An important stage in the design of robotic cyber-physical immunosensors systems is the development and research of their mathematical models, which would adequately reflect the important, from the point of view of the problems of research, aspects of the spatial structure of immunopixels. After all, the quality of the model determines the effectiveness of their processing methods in immunosensors systems. The peculiarities of the laser distance sensors application for the detection of obstacles and positioning of a mobile robotic platform in space is considered. The work developed a robotic platform using laser distance sensors. A method of determining dynamic obstacles and a method of positioning are proposed. The calculation of non-contact sensors of the distance of the robotic platform, the scheme of placement of sensors and positioning of the mobile robotic platform in space are described There is a mobile robotic platform in which a complex of infrared distance sensors is used to determine parallelism, distance to an obstacle and positioning.
The planning the movement of a mobile robotic platform, determining obstacles and positioning in
space are one of the most important problems of the operation of robotic platforms and one of the
areas of modern scientific and practical knowledge that is being investigated. Robot navigation is
the problem of finding a path for a robot to move from a start location to a goal location in an
environment, while avoiding obstacles and minimizing costs [
Bug algorithms can be classified into two categories: contact-based and range-based.
Contactbased bug algorithms use only tactile sensors, such as bumpers or whiskers, to detect obstacles.
Range-based bug algorithms use distance sensors, such as sonar or laser, to measure the distance to
obstacles and the goal [
The main features, advantages, and disadvantages of different approaches to bug algorithms
constructions, the discuss their performance and applicability in various scenarios and also some
examples of practical applications are presented in [
Range-based bug algorithms are more advanced and efficient type of bug algorithms. They were first proposed by Khatib (1986), who introduced a variant called Potential Field Method (PFM). These algorithms assume that the robot has a perfect compass and a distance sensor that can measure the distance to obstacles and the goal. Range-based bug algorithms use the distance sensor information to create a potential field, which is determined with a function that assigns some values to each point in the environment. The potential field is composed of two components: an attractive component, which pulls the robot toward the goal, and a repulsive component, which pushes the robot away from obstacles. The robot’s motion is determined by the gradient of the potential field, which indicates the direction of the steepest ascent or descent. The robot moves along the direction of the negative gradient, which leads to the minimum of the potential field.
Range-based bug algorithms are faster and more efficient than contact-based bug algorithms, as they permit to avoid obstacles without touching them and find shorter or optimal paths to the goal. However, range-based bug algorithms may suffer from some drawbacks, concerning local minima, oscillations, and sensitivity to sensor noise and errors.
Bug navigation algorithms are based on some mathematical concepts that describe the robot’s motion, sensing, and decision making. For example: 1. 2.
The robot’s position is represented by a vector p=( x , y ) in a Cartesian coordinate system, where x and y are the horizontal and vertical coordinates, respectively.
The robot’s orientation is represented by an angle θ measured from the positive x-axis in a counterclockwise direction.
The robot’s goal position is represented by another vector g=( xg , y g), which is assumed to be known and fixed.
The robot’s motion is controlled by two inputs: a linear velocity v and an angular velocity ω. The robot’s kinematic model is given by: where i and j are the unit vectors along the x-axis and y-axis, respectively. The robot’s distance to the goal is given by the Euclidean norm of the difference between p and g: dp =v cos θ i + v sin θ j, dt dθ =ω, dx d ( p , g )=‖p− g‖=√( x− x g)2+( y − y g)2, (1) (2) (3) The robot’s heading error is given by the difference between θ and α ( p , g ):
The robot’s distance sensor measures the distance to the nearest obstacle in a given direction β, which is relative to the robot’s orientation. The sensor model is given by: α ( p , g )=arctan y g− y xg− x
, e ( p , θ , g )=θ−α ( p , g ), r ( β )=d ( p , o ( β ))+n ( β ),
s=f ( d ( p , g ))+m,
The robot’s direction to the goal is given by the angle between the vector p-g and the positive x - axis: (4) (5) (6) (7) (8) (9) where o ( β ) is the position of the obstacle point in direction β, and n ( β ) is the sensor noise, which is assumed to be zero-mean Gaussian with variance σ 2. The robot’s intensity sensor measures the signal strength from the goal, which depends on the distance and the signal intensity function f ( d ). The sensor model is given by: where m is the sensor noise, which is assumed to be zero-mean Gaussian with variance τ 2.
The robot’s decision making is based on switching between two modes: move-to-goal (MTG) and follow-boundary (FB). The switching conditions are given by:
MTG → FB : r ( 0)< d s,
FB → MTG : d ( p , g )< d (l , g ) or s > smax, where d s is a safety distance threshold, l is the leave point, and smax is a maximum intensity threshold.
Thе control unit considered is designed to control the robotic platform shown in Figure 1.
The first action after the initialization of the components is to poll the distance sensors and process the data that will arrive from the ADC to the controller. The next step will be to determine the direction of rotation of the DC motor, at the same time the position of the servo is set. After these operations are completed, a control signal is sent to the DC motor, causing it to start.
