Operating principle (lyrics)
First task of our system is to find a pet in the room. We decide to use something like triangulation to make this issue. We need to attach the transmitter on the pet’s collar. Thus, we assume:
1) the pet is the material point;
2) the pet is located in the same place with it’s collar.
Then, we place two sensors along the wall. They measure the distance to the transmitter (= to the pet) and then transfer these values further.
Our proposing system has one difference with the classical triangulation systems: we use only two sensors instead of three. As we know, two circles have two intersection points. In common situation it’s not enough to identify the object location. But we can use one of intersection points characteristics: they are symmetric about the straight line between centers. As we place two sensors along the wall, we guarantee that one of these intersection points is out of room, so we can define that the pet is in the other point. You can see our “triangulation” math model below (pic. 2).
Pic. 2. Pet triangulation
We have two output signals from this sensors - “a” and “b”, what means distance from our pet to sensors. Now we should evaluate the Decart coordinates of the pet. Let the origin be in the center between two sensors on the wall. The X-axis is along the wall with sensors. The Y-axis is perpendicularly to it directly to the room (pic. 3).
Pic. 3. Decart coordinates in the room
Let OA=OB=L. The systems of equations links output sensor signals and Decart coordinates of the pet:
where “L” - system parameter, “a” and “b” - independent variables, “x” and “y” - dependent variables. These evaluations are occurring inside the Arduino controller.
We have no aim to rotate the laser directly on the pet. The laser target is the point next to it (on the distance “d”, let it be 20 cm) on the pet’s route. That’s why we should define the direction of pet’s speed. We can get two components of the speed by differentiating pet’s coordinates. So below you can see the formulas of defining the coordinates of target for laser.
Laser is turning by two rotatory drivers placed on the height “h”. Each of them moves the laser point along its own axis. They are equipped by two angle sensors. These sensors measure actual angles (alpha and beta) of driver’s rotating. We propose the next method to define the laser point actual coordinates (pic. 4 and pic. 5).
Pic. 4. Defining of Y-coordinate of the laser point
Pic. 5. Defining of X-coordinate of the laser point
Then we find the difference between target position and actual position of the laser point:
These deltas are inputs for the PID-controller. It aims to make them equal to zero.
Thus, we guarantee that our system will make the laser point run away from the pet.
