Formal Reports: Robotic Mouse Group

The purpose of this project is to design an autonomous robotic mouse that is able to navigate through a maze, locate a doll, and transport the doll to the beginning of the maze. This opportunity will provide students an application in everthing they have learned in their electrical, mechanical, and computer engineering courses. The concept for this project was originally taken from the IEEE (Institute of Electrical and Electronics Engineering) robotic mouse competition held ammally in Japan, which is a competition in how quickly a robotic mouse can solve a maze. We decided to add a realistic component to the design and simulate a search and rescue mission, hence including the need to rescue a doll and return it to the start of the maze. This project will also lay a foundation for fuhu-e Trinity engineers who wish to compete in IEEE Micromouse Competitions or in developing similar projects. The Micromouse itself is a three-tiered, circular robot (about 10 centimeters to a side) with two wheels on both sides and a single ball bearing located towards the back of the body which provides balance for the robot. The chassis is made of 118th inch Plexiglas and is cut into two tiered sheets in order to provide a body for the robot. The major hardware components of our design include sensors, servo motors, DC motors, encoders, wheels, a microcontroller, chassis, battery and a gripper. Three sensors are attached to the front of the robot in order to help locate the walls of the maze and orient the robot. The DC motors are tucked within the body of the robot and are used to power the wheels. The battery is stored within the body of the mouse and is positioned by the Plexiglas columns connecting the three tiers of the chassis. A project control board (PCB) is located in the middle tier and contains all of the electrical components that are necessary to complete our design. Encoders are located on either side of the middle tier and are also used to help the robot determine how far it has travelled in order to navigate the maze. The gripper will be attached to the top tier of the Micromouse and will rotate downwards to pick up the doll when it is within a certain range. Four prototypes have been developed in order to reach our final design. A wall follower was developed as the first prototype and worked properly. The second prototype failed because the hand soldered board was causing issues when all the components were co1mected to each other. Prototype #3 included a gripper circuit as well as a robotic circuit that was supposed to navigate the maze. The gripper circuit was developed and worked properly, but similar issues that had occurred with Prototype #2 were apparent within the robotic circuit of Prototype #3. These issues were eventually fixed by including encoders which would help the robot trace how far it has travelled while navigating the maze. Multiple microcontrollers were also destroyed in the process of developing prototype #3. It was determined that by hooking the motors up to the same power source as the microcontroller, a back-EMF voltage was being applied, which was causing the microcontroller to stop working. By isolating the power sources using two individual batteries, this problem was solved. After testing our final design, the robot was able to navigate the maze, locate the doll, pick up the doll and then return it to the start of the maze within 15 minutes. It was able to this autonomously without leaving any parts behind. Unfortunately, our design was not as robust as we would have liked. On average, the robot was able to complete the objective perfectly every fifth time it was tested. Because of this, we were not able to complete the objective three times in a row without fail. Nevertheless, our robot was able to accomplish four out of the five objectives that we initially stated in our project charter while adhering to all of the project constraints

Mathematical modeling with digital technological tools for interpretation of contextual situations

This article has the goal of proposing physical contextual situations modeling as a way to interpret mathematical representations that are produced by digital technological tools. Thus, there is an experimental situation-problem about a physical phenomenon that is modeled through video analysis and dynamic geometry software; the methodological model Cuvima conducts the experimental activity. Pre-testing and post-testing measuring instruments were designed to obtain the information and previous conceptions of ten graduate students in Mathematical Education, which showed a conceptual change. Similarly, results prove that digital technology, from a didactical sequence, supports and strengthens experimental work simplifying modeling processes of a physical phenomenon, promoting the use of mathematical representations to solve a situation-problem

Rare Kaon Decay to Missing Energy: Implications of the NA62 Result for a Z′Z^\prime Model

Meson decays offer a good opportunity to probe new physics. The rare kaon decay $K^+ \rightarrow \pi^+ \nu\bar{\nu}$ is one of the cleanest of them and, for this reason, is rather sensitive to new physics, in particular, vector mediators. NA62 collaboration, running a fixed-target experiment at CERN, recently reported an unprecedented sensitivity to this decay, namely a branching fraction of $BR(K^+ \rightarrow \pi^+ \nu\bar{\nu}) = (11^{+4.0}_{-3.5})\times 10^{-11}$ at 68\% C.L. Vector mediators that couple to neutrinos may yield a sizeable contribution to this decay. Motivated by the new measurement, we interpret this result in the context of a concrete $Z^\prime$ model, and put our findings into perspective with the correlated $K_L \rightarrow \pi^0 \nu \bar{\nu}$ decay measured by KOTO collaboration, current, and future colliders, namely the High-Luminosity and High-Energy LHC