilization of internal dynamics during trajectory tracking and posture stabilization, unlike the previous research [16,17,18,19]. Furthermore, the proposed method used an exact model of nonlinear internal dynamics rather than a linear approximation of internal dynamics [5].
- This paper proposes a novel recursive integral backstepping control based on generalized nontriangular normal form structure for differential drive WMR. The proposed single controller can perform trajectory tracking and posture stabilization better than existing backstepping-based tracking/stabilization controllers [3,22,23,24,25,38]. Using a normal form representation of WMR makes the proposed algorithm simpler because of the features of regular backstepping technique as compared with modified backstepping control [20] and block-backstepping [37]. Moreover, the proposed controller provides a solution for the kinematic model cascaded with the dynamic model of WMR, as compared with previously designed controllers for kinematic and/or dynamics models [6,37,39]. In our approach, the actual robot motion commands are the wheel velocities rather than robot driving and steering velocities, calculated from the motor torques based on a dynamic model. Therefore, it would be more appropriate to represent the robot’s dynamic equations of motion based on wheel velocities to have a modular control structure unlike [37].
2. Modeling of Nonholonomic WMR
2.1. Kinematic Model of WMR
2.2. Dynamic Model of WMR
2.3. State Space Model of WMR
3. Input-Output Feedback Linearization: Normal form for WMR
4. Backstepping Control Design for Trajectory Tracking
- C1.
- , for all
5. Backstepping Control Design for Posture Stabilization
- C1.
- C2.
- for all
6. Simulation Results
6.1. Simulation Results for Trajectory Tracking
6.2. Simulation Results for Posture Stabilization
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
WMR | Wheeled Mobile Robot |
MIMO | Multiple Input Multiple Output |
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Parameter | Description | Value |
---|---|---|
r | Radius of wheels | 0.05 m |
Distance between two driving wheels | 0.27 m | |
m | Mass of robot | 4 kg |
I | Moment of inertia of whole robot | 2.5 kg·m |
d | Distance from point to point | 0.05 m |
Parameter | Trajectory Tracking | Posture Stabilization |
---|---|---|
2.5 | 2.5 | |
8 | 6 | |
6.5 | 6 | |
60 | 20 | |
9 | 10 | |
5 (rad/s) | 0 | |
(0.3, −0.7, ) | (−5, −5, ), Figure 7 and Figure 8 and | |
(0, −1, ), Figure 9 and Figure 10 |
Parameter | Circular Trajectory | Lamniscate Curve Trajectory |
---|---|---|
x (m) | 0.0114 | 0.0123 |
y (m) | 0.0117 | 0.0123 |
(rad) | 0.0097 | 0.0109 |
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Rabbani, M.J.; Memon, A.Y. Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control. Electronics 2021, 10, 1992. https://doi.org/10.3390/electronics10161992
Rabbani MJ, Memon AY. Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control. Electronics. 2021; 10(16):1992. https://doi.org/10.3390/electronics10161992
Chicago/Turabian StyleRabbani, Muhammad Junaid, and Attaullah Y. Memon. 2021. "Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control" Electronics 10, no. 16: 1992. https://doi.org/10.3390/electronics10161992
APA StyleRabbani, M. J., & Memon, A. Y. (2021). Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control. Electronics, 10(16), 1992. https://doi.org/10.3390/electronics10161992