As the use of simulation increases across many diff erent application domains, the need for high- fidelity three-dimensional virtual representations of real-world environments has never been greater. This need has driven the research and development of both faster and easier methodologies for creating such representations. In this research, we present two diff erent inference-based geometric modeling techniques that support the automatic construction of complex cluttered environments. The fi rst method we present is a surface reconstruction-based approach that is capable of reconstructing solid models from a point cloud capture of a cluttered environment. Our algorithm is capable of identifying objects of interest amongst a cluttered scene, and reconstructing complete representations of these objects even in the presence of occluded surfaces. This approach incorporates a predictive modeling framework that uses a set of user provided models for prior knowledge, and applies this knowledge to the iterative identifi cation and construction process. Our approach uses a local to global construction process guided by rules for fi tting high quality surface patches obtained from these prior models. We demonstrate the application of this algorithm on several synthetic and real-world datasets containing heavy clutter and occlusion. The second method we present is a generative modeling-based approach that can construct a wide variety of diverse models based on user provided templates. This technique leverages an inference-based construction algorithm for developing solid models from these template objects. This algorithm samples and extracts surface patches from the input models, and develops a Petri net structure that is used by our algorithm for properly fitting these patches in a consistent fashion. Our approach uses this generated structure, along with a defi ned parameterization (either user-defi ned through a simple sketch-based interface or algorithmically de fined through various methods), to automatically construct objects of varying sizes and con figurations. These variations can include arbitrary articulation, and repetition and interchanging of parts sampled from the input models. Finally, we affim our motivation by showing an application of these two approaches. We demonstrate how the constructed environments can be easily used within a physically-based simulation, capable of supporting many diff erent application domains.

Pursuit-evasion problems comprise a set of pursuers that strive to catch oneor several evaders, often in a constrained environment. This thesis proposesand compares heuristic algorithms for pursuit-evasion problems wherein several double integrator agents pursue a single evader in a bounded subset of theEuclidean plane. Different methods for assigning surrounding target points tothe pursuers are tested numerically. In addition, a method which finds the timeoptimal strategy for pursuing a static target in an unconstrained setting is presented, and is then used to pursue the assigned, dynamic, target. Numericalresults show that the time optimal strategy for pursuing a static target translateswell to the dynamic problem.

This thesis provides a comparison between instance segmentation methods using point clouds and depth images. Specifically, their performance on cluttered scenes of irregular objects in an industrial environment is investigated. Recent work by Wang et al. [1] has suggested potential benefits of a point cloud representation when performing deep learning on data from 3D cameras. However, little work has been done to enable quantifiable comparisons between methods based on different representations, particularly on industrial data. Generating synthetic data provides accurate grayscale, depth map, and point cloud representations for a large number of scenes and can thus be used to compare methods regardless of datatype. The datasets in this work are created using a tool provided by SICK. They simulate postal packages on a conveyor belt scanned by a LiDAR, closely resembling a common industry application. Two datasets are generated. One dataset has low complexity, containing only boxes.The other has higher complexity, containing a combination of boxes and multiple types of irregularly shaped parcels. State-of-the-art instance segmentation methods are selected based on their performance on existing benchmarks. We chose PointGroup by Jiang et al. [2], which uses point clouds, and Mask R-CNN by He et al. [3], which uses images. The results support that there may be benefits of using a point cloud representation over depth images. PointGroup performs better in terms of the chosen metric on both datasets. On low complexity scenes, the inference times are similar between the two methods tested. However, on higher complexity scenes, MaskR-CNN is significantly faster.