3.16.2. Odometry We are using encoders in our wheels as instruments of measuring our robot’s movements to determine its location in the course. In order to do this, we will need to use an odometer model to convert the information read from the encoders to real world coordinates. The model we intend to use is detailed below. Begin with the following equations relating the change in position of the wheels to the circular arc of the turning axis as seen in Figure 3.21. Eq(1): Δsl = Rα Eq(2): Δsr = (R+2L)α Eq(3): Δs = (R+L)α Figure 3.21: Odometry p1- Example showing the relations of variables (Permission Requested from Princeton) Use Eq(1) and Eq(2) 2 to solve for the distance from the right and left wheels to the axis of the turn. Eq(4): Rα = Δsl Eq(5): Lα = (Δsr - Rα)/2 = Δsr /2 – Δsl /2 Substituting Eq(4) and Eq(5) into Eq(3) we represent Δs as a function of Δsl and Δsr. Δs = (R+L)α = R α + L= Δsl + Δsr /2 – Δsl /2 = Δsl /2 + Δsr /2 Δs = (Δsl + Δsr) /2 To calculate the change of the angle of the robot’s orientation Δθ, is equal to the circular arc’s center point as seen in Figure 3.22. Δθ = α Figure 3.22: Odometry p2- Example relating circular α to the orientation (Permission Requested from Princeton) Then solve for α by equating α from Eq(1) and Eq(2). Δθ = (Δsr - Δsl ) /2L With Δθ and Δs we are able to calculate the position change in real world coordinates. Using trigonometry to model the Δx and Δy as functions of Δd. Δx = Δd cos(θ + Δθ/2) Δy = Δd sin(θ + Δθ/2)
Dimension Engineering has only been utilized for some specific that cannot be purchased at other retailers. For example, the 5V switching regulator was a piece that was specifically developed by Dimension Engineering. Therefore, the only place to order this product was on their website. This was the best regulator that was found within our price range for the proposed system. 4. Related Standards and Design Constraints In this section, there are several different standards that will be used in order to make this project successful. There are some related standards out in the market, it is important to compare these standards in order to be able to prove that the project is safe, usable and stable. This section will explore the different types of standards that are related to our project as well as discuss the possible design constraints that this project may face. 4.1. Standards Research For related standards research, there are plenty of standards that can be compared to this project. In this section, one standard is researched through details and analyzing so there is a better sense of how to read and use a standard and a table is provided for the other standards that can be researched and used. The first related standard for our project is an IEEE standard denoted “1873-2015 - IEEE Standard for Robot Map Data Representation for Navigation.” One of the methods that the battlebot robot in our project will implemented is the use of 2D mapping. Therefore, this related standard can be used and compared to the robot project. Although this topic is very broad, the standard provides a scope of what exactly is being standardized. This standard is used for defining terminologies related to 2D robot maps of navigation in indoor and outdoor environments. It also specifies a data model for each element and defines a format used to exchange this data among other computers and robots. The importance of this standard is to set a common representation for robot map data in a way that can allow an accessible use of software exchange among other robotic systems. This standard is used in order to expand the range of application and operational use among robots. There is also a section of definitions containing word definitions and mathematical definitions in order for the reader using this standard to understand the terms being presented as well as define specific words that makes following the standard less confusing. There are several tables in the standard, labeled M/O which defines how often a variable or element is to be used. M is for mandatory and O is for optional. There are also detailed descriptions for how to format the data between the different type of mapping such as metric and topological mapping.