A GROWTH-BASED APPROACH TO THE AUTOMATIC GENERATION OF NAVIGATION MESHES

Providing an understanding of space in game and simulation environments is one of the major challenges associated with moving artificially intelligent characters through these environments. The usage of some form of navigation mesh has become the standard method to provide a representation of the walkable space in game environments to characters moving around in that environment. There is currently no standardized best method of producing a navigation mesh. In fact, producing an optimal navigation mesh has been shown to be an NP-Hard problem. Current approaches are a patchwork of divergent methods all of which have issues either in the time to create the navigation meshes (e.g., the best looking navigation meshes have traditionally been produced by hand which is time consuming), generate substandard quality navigation meshes (e.g., many of the automatic mesh production algorithms result in highly triangulated meshes that pose problems for character navigation), or yield meshes that contain gaps of areas that should be included in the mesh and are not (e.g., existing growth-based methods are unable to adapt to non-axis-aligned geometry and as such tend to provide a poor representation of the walkable space in complex environments). We introduce the Planar Adaptive Space Filling Volumes (PASFV) algorithm, Volumetric Adaptive Space Filling Volumes (VASFV) algorithm, and the Iterative Wavefront Edge Expansion Cell Decomposition (Wavefront) algorithm. These algorithms provide growth-based spatial decompositions for navigation mesh generation in either 2D (PASFV) or 3D (VASFV). These algorithms generate quick (on demand) decompositions (Wavefront), use quad/cube base spatial structures to provide more regular regions in the navigation mesh instead of triangles, and offer full coverage decompositions to avoid gaps in the navigation mesh by adapting to non-axis-aligned geometry. We have shown experimentally that the decompositions offered by PASFV and VASFV are superior both in character navigation ability, number of regions, and coverage in comparison to the existing and commonly used techniques of Space Filling Volumes, Hertel-Melhorn decomposition, Delaunay Triangulation, and Automatic Path Node Generation. Finally, we show that our Wavefront algorithm retains the superior performance of the PASFV and VASFV algorithms while providing faster decompositions that contain fewer degenerate and near degenerate regions. Unlike traditional navigation mesh generation techniques, the PASFV and VASFV algorithms have a real time extension (Dynamic Adaptive Space Filling Volumes, DASFV) which allows the navigation mesh to adapt to changes in the geometry of the environment at runtime. In addition, it is possible to use a navigation mesh for applications above and beyond character path planning and navigation. These multiple uses help to increase the return on the investment in creating a navigation mesh for a game or simulation environment. In particular, we will show how to use a navigation mesh for the acceleration of collision detection

Geometric Path-Planning Algorithm in Cluttered 2D Environments Using Convex Hulls

Routing or path planning is the problem of finding a collision-free path in an environment usually scattered with multiple objects. Finding the shortest route in a planar (2D) or spatial (3D) environment has a variety of applications such as robot motion planning, navigating autonomous vehicles, routing of cables, wires, and harnesses in vehicles, routing of pipes in chemical process plants, etc. The problem often times is decomposed into two main sub-problems: modeling and representation of the workspace geometrically and optimization of the path. Geometric modeling and representation of the workspace are paramount in any path planning problem since it builds the data structures and provides the means for solving the optimization problem. The optimization aspect of the path planning involves satisfying some constraints, the most important of which is to avoid intersections with the interior of any object and optimizing one or more criteria. The most common criterion in path planning problems is to minimize the length of the path between a source and a destination point of the workspace while other criteria such as minimizing the number of links or curves could also be taken into account. Planar path planning is mainly about modeling the workspace of the problem as a collision-free graph. The graph is, later on, searched for the optimal path using network optimization techniques such as branch-and-bound or search algorithms such as Dijkstra\u27s. Previous methods developed to construct the collision-free graph explore the entire workspace of the problem which usually results in some unnecessary information that has no value but to increase the time complexity of the algorithm, hence, affecting the efficiency significantly. For example, the fastest known algorithm to construct the visibility graph, which is the most common method of modeling the collision-free space, in a workspace with a total of n vertices has a time complexity of order O(n2). In this research, first, the 2D workspace of the problem is modeled using the tessellated format of the objects in a CAD software which facilitates handling of any free-form object. Then, an algorithm is developed to construct the collision-free graph of the workspace using the convex hulls of the intersecting obstacles. The proposed algorithm focuses only on a portion of the workspace involved in the straight line connecting the source and destination points. Considering the worst case that all the objects of the workspace are intersecting, the algorithm yields a time complexity of O(nlog(n/f)), with n being the total number of vertices and f being the number of objects. The collision-free graph is later searched for the shortest path between the two given nodes using a search algorithm known as Dijkstra\u27s

