Discussion and conclusion
We were able to create a lane keeping algorithm for autonomous vehicles based on traditional computer vision techniques, that is robust to illumination changes and manages to detect and track lanes under different conditions such as: lane markings with two different colors (yellow and white), lane markings exposed to direct sunlight, shadows and transitions between asphalts of different color. Also, the system can react to the two main lane types, straight and curved. Furthermore, the system controls the vehicle’s heading, based on a short-term trajectory generation and the Ackermann Kinematic model so the vehicle stays in the center of the lane, which is an added capability compared to Lane Departure warning systems presented in [2], [3] and [4].
We also highlight the use of sliding windows versus the Hough Line transform and its variants used in [2], [3] and [4] since we are able to model with a fixed number of sliding windows each lane marking by representing them as series of points. The main problem with the use of the Hough Line Transform is the detection of only straight lines. Thus, to detect curved features the system needs to either detect small segments of the curved line and piece them together to create the lane model, or it needs to do a rough approximation of a curve with a straight line, which could not be an optimal model.
For future work, we recommend doing a comparative analysis between our method and the ones presented on previous work, focused on the computational cost and real-time performance. Also, given the current trend on the Computer Vision field, it would be interesting to see the Deep Learning-based approaches to both the perception and decision modules.
References
[1] S. P. Narote, P. N. Bhujbal, A. S. Narote, and D. M. Dhane, “A review of recent advances in lane detection and departure warning system”, Pattern Recognit., vol. 73, pp. 216-234, 2018. doi: 10.1016/j.patcog.2017.08.014
[2] J. Son, H. Yoo, S. Kim, and K. Sohn, “Real-time illumination invariant lane detection for lane departure warning system”, Expert Syst. Appl., vol. 42, n. 4, pp. 1816-1824, 2015. doi: 10.1016/j.eswa.2014.10.024
[3] N. Madrid, P. Hurtik, “Lane departure warning for mobile devices based on a fuzzy representation of images”, Fuzzy Sets Syst., vol. 291, pp. 144-159, 2016. doi: 10.1016/j.fss.2015.09.009
[4] A. Mammeri, A. Boukerche, and Z. Tang, “A real-time lane marking localization, tracking and communication system”, Comput. Commun., vol. 73, n. A, pp. 132-143, 2016. doi: 10.1016/j.comcom.2015.08.010
[5] E. Ackerman, “Study: Intelligent Cars Could Boost Highway Capacity by 273 %”, 2012. [Online]. Available: https://spectrum.ieee.org/automaton/robotics/artificial-intelligence/intelligent-cars-could-boost-highway-capacity-by-273. [Accessed:16-May-2019].
[6] Udacity, “Lane finding project for self-driving car ND”, 2017. [Online]. Available: https://github.com/udacity/CarND-LaneLines-P1. [Accessed: 16-May-2019].
[7] P. Viola, and M. Jones, “Rapid object detection using a boosted cascade of simple features”, in Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR, Vol. II, A. Jacobs, and T. Baldwin, Eds. Kawai, Hawaii: IEEE Computer Society, 2001, pp. 511-518 [Online]. Available: http://ieeexplore.ieee.org/document/990517/
[8] R. E. Kalman, “A New Approach to Linear Filtering and Prediction Problems”, J. Basic Eng., vol. 82, n. 1, pp. 35-45, 1960. doi: 10.1115/1.3662552
[9] M. A. Saavedra Ruiz, y A. M. Pinto Vargas, “Desarrollo de un sistema de aterrizaje autónomo para un vehículo aéreo no tripulado sobre un vehículo terrestre”, tesis de pregrado, Universidad Autónoma de Occidente, Cali, Valle del Cauca, 2019 [En línea]. Disponible en: http://hdl.handle.net/10614/10754
[10] K. Ogata, “Ingeniería de control moderna”, 5a. Edición, Madrid: Pearson Educación. 2010.
Design and implementation of a PID controller for a didactic pneumatic levitation system monitored by smartphone
Johan Fernández Zorro,1, γ, Yefferson Caleño Barrera1, Nicolás Niño Viancha1, Camilo Sanabria Totaitive1, Liliana Fernández-Samacá1
1 Electronics Engineering School, Signal Processing Research Group, Universidad Pedagógica y Tecnológica de Colombia, Sogamoso, Colombia.
