Controlling an Underactuated Two-Wheeled Mobile Robot: A Constraint-Following Approach

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Hui Yin ◽  
Ye-Hwa Chen ◽  
Dejie Yu
Keyword(s):  
Mobile Robot ◽  
Degrees Of Freedom ◽  
Control Design ◽  
Nonholonomic Constraints ◽  
Linear Quadratic Regulator ◽  
Wheeled Mobile Robot ◽  
Linear Quadratic ◽  
Control Goal ◽  
Standard Linear ◽  
Following Error

Controlling underactuated systems is a challenging problem in control engineering. This paper presents a novel constraint-following approach for control design of an underactuated two-wheeled mobile robot (2 WMR), which has two degrees-of-freedom (DOF) to be controlled but only one actuator. The control goal is to drive the 2 WMR to follow a set of constraints, which may be holonomic or nonholonomic constraints. The constraint is considered in a more general form than the previous studies on constraint-following control (hence including a wider range of constraints). No auxiliary variables or pseudo variables are required for the control design. The proposed control only uses physical variables. We show that the proposed control is able to deal with both holonomic and nonholonomic constraints by forcing the constraint-following error to converge to zero, even if the system is not initially on the constraint manifold. Using this control design, we investigate two cases regarding different constraints on the 2 WMR motion, one for a holonomic constraint and the other for a nonholonomic constraint. Simulation results show that the proposed control is able to drive the 2 WMR to follow the constraints in both cases. Furthermore, the standard linear quadratic regulator (LQR) control is applied as a comparison in the simulations, which reflects the advantage of the proposed control.

scholarly journals Linear and Non-Linear Control Design of Skid Steer Mobile Robot on an Embedded

2018 ◽  
Vol 7 (3) ◽  
pp. 185
Author(s):  
Jharna Majumdar ◽  
Sudip C Gupta ◽  
B Prassanna Prasath
Keyword(s):  
Mobile Robot ◽  
Pid Controller ◽  
Control Design ◽  
Linear Quadratic Regulator ◽  
Performance Comparison ◽  
Linear Control ◽  
Proportional Integral Derivative ◽  
Linear Quadratic ◽  
Non Linear ◽  
Lqr Controller

A detailed approach for a linear Proportional-Integral-Derivative (PID) controller and a non-linear controller - Linear Quadratic Regulator (LQR) is discussed in this paper. By analyzing several mathematical designs for the Skid Steer Mobile Robot (SSMR), the controllers are implemented in an embedded microcontroller - Mbed LPC1768. To verify the controllers, MATLAB-Simulink is used for the simulation of both the controllers involving motors - Maxon RE40. This paper compares between PID and LQR controller along with the performance comparison between Homogenous and Non-Homogenous LQR controllers.

scholarly journals A Model-Based Control Design Approach for Linear Free-Piston Engines

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
T. N. Kigezi ◽  
J. F. Dunne
Keyword(s):  
Control Design ◽  
Linear Quadratic Regulator ◽  
Design Approach ◽  
Linear Quadratic ◽  
Free Piston ◽  
Model Based Control ◽  
Model Based ◽  
Bottom Dead Center ◽  
Free Piston Engine ◽  
Advanced Control

A general design approach is presented for model-based control of piston position in a free-piston engine (FPE). The proposed approach controls either “bottom-dead-center” (BDC) or “top-dead-center” (TDC) position. The key advantage of the approach is that it facilitates controller parameter selection, by the way of deriving parameter combinations that yield both stable BDC and stable TDC. Driving the piston motion toward a target compression ratio is, therefore, achieved with sound engineering insight, consequently allowing repeatable engine cycles for steady power output. The adopted control design approach is based on linear control-oriented models derived from exploitation of energy conservation principles in a two-stroke engine cycle. Two controllers are developed: A proportional integral (PI) controller with an associated stability condition expressed in terms of controller parameters, and a linear quadratic regulator (LQR) to demonstrate a framework for advanced control design where needed. A detailed analysis is undertaken on two FPE case studies differing only by rebound device type, reporting simulation results for both PI and LQR control. The applicability of the proposed methodology to other common FPE configurations is examined to demonstrate its generality.

Lateral Stability Analysis for Car-Trailer Combinations

2016 ◽  
Author(s):  
Eungkil Lee ◽  
Tao Sun ◽  
Yuping He
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Parametric Study ◽  
Degrees Of Freedom ◽  
Linear Quadratic Regulator ◽  
Lateral Stability ◽  
Linear Quadratic ◽  
Lqr Control ◽  
Ct System

This paper presents a parametric study of linear lateral stability of a car-trailer (CT) combination in order to examine the fidelity, complexity, and applicability for control algorithm development for CT systems. Using MATLAB software, a linear yaw-roll model with 5 degrees of freedom (DOF) is developed to represent the CT combination. In the case of linear stability analysis, a parametric study was carried out using eigenvalue analysis based on a linear yaw-roll CT model with varying parameters. Built upon the linear stability analysis, an active trailer differential braking (ATDB) controller was designed for the CT system using the linear quadratic regulator (LQR) technique. The simulation study presented in this paper shows the effectiveness of the proposed LQR control design and the influence of different trailer parameters.