When the control is carried out, it is possible to change the position of the servo drive, control the speed and direction of rotation of the direct current motor using an encoder.
The principle of operation of the infrared sensor Sharp GP2Y0A02YK0F is based on the use of an infrared beam that is reflected from an object to measure the distance.
The distance is calculated using the triangulation method [16, 17]. The sensor consists of an infrared LED and PSD element [18]. The emitted light beam is reflected from the object, the reflected beam reaches the PSD of the element on which a "light spot" is formed. When the position of the object changes, the angle of reflection of the beam changes Figure 2.
The sensor has a built-in circuit for processing the signal, which allows you to determine the distance to the object. The measured distance is represented as an analog signal.
To determine the calibration characteristic of a non-contact distance sensor, we turn to the experimentally determined dependences of the output voltage on the distance to the reflecting surface. The dependencies for the surfaces with different reflective characteristics are shown in Figure 3.
As one can see from Figure 3, it is possible to specify the operating ranges for which the dependence of the sensor voltage from the distance measured are acceptable.
An example of an approximate distance determination based on information received from a sensor is shown in Figure 4.
Lmax – is the maximum distance from the sensor to the measurement object.
Vmax – is the voltage we get when measuring the maximum possible distance to the object.
For the most optimal distance measurement modes we will operate with the next data: 150 centimeters to the measuring object will equal 0 volts of the output signal, and 0 centimeters equals 2.2 volts.
Sensor characteristic coefficients after approximation by a 5th order polynomial: [-3. 83, -645.2215, -3849.3362, -1230, 150]
Minimal error of Approximation: 0.0014 cm Mean error of Approximation: 2.6278 cm Maximal error of Approximation: 9.1994 cm Blue Pill ADC resolution = 12-bits
These error metrics are comparable to those achieved in complex systems modeling using numerical simulation and parameter identification techniques, where mean approximation errors below 5% are considered acceptable for real-time applications [19]. The use of polynomial approximation and signal linearization in sensor calibration mirrors approaches used in the analysis of complex systems dynamics, where accurate signal reconstruction is essential [20].
ADC resolution of the microcontroller:
32.132 =0.0008 bVit , 0.0008 ( 0.0187 )=0.043 cm, (11) (12)
Methods of accurate distance measurement and determination of the parallelism of mobile robotic platforms to obstacles and objects in real time are an important component in the tasks set for modern robotic platforms [21].
Analysis of the interference of mobile robotic platforms in space is carried out with the help of four infrared sensors Sharp GP2Y0A02YK0F. The arrangement of sensors is shown in Figure 6. a) b)
The distance to the obstacles and parallelism measurement of the mobile robotic platform to objects is determined from an isosceles right triangle. The distance is determined by finding the bisector (B) according to the formula (13)
Since, while maintaining the required accuracy based on the characteristics of the sensor, we can measure the distance (a, b) in the range from 15 to 150 cm, the considered scheme allows us to determine the distance to the obstacle and the parallelism from 0 to106 cm.
To determine parallelism, we define (aex) the experimental distance and compare with the real (a)
B=√2 ab ,
a+b a=
B cos 45 °
, a α1=atan ( ),
b α1=atan α1=atan 2 B−a √3 B (17)
The angle α is determined using the formula
where aex is the experimentally determined leg length of an isosceles right triangle. a – the actual length of the leg of the studied triangle. α 1 – angle of deviation from the object.
B – bisector of the studied triangle.
α – valid angle to the object is 45°.
Thus, the work algorithm is as follows. The mobile robotic platform distance to the obstacle and parallelism calculation is carried out from the measured distances of the isosceles right triangle as in figure 6 b). The distance to the object is determined by the bisector estimating. After finding the bisector the experimental dynamic distance in motion to the object and compare it with the real one. If the experimental distance differs from the real one, then the angle α1 is determined, if (α1)>( α ) then the angle α1 is determined. If (α1)<( α ) then we determine the angle α1. When performing all angle determinations, we compare it with the actual angle to object 45°.
The proposed method of measuring distance and parallelism allows to carry out these operations using a small number of sensors, and also allows to make measurements quite accurately based on the basic characteristics of the sensors. The obtained results are useful for the tasks described in [22,23].
A method of determining dynamic obstacles and a method of robotic platform positioning are proposed considered. The approach proposed is established on the laser distance sensors using for the obstacles detecting and positioning a mobile robotic platform in the space. The calculation of non-contact sensors of the distance of the robotic platform, the scheme of placement of sensors and positioning of the mobile robotic platform in space are described.
The method proposed of using laser distance sensors for determining obstacles and positioning a mobile robotic platform in the space allows to determine the coordinates of the location and course of a mobile robotic platform using infrared distance sensors. The above functions in various combinations can be performed by a positioning system, an inertial navigation system capable of calculating the distance to obstacles, calculating the parallelism of the mobile robotic platform to the plane, and calculating the course of the mobile robotic platform.