Student: Prithvi Akella
Professor/Sponsor: Professor Oliver O’Reilly
Mentor: Evan Hemingway
Research Project Title: A Visualization Tool for the Vibration of Euler-Bernoulli and Timoshenko Beams
Final Paper
Student: Prithvi Akella
Professor/Sponsor: Professors Oliver O’Reilly & Kameshwar Poolla
Mentor: Evan Hemingway
Research Project Title: Dynamics of Deformed Beams // Linearization of Neural Networks
Abstracts:
Deformation of Beams
Timoshenko beam deformation is widely considered an upper-division/graduate level topic in the study of beam deformation, while its counterpart, Bernoulli-Euler, is oftentimes taught in lower division undergraduate classes. The aim of our work is to generate Mathematica code to portray both static and vibrational deformation under both prevailing theories. Our intended goal is to create software that assists in the intuition and visualization of deformation under these theories in an effort to facilitate their instruction to an undergraduate audience. To that effect, we hope to publish our work on the Mathematica demonstrations site soon.
Linearization of Neural Networks
In practice, the functionality of Neural Networks is oftentimes abstracted to a form of linear regression. Our work aims to validate that abstraction by establishing an analytic map between the functionality of each layer in a Net and each successive independent function in a linear regressor. We hope that doing so can not only elucidate why Neural Networks work as well as they do, but also drastically reduce training and estimation times for small data-sizes. If successful, we hope to create linear predictors for stock-market data to validate the functionality of the regressor on highly-variable, real-world data.
Student: Loren Newton
Professor/Sponsor: Professor Fai Ma
Mentor:
Research Project Title: Computationally Feasible Damped Mode Fitting for Analysis of Damped 1D Systems
Abstract:
Conventional modal analysis for undamped oscillating systems invokes a coordinate transform to enable convenient analysis of these systems in frequency domain as well as computationally efficient approximation of their responses to arbitrary initial conditions. Analogous analysis for damped systems is complicated by the fact that the coordinate mapping, or “damped modes,” are time variant. In a previous research effort, a damped modal coordinate fit was constructed in MATLAB to estimate damped systems’ responses as a linear combination of damped modal responses, fitting the initial conditions to a set of modal coordinates considering both the premultiplication factor of each damped mode as well as its time delay to account for time variance. This algorithm was successful in identifying responses to linear combinations of initial conditions specifically tailored to excite certain modes; however, it returned less-than-desired quality for more arbitrary initial conditions. A limiting factor in the algorithm’s applicability was determined to be its exponentially increasing complexity with regards to the number of modes simulated. A more intelligent algorithm to circumvent these computational limitations was created in this investigation. The previous method was parameterized in physical units, namely time rather than step delays, to facilitate a bisection search in time delays for each damped mode shape. In each iteration of the new algorithm, the solver converges around the time delays for each damped mode that linearly map to a response approximation producing minimum deviation from a numerical solution truth source. Compared to the previous algorithm, this approach drastically increased the solution time for the previously solved mode excitation initial conditions, and notably increased the fidelity of the arbitrary initial condition case. However, further work is required to approach the level of accuracy achieved for the known modal excitation setup
Student: Loren Newton
Professor/Sponsor: Professor Fai Ma
Research Project Title: Response Approximation of Damped Systems by Damped Mode Fitting
Abstract
Student: Isabel Paredes
Professor/Sponsor: Koushil Sreenath
Mentor: Ayush Agrawal
Research Project Title: Generation of Optimized Periodic Trajectories for Cassie
Abstract
Student: Tung Phan
Professor/Sponsor: Professor Oliver O’Reilly
Mentor: Alyssa Novelia
Research Project Title: Dynamic Simulation of Rigid Bodies using JavaScript
Abstract:
This project involves programming several interactive animations of rigid bodies using JavaScript. The resulting animation modules feature arbitrary rotations of rigid bodies and will be showcased on the instructional website http://rotations.berkeley.edu/. The first module features a simulation of a solid block thrown into empty space and can be used to demonstrate the well-known instability of rotation about the intermediate axis. The interface allows the user to adjust the initial angular and linear velocities as well as the gravitational acceleration. The module can be used to show the evolution of the system’s variables with time, and draw the trajectory of the center of mass of the block. The second module involves Euler’s representation of a rotation in terms of an axis of rotation and an angle of rotation. The module features two coordinate systems whose rotation can be controlled by the user and a third fixed system that serves as a reference. To use the program, the user needs to input two pairs of axes and angles of rotation for the two controllable sets of axes. Upon the user’s command, an animation is shown to help them visualize the results of their inputs and enables them to compare two different rotations.
Student: Kimberly A. Sover
Professor/Sponsor: Professor Alice Agogino
Mentor: Andrew P. Sabelhaus
Research Project Title: Mechanical and Electrical Design of a Fixture to Test Modeling Methods and Control of a Tensegrity Spine
Abstract:
Flexible spines for quadruped robots are a growing technology in the soft robotics field. The Berkeley Emergent Space Tensegrities Lab is currently conducting research on a tensegrity-based spine that consists of interlaced rigid cores connected by cables to create movement that mimics that of a vertebrate spine. The spine can be actuated by adjusting the lengths of the cables attached to ends of the vertebrae on the top, bottom, and sides to bend in the sagittal and coronal planes. This paper discusses the development of simplified hardware to robustly test modeling methods and control designs for the current spine prototype. As the semester began, it became clear that the current three-dimensional prototype would not be able to provide accurate data for detailed investigations into the techniques used to construct the governing state equations of the model or the development of control strategies. A stand-alone hardware setup was developed to create and capture the dynamics of a single vertebrae. Mechanically, this test setup was designed to accurately represent a core with cable attachments in two dimensions and eliminate sources of error, such as out of plane motion and fictional effects. Electrically, it was designed to have the ability to precisely dictate the forces the cables apply by using motors to change cable lengths. In addition, there is a camera vision component to the test setup that relays information about the position and rotation of the spine for closed loop control testing. Initial testing of the system, shows that we will be able to move the vertebrae by commanding the motors while tracking the state the vertebrae in real time to perform a variety of tests in both open and closed loop for verification of continued research in the lab. Future work will focus on increased performance and robustness of the test setup for application to a wider range testing possibilities.
Student: Dennis Tan
Professor/Sponsor: Professor Oliver O’Reilly
Research Project Title: 3D Soft Robot Tracking Using Microsoft Kinect
Abstract:
In dynamics field research study, having the capability to track and measure the movement of a body is very beneficial. For a soft robot, we want to calculate the motion of a specific point on the body which can be challenging because of the small size of the robot. By marking a specific point with a contrasting color to the soft robot body, and using the depth measurement feature in Microsoft Kinect, we can process the captured image using the image processing toolbox in MatLab and determine the three-dimensional location of the specific point. The collected location data of our point can then be further process to gather more information such as the velocity and acceleration of the point throughout the run, as well as the orientation of the body. Compared to other motion tracking methods such as multi-camera motion tracking, this approach costs less and is more portable, allowing us to conduct the data collection at different locations wherever access to good lighting is available.