Mobile robots are complex systems that assist one or more specific tasks. In the agricultural case, challenging environmental conditions affect movement and task performing. In this chapter, state feedback and fuzzy controllers were developed for Ceres -an agricultural robot with 200Kg of payload. Controllers were designed after a dynamical modeling stage using system identification techniques with open-loop data acquired from the real plant to refine the model parameters. The fuzzy controller is desired to obtain a faster response concerning classical controllers and to compensate nonlinear and/or unmodeled dynamics. To get a zero steady-state error, an FPD+I architecture was implemented. Simulations were performed, and a faster response was obtained with the fuzzy controller. Results have shown a control signal according to the ranges used in the motor drivers embedded in the robot Ceres. Future works will integrate the fuzzy controller to the robot by using the Robot Operating System (ROS).

Keywords: Mobile robot, control, agricultural robot, fuzzy controller, feedback controller.

Introduction

Mobile robots are used to perform assistance tasks such as indoor guiding, payload movement, and recently, agricultural tasks [1]. However, agrarian field robots have an important lack compared to the high potential of this technology [2]. Environmental conditions, rough terrains, obstacles environment, and sloped terrains, are some of the challenges to develop such robots [3]. On the other hand, the growing food demand implies the need to increase the field size and crop productivity, while reducing agricultural costs [4]. The use of vehicles to assist tasks such as harvesting, weeding, fertilizing, and fumigating have obtained prominent results in different fields such as rice [5], citrus [6] and grapes [7].

Two main subsystems are required to obtain a useful robot to assist agricultural tasks. Firstly, a mobile platform that allows performing the job in the whole crop, with a localization system and guidance systems. The second subsystem is related to the primary purpose of the robot and can be tools for weeding, seeding, harvesting, sensing agricultural variables, or other tasks [8].

Mobility requirements must be able to control linear and angular velocities of the robot commonly named guidance, taking into account velocity limits, crop lines, and robot dynamics. Due to localization and path following requirements, the guidance performance needs to be assured. A complete hierarchy for an autonomous robot is described in [9].

This work compares a state feedback technique and a fuzzy logic technique for guidance navigation for our 200 Kg payload capability - agricultural robot CERES. Some relevant approaches in the same directions are the agricultural low size tractor for visual navigation [10], a custom-designed robot for fertilizing potato fields [11] and a robotic platform for beets fumigation that achieved a 12 % of herbicides reduction [12].

Methods

We have designed our robot Ceres – Agrobot to face three agricultural challenges, i.e., weeding, fertilizing, and fumigating. A setup of three linear actuators is located in the bottom part of the robot with the farming tools. To move the robot across the crops, a differential locomotion scheme is used, with two brushless motors in the front part and two freewheels (castor wheel type) in the rear section. To increase the crop navigation performance, a high capability inertial measurement unity (IMU) is placed. The kinematic and dynamic analyses for the Ceres robot are carried out in this section. Then, control techniques are applied and compared to obtain the reference velocities.

Figure 1

Ceres robot

(Left): Agricultural robotic platform electrically powered with differential traction, a payload of 100 Kg of solid fertilizer, 20 liters for disinfecting purposes, and a weeding system. (Right): Principal forces of Ceres robot used for modeling purposes. Source: Prepared by the authors

Modeling

Navigation into the crops requires a low error system to preserve the field integrity and perform the necessary tasks. Such level of performance is why a conventional control process is done, including mathematical modeling of the robot dynamics, design, and simulation. This section tackles the robot two-stage modeling step.

First, kinematic analysis and then a dynamic analysis using the Euler-Lagrange approach [13] are performed. For this purpose, forces and dimensions are defined as shown in Figure 1 (right). Considering as the wheel velocity, a simplified model of Ceres robot is described by

Where:

Notice that no slip between the wheel and the ground is considered. Beta parameters are constant and only depend on robot physics. However, they contain uncertainties that need be reduced.

Physical parameters are obtained from the Ceres CAD model, where the materials and payload are taken into account. These parameters are mass M=530Kg, inertia at the center of gravity ICG=47*109 Kg.m2, inertia at the wheel Iwheel=219*106 Kg.m2, distance from the center of gravity to each wheel a=1,2m, wheel radius r=0,28m and an estimated friction β between the wheel and the specific terrain. To find the values of βxx, and the coefficients in the previous equations, open loop data is captured in real tests over solid ground. Inputs (voltages to motor drivers) and outputs (velocities) are registered using ROS. In order to excite the system, pseudo-random binary signals are applied to the motors. Then, an algorithm of parametric estimation such as Recursive Least Squares (RLS) was applied. By several simulations with combinations of the obtained parameters we determine that the dominant dynamics of Ceres is related to β11, β22, while β12 and β21 are only the 13 % of the β11, β22 value. These results mean that there are no couplings between right and left wheels.

