Patching Neural Barrier Functions Using Hamilton-Jacobi Reachability

Learning-based control algorithms have led to major advances in robotics at the cost of decreased safety guarantees. Recently, neural networks have also been used to characterize safety through the use of barrier functions for complex nonlinear systems. Learned barrier functions approximately encode and enforce a desired safety constraint through a value function, but do not provide any formal guarantees. In this paper, we propose a local dynamic programming (DP) based approach to "patch" an almost-safe learned barrier at potentially unsafe points in the state space. This algorithm, HJ-Patch, obtains a novel barrier that provides formal safety guarantees, yet retains the global structure of the learned barrier. Our local DP based reachability algorithm, HJ-Patch, updates the barrier function "minimally" at points that both (a) neighbor the barrier safety boundary and (b) do not satisfy the safety condition. We view this as a key step to bridging the gap between learning-based barrier functions and Hamilton-Jacobi reachability analysis, providing a framework for further integration of these approaches. We demonstrate that for well-trained barriers we reduce the computational load by 2 orders of magnitude with respect to standard DP-based reachability, and demonstrate scalability to a 6-dimensional system, which is at the limit of standard DP-based reachability.Comment: 8 pages, submitted to IEEE Conference on Decision and Control (CDC), 202

Efficient Control Barrier Refinement Using Local Hamilton-Jacobi Reachability

Safe control policies for nonlinear dynamic systems are notoriously challenging to derive. Hamilton-Jacobi reachability analysis (HJ reachability) provides guaranteed safety in the form of the optimal control policy, but its compute cost scales exponentially with state space. Neural learning provides an alternative approach with its compute scaling only against problem complexity, but yields only approximate results. Recently, neural policies in the form of control barrier functions (CBFs) have been used to warmstart HJ reachability, yielding a guaranteed safe result more efficiently. However, a significant amount of compute is still spent to shape the CBF into the HJ reachability result. This paper introduces HJ Boundary Marching, which adapts the mechanics of warmstarted HJ reachability to refine erroneous control barrier function boundaries by minimally reshaping them to the nearest interior control-invariant boundary. This yields a guaranteed safe CBF for the same set as HJ reachability, with up to two orders of magnitude faster compute. A demonstration is provided on a 4-dimensional system with a learned neural CBF

Development and Validation of a Two Factor Model of Adult Career Orientation

Subjects in this study were 5,523 respondents from a survey which was sent to households throughout the United States. The purpose of this study was to examine two basic components of career orientation: career indecision and career insight. Correlational analyses found relationships between career indecision and average job tenure, industry leaving intentions, industry staying intentions, and job satisfaction. Correlational analyses found relationships between career insight, industry staying intentions and job satisfaction. Multiple regression analyses were run using both career indecision and career insight as independent variables found that they had useful levels of incremental validity in predicting industry leaving intentions and job satisfaction. Potential uses of the two-dimensional career indecision - career insight model are discussed

Grafted city. Re-forming Porta Genova rail yard, Milano

LAUREA MAGISTRALEQuesta tesi ha lo scopo di proporre un'idea su come riformare e trasformare il cantiere ferroviario di Porta Genova abbandonato in uno spazio sociale interattivo, con l'intenzione di coinvolgere questo sito abbandonato con il suo contesto. Il progetto offre l'opportunità di ripensare i valori di un cantiere ferroviario abbandonato nella città di Milano rispetto ai suoi valori spaziali come un cantiere urbano esistente, ma rifiuta il punto di vista romantico di lasciarlo intatto per sempre. Questo progetto è intrapreso con l'intento di esplorare le possibilità di generare un nuovo concetto e tipologia per il cantiere ferroviario di Porta Genova, affrontandolo come uno dei sette cantieri ferroviari dismessi di Milano. Il mio obiettivo è di sfruttare l'architettura per scoprire l'essenza nascosta di questo sito, fondere i suoi valori sensibili con il suo delicato contesto con la speranza di una più ampia influenza urbana non solo sull'intero distretto ma anche su scala metropolitana. L'architettura risultante tenta di tracciare ombre del passato, adeguate alle principali trasformazioni urbane dell'era postindustriale, lasciando aperto il futuro per ulteriori interpretazioni e appropriazioni come il progetto "SCALI MILANO". Il design suggerisce un nuovo modo di vedere e pianificare la città. Questa nuova prospettiva offre una potenziale interazione a livello locale, in modo tale che la città sia generata dal basso verso l'alto, non dal modello tradizionale di pianificazione urbana top-down. Ci sono diverse considerazioni che sono alla base dello sviluppo della progettazione architettonica di accompagnamento, tra cui: La teoria concettuale di "Terrain Vague". H2020 Riciclaggio in Italia Ri-formare Milano Scali Milano Distretto di Porta Genova | Valori storici, trasformazioni contemporanee e opportunità future. Stazione di Porta GenovaThis thesis aims to propose an idea about how to re-form and transform the abandoned Porta Genova rail yard into a social interactive space, with an intention to engage this abandoned site with its context. The project provides an opportunity to rethink values of an abandoned rail yard in the city of Milan with respect to its spatial values as an existing urban yard but refuses the romantic point of view of leaving it untouched forever. This project is undertaken with the intention of exploring the possibilities of generating a new concept and typology for Porta Genova rail yard, addressing it as one of the seven unused railway yards of Milan. My aim is to advantage architecture to uncover the hidden essence of this site, merge its sensitive values with its delicate context with hope of wider urban influence not only on entire district but also on metropolitan scale. The resulting architecture attempts to trace shadows of the past, adequate with major urban transformations of post-industrial era whilst leaving the future open for further interpretation and appropriation as so called “SCALI MILANO” project. The design suggests a new way of seeing and planning the city. This new perspective offers a potential interaction in local scale, such that the city is generated from the bottom-up, not the traditional model of top-down urban planning. There are several considerations which underpin the development of the accompanying architectural design, including: The conceptual theory of “Terrain Vague”. H2020 Re-cycling Italy Ri-formare Milano Scali Milano Porta Genova District | Historical values, contemporary transformations and future opportunities. Porta Genova Statio