Isaac Miller

Efficient Unbiased Tracking of Multiple Dynamic Obstacles Under Large Viewpoint Changes

A novel-tracking algorithm is presented as a computationally feasible, real-time solution to the joint estimation problem of data assignment and dynamic obstacle tracking from a potentially moving robotic platform. The algorithm implements a Rao-Blackwellized particle filter (RBPF) to factorize the joint estimation problem into 1) a data assignment problem solved via particle filter and 2) a multiple dynamic obstacle-tracking problem solved with efficient parametric filters. The parametric filters make use of a new target representation and stable features developed specifically for tracking full-size vehicles in a dense traffic environment. The algorithm is validated in real time, both in controlled experiments with full-size robotic vehicles and on data collected at the 2007 Defense Advanced Research Projects Agency (DARPA) Urban Challenge.

Cornell university's 2005 DARPA grand challenge entry

The 2005 DARPA Grand Challenge required teams to design and build autonomous off-road vehicles capable of handling harsh terrain at high speeds while following a loosely-defined path. This paper discusses the critical subsystems of Cornell University’s entry, an autonomous Spider Light Strike Vehicle. An attitude and position estimator is presented with modifications for specific problems associated with high-speed autonomous ground vehicles, including GPS signal loss and reacquisition. A novel terrain estimation algorithm is presented to combine attitude and position estimates with terrain sensors to generate a detailed elevation model. The elevation model is combined with a spline-based path planner in a sensing / action feedback loop to generate smooth, human-like paths that are consistent with vehicle dynamics. The performance of these subsystems is validated in a series of demonstrative experiments, along with an evaluation of the full system at the Grand Challenge.

Map-aided localization in sparse global positioning system environments using vision and particle filtering

A map-aided localization approach using vision, inertial sensors when available, and a particle filter is proposed and empirically evaluated. The approach, termed PosteriorPose, uses a Bayesian particle filter to augment global positioning system (GPS) and inertial navigation solutions with vision-based measurements of nearby lanes and stop lines referenced against a known map of environmental features. These map-relative measurements are shown to improve the quality of the navigation solution when GPS is available, and they are shown to keep the navigation solution converged in extended GPS blackouts. Measurements are incorporated with careful hypothesis testing and error modeling to account for non-Gaussian and multimodal errors committed by GPS and vision-based detection algorithms. Using a set of data collected with Cornells autonomous car, including a measure of truth via a high-precision differential corrections service, an experimental investigation of important design elements of the PosteriorPose estimator is conducted. The algorithm is shown to statistically outperform a tightly coupled GPS/inertial navigation solution both in full GPS coverage and in extended GPS blackouts. Statistical performance is also studied as a function of road type, filter likelihood models, bias models, and filter integrity tests.

Particle filtering for map-aided localization in sparse GPS environments

This study presents the PosteriorPose algorithm, a Bayesian particle filtering approach for augmenting GPS and inertial navigation solutions with vision-based measurements of nearby lanes and stoplines referenced against a known map of environmental features. These relative measurements are shown to improve the quality of the navigation solution when GPS is available, and they are shown to keep the navigation solution converged in extended GPS blackouts. Measurements are incorporated with careful hypothesis testing and error modeling to account for non-Gaussian errors committed by vision-based detection algorithms. The PosteriorPose algorithm is implemented and validated in real-time on Cornell Universitys 2007 DARPA Urban Challenge entry; experimental data is presented showing the algorithm outperforming a tightly- coupled GPS/inertial navigation solution both in full GPS coverage and in an extended GPS blackout.

A Mixture-Model Based Algorithm for Real-Time Terrain Estimation

A real-time terrain mapping and estimation algorithm using Gaussian sum elevation densities to model terrain variations in a planar gridded elevation model is presented. A formal probabilistic analysis of each individual sensor measurement allows the modeling of multiple sources of error in a rigorous manner. Measurements are associated to multiple locations in the elevation model using a Gaussian sum conditional density to account for uncertainty in measured elevation as well as uncertainty in the in-plane location of the measurement. The approach is constructed such that terrain estimates and estimation error statistics can be constructed in real-time without maintaining a history of sensor measurements. The algorithm is validated experimentally on the 2005 Cornell University DARPA Grand Challenge ground vehicle, demonstrating accurate and computationally feasible elevation estimates on dense terrain models, as well as estimates of the errors in the terrain model.

Rao-Blackwellized Particle Filtering for Mapping Dynamic Environments

A general method for mapping dynamic environments using a Rao-Blackwellized particle filter is presented. The algorithm rigorously addresses both data association and target tracking in a single unified estimator. The algorithm relies on a Bayesian factorization to separate the posterior into: 1) a data association problem solved via particle filter; and 2) a tracking problem with known data associations solved by Kalman filters developed specifically for the ground robot environment. The algorithm is demonstrated in simulation and validated in the real world with laser range data, showing its practical applicability in simultaneously resolving data association ambiguities and tracking moving objects.