Finally, a similar identification process is performed to obtain a transfer function relating the voltage applied to motor drivers to the obtained torque (proportional to angular velocity). Besides, by using kinematics equations for wheeled robots, the linear and angular velocity of the robot is obtained from each wheel velocity.

Controller’s design

To obtain an autonomous robot, we must design and implement controllers, including velocity controllers, path-following controllers, and a path-planning algorithm. This subsection describes the state feedback and fuzzy controllers designed for linear velocity and angular position, obtained by direct integration of angular velocity model, on Ceres robot.

Figure 2

Controller structure

(Left): State feedback controller structure. (Right): Fuzzy Logic controller structure. Source: Own elaboration

State feedback controller

The design of the first controller started from the state space model that can be viewed in Figure 2-left. In this scheme, the states are the linear velocity and angular position. Integral feedback is used to obtain zero steady-state error. As control objectives, a stabilization time of 5 seconds and a damping factor ζ= 0.9 is defined according to the open-loop response obtained by applying steps to each variable in the real plant and measuring outputs with the embedded IMU. These objectives to achieve similar closed-loop behavior with low control effort. With the described requirements and to get a Hurwitz matrix, the closed-loop dynamic is established. To obtain small control efforts, the natural dynamics is taken into account to find the state feedback controller coefficients.

Fuzzy controllers

A vast number of architectures are used with fuzzy controllers to supervise, complement, or replace PID controllers. In this case, replacing the PID controller can improve the performance in several operating points in nonlinear systems [14]. However, in robotics, a low tracking error of the reference signal is required. This requirement is fulfilled typically with an integral gain. Besides, fuzzy controllers with integral action are challenging to design for an error input due to the uncertainty over the steady-state value, that affects assigning membership values [15]. To avoid the fuzzification process of integral error, an FPI+D architecture is chosen [16]. This structure attributes a fixed gain over the integral error which is added to the fuzzy control signal to obtain a zero steady-state error.

The membership functions at the input are selected triangular to obtain a lower computational time in the implementation stage. Moreover, input functions are designed to avoid overlapping of more than two membership functions. In that condition, a value can never be assigned to more than two groups. Finally, the center membership function is designed with a higher slope for the fastest rising time [15].

Then, a tuning process is performed starting by the gain conversion between a classical PID and fuzzy controller proposed in [16]. The control objectives are the same as in the state feedback design, i.e., a response time similar to the open-loop response (5 seconds) and a low signal to each wheel with non-reverse commands.

Results

Simulations are carried out to compare the performance of the designed controllers with multi-step signals. This section compares and analyzes the results before a future integration stage to the Ceres robot.

After applying the fuzzy and state feedback controllers to the previous model, the results shown in Figure 3 were obtained. Figure 3-upper left shows the angular position of the robot; here, the response of the fuzzy controller was approximately 5s faster than the reaction of the state feedback controller. On the other hand, Figure 3-upper right shows the linear velocity of the Ceres robot where the response of the fuzzy controller was 2s faster than the reaction of the state feedback controller. However, the former has some overshoots due to saturations of control signals, as shown in Figure 3 (bottom left). The first overshoot at t= 2s occurs because of the saturation of the right and left voltage in motor drivers; the second overshoot at t= 16s is due to the saturation of the left wheel voltage applied to the motor (angular position reference). This saturation affects the linear velocity at t=16 because of the existing coupling between the dynamic model states.

It is important to remark that the angular velocities of the wheels are proportional to the input voltages, so the effect of the saturation of the motor voltages at the input of the motor drivers is reflected in the linear and angular velocities limitations. We use a saturation between 0 and 10 V. The lower limit was chosen not to have a reversal of rotation in the motors, while the upper limit considers the maximum limits of the motor drivers. Then, the control signals saturate when the amplitude of steps changes, i.e., when the control signal is at its highest value. Furthermore, bearing in mind that the fuzzy controller response is faster than in the state feedback, the control signal is stronger, as seen in Figure 3 (bottom left). Finally, in Figure 3 (bottom right), the control objective was achieved, i.e., an error in steady-state equal to 0, at the time of 5 seconds. Notice that the fuzzy control acted faster than the state feedback.

Figure 3

Comparison of the results obtained with the two types of control

(Upper left): Angular velocities. (upper right): Linear velocities. (bottom left): Wheels commands. (bottom right): Velocities errors. Source: Own elaboration

Conclusions

This paper summarizes two control techniques used to guide an agricultural robot that moves at a constant speed and the desired orientation. The dynamic model is described by the Lagrange approach. Identification techniques were applied to have a more accurate model. Considering two single-input single-output systems, the control techniques were developed. The first one was based on state feedback control, and the second one was based on fuzzy logic control. The fuzzy controller has an FPD+I structure based on the error and its derivative with an integral term added. The control law is given by the sum of fuzzy PD and integral contributions.

