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Brian Williams

Brian Williams appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Roboticsastro-ph.COeess.SYSystems and ControlMachine Learningmath.OCQuantitative MethodsArtificial Intelligenceastro-ph.IMastro-ph.EPastro-ph.GAastro-ph.HECell BehaviorSymbolic Computation

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Published work

21 published item(s)

preprint2026arXiv

MoMo: Conditioned Contrastive Representation Learning for Preference-Modulated Planning

Temporally contrastive representation learning induces a latent structure capable of reducing long-horizon planning to inference in a low-dimensional linear system. However, existing contrastive planning work learns a single latent geometry which cannot distinguish multiple valid behaviors trading task efficiency against risk exposure for the same start-goal query. We introduce MoMo, a preference-conditioned contrastive planner allowing a scalar user preference to continuously modulate plan conservativeness at inference time, without retraining. MoMo learns a joint conditioning of the representation geometry and latent prediction operator via Feature-Wise Linear Modulation and low-rank neural modulation, respectively. We show that our formulation preserves the probability density ratio encoded in the representation space that is required for inference-driven contrastive planning, further retaining its inference-time efficiency. Across six environments, MoMo smoothly adapts plan safety according to user preferences, yielding improved temporal and preferential consistency over state augmentation baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Automatic Curricula via Expert Demonstrations

We propose Automatic Curricula via Expert Demonstrations (ACED), a reinforcement learning (RL) approach that combines the ideas of imitation learning and curriculum learning in order to solve challenging robotic manipulation tasks with sparse reward functions. Curriculum learning solves complicated RL tasks by introducing a sequence of auxiliary tasks with increasing difficulty, yet how to automatically design effective and generalizable curricula remains a challenging research problem. ACED extracts curricula from a small amount of expert demonstration trajectories by dividing demonstrations into sections and initializing training episodes to states sampled from different sections of demonstrations. Through moving the reset states from the end to the beginning of demonstrations as the learning agent improves its performance, ACED not only learns challenging manipulation tasks with unseen initializations and goals, but also discovers novel solutions that are distinct from the demonstrations. In addition, ACED can be naturally combined with other imitation learning methods to utilize expert demonstrations in a more efficient manner, and we show that a combination of ACED with behavior cloning allows pick-and-place tasks to be learned with as few as 1 demonstration and block stacking tasks to be learned with 20 demonstrations.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Non-Gaussian Risk Bounded Trajectory Optimization for Stochastic Nonlinear Systems in Uncertain Environments

We address the risk bounded trajectory optimization problem of stochastic nonlinear robotic systems. More precisely, we consider the motion planning problem in which the robot has stochastic nonlinear dynamics and uncertain initial locations, and the environment contains multiple dynamic uncertain obstacles with arbitrary probabilistic distributions. The goal is to plan a sequence of control inputs for the robot to navigate to the target while bounding the probability of colliding with obstacles. Existing approaches to address risk bounded trajectory optimization problems are limited to particular classes of models and uncertainties such as Gaussian linear problems. In this paper, we deal with stochastic nonlinear models, nonlinear safety constraints, and arbitrary probabilistic uncertainties, the most general setting ever considered. To address the risk bounded trajectory optimization problem, we first formulate the problem as an optimization problem with stochastic dynamics equations and chance constraints. We then convert probabilistic constraints and stochastic dynamics constraints on random variables into a set of deterministic constraints on the moments of state probability distributions. Finally, we solve the resulting deterministic optimization problem using nonlinear optimization solvers and get a sequence of control inputs. To our best knowledge, it is the first time that the motion planning problem to such a general extent is considered and solved. To illustrate the performance of the proposed method, we provide several robotics examples.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Optimal Mixed Discrete-Continuous Planning for Linear Hybrid Systems

