Robot navigation in dense crowds : statistical models and experimental studies of human robot cooperation

This thesis explores the problem of mobile robot navigation in dense human crowds. We begin by considering a fundamental impediment to classical motion planning algorithms called the freezing robot problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing predictive uncertainty by employing higher fidelity individual dynamics models or heuristically limiting the individual predictive covariance to prevent overcautious navigation. We demonstrate that both the individual prediction and the individual predictive uncertainty have little to do with this undesirable navigation behavior. Additionally, we provide evidence that dynamic agents are able to navigate in dense crowds by engaging in joint collision avoidance, cooperatively making room to create feasible trajectories. We accordingly develop interacting Gaussian processes, a prediction density that captures cooperative collision avoidance, and a "multiple goal" extension that models the goal driven nature of human decision making. Navigation naturally emerges as a statistic of this distribution.

Most importantly, we empirically validate our models in the Chandler dining hall at Caltech during peak hours, and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (collecting data on 488 runs). The multiple goal interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities nearing 1 person/m², while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as the multiple goal extension, and twice as often as the basic interacting Gaussian process approach. Furthermore, a reactive planner based on the widely used dynamic window approach proves insufficient for crowd densities above 0.55 people/m². We also show that our noncooperative planner or our reactive planner capture the salient characteristics of nearly any dynamic navigation algorithm. For inclusive validation purposes, we show that either our non-interacting planner or our reactive planner captures the salient characteristics of nearly any existing dynamic navigation algorithm. Based on these experimental results and theoretical observations, we conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.

Finally, we produce a large database of ground truth pedestrian crowd data. We make this ground truth database publicly available for further scientific study of crowd prediction models, learning from demonstration algorithms, and human robot interaction models in general.

Convex model predictive control for vehicular systems

In this work, the author presents a method called Convex Model Predictive Control (CMPC) to control systems whose states are elements of the rotation matrices SO(n) for n = 2, 3. This is done without charts or any local linearization, and instead is performed by operating over the orbitope of rotation matrices. This results in a novel model predictive control (MPC) scheme without the drawbacks associated with conventional linearization techniques such as slow computation time and local minima. Of particular emphasis is the application to aeronautical and vehicular systems, wherein the method removes many of the trigonometric terms associated with these systems’ state space equations. Furthermore, the method is shown to be compatible with many existing variants of MPC, including obstacle avoidance via Mixed Integer Linear Programming (MILP).

Dynamic characterization of micro-particle systems

Ordered granular systems have been a subject of active research for decades. Due to their rich dynamic response and nonlinearity, ordered granular systems have been suggested for several applications, such as solitary wave focusing, acoustic signals manipulation, and vibration absorption. Most of the fundamental research performed on ordered granular systems has focused on macro-scale examples. However, most engineering applications require these systems to operate at much smaller scales. Very little is known about the response of micro-scale granular systems, primarily because of the difficulties in realizing reliable and quantitative experiments, which originate from the discrete nature of granular materials and their highly nonlinear inter-particle contact forces.

In this work, we investigate the physics of ordered micro-granular systems by designing an innovative experimental platform that allows us to assemble, excite, and characterize ordered micro-granular systems. This new experimental platform employs a laser system to deliver impulses with controlled momentum and incorporates non-contact measurement apparatuses to detect the particles’ displacement and velocity. We demonstrated the capability of the laser system to excite systems of dry (stainless steel particles of radius 150 micrometers) and wet (silica particles of radius 3.69 micrometers, immersed in fluid) micro-particles, after which we analyzed the stress propagation through these systems.

We derived the equations of motion governing the dynamic response of dry and wet particles on a substrate, which we then validated in experiments. We then measured the losses in these systems and characterized the collision and friction between two micro-particles. We studied wave propagation in one-dimensional dry chains of micro-particles as well as in two-dimensional colloidal systems immersed in fluid. We investigated the influence of defects to wave propagation in the one-dimensional systems. Finally, we characterized the wave-attenuation and its relation to the viscosity of the surrounding fluid and performed computer simulations to establish a model that captures the observed response.

The findings of the study offer the first systematic experimental and numerical analysis of wave propagation through ordered systems of micro-particles. The experimental system designed in this work provides the necessary tools for further fundamental studies of wave propagation in both granular and colloidal systems.

Cosmic Explosions: Observations Of Infant Hydrogen-Free Supernovae Towards An Understanding Of Their Parent Systems

Radiation in the first days of supernova explosions contains rich information about physical properties of the exploding stars. In the past three years, I used the intermediate Palomar Transient Factory to conduct one-day cadence surveys, in order to systematically search for infant supernovae. I show that the one-day cadences in these surveys were strictly controlled, that the realtime image subtraction pipeline managed to deliver transient candidates within ten minutes of images being taken, and that we were able to undertake follow-up observations with a variety of telescopes within hours of transients being discovered. So far iPTF has discovered over a hundred supernovae within a few days of explosions, forty-nine of which were spectroscopically classified within twenty-four hours of discovery.

Our observations of infant Type Ia supernovae provide evidence for both the single-degenerate and double-degenerate progenitor channels. On the one hand, a low-velocity Type Ia supernova iPTF14atg revealed a strong ultraviolet pulse within four days of its explosion. I show that the pulse is consistent with the expected emission produced by collision between the supernova ejecta and a companion star, providing direct evidence for the single degenerate channel. By comparing the distinct early-phase light curves of iPTF14atg to an otherwise similar event iPTF14dpk, I show that the viewing angle dependence of the supernova-companion collision signature is probably responsible to the difference of the early light curves. I also show evidence for a dark period between the supernova explosion and the first light of the radioactively-powered light curve. On the other hand, a peculiar Type Ia supernova iPTF13asv revealed strong near-UV emission and absence of iron in the spectra within the first two weeks of explosion, suggesting a stratified ejecta structure with iron group elements confined to the slow-moving part of the ejecta. With its total ejecta mass estimated to exceed the Chandrasekhar limit, I show that the stratification and large mass of the ejecta favor the double-degenerate channel.

In a separate approach, iPTF found the first progenitor system of a Type Ib supernova iPTF13bvn in the pre-explosion HST archival mages. Independently, I used the early-phase optical observations of this supernova to constrain its progenitor radius to be no larger than several solar radii. I also used its early radio detections to derive a mass loss rate of 3e-5 solar mass per year for the progenitor right before the supernova explosion. These constraints on the physical properties of the iPTF13bvn progenitor provide a comprehensive data set to test Type Ib supernova theories. A recent HST revisit to the iPTF13bvn site two years after the supernova explosion has confirmed the progenitor system.

Moving forward, the next frontier in this area is to extend these single-object analyses to a large sample of infant supernovae. The upcoming Zwicky Transient Facility with its fast survey speed, which is expected to find one infant supernova every night, is well positioned to carry out this task.