Persistent Robotic Tasks: Monitoring and Sweeping in Changing Environments

In this paper, we present controllers that enable mobile robots to persistently monitor or sweep a changing environment. The environment is modeled as a field that is defined over a finite set of locations. The field grows linearly at locations that are not within the range of a robot and decreases linearly at locations that are within range of a robot. We assume that the robots travel on given closed paths. The speed of each robot along its path is controlled to prevent the field from growing unbounded at any location. We consider the space of speed controllers that are parametrized by a finite set of basis functions. For a single robot, we develop a linear program that computes a speed controller in this space to keep the field bounded, if such a controller exists. Another linear program is derived to compute the speed controller that minimizes the maximum field value over the environment. We extend our linear program formulation to develop a multirobot controller that keeps the field bounded. We characterize, both theoretically and in simulation, the robustness of the controllers to modeling errors and to stochasticity in the environment

Rebalancing the Rebalancers: Optimally Routing Vehicles and Drivers in Mobility-on-Demand Systems

In this paper we study rebalancing strategies for a mobility-on-demand urban transportation system blending customer-driven vehicles with a taxi service. In our system, a customer arrives at one of many designated stations and is transported to any other designated station, either by driving themselves, or by being driven by an employed driver. The system allows for one-way trips, so that customers do not have to return to their origin. When some origins and destinations are more popular than others, vehicles will become unbalanced, accumulating at some stations and becoming depleted at others. This problem is addressed by employing rebalancing drivers to drive vehicles from the popular destinations to the unpopular destinations. However, with this approach the rebalancing drivers themselves become unbalanced, and we need to "rebalance the rebalancers" by letting them travel back to the popular destinations with a customer. Accordingly, in this paper we study how to optimally route the rebalancing vehicles and drivers so that stability (in terms of boundedness of the number of waiting customers) is ensured while minimizing the number of rebalancing vehicles traveling in the network and the number of rebalancing drivers needed; surprisingly, these two objectives are aligned, and one can find the optimal rebalancing strategy by solving two decoupled linear programs. Leveraging our analysis, we determine the minimum number of drivers and minimum number of vehicles needed to ensure stability in the system. Interestingly, our simulations suggest that, in Euclidean network topologies, one would need between 1/3 and 1/4 as many drivers as vehicles.Comment: Extended version of 2013 American Control Conference pape

Idempotent splittings, colimit completion, and weak aspects of the theory of monads

We show that some recent constructions in the literature, named `weak' generalizations, can be systematically treated by passing from 2-categories to categories enriched in the Cartesian monoidal category of Cauchy complete categories.Comment: LaTeX source 23 pages; v3 final version, minor corrections only, to appear in Journal of Pure and Applied Algebr

Social Misdirection Fails to Enhance a Magic Illusion

Visual, multisensory and cognitive illusions in magic performances provide new windows into the psychological and neural principles of perception, attention, and cognition. We investigated a magic effect consisting of a coin “vanish” (i.e., the perceptual disappearance of a coin after a simulated toss from hand to hand). Previous research has shown that magicians can use joint attention cues such as their own gaze direction to strengthen the observers’ perception of magic. Here we presented naïve observers with videos including real and simulated coin tosses to determine if joint attention might enhance the illusory perception of simulated coin tosses. The observers’ eye positions were measured, and their perceptual responses simultaneously recorded via button press. To control for the magician’s use of joint attention cues, we occluded his head in half of the trials. We found that subjects did not direct their gaze at the magician’s face at the time of the coin toss, whether the face was visible or occluded, and that the presence of the magician’s face did not enhance the illusion. Thus, our results show that joint attention is not necessary for the perception of this effect. We conclude that social misdirection is redundant and possibly detracting to this very robust sleight-of-hand illusion. We further determined that subjects required multiple trials to effectively distinguish real from simulated tosses; thus the illusion was resilient to repeated viewing

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Collisional N-Body Dynamics Coupled to Self-Gravitating Magnetohydrodynamics Reveals Dynamical Binary Formation

We describe a star cluster formation model that includes individual star formation from self-gravitating, magnetized gas, coupled to collisional stellar dynamics. The model uses the Astrophysical Multi-purpose Software Environment (AMUSE) to integrate an adaptive-mesh magnetohydrodynamics code (FLASH) with a fourth order Hermite N-body code (ph4), a stellar evolution code (SeBa), and a method for resolving binary evolution (multiples). This combination yields unique star formation simulations that allow us to study binaries formed dynamically from interactions with both other stars and dense, magnetized gas subject to stellar feedback during the birth and early evolution of stellar clusters. We find that for massive stars, our simulations are consistent with the observed dynamical binary fractions and mass ratios. However, our binary fraction drops well below observed values for lower mass stars, presumably due to unincluded binary formation during initial star formation. Further, we observe a build up of binaries near the hard-soft boundary that may be an important mechanism driving early cluster contraction.Comment: 14 pages, 12 figures. Submitted to Ap

Simulating Radiating and Magnetized Flows in Multi-Dimensions with ZEUS-MP

This paper describes ZEUS-MP, a multi-physics, massively parallel, message- passing implementation of the ZEUS code. ZEUS-MP differs significantly from the ZEUS-2D code, the ZEUS-3D code, and an early "version 1" of ZEUS-MP distributed publicly in 1999. ZEUS-MP offers an MHD algorithm better suited for multidimensional flows than the ZEUS-2D module by virtue of modifications to the Method of Characteristics scheme first suggested by Hawley and Stone (1995), and is shown to compare quite favorably to the TVD scheme described by Ryu et. al (1998). ZEUS-MP is the first publicly-available ZEUS code to allow the advection of multiple chemical (or nuclear) species. Radiation hydrodynamic simulations are enabled via an implicit flux-limited radiation diffusion (FLD) module. The hydrodynamic, MHD, and FLD modules may be used in one, two, or three space dimensions. Self gravity may be included either through the assumption of a GM/r potential or a solution of Poisson's equation using one of three linear solver packages (conjugate-gradient, multigrid, and FFT) provided for that purpose. Point-mass potentials are also supported. Because ZEUS-MP is designed for simulations on parallel computing platforms, considerable attention is paid to the parallel performance characteristics of each module. Strong-scaling tests involving pure hydrodynamics (with and without self-gravity), MHD, and RHD are performed in which large problems (256^3 zones) are distributed among as many as 1024 processors of an IBM SP3. Parallel efficiency is a strong function of the amount of communication required between processors in a given algorithm, but all modules are shown to scale well on up to 1024 processors for the chosen fixed problem size.Comment: Accepted for publication in the ApJ Supplement. 42 pages with 29 inlined figures; uses emulateapj.sty. Discussions in sections 2 - 4 improved per referee comments; several figures modified to illustrate grid resolution. ZEUS-MP source code and documentation available from the Laboratory for Computational Astrophysics at http://lca.ucsd.edu/codes/currentcodes/zeusmp2