Hierarchical path-finding for Navigation Meshes (HNA*)

Path-finding can become an important bottleneck as both the size of the virtual environments and the number of agents navigating them increase. It is important to develop techniques that can be efficiently applied to any environment independently of its abstract representation. In this paper we present a hierarchical NavMesh representation to speed up path-finding. Hierarchical path-finding (HPA*) has been successfully applied to regular grids, but there is a need to extend the benefits of this method to polygonal navigation meshes. As opposed to regular grids, navigation meshes offer representations with higher accuracy regarding the underlying geometry, while containing a smaller number of cells. Therefore, we present a bottom-up method to create a hierarchical representation based on a multilevel k-way partitioning algorithm (MLkP), annotated with sub-paths that can be accessed online by our Hierarchical NavMesh Path-finding algorithm (HNA*). The algorithm benefits from searching in graphs with a much smaller number of cells, thus performing up to 7.7 times faster than traditional A¿ over the initial NavMesh. We present results of HNA* over a variety of scenarios and discuss the benefits of the algorithm together with areas for improvement.Peer ReviewedPostprint (author's final draft

Simplex Control Methods for Robust Convergence of Small Unmanned Aircraft Flight Trajectories in the Constrained Urban Environment

Constrained optimal control problems for Small Unmanned Aircraft Systems (SUAS) have long suffered from excessive computation times caused by a combination of constraint modeling techniques, the quality of the initial path solution provided to the optimal control solver, and improperly defining the bounds on system state variables, ultimately preventing implementation into real-time, on-board systems. In this research, a new hybrid approach is examined for real-time path planning of SUAS. During autonomous flight, a SUAS is tasked to traverse from one target region to a second target region while avoiding hard constraints consisting of building structures of an urban environment. Feasible path solutions are determined through highly constrained spaces, investigating narrow corridors, visiting multiple waypoints, and minimizing incursions to keep-out regions. These issues are addressed herein with a new approach by triangulating the search space in two-dimensions, or using a tetrahedron discretization in three-dimensions to define a polygonal search corridor free of constraints while alleviating the dependency of problem specific parameters by translating the problem to barycentric coordinates. Within this connected simplex construct, trajectories are solved using direct orthogonal collocation methods while leveraging navigation mesh techniques developed for fast geometric path planning solutions. To illustrate two-dimensional flight trajectories, sample results are applied to flight through downtown Chicago at an altitude of 600 feet above ground level. The three-dimensional problem is examined for feasibility by applying the methodology to a small scale problem. Computation and objective times are reported to illustrate the design implications for real-time optimal control systems, with results showing 86% reduction in computation time over traditional methods

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

Simplex Solutions for Optimal Control Flight Paths in Urban Environments

This paper identifies feasible fight paths for Small Unmanned Aircraft Systems in a highly constrained environment. Optimal control software has long been used for vehicle path planning and has proven most successful when an adequate initial guess is presented flight to an optimal control solver. Leveraging fast geometric planning techniques, a large search space is discretized into a set of simplexes where a Dubins path solution is generated and contained in a polygonal search corridor free of path constraints. Direct optimal control methods are then used to determine the optimal flight path through the newly defined search corridor. Two scenarios are evaluated. The first is limited to heading rate control only, requiring the air vehicle to maintain constant speed. The second allows for velocity control which permits slower speeds, reducing the vehicles minimum turn radius and increasing the search domain. Results illustrate the benefits gained when including speed control to path planning algorithms by comparing trajectory and convergence times, resulting in a reliable, hybrid solution method to the SUAS constrained optimal control problem

Study and Development of Hierarchical Path Finding to Speed Up Crowd Simulation

We propose a new hierarchical path finding solution for large environments. We use a navigation mesh as abstract data structure to partition the 3D world. Then, we build a hierarchy of graphs that allow us to perform faster path finding calculations than a common A*

PHYSICS-BASED SHAPE MORPHING AND PACKING FOR LAYOUT DESIGN

The packing problem, also named layout design, has found wide applications in the mechanical engineering field. In most cases, the shapes of the objects do not change during the packing process. However, in some applications such as vehicle layout design, shape morphing may be required for some specific components (such as water and fuel reservoirs). The challenge is to fit a component of sufficient size in the available space in a crowded environment (such as the vehicle under-hood) while optimizing the overall performance objectives of the vehicle and improving design efficiency. This work is focused on incorporating component shape design into the layout design process, i.e. finding the optimal locations and orientations of all the components within a specified volume, as well as the suitable shapes of selected ones. The first major research issue is to identify how to efficiently and accurately morph the shapes of components respecting the functional constraints. Morphing methods depend on the geometrical representation of the components. The traditional parametric representation may lend itself easily to modification, but it relies on assumption that the final approximate shape of the object is known, and therefore, the morphing freedom is very limited. To morph objects whose shape can be changed arbitrarily in layout design, a mesh based morphing method based on a mass-spring physical model is developed. For this method, there is no need to explicitly specify the deformations and the shape morphing freedom is not confined. The second research issue is how to incorporate component shape design into a layout design process. Handling the complete problem at once may be beyond our reach,therefore decomposition and multilevel approaches are used. At the system level, a genetic algorithm (GA) is applied to find the positions and orientations of the objects, while at the sub-system or component level, morphing is accomplished for select components. Although different