Gaussian Sum Reapproximation for Use in a Nonlinear Filter

A new method has been developed to approximate one Gaussian sum by another. This algorithm is being developed as part of an effort to generalize the concept of a particle filter. In a traditional particle filter, the underlying probability density function is described by particles: Dirac delta functions with infinitesimal covariances. This paper develops an important component of a more general filter, which uses a Gaussian sum with “fattened” finite-covariance “blobs” (i.e., Gaussian components), which replace infinitesimal particles. The goal of such a filter is to save computational effort by using many fewer Gaussian components than particles. Most of the techniques necessary for this type of filter exist. The one missing technique is a resampling algorithm that bounds the covariance of each Gaussian component while accurately reproducing the original probability distribution. The covariance bounds keep the blobs from becoming too “fat” to ensure low truncation error in extended Kalman filter or unsc...

Probabilistic estimation of Multi-Level terrain maps

Recent research has shown that robots can model their world with Multi-Level (ML) surface maps, which utilize ‘patches’ in a 2D grid space to represent various environment elevations within a given grid cell. Though these maps are able to produce 3D models of the environment while exploiting the computational feasibility of single elevation maps, they do not take into account in-plane uncertainty when matching measurements to grid cells or when grouping those measurements into ‘patches.’ To respond to these drawbacks, this paper proposes to extend these ML surface maps into Probabilistic Multi-Level (PML) surface maps, which uses formal probability theory to incorporate estimation and modeling errors due to uncertainty. Measurements are probabilistically associated to cells near the nominal location, and are categorized through hypothesis testing into ‘patches’ via classification methods that incorporate uncertainty. Experimental results comparing the performances of the PML and ML surface mapping algorithms on representative objects found in both indoor and outdoor environments show that the PML algorithm outperforms the ML algorithm in most cases including in the presence of noisy and sparse measurements. The experimental results support the claim that the PML algorithm produces more densely populated, conservative representations of its environment with fewer measurements than the ML algorithm.

Posterior representation with a multi-modal likelihood using the gaussian sum filter for localization in a known map

A Gaussian sum filter (GSF) with component extended Kalman filters (EKF) is proposed as an approach to localizing an autonomous vehicle in an urban environment with limited GPS availability. The GSF uses vehicle-relative vision-based measurements of known map features coupled with inertial navigation solutions to accomplish localization in the absence of GPS. The vision-based measurements have multimodal measurement likelihood functions that are well represented as weighted sums of Gaussian densities. The GSF is used because of its ability to represent the posterior distribution of the vehicle pose with better efficiency (fewer terms, less computational complexity) than a corresponding bootstrap particle filter with various numbers of particles because of the interaction with measurement hypothesis tests. The expectation-maximization algorithm is used off line to determine the representational efficiency of the particle filter in terms of an effective number of Gaussian densities. In comparison, the GSF, which uses an iterative condensation procedure after each iteration of the filter to maintain real-time capabilities, is shown through a series of in-depth empirical studies to more accurately maintain a representation of the posterior distribution than the particle filter using 37 min of recorded data from Cornell Universitys autonomous vehicle driven in an urban environment, including a 32 min GPS blackout.

Gaussian Mixture Approximation by Another Gaussian Mixture for "Blob" Filter Re-Sampling

A new method has been developed to approximate one Gaussian mixture by another in a process that generalizes the idea of importance re-sampling in a particle filter. This algorithm is being developed as part of an effort to generalize the concept of a particle filter. In a traditional particle filter, the underlying probability density function is described by particles: Dirac delta functions with infinitesimal covariances. This paper develops an important component of a “blob” filter, which uses a Gaussian mixture of “fattened,” finitecovariance blobs instead of infinitesimal particles. The goal of a blob filter is to save computational effort for a given level of probability density precision by using many fewer blobs than particles. Most of the techniques necessary for this type of filter have already been developed. The one missing component is developed in this paper: a re-sampling algorithm that bounds the covariance of each element while accurately re-producing the original probability distribution. The covariance bounds are needed in order to keep the blobs from becoming too “fat”; otherwise, Extended Kalman Filter (EKF) or Unscented Kalman Filter dynamic propagation and measurement update calculations would cause excessive truncation error for each blob. The re-sampling algorithm is described in detail, and its performance is studied using several simulated test cases. Also discussed is the usefulness of a Gaussian mixture and EKF-like techniques for nonlinear dynamic propagation and nonlinear measurement update of probability distributions.