γ. Corresponding author: johan.fernandez@uptc.edu.co
Abstract
This work presents a prototype of a vertical pneumatic levitator as an educational resource for encouraging control learning. The objective is to control the position of a ball inside of a pipe, by an airflow. This paper shows a learning experience developed in an undergraduate course, where students construct the prototype plant, obtain its mathematical model, and design a digital PID controller. In this exercise, students work in a team in a Project-Based Learning experience focused on comparing the behavior of a simulation model to the actual plant. For observing changes in the ball position inside the pipe when the user changes the set point, the team develops an App in Android that facilitates the interaction with the prototype.
Keywords: Pneumatic levitator; digital PID; App Android; Step-test.
Introduction
The suspension of a body in the air is a phenomenon known as levitation; this suspension can be achieved through a pushing force by different means so that that levitation can be magnetic, acoustic, optical, electrostatic, or pneumatic. In the case of pneumatic levitators, the object is lifted by the action of an airflow. Usually provides the flow, which passes through a grid that makes it laminar. Currently, pneumatic levitation systems are widely used in the transport of materials like food or medicines, which have strict hygiene parameters or require low friction of materials that are being moved [1].
When the pneumatic levitators are considered as an academic resource for control learning, the control objective is to keep the position of a ball inside of a pipe; where a sensor measures the ball position. Figure 1 shows an example of a structure for a pneumatic levitator. For estimating the mathematical model, researchers generally neglect the porosities and imperfections of the object, and effects of the friction forces in the horizontal movement and rotational movements resulting from the Magnus effect, [2]. Likewise, they approximate some physical constants such as the drag coefficient and the density of the object and pay attention to aspects such as the dead zones of the sensor and fan, which generates a range of positions that cannot be controlled, see Figure 1.
Different structures and controllers have been implemented for pneumatic levitator. For example, in [2], the authors show the identification and position control of a pneumatic levitation system using a compressor driven by a variable velocity drive; they compare the results obtained of implementing an H∞ control, a PID control and an incremental fuzzy control. Reference [3] presents the mathematical model and a controller for a pneumatic levitation system as well as the construction of a prototype for the experimental validation of a linear controller which is implemented by using the state feedback. In [4], the performance of a conventional PID controller and an expert FUZZY controller are evaluated for reference tracking and in rejection of disturbances. In [5], an experimental study of different nonlinear PI controllers is presented, for that, authors use an academic platform based on an air levitation system.
The pneumatic levitator has also been used to perform different stability analysis tests for rejecting disturbances. For example, reference [6] shows the design and construction of a virtual laboratory where the behavior of a remote pneumatic levitation system is observed in real-time. Likewise, the authors of [7] describe a pneumatic levitation system to help students visualize and understand theoretical concepts in control engineering. Likewise, in [1], authors describe a mathematical model and a 3D simulation of a pneumatic levitator, in the experiment the forces involved in the system are increased for calculating the parameters of a real levitator. Finally, the most significant advance is the patent that exists on a pneumatic levitation train known as Hyperloop, which aims to transport people at speeds never reached. The patent is not yet available; however, in [8], a general description of the project is discussed.
Figure 1
Vertical Pneumatic Levitator
Source: Own elaboration
This article presents the design of a prototype of pneumatic levitator that is used as a plant for control education. This prototype is characterized for having a size for facilitate its use in the classrooms, it is a practical tool, playful resource and inexpensive lab set-up. Moreover, the prototype has a human-machine interface, which allows to the user operate the prototype in a remote way.
The rest of the paper is organized as follows, Section 2 show the modeling of the system and its linearization at an operating point, the design of a digital position PID controller by means of pole assignment and the simulation results; in Section 3 presents the performance of the designed controller and the use of App for monitoring the variables. Finally, Section 4 shows conclusions.
Prototype description
After reviewing the state of art of the pneumatic levitator, students obtain the mathematical model by using the studied theory. Based on the model, they build the prototype, firstly a designing a model in a graphic editor, this information is used to cut the pieces that will comprise it; later, selecting the appropriate materials and devices like sensor, actuator, digital platforms (e.g., Arduino) and power supplies; and Finally, they implement and adjust the prototype components to have a final version. Once the prototype is finished, students test its performance and behavior before to design the controllers.
