Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search

Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular approximations include graphs and random samples, as respectively used by informed graph-based searches and anytime sampling-based planners. Informed graph-based searches, such as A*, traditionally use heuristics to search a priori graphs in order of potential solution quality. This makes their search efficient but leaves their performance dependent on the chosen approximation. If its resolution is too low then they may not find a (suitable) solution but if it is too high then they may take a prohibitively long time to do so. Anytime sampling-based planners, such as RRT*, traditionally use random sampling to approximate the problem domain incrementally. This allows them to increase resolution until a suitable solution is found but makes their search dependent on the order of approximation. Arbitrary sequences of random samples approximate the problem domain in every direction simultaneously and but may be prohibitively inefficient at containing a solution. This paper unifies and extends these two approaches to develop Batch Informed Trees (BIT*), an informed, anytime sampling-based planner. BIT* solves continuous path planning problems efficiently by using sampling and heuristics to alternately approximate and search the problem domain. Its search is ordered by potential solution quality, as in A*, and its approximation improves indefinitely with additional computational time, as in RRT*. It is shown analytically to be almost-surely asymptotically optimal and experimentally to outperform existing sampling-based planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16 Figure

Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.Comment: 8 pages, 11 figures. Videos available at https://www.youtube.com/watch?v=d7dX5MvDYTc and https://www.youtube.com/watch?v=nsl-5MZfwu

Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs

In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT). BIT* uses a heuristic to efficiently search a series of increasingly dense implicit RGGs while reusing previous information. It can be viewed as an extension of incremental graph-search techniques, such as Lifelong Planning A* (LPA*), to continuous problem domains as well as a generalization of existing sampling-based optimal planners. It is shown that it is probabilistically complete and asymptotically optimal. We demonstrate the utility of BIT* on simulated random worlds in $\mathbb{R}^2$ and $\mathbb{R}^8$ and manipulation problems on CMU's HERB, a 14-DOF two-armed robot. On these problems, BIT* finds better solutions faster than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster anytime convergence towards the optimum, especially in high dimensions.Comment: 8 Pages. 6 Figures. Video available at http://www.youtube.com/watch?v=TQIoCC48gp

On Recursive Random Prolate Hyperspheroids

This technical note analyzes the properties of a random sequence of prolate hyperspheroids with common foci. Each prolate hyperspheroid in the sequence is defined by a sample drawn randomly from the previous volume such that the sample lies on the new surface (Fig. 1). Section 1 defines the prolate hyperspheroid coordinate system and the resulting differential volume, Section 2 calculates the expected value of the new transverse diameter given a uniform distribution over the existing prolate hyperspheroid, and Section 3 calculates the convergence rate of this sequence. For clarity, the differential volume and some of the identities used in the integration are verified in Appendix A through a calculation of the volume of a general prolate hyperspheroid.Comment: 11 pages, 2 figure

The TeV spectrum of H1426+428

The BL Lac object H1426+428 was recently detected as a high energy gamma-ray source by the VERITAS collaboration (Horan et al. 2002). We have reanalyzed the 2001 portion of the data used in the detection in order to examine the spectrum of H1426+428 above 250 GeV. We find that the time-averaged spectrum agrees with a power law of the shape dF/dE = 10^(-7.31 +- 0.15(stat) +- 0.16(syst)) x E^(-3.50 +- 0.35(stat) +- 0.05(syst)) m^(-2)s^(-1)TeV^(-1) The statistical evidence from our data for emission above 2.5 TeV is 2.6 sigma. With 95% c.l., the integral flux of H1426+428 above 2.5 TeV is larger than 3% of the corresponding flux from the Crab Nebula. The spectrum is consistent with the (non-contemporaneous) measurement by Aharonian et al. (2002) both in shape and in normalization. Below 800 GeV, the data clearly favours a spectrum steeper than that of any other TeV Blazar observed so far indicating a difference in the processes involved either at the source or in the intervening space.Comment: LaTeX, 8 pages, 4 figures, accepted for publication in Ap

The 1999 international emergency humanitarian evacuation of the Kosovars to Canada: A qualitative study of service providers' perspectives at the international, national and local levels

BACKGROUND: In response to the Kosovo crisis, Canada received 5,500 Albanian Kosovar refugees in 1999 as part of the emergency humanitarian evacuation and settlement effort. This study attempts to describe the experiences of service providers at the international, national, and local levels, involved in the organization and delivery of health and settlement services in Canada for the Kosovar refugees. METHODS: A qualitative case study design using key informant interviews was used. Nominated sampling was used to identify 17 individuals involved in the organization and delivery of health and settlement. Key themes were identified and recommendations made to provide a framework for the development of policy to guide response to future humanitarian emergencies. RESULTS: Six themes emerged: (1) A sense of being overwhelmed, (2) A multitude of health issues, (3) critical challenges in providing health care, (4) access to health and settlement services, (5) overall successes and (6) need for a coordinated approach to migration health. CONCLUSIONS: For those involved, the experience was overwhelming but rewarding. Interviewees' major concerns were the need for a more comprehensive and coordinated approach to the flow of medical information and handling of specific health problems