scholarly journals DYNAMICS BASED CONTROL OF A SKID STEERING MOBILE ROBOT

2016 ◽  
Vol 9 (2) ◽  
pp. 70 ◽  
Author(s):  
Osama Elshazly ◽  
Hossam Abbas ◽  
Zakarya Zyada
Keyword(s):  
Mobile Robot ◽  
Inverse Dynamics ◽  
Linear Quadratic Regulator ◽  
Nonlinear Controller ◽  
Linear Quadratic ◽  
Reduced Order ◽  
Lqr Control ◽  
Control Schemes ◽  
Skid Steering ◽  
Drive Model

In this paper, development of a reduced order, augmented dynamics-drive model that combines both the dynamics and drive subsystems of the skid steering mobile robot (SSMR) is presented. A Linear Quadratic Regulator (LQR) control algorithm with feed-forward compensation of the disturbances part included in the reduced order augmented dynamics-drive model is designed. The proposed controller has many advantages such as its simplicity in terms of design and implementation in comparison with complex nonlinear control schemes that are usually designed for this system. Moreover, the good performance is also provided by the controller for the SSMR comparable with a nonlinear controller based on the inverse dynamics which depends on the availability of an accurate model describing the system. Simulation results illustrate the effectiveness and enhancement provided by the proposed controller.

Optimal Error-Clamping Design for Position-Based Visual Servoing of a 2-DOF Model Helicopter

2011 ◽  
Author(s):  
M. Alizadeh ◽  
C. Ratanasawanya ◽  
M. Mehrandezh ◽  
R. Paranjape
Keyword(s):  
Visual Servoing ◽  
Degrees Of Freedom ◽  
Vision System ◽  
Physical Space ◽  
Linear Quadratic Regulator ◽  
Image Plane ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Feed Forward ◽  
Model Helicopter

A vision-based servoing technique is proposed for a 2 degrees-of-freedom (dof) model helicopter equipped with a monocular vision system. In general, these techniques can be categorized as image- and position-based, where the task error is defined in the image plane in the former and in the physical space in the latter. The 2-dof model helicopter requires a configuration-dependent feed-forward control to compensate for gravitational forces when servoing on a ground target. Therefore, a position-based visual servoing deems more appropriate for precision control. Image information collected from a ground object, with known geometry a priori, is used to calculate the desired pose of the camera and correspondingly the desired joint angles of the model helicopter. To assure a smooth servoing, the task error is parameterized, using the information obtained from the linearaized image Jacobian, and time scaled to form a moving reference trajectory. At the higher level, a Linear Quadratic Regulator (LQR), augmented with a feed-forward term and an integrator, is used to track this trajectory. The discretization of the reference trajectory is achieved by an error-clamping strategy for optimal performance. The proposed technique was tested on a 2-dof model helicopter capable of pitch and yaw maneuvers carrying a light-weight off-the-shelf video camera. The test results show that the optimized controller can servo the model helicopter to a hovering pose for an image acquisition rate of as low as 2 frames per second.

HOLONOMIC AND OMNIDIRECTIONAL LOCOMOTION SYSTEMS FOR WHEELED MOBILE ROBOTS: A REVIEW

2015 ◽  
Vol 77 (28) ◽  
Author(s):  
M. Juhairi Aziz Safar
Keyword(s):  
Mobile Robot ◽  
Mobile Robots ◽  
Degrees Of Freedom ◽  
Wheeled Mobile Robot ◽  
Arbitrary Direction ◽  
Current Position ◽  
Wheeled Mobile Robots ◽  
Future Improvement ◽  
Position And Orientation ◽  
Three Degrees Of Freedom

Holonomic and omnidirectional locomotion systems are best known for their capability to maneuver at any arbitrary direction regardless of their current position and orientation with a three degrees of freedom mobility. This paper summarizes the advancement of holonomic and omnidirectional locomotion systems for wheeled mobile robot applications and discuss the issues and challenges for future improvement.

Backstepping Controller Design for a 5 DOF Spherical Inverted Pendulum

2019 ◽  
Vol 41 ◽  
pp. 37-50 ◽  
Author(s):  
Soukaina Krafes ◽  
Zakaria Chalh ◽  
Abdelmjid Saka
Keyword(s):  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Linear Quadratic Regulator ◽  
Performance Comparison ◽  
Virtual Reality Environment ◽  
Linear Quadratic ◽  
Control Scheme ◽  
Linearized System ◽  
Backstepping Controller

This paper presents a Backstepping controller for five degrees of freedom Spherical Inverted Pendulum. Since the system is nonlinear, unstable, underactuated and MIMO and has a nonsquare form, the classic control design cannot be applied to control it. In order to remedy this problem, we propose in this paper a new method based on hierarchical steps of the Backstepping controller taking into a count the nonlinearities that cannot be neglected. Furthermore, a Linear Quadratic Regulator controller and LQR + PID based on the linearized system model are also designed for performance comparison. Finally, a simulation study is carried out to prove the effectiveness of proposed control scheme and is validated using the virtual reality environment that proves the performance of the Backstepping controller over the linear ones where it brings the pendulum from any initial condition in the upper hemisphere while the base is brought to the origin of the coordinates.

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