Timely Near-Optimal Path Generation for an Unmanned Aerial System in a Highly Constrained Environment

A current challenge in path planning is the ability to efficiently calculate a near-optimum path solution through a highly-constrained environment in near-real time. In addition, computing performance on a small unmanned aerial vehicle is typically limited due to size and weight restrictions. The proposed method determines a solution quickly by first mapping a highly constrained three-dimensional environment to a two-dimensional weighted node surface in which the weighting accounts for both the terrain gradient and the vehicle\u27s performance. The 2D surface is then discretized into triangles which are sized based upon the vehicle maneuverability and terrain gradient. The shortest feasible path between the nodes of the two-dimensional triangulated surface is determined using an A* algorithm. An optimal path is then chosen through the unconstrained corridor to yield a quick near-optimal path solution in three-dimensional space. This technique requires prior knowledge of the terrain map and vehicle performance. The cost to traverse each segment of the map is independent of the starting position on the map and can be pre-calculated once the goal position is known. The proposed method allows for a rapid path solution from any start position to a goal position while satisfying all constraints. It was shown that employing the methodology herein resulted in near-optimal solutions in less than a couple seconds for the scenarios tested. The future work section proposes methods for improving the algorithms efficiency even further

Practical motion planning for aerial-like virtual agents in Meta!Blast: A full and complex three dimensional virtual environment

Motion planning, or enabling agents to navigate around a virtual environment autonomously, is an essential requirement for video games and simulations. A well implemented motion planning technique can create a realistic and immersive user experience. If motion planning is not implemented properly, agents will exhibit unrealistic behavior and cause a distraction for the user. Motion planning is often difficult to implement due to the agents\u27 movement capabilities and the complexity of the virtual environment in which the agents exist. In a traditional three dimensional video game in which the agents are bound by gravity, the agents\u27 motion takes place mostly in the XZ-plane. In other words, the agents\u27 degree of freedom (DOF) is three. In this case, motion planning is translated into a two-dimensional problem, which is relatively easier to compute. However, when the agents can move in any three dimensional direction or to any three dimensional position in space, motion planning is much more complex. Meta!Blast is a three dimensional educational video game. Implementing motion planning in Meta!Blast is challenging for three reasons: The first reason is the agents have at least six degrees of freedom and can be translated or rotated about any axis in the three dimensional virtual environment. The second reason is the agents exist in a dense environment with many irregularly shaped models that need to be considered during planning. Lastly, Meta!Blast will be deployed in the high school classroom where computer hardware resources are limited, eliminating some planning techniques found in the literature. This thesis provides a practical solution for high DOF agents in dense environments using a combination of octree space partitioning, A* path-planning, and steering behaviors

Efficient mobile robot path planning by Voronoi-based heuristic

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ALGORITHM FOR GRAPH VISIBILITY OBTAINMENT FROM A MAP OF NON-CONVEX POLYGONS

Visibility graphs are basic planning algorithms,widely used in mobile robotics and other disciplines. The construction of a visibility graph can be considered a tool based on geometry that provides support to planning strategies in mobile robots. Visually, the method is used to solve that planning, which is quite extended due to the simplicity of operating with polygons, that represent obstacles in the environment. The cost of these algorithms tend to be quite low. The most sensitive issue of obtaining visibility between polygons is in cases in which the polygons are non-convex. In such cases, it is obligatory to know whether the area where one vertex of the polygon is found, is located in a convex or non-convex area, being desirable to distinguish between both situations in a simple way, issue that was not possible up to now. To obtain the visibility of non-convex polygons, the authors have developed a visual and intuitive method which gives the machine the ability to interpret the visibility with a simplicity similar to the human mind