Mathematical model of the plant
Taking into account the literature review, the students obtain a nonlinear mathematical model of the plant in state space, Equation (1), taking into account the physical considerations shown in Figure 2. After that, students define an operating point, for obtaining a linear model of the system in state space Equation (4) and (5).
In Figure 2(a), the reader can observe the prototype, in (b) the set-point signal (in yellow) vs. the output system (in green), these signals are directly measured with the oscilloscope in the plant.
Figure 2
(a) Pneumatic levitation plant; (b) plant response seen from the oscilloscope
Source: Prepared by the authors
Non-linear mode.
The mathematical model of a pneumatic levitation system involves mechanical, electrical and aerodynamic principles, such as: i) principle of continuity because the air flow is constant through the cylinder; ii) Bernoulli principle because the force applied by the flow of Air to the object depends solely on the kinetic energy, Euler-Lagrange equations because with these any system can be represented with respect to its energy variation; and iii) Raleigh dissipation function for the modeling of the viscous friction experienced by the object, number of Reynolds (Re) quantity to be taken into account for the calculation of the drag coefficient CD.
The non-linear in state space representation of the system is in Equation (1).
(1)
Where, x1, x2 are the position and speed of Object, respectively; Af is transversal area of the tube; Vf is air velocity in the cross section of the fan; ρa is air density; CD is drag coefficient; Ab is transversal area of the levitating object; mb is Mass of the levitating object and g the gravity constant.
Linear model.
To use the linear control techniques, linear model is obtained for a operating point. The Equation (2) describes the process to obtain the equilibrium points in Equation (3) the expression for Jacobian.
(2)
(3)
Where:
Finally, the linear model in state space representation of the system is described by Equation (4).
(4)
(5)
Taking into account the actual parameters of the plant, the system transfer function is:
(6)
The system has a pole at zero, which provokes an integrator effect; for this reason, the response in closed-loop (see Figure 3) was analyzed to determine which parameters could be improved. The response of the system scaled in volts is shown in Figure 3, where 0 cm equals to 0V and 53 cm equals 5V. A step-test was used to obtain an experimental model, changing the input signal from 10.6 cm (1V) to 31.8 cm (3V), an over peak of was observed in the output signal and a stabilization time of Mp%=58 % and a ts = 9.33 [s].
Figure 3
System response to a reference change in closed loop without controller, using Matlab2014
Source: Own elaboration
PID controller design
As desired parameters for system, student define:
Using Diophantine Equation that compares the closed-loop characteristic polynomial to desired polynomial the constants for the PID controller are:
To choose the sampling time, the Nyquist-Shannon theorem is used, choosing for this case a sampling time twenty times faster than the of system. Having the sampling time and the analog constants of the PID, the constants for the digital controller are obtained and these are:
Finally, the control law that is implemented in the microcontroller is:
Figure 4, shows the controlled system response (blue) after making a set-point change from 10.6 cm (1V) to 31.8 cm (3V). Here it is shown how the system response has improved considerably, having a behavior as desired, with Mp% = 25 % and also the settling time is less than expected.
Figure 4
System response to a reference change in closed loop with controller, using Matlab 2014
Source: Own elaboration
Results
Figure 5 shows the comparison of the controlled system response (blue line) and the set-point (yellow line), when the set-point is changes from 6.36 cm (0.6V) to 33.92 cm (3.2V), the reader can observe that some parameters of actual response are little different to those obtained in the simulation.
Figure 5
System response to a reference change in closed loop with controller, using oscilloscope
Source: Own elaboration
Figure 6, shows the response of the closed loop system with controller (green graph), vs the reference change (yellow graph), since the android application. The application has a graphical user-friendly interface, it also has a menu that allows: connection to the Bluetooth device, choose the position of the levitator object, see the graph of the reference and control signals, and see the status variables, all in real time.
The oscillations in steady state are due to the resistive forces that are generated when the air flow hits the sphere, to improve this, an advanced control that compensates for the non-linearities of the system is required. The application has a graphical user-friendly interface developed in App Inventor, which has a menu that allows connecting Bluetooth devices. The user can change the set-point for the system by using the option available in the menu. Figure 6 shows the final view of the user interface, which also has a plotter to observe the set-point (yellow line) and system output signal (green line) in real-time.
Figure 6
App in Android for monitoring the signals and adjusting the set-point
Source: Own elaboration
Conclusions
Considering that the PID controller was designed using the linear model of the system, whose non-linear model is an approximation to its actual behavior. Researchers observed that the performance of the controller was the expected, which was observed for an abrupt change of set point was applied during the testing stage, where a maximum overshoot of 32 % and a stabilization time of 2.5 was calculated for these operating conditions indicating an improving of the system response.
The application on Android allows observes what is happening with the plant in real time; in addition, it is possible that the user selects the position in which he/she wants to place the levitation object. This application has a very easy to use and results a didactic tool to observe the variable behavior of the plant.
References
[1] J. García, y M. Arroyave, “Modelación, simulación y control de un levitador neumático”, Revista Politécnica, vol. 11, n. 20, pp. 59-66, 2015 [En línea]. Disponible en: https://revistas.elpoli.edu.co/index.php/pol/article/view/489/515
[2] J. Escaño, y D. Algarín, “Identificación y control de posición de un sistema de levitación neumática”, en XXV Jornada de Automática Ciudad Real, J. A. Somolinos, Ed. Ciudad Real, España: CEA, 2004, [En línea]. Disponible en: https://intranet.ceautomatica.es/old/actividades/jornadas/XXV/documentos/39-anessiuore.pdf
[3] F. G. Rojas-Contreras, R. Reyes-Báez, L. Ferrer-García, S. Romero-Hernández, y E. Rosario, Control por retroalimentación de salida de un sistema de levitación de aire. 12° Congreso interamericano de computación aplicado a la industria de procesos (CAIP), Cartagena, Colombia: Universidad Libre, 2015.
[4] D. F. Ordoñez, M. Jacome, y F. A. González, “Implementación y estudio comparativo de técnicas de control PID y Fuzzy en controladores lógicos programables”, Reset UTS, vol. 1, n. 4, pp. 21-28, 2009 [En línea]. Disponible en: http://historico.uts.edu.co/portal/files/ARTICULORESET4.pdf
[5] J. Chacón, H. Vargas, S. Dormido, and J. Sánchez, “Experimental study of nonlinear PID controllers in an air levitation system”, in Preprints of the3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control, D. Rodríguez, Ed. Ghent, Belgium: IFAC, 2018, pp. 304-309 [Online]. Available: https://folk.ntnu.no/skoge/prost/proceedings/PID-2018/0098.PDF
[6] J. Saenz, J. Chacón, L. De la Torre, and S. Dormido, “An open software-open hard ware lab of the air levitation system”, IFAC-PapersOnLine, vol. 50, n. 1, pp. 9168-9173, 2017. doi: 10.1016/j.ifacol.2017.08.1727
[7] J. C. Kuzhandairaj. Development, control and testing of an air levitation system for educational purpose. Master’s thesis, Politecnico Milano, Milan, Italy, 2018.
[8] R. Garcia, J. Carril, A. Catoira, y J. Gómez, Dispositivo de sustentación mediante levitación neumática para trenes, rail y sistema que comprende ambos. Oficina de Patentes de España, P201230593, 23 octubre 2013.
Virtual navigation of a micro robot guided by haptic interface
María Alejandra Gutiérrez Peñafiel, Juan José Rosero Calderón, Martín Alonso Muñoz Medina, Oscar Andrés Vivas Albán
Universidad del Cauca, Popayán, Colombia
Corresponding author: mariafe@unicauca.edu.co
Abstract
The theoretical and experimental advances of micro robotics have grown at a high speed in recent years, perceived as a technology that will revolutionize in the near future medical procedures as diverse as the performance of tests that were generally invasive, the administration of medicines and the monitoring of some vital organs, etc. In this article we will present a field of application of micro robotics, called virtual navigation of a micro robot through a software platform guided by a haptic interface. This interface provides the surgeon with convincing haptic sensations about the interaction between the micro robot and the pancreatic duct, and allows him to intuitively control the position of the micro robot in a 3D space. Virtual designed navigation simulates both the trajectory and its collisions with the pancreatic duct, providing realism in the exploration of this organ.
Keywords: Virtual simulation, haptic interface, micro robots, virtual navigation, 3D modeling.