Lab 2-Visual Odometry

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Texas A&M University *

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Physics

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Apr 3, 2024

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LAB 2: Visual Odometry Victoria Applegate, Alissa Ordway, Carlos Velazquez Texas A&M University College Station, TX 77843, US. Abstract In this report we will demonstrate how to use the tracking camera to convert pixels to SI units and determine the value of gravitational acceleration. The tracking camera recorded the pixels between two different points on a meter stick that can be used to find a conversion between pixels and millimeters and its uncertainty. This conversion is used to convert our data for position into SI units so that it can be further used to find the velocity and acceleration of the moving object in SI units. Once acceleration is found it can be used to calculate gravitational acceleration and its uncertainty, which is the purpose of the lab. Keywords: Tracking Camera, Velocity, Position, Acceleration, Gravity 1. Introduction In this lab, we will be investigating gravitational acceleration. Our first task is to use the tracking camera to track the distance of two stickers on a meter stick and determine the distance between them by converting from pixels to SI units. Our second task is to determine a value for gravitational acceleration of a sticker on a hockey puck sliding down an inclined plane. General physics concepts that we are going to use are gravity, finite difference, and Taylor series, position, velocity, and acceleration vectors. When we are finding the distance between the two stickers on the meter stick, we will use D=√(x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 Equation 1 where (x 1 ,y 1 ) and (x 2 ,y 2 ) are the coordinates of the stickers and then 0.82 mm / 1 pixel Equation 2 Is used to convert from pixels to mm. For finding the value for gravitational acceleration, we first find velocity by using v = r 2 - r 1 / t 2 - t 1 Equation 3 where r 1 and r 2 are the positions of the stickers and t 1 and t 2 are time. Next, We will find acceleration by using a = v 2 - v 1 / t 2 - t 1 Equation 4 where v 2 and v 1 are the velocities of the stickers and t 1 and t 2 are time. Finally, we will use g = a g / sin 𝛳 Equation 5

where a g is the acceleration and sin 𝛳 is the angle of the inclined plane. There will be uncertainty when calculating the gravitational acceleration, which is 0.0098 mm/ms 2 , as the data collection cannot be perfect. 2. Experimental Procedure To begin the experiment take a meter stick and place two different color tracking stickers on opposing ends of the meter stick. Once this is done place the meter stick with the tracking stickers facing up under the camera of the visualization studio. When ready to collect data connect and unlock Jetson. Once connected to Jetson, make a directory for the lab and give it a reasonable name. Then use the copy command followed by examples/tracking/4_track_and_print_with_camera_input.py . Be sure to change the directory to the name you chose above. To run the experiment, type python3 4_track_and_print_with_camera_input.py into the user window to start running the program. Once running, collect a few seconds of data then stop running the program with Ctrl+C . This is the data that will be used to determine the pixels to SI unit conversion. To start the second part of the lab turn on the visualization studio and adjust the angle of the table to 3.6 degrees (the steepest angle it will go) and then run the code the same way you did before. Have one team member at the top of the incline with the object you intend to slide down and another at the bottom of the inclined to stop the object from bouncing off the bottom. The team member with the object needs to place it flat at the top of the incline and let go and the team member at the bottom needs to stop the object from bouncing off the wall at the bottom. Repeat this until you have a usable data set then end the code. This is the data you will use to find gravitational acceleration. 3. Results and Analysis From our data we calculated that our average acceleration is -0.00048 mm/ms^2 with an error of +- 0.000613. The value that we calculated for gravity is 0.001078 mm/ms^2 with an error value of +- 0.001385. Our expected value of gravity is 0.0098 mm/ms^2. Our data is noisy, when one looks at the provided velocity and acceleration graphs it is easily seen that the y-component of the graph has most of the noisy data and errors. The x-component of the data is less noisy and has minimal error when compared to our y-component. Table 1: Describes the Found Acceleration and Gravity Average Acceleration(mm/ms^2) X: -0.000032679+-0.000137 Y: -0.00048 +- 0.000613 Average Gravity(mm/ms^2) 0.001078 +- 0.001385

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