Jonathan R. Schoenberg

Segmentation of dense range information in complex urban scenes

In this paper, an algorithm to segment 3D points in dense range maps generated from the fusion of a single optical camera and a multiple emitter/detector laser range finder is presented. The camera image and laser range data are fused using a Markov Random Field to estimate a 3D point corresponding to each image pixel. The textured 3D dense point cloud is segmented based on evidence of a boundary between regions of the textured point cloud. Clusters are discriminated based on Euclidean distance, pixel intensity and estimated surface normal using a fast, deterministic and near linear time segmentation algorithm. The algorithm is demonstrated on data collected with the Cornell University DARPA Urban Challenge vehicle. Performance of the proposed dense segmentation routine is evaluated in a complex urban environment and compared to segmentation of the sparse point cloud. Results demonstrate the effectiveness of the dense segmentation algorithm to avoid over-segmentation better than incorporating color and surface normal data in the sparse point cloud.

Scalable Bayesian human-robot cooperation in mobile sensor networks

In this paper, scalable collaborative human-robot systems for information gathering applications are approached as a decentralized Bayesian sensor network problem. Human-computer augmented nodes and autonomous mobile sensor platforms are collaborating on a peer-to-peer basis by sharing information via wireless communication network. For each node, a computer (onboard the platform or carried by the human) implements both a decentralized Bayesian data fusion algorithm and a decentralized Bayesian control negotiation algorithm. The individual node controllers iteratively negotiate anonymously with each other in the information space to find cooperative search plans based on both observed and predicted information that explicitly consider the platforms (humans and robots) motion models, their sensors detection functions, as well as the target arbitrary motion model. The results of a collaborative multi-target search experiment conducted with a team of four autonomous mobile sensor platforms and five humans carrying small portable computers with wireless communication are presented to demonstrate the efficiency of the approach.

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...

Fast Weighted Exponential Product Rules for Robust General Multi-Robot Data Fusion

This paper considers the distributed data fusion (DDF) problem for general multi-agent robotic sensor networks in applications such as 3D mapping and target search. In particular, this paper focuses on the use of conservative fusion via the weighted exponential product (WEP) rule to combat inconsistencies that arise from double-counting common information between fusion agents. WEP fusion is ideal for fusing arbitrarily distributed estimates in ad-hoc communication network topologies, but current WEP rule variants have limited applicability to general multi-robot DDF. To address these issues, new information-theoretic WEP metrics are presented along with novel optimization algorithms for efficiently performing DDF within a recursive Bayesian estimation framework. While the proposed WEP fusion methods are generalizable to arbitrary probability distribution functions (pdfs), emphasis is placed here on widely-used Bernoulli and Gaussian mixture pdfs. Experimental results for multi-robot 3D mapping and target search applications show the effectiveness of the proposed methods.

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.

Localization with multi-modal vision measurements in limited GPS environments using Gaussian Sum Filters

A Gaussian Sum Filter (GSF) with component extended Kalman filters (EKF) is proposed as an approach to localize 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 are shown to have multi-modal measurement likelihood functions that are well represented as a weighted sum of Gaussian densities and the GSF is ideally suited to accomplish recursive Bayesian state estimation for this problem. A sequential merging technique is used for Gaussian mixture condensation in the posterior density approximation after fusing multi-modal measurements in the GSF to maintain mixture size over time. The representation of the posterior density with the GSF is compared over a common dataset against a benchmark particle filter solution. The Expectation-Maximization (EM) algorithm is used offline to determine the representational efficiency of the particle filter in terms of an effective number of Gaussian densities. The GSF with vision-based vehicle relative measurements is shown to remain converged using 37 minutes of recorded data from the Cornell University DARPA Urban Challenge (DUC) autonomous vehicle in an urban environment that includes a 32 minute GPS blackout.