The research presented in this Honors Thesis provides development in machine learning models which predict future states of a system with unknown dynamics, based on observations of the system. Two case studies are presented for (1) a non-conservative pendulum and (2) a differential game dictating a two-car uncontrolled intersection scenario. In the paper we investigate how learning architectures can be manipulated for problem specific geometry. The result of this research provides that these problem specific models are valuable for accurate learning and predicting the dynamics of physics systems.<br/><br/>In order to properly model the physics of a real pendulum, modifications were made to a prior architecture which was sufficient in modeling an ideal pendulum. The necessary modifications to the previous network [13] were problem specific and not transferrable to all other non-conservative physics scenarios. The modified architecture successfully models real pendulum dynamics. This case study provides a basis for future research in augmenting the symplectic gradient of a Hamiltonian energy function to provide a generalized, non-conservative physics model.<br/><br/>A problem specific architecture was also utilized to create an accurate model for the two-car intersection case. The Costate Network proved to be an improvement from the previously used Value Network [17]. Note that this comparison is applied lightly due to slight implementation differences. The development of the Costate Network provides a basis for using characteristics to decompose functions and create a simplified learning problem.<br/><br/>This paper is successful in creating new opportunities to develop physics models, in which the sample cases should be used as a guide for modeling other real and pseudo physics. Although the focused models in this paper are not generalizable, it is important to note that these cases provide direction for future research.
High-entropy alloys possessing mechanical, chemical, and electrical properties that far exceed those of conventional alloys have the potential to make a significant impact on many areas of engineering. Identifying element combinations and configurations to form these alloys, however, is a difficult, time-consuming, computationally intensive task. Machine learning has revolutionized many different fields due to its ability to generalize well to different problems and produce computationally efficient, accurate predictions regarding the system of interest. In this thesis, we demonstrate the effectiveness of machine learning models applied to toy cases representative of simplified physics that are relevant to high-entropy alloy simulation. We show these models are effective at learning nonlinear dynamics for single and multi-particle cases and that more work is needed to accurately represent complex cases in which the system dynamics are chaotic. This thesis serves as a demonstration of the potential benefits of machine learning applied to high-entropy alloy simulations to generate fast, accurate predictions of nonlinear dynamics.
To achieve this goal, a model of a swarm performing a collective transport task in a bounded domain featuring convex obstacles was simulated in MATLAB/ Simulink®. The closed-loop dynamic equations of this model were linearized about an equilibrium state with angular acceleration and linear acceleration set to zero. The simulation was run over 30 times to confirm system ability to successfully transport the payload to a goal point without colliding with obstacles and determine ideal operating conditions by testing various orientations of objects in the bounded domain. An additional purely MATLAB simulation was run to identify local minima of the Hessian of the navigation-like potential function. By calculating this Hessian periodically throughout the system’s progress and determining the signs of its eigenvalues, a system could check whether it is trapped in a local minimum, and potentially dislodge itself through implementation of a stochastic term in the robot controllers. The eigenvalues of the Hessian calculated in this research suggested the model local minima were degenerate, indicating an error in the mathematical model for this system, which likely incurred during linearization of this highly nonlinear system.
This paper analyzes responses to deviated Trolley Problem scenarios [5] in a simulated driving environment and still images from MIT’s moral machine website [8] to better understand how humans respond to various crashes. Also included is participants driving habits and personal values, however the bulk of that analysis is not included here. The results of the simulation prove that for the most part in driving scenarios, people would rather sacrifice themselves over people outside of the vehicle. The moral machine scenarios prove that self-sacrifice changes as the trend to harm one’s own vehicle was not so strong when passengers were introduced. Further defending this idea is the importance placed on Family Security over any other value.
Suggestions for implementing ethics into autonomous vehicle crashes stem from the results of this experiment but are dependent on more research and greater sample sizes. Once enough data is collected and analyzed, a moral baseline for human’s moral domain may be agreed upon, quantified, and turned into hard rules governing how self-driving cars should act in different scenarios. With these hard rules as boundary conditions, artificial intelligence should provide training and incremental learning for scenarios which cannot be determined by the rules. Finally, the neural networks which make decisions in artificial intelligence must move from their current “black box” state to something more traceable. This will allow researchers to understand why an autonomous vehicle made a certain decision and allow tweaks as needed.
The work presents the nonlinear equations of motion of a quadcopter. This includes the translational and rotational equations of motion, as well as an analysis of the nonlinear actuator dynamics. The work then analyzes the static properties of a quadcopter in forward flight equilibrium and shows how static properties change as physical properties of the vehicle are varied. Next, the dynamics of forward flight are linearized, and a dynamic analysis is provided.
After dynamic analysis, the work shows detailed hierarchical control system design trade studies, which includes attitude and translational inner-outer loop control. Among other designs, the following are presented: PD control, proportional control, pole-placement control. Each of these control architectures are employed for the inner loops and outer loops. The work also analyzes linear versus nonlinear simulation performance of a quadcopter, specifically for a step x-axis reference command. It is found that the nonlinear dynamics of the actuator cause significant discrepancy between linear and nonlinear simulation.
Finally, this thesis establishes directions for future graduate research. This includes hardware design, as well as moving toward design of a highly-maneuverable thrust-vectoring quadrotor which will be the focus of the proposed graduate PhD research. In summary, this thesis provides the beginning of a cohesive framework to model, analyze, control, and design quadcopters. It also lays the groundwork for graduate research and beyond.