The fuzzy control manages to compensate for nonlinear dynamics or not completely modeled dynamics such that the controller’s performance from a temporary response objective is improved. The controllers designed and the simulation tests show appropriate control signals and allow them to reach real robot movements.

Furthermore, path-following controllers will be designed to obtain a complete locomotion scheme that allows crop lines following from GPS coordinates.

Acknowledgment

This work is supported by the project INV-ING 2990 “Self-driving for mission execution in outdoor, dynamic and unstructured environments for a differential robot Ceres-Agrobot” financed by the Universidad Militar Nueva Granada in Bogotá-Colombia. Academic cooperation with Universidad Nacional de Colombia – Bogotá Campus is also recognized.

References

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[2] D. R. Heldman, D. B. Lund, and C. Sabliov, Handbook of Food Engineering, Boca Ratón, Fl, USA: CRC Press, 2018.

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[10] D. Ball et al., “Robotics for Sustainable Broad-Acre Agriculture”, in Springer Tracts in Advanced Robotics, vol. 105, L. Mejias, P. Corke, and J. Roberts, Eds. Switzerland: Springer, 2015, pp. 439-453 [Online]. Available: https://link.springer.com/chapter/10.1007/978-3-319-07488-7_30#citeas

[11] P. F. Martín Gómez, O. S. Hernández, y J. S. Toquica, “Diseño y simulación de un vehículo prototipo para la distribución automática de fertilizantes agrícolas”, Épsilon, n. 24, pp. 49-70, 2015 [En línea]. Disponible en: http://oaji.net/articles/2015/2065-1443974897.pdf

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Sección II
Resúmenes extendidos

En esta sección se encuentra la información que respalda las ponencias realizadas en LACAR2019, en las que se presentaron resultados preliminares de proyectos de investigación y desarrollo tecnológico efectuados en distintas universidades de Latinoamérica.

A Vision-Based System for Evaluating the Quality of the Coloration of Thick Blood Smears in Malaria Diagnosis

Wendy M. Fong Amarís, Carol V. Martínez Luna, Daniel R. Suárez Venegas γ

Department of Industrial Engineering, Pontificia Universidad Javeriana, Bogotá, Colombia.

γ. Autor corresponsal: d-suarez@javeriana.edu.co

Keywords: Malaria, quality, diagnosis, automatic, thick blood smears.

Background, Motivation and Objective

Malaria is an infectious disease and a serious problem of public health. In regard to Colombia, during 2018 a total of 62141 cases of Malaria were reported [1]. For carry out the malaria diagnosis, a blood sample is spread with square shape, above a smear. This technique is named thick blood smear and is the reference method chosen as first option for malaria diagnosis. This thick smear is dyed to allow the parasites visualization. The microscopic malaria diagnosis takes around 1 hour since the sampling to diagnosis statement. Additionally, 15-30 minutes more are required by the microscopist to analyze the smear. In published reports, the WHO has emphasized the need for all laboratories responsible for malaria diagnosis to fully comply with a strict inspection of the diagnostic techniques they implement to guarantee the correct diagnosis [2]. Figure 1 shows an example of two blood smears (images in the second column), and their corresponding microscopic image (First column). The first row shows a properly stained smear. As a result, leukocytes and platelets are perceived. However, the second row shows an example of what is perceived when the staining process of the smear is not properly done; no leukocytes, neither platelets are visualized.

Taking into account the influence of the staining procedure in all the malaria diagnosis process, this project proposes an image analysis system for the automatic evaluation of the staining process, by analyzing the quality of the coloration of the thick blood smear. The system will automatically determine if the smear complies with the minimum requirements of quality to be analyzed by the microscopist, in terms of coloration stablished in WHO [2] and INS & MinSalud [3].

Image analysis in Malaria diagnosis has been studied before. However, to the author’s knowledge, the evaluation of the staining procedure of the smear, which is crucial to ensure the visualization of the parasite by microscopy, has not been studied before by the research community.

Figure 1

Problems in the staining process of the smear

Note: First row shows the smear and its corresponding image when it is correctly stained. The second row shows a smear that was not properly stained (elements of interest are not visualized, e. g. no leukocytes, neither platelets). Source: Prepared by the authors.

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Alexander Martínez

La gestión de proyectos en el Perú. Análisis de madurez 2015-2016

Automática y Robótica en Latinoamérica

Comparison of fuzzy FPD+I and state feedback controller for a differential agricultural robot

Abstract