Planning in hybrid systems with both discrete and continuous control variables is important for dealing with real-world applications such as extra-planetary exploration and multi-vehicle transportation systems. Meanwhile, generating high-quality solutions given certain hybrid planning specifications is crucial to building high-performance hybrid systems. However, since hybrid planning is challenging in general, most methods use greedy search that is guided by various heuristics, which is neither complete nor optimal and often falls into blind search towards an infinite-action plan. In this paper, we present a hybrid automaton planning formalism and propose an optimal approach that encodes this planning problem as a Mixed Integer Linear Program (MILP) by fixing the action number of automaton runs. We also show an extension of our approach for reasoning over temporally concurrent goals. By leveraging an efficient MILP optimizer, our method is able to generate provably optimal solutions for complex mixed discrete-continuous planning problems within a reasonable time. We use several case studies to demonstrate the extraordinary performance of our hybrid planning method and show that it outperforms a state-of-the-art hybrid planner, Scotty, in both efficiency and solution qualities.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Fast Certification of Collision Probability Bounds with Uncertain Convex Obstacles

To operate reactively in uncertain environments, robots need to be able to quickly estimate the risk that they will collide with their environment. This ability is important for both planning (to ensure that plans maintain acceptable levels of safety) and execution (to provide real-time warnings when risk exceeds some threshold). Existing methods for estimating this risk are often limited to models with simplified geometry (e.g. point robots); others handle complex geometry but are too slow for many applications. In this paper, we present two algorithms for quickly computing upper bounds on the risk of collision between a robot and uncertain obstacles by searching for certificate regions that capture collision probability mass while avoiding the robot. These algorithms come with strong theoretical guarantees that the true risk does not exceed the estimated value, support arbitrary geometry via convex decomposition, and provide fast query times ($<200μ$s) in representative scenarios. We characterize the performance of these algorithms in environments of varying complexity, demonstrating at least an order of magnitude speedup over existing techniques.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Fast Risk Assessment for Autonomous Vehicles Using Learned Models of Agent Futures

This paper presents fast non-sampling based methods to assess the risk of trajectories for autonomous vehicles when probabilistic predictions of other agents' futures are generated by deep neural networks (DNNs). The presented methods address a wide range of representations for uncertain predictions including both Gaussian and non-Gaussian mixture models for predictions of both agent positions and controls. We show that the problem of risk assessment when Gaussian mixture models (GMMs) of agent positions are learned can be solved rapidly to arbitrary levels of accuracy with existing numerical methods. To address the problem of risk assessment for non-Gaussian mixture models of agent position, we propose finding upper bounds on risk using Chebyshev's Inequality and sums-of-squares (SOS) programming; they are both of interest as the former is much faster while the latter can be arbitrarily tight. These approaches only require statistical moments of agent positions to determine upper bounds on risk. To perform risk assessment when models are learned for agent controls as opposed to positions, we develop TreeRing, an algorithm analogous to tree search over the ring of polynomials that can be used to exactly propagate moments of control distributions into position distributions through nonlinear dynamics. The presented methods are demonstrated on realistic predictions from DNNs trained on the Argoverse and CARLA datasets and are shown to be effective for rapidly assessing the probability of low probability events.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Moment State Dynamical Systems for Nonlinear Chance-Constrained Motion Planning

Chance-constrained motion planning requires uncertainty in dynamics to be propagated into uncertainty in state. When nonlinear models are used, Gaussian assumptions on the state distribution do not necessarily apply since almost all random variables propagated through nonlinear dynamics results in non-Gaussian state distributions. To address this, recent works have developed moment-based approaches for enforcing chance-constraints on non-Gaussian state distributions. However, there still lacks fast and accurate moment propagation methods to determine the necessary statistical moments of these state distributions. To address this gap, we present a framework that, given a stochastic dynamical system, can algorithmically search for a new dynamical system in terms of moment state that can be used to propagate moments of disturbance random variables into moments of the state distribution. The key algorithm, TreeRing, can be applied to a large class of nonlinear systems which we refer to as trigonometric polynomial systems. As an example application, we present a distributionally robust RRT (DR-RRT) algorithm that propagates uncertainty through the nonlinear Dubin's car model without linearization.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Non-Gaussian Chance-Constrained Trajectory Planning for Autonomous Vehicles under Agent Uncertainty