Search for High Energy Gamma Rays from an X-ray Selected Blazar Sample

Our understanding of blazars has been greatly increased in recent years by extensive multi-wavelength observations, particularly in the radio, X-ray and gamma-ray regions. Over the past decade the Whipple 10m telescope has contributed to this with the detection of 5 BL Lacertae objects at very high gamma-ray energies. The combination of multi-wavelength data has shown that blazars follow a well-defined sequence in terms of their broadband spectral properties. Together with providing constraints on emission models, this information has yielded a means by which potential sources of TeV emission may be identified and predictions made as to their possible gamma-ray flux. We have used the Whipple telescope to search for TeV gamma-ray emission from eight objects selected from a list of such candidates. No evidence has been found for VHE emission from the objects in our sample, and upper limits have been derived for the mean gamma-ray flux above 390GeV. These flux upper limits are compared with the model predictions and the implications of our results for future observations are discussed.Comment: 15 pages, 2 figures, Accepted for publication in Ap

A Search for TeV Gamma-Ray Emission from High-Peaked Flat Spectrum Radio Quasars Using the Whipple Air-Cherenkov Telescope

Blazars have traditionally been separated into two broad categories based upon their optical emission characteristics; BL Lacs, with faint or no emission lines, and flat spectrum radio quasars (FSRQs) with prominent, broad emission lines. The spectral energy distribution of FSRQs has generally been thought of as being more akin to the low-peaked BL Lacs, which exhibit a peak in the infrared region of the spectrum, as opposed to high-peaked BL Lacs (HBLs), which exhibit a peak in UV/X-ray region of the spectrum. All blazars currently confirmed as sources of TeV emission are HBLs. Recent surveys have found several FSRQs exhibiting spectral properties similar to HBLs, particularly the synchrotron peak frequency. These objects are potential sources of TeV emission according to several models of blazar jet emission and blazar evolution. Measurements of TeV flux or upper limits could impact existing theories explaining the links between different blazar types and could have a significant impact on our understanding of the nature of objects that are capable of TeV emission. In particular, the presence (or absence) of TeV emission from FSRQs could confirm (or cast doubt upon) recent evolutionary models that expect intermediate objects in a transitionary state between FSRQ and BL Lac. The Whipple 10 meter imaging air-Cherenkov gamma-ray telescope is well suited for TeV gamma-ray observations. Using the Whipple telescope, we have taken data on a small selection of nearby(z<0.1 in most cases), high-peaked FSRQs. Although one of the objects, B2 0321+33, showed marginal evidence of flaring, no significant emission was detected. The implications of this paucity of emission and the derived upper limits are discussed.Comment: accepted for publication in Astrophysical Journa

A Multi-wavelength View of the TeV Blazar Markarian 421: Correlated Variability, Flaring, and Spectral Evolution

We report results from a multi-wavelength monitoring campaign on Mrk 421 over the period of 2003-2004. The source was observed simultaneously at TeV and X-ray energies, with supporting observations frequently carried out at optical and radio wavelengths. The large amount of simultaneous data has allowed us to examine the variability of Mrk 421 in detail. The variabilities are generally correlated between the X-ray and gamma-ray bands, although the correlation appears to be fairly loose. The light curves show the presence of flares with varying amplitudes on a wide range of timescales both at X-ray and TeV energies. Of particular interest is the presence of TeV flares that have no coincident counterparts at longer wavelengths, because the phenomenon seems difficult to understand in the context of the proposed emission models for TeV blazars. We have also found that the TeV flux reached its peak days before the X-ray flux during a giant flare in 2004. Such a difference in the development of the flare presents a further challenge to the emission models. Mrk 421 varied much less at optical and radio wavelengths. Surprisingly, the normalized variability amplitude in optical seems to be comparable to that in radio, perhaps suggesting the presence of different populations of emitting electrons in the jet. The spectral energy distribution (SED) of Mrk 421 is seen to vary with flux, with the two characteristic peaks moving toward higher energies at higher fluxes. We have failed to fit the measured SEDs with a one-zone SSC model; introducing additional zones greatly improves the fits. We have derived constraints on the physical properties of the X-ray/gamma-ray flaring regions from the observed variability (and SED) of the source. The implications of the results are discussed. (Abridged)Comment: 32 pages, 12 figures, to appear in Ap