Agent behavior is arguably the greatest source of uncertainty in trajectory planning for autonomous vehicles. This problem has motivated significant amounts of work in the behavior prediction community on learning rich distributions of the future states and actions of agents. However, most current works on chance-constrained trajectory planning under agent or obstacle uncertainty either assume Gaussian uncertainty or linear constraints, which is limiting, or requires sampling, which can be computationally intractable to encode in an optimization problem. In this paper, we extend the state-of-the-art by presenting a methodology to upper-bound chance-constraints defined by polynomials and mixture models with potentially non-Gaussian components. Our method achieves its generality by using statistical moments of the distributions in concentration inequalities to upper-bound the probability of constraint violation. With this method, optimization-based trajectory planners can plan trajectories that are chance-constrained with respect to a wide range of distributions representing predictions of agent future positions. In experiments, we show that the resulting optimization problem can be solved with state-of-the-art nonlinear program solvers to plan trajectories fast enough for use online.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Provably Safe Trajectory Optimization in the Presence of Uncertain Convex Obstacles

Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of safety as the robot moves, even when the exact locations of nearby obstacles are not known. In this paper, we solve this chance-constrained motion planning problem using a sequential convex optimization framework. To constrain the risk of collision incurred by planned movements, we employ geometric objects called $ε$-shadows to compute upper bounds on the risk of collision between the robot and uncertain obstacles. We use these $ε$-shadow-based estimates as constraints in a nonlinear trajectory optimization problem, which we then solve by iteratively linearizing the non-convex risk constraints. This sequential optimization approach quickly finds trajectories that accomplish the desired motion while maintaining a user-specified limit on collision risk. Our method can be applied to robots and environments with arbitrary convex geometry; even in complex environments, it runs in less than a second and provides provable guarantees on the safety of planned trajectories, enabling fast, reactive, and safe robot motion in realistic environments.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

The Quiescent Intracluster Medium in the Core of the Perseus Cluster

Clusters of galaxies are the most massive gravitationally-bound objects in the Universe and are still forming. They are thus important probes of cosmological parameters and a host of astrophysical processes. Knowledge of the dynamics of the pervasive hot gas, which dominates in mass over stars in a cluster, is a crucial missing ingredient. It can enable new insights into mechanical energy injection by the central supermassive black hole and the use of hydrostatic equilibrium for the determination of cluster masses. X-rays from the core of the Perseus cluster are emitted by the 50 million K diffuse hot plasma filling its gravitational potential well. The Active Galactic Nucleus of the central galaxy NGC1275 is pumping jetted energy into the surrounding intracluster medium, creating buoyant bubbles filled with relativistic plasma. These likely induce motions in the intracluster medium and heat the inner gas preventing runaway radiative cooling; a process known as Active Galactic Nucleus Feedback. Here we report on Hitomi X-ray observations of the Perseus cluster core, which reveal a remarkably quiescent atmosphere where the gas has a line-of-sight velocity dispersion of 164+/-10 km/s in a region 30-60 kpc from the central nucleus. A gradient in the line-of-sight velocity of 150+/-70 km/s is found across the 60 kpc image of the cluster core. Turbulent pressure support in the gas is 4% or less of the thermodynamic pressure, with large scale shear at most doubling that estimate. We infer that total cluster masses determined from hydrostatic equilibrium in the central regions need little correction for turbulent pressure.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Time Resource Networks

The problem of scheduling under resource constraints is widely applicable. One prominent example is power management, in which we have a limited continuous supply of power but must schedule a number of power-consuming tasks. Such problems feature tightly coupled continuous resource constraints and continuous temporal constraints. We address such problems by introducing the Time Resource Network (TRN), an encoding for resource-constrained scheduling problems. The definition allows temporal specifications using a general family of representations derived from the Simple Temporal network, including the Simple Temporal Network with Uncertainty, and the probabilistic Simple Temporal Network (Fang et al. (2014)). We propose two algorithms for determining the consistency of a TRN: one based on Mixed Integer Programing and the other one based on Constraint Programming, which we evaluate on scheduling problems with Simple Temporal Constraints and Probabilistic Temporal Constraints.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Drake: An Efficient Executive for Temporal Plans with Choice

This work presents Drake, a dynamic executive for temporal plans with choice. Dynamic plan execution strategies allow an autonomous agent to react quickly to unfolding events, improving the robustness of the agent. Prior work developed methods for dynamically dispatching Simple Temporal Networks, and further research enriched the expressiveness of the plans executives could handle, including discrete choices, which are the focus of this work. However, in some approaches to date, these additional choices induce significant storage or latency requirements to make flexible execution possible. Drake is designed to leverage the low latency made possible by a preprocessing step called compilation, while avoiding high memory costs through a compact representation. We leverage the concepts of labels and environments, taken from prior work in Assumption-based Truth Maintenance Systems (ATMS), to concisely record the implications of the discrete choices, exploiting the structure of the plan to avoid redundant reasoning or storage. Our labeling and maintenance scheme, called the Labeled Value Set Maintenance System, is distinguished by its focus on properties fundamental to temporal problems, and, more generally, weighted graph algorithms. In particular, the maintenance system focuses on maintaining a minimal representation of non-dominated constraints. We benchmark Drakes performance on random structured problems, and find that Drake reduces the size of the compiled representation by a factor of over 500 for large problems, while incurring only a modest increase in run-time latency, compared to prior work in compiled executives for temporal plans with discrete choices.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Elimination of HIV in South Africa through expanded access to antiretroviral therapy: Cautions, caveats and the importance of parsimony

In a recent article Hontelez and colleagues investigate the prospects for elimination of HIV in South Africa through expanded access to antiretroviral therapy (ART) using STDSIM, a micro-simulation model. One of the first published models to suggest that expanded access to ART could lead to the elimination of HIV, referred to by the authors as the Granich Model, was developed and implemented by the present author. The notion that expanded access to ART could lead to the end of the AIDS epidemic gave rise to considerable interest and debate and remains contentious. In considering this notion Hontelez et al. start by stripping down STDSIM to a simple model that is equivalent to the model developed by the present author3 but is a stochastic event driven model. Hontelez and colleagues then reintroduce levels of complexity to explore ways in which the model structure affects the results. In contrast to our earlier conclusions Hontelez and colleagues conclude that universal voluntary counselling and testing with immediate ART at 90% coverage should result in the elimination of HIV but would take three times longer than predicted by the model developed by the present author. Hontelez et al. suggest that the current scale-up of ART at CD4 cell counts less than 350 cells/microL will lead to elimination of HIV in 30 years. I disagree with both claims and believe that their more complex models rely on unwarranted and unsubstantiated assumptions.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Ending AIDS in Gabon: How long will it take? How much will it cost?

The prevalence of HIV in West Africa is lower than elsewhere in Africa but Gabon has one of the highest rates of HIV in that region. Gabon has a small population and a high per capita gross domestic product making it an ideal place to carry out a programme of early treatment for HIV. The effectiveness, availability and affordability of triple combination therapy make it possible to contemplate ending AIDS deaths and HIV transmission in the short term and HIV prevalence in the long term. Here we consider what would have happened in Gabon without the development of potent anti-retroviral therapy (ART), the impact that the current roll-out of ART has had on HIV, and what might be possible if early treatment with ART becomes available to all. We fit a dynamic transmission model to trends in the adult prevalence of HIV and infer trends in incidence, mortality and the impact of ART. The availability of ART has reduced the prevalence of HIV among adults not on ART from 4.2% to 2.9%, annual incidence from 0.43% to 0.27%, and the proportion of adults dying from AIDS illnesses each year from 0.36% to 0.13% saving the lives of 2.3 thousand people in 2013 alone. The provision of ART has been highly cost effective saving the country at least $18 million up to 2013.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Destriping Cosmic Microwave Background Polarimeter data

Destriping is a well-established technique for removing low-frequency correlated noise from Cosmic Microwave Background (CMB) survey data. In this paper we present a destriping algorithm tailored to data from a polarimeter, i.e. an instrument where each channel independently measures the polarization of the input signal. We also describe a fully parallel implementation in Python released as Free Software and analyze its results and performance on simulated datasets, both the design case of signal and correlated noise, and with additional systematic effects. Finally we apply the algorithm to 30 days of 37.5 GHz polarized microwave data gathered from the B-Machine experiment, developed at UCSB. The B-Machine data and destriped maps are made publicly available. The purpose is the development of a scalable software tool to be applied to the upcoming 12 months of temperature and polarization data from LATTE (Low frequency All sky TemperaTure Experiment) at 8 GHz and to even larger datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

HIV, TB and ART: the CD4 enigma

The concentration of CD4 T-lymphocytes (CD4 count), in a person's plasma is widely used to decide when to start HIV-positive people on anti-retroviral therapy (ART) and to predict the impact of ART on the future course of HIV and tuberculosis (TB). However, CD4 cell-counts vary widely within and among populations and depend on many factors besides HIV-infection. The way in which CD4 counts decline over the course of HIV infection is neither well understood nor widely agreed. We review what is known about CD4 counts in relation to HIV and TB and discuss areas in which more research is needed to build a consensus on how to interpret and use CD4 counts in clinical practice and to develop a better understanding of the dynamics and control of HIV and HIV-related TB.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Mission to the Trojan Asteroids: lessons learned during a JPL Planetary Science Summer School mission design exercise

The 2013 Planetary Science Decadal Survey identified a detailed investigation of the Trojan asteroids occupying Jupiter's L4 and L5 Lagrange points as a priority for future NASA missions. Observing these asteroids and measuring their physical characteristics and composition would aid in identification of their source and provide answers about their likely impact history and evolution, thus yielding information about the makeup and dynamics of the early Solar System. We present a conceptual design for a mission to the Jovian Trojan asteroids: the Trojan ASteroid Tour, Exploration, and Rendezvous (TASTER) mission, that is consistent with the NASA New Frontiers candidate mission recommended by the Decadal Survey and the final result of the 2011 NASA-JPL Planetary Science Summer School. Our proposed mission includes visits to two Trojans in the L4 population: a 500 km altitude fly-by of 1999 XS143, followed by a rendezvous with and detailed observations of 911 Agamemnon at orbital altitudes of 1000 - 100 km over a 12 month nominal science data capture period. Our proposed instrument payload - wide- and narrow-angle cameras, a visual and infrared mapping spectrometer, and a neutron/gamma ray spectrometer - would provide unprecedented high-resolution, regional-to-global datasets for the target bodies, yielding fundamental information about the early history and evolution of the Solar System. Although our mission design was completed as part of an academic exercise, this study serves as a useful starting point for future Trojan mission design studies. In particular, we identify and discuss key issues that can make large differences in the complex trade-offs required when designing a mission to the Trojan asteroids.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

The Coyote Universe III: Simulation Suite and Precision Emulator for the Nonlinear Matter Power Spectrum

Many of the most exciting questions in astrophysics and cosmology, including the majority of observational probes of dark energy, rely on an understanding of the nonlinear regime of structure formation. In order to fully exploit the information available from this regime and to extract cosmological constraints, accurate theoretical predictions are needed. Currently such predictions can only be obtained from costly, precision numerical simulations. This paper is the third in a series aimed at constructing an accurate calibration of the nonlinear mass power spectrum on Mpc scales for a wide range of currently viable cosmological models, including dark energy. The first two papers addressed the numerical challenges, and the scheme by which an interpolator was built from a carefully chosen set of cosmological models. In this paper we introduce the "Coyote Univers"' simulation suite which comprises nearly 1,000 N-body simulations at different force and mass resolutions, spanning 38 wCDM cosmologies. This large simulation suite enables us to construct a prediction scheme, or emulator, for the nonlinear matter power spectrum accurate at the percent level out to k~1 h/Mpc. We describe the construction of the emulator, explain the tests performed to ensure its accuracy, and discuss how the central ideas may be extended to a wider range of cosmological models and applications. A power spectrum emulator code is released publicly as part of this paper.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Resistance to TB drugs in KwaZulu-Natal: causes and prospects for control

In 2005 there was an outbreak of XDR (extensively drug resistant) TB in Tugela Ferry, which is served by the Church of Scotland Hospital (COSH), in the uMzinyathi District, KwaZulu-Natal, South Africa. An investigation was carried out to determine if XDR TB was occurring elsewhere in the province, and to develop hypotheses for the rise in drug resistance with a view to developing a strategy for the control of MDR (multi-drug resistant) and XDR TB in the province and elsewhere. TB incidence and treatment success rates, for each of the 11 districts in the province, were obtained from the provincial electronic TB register for the years 2002-2007. The results of culture and drug sensitivity tests for the years 2002 to 2007 in each of the districts were compiled and culture taking practices were compared to the number of MDR TB cases. Interviews were conducted with key personnel in affected sites. In 2007, 2799, or 2.3% of 119,218 notified TB cases in the province were multi-drug resistant (MDR), and of these 270 (9.6%) were XDR. The two worst affected districts were uMzinyathi where 226 (4.1%) of 5522 notified TB cases were MDR, and of these 120 (53%) were extensively drug resistant (XDR), and uMkhanyakude where 337 (4.8%) of 6991 notified TB cases were MDR, but of these only four or (1.2%) were XDR. The worst affected medical centre was COSH where 164 or 9.8% of notified TB cases were MDR and of these 99 (60%) were XDR. Very high rates of XDR TB in the province are only found in uMzinyathi district even though MDR TB is common in most other districts. XDR may arisen at COSH because of the early and effective integration of the TB and HIV programmes in overcrowded and poorly ventilated facilities particular to COS.H To control XDR TB better management of both susceptible and resistant forms of TB is needed including treatment supervision, infection control and HIV management.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

Modeling the frequency response of microwave radiometers with QUCS

Characterization of the frequency response of coherent radiometric receivers is a key element in estimating the flux of astrophysical emissions, since the measured signal depends on the convolution of the source spectral emission with the instrument band shape. Laboratory Radio Frequency (RF) measurements of the instrument bandpass often require complex test setups and are subject to a number of systematic effects driven by thermal issues and impedance matching, particularly if cryogenic operation is involved. In this paper we present an approach to modeling radiometers bandpasses by integrating simulations and RF measurements of individual components. This method is based on QUCS (Quasi Universal Circuit Simulator), an open-source circuit simulator, which gives the flexibility of choosing among the available devices, implementing new analytical software models or using measured S-parameters. Therefore an independent estimate of the instrument bandpass is achieved using standard individual component measurements and validated analytical simulations. In order to automate the process of preparing input data, running simulations and exporting results we developed the Python package python-qucs and released it under GNU Public License. We discuss, as working cases, bandpass response modeling of the COFE and Planck Low Frequency Instrument (LFI) radiometers and compare results obtained with QUCS and with a commercial circuit simulator software. The main purpose of bandpass modeling in COFE is to optimize component matching, while in LFI they represent the best estimation of frequency response, since end-to-end measurements were strongly affected by systematic effects.

0 citations0 reviewsNo code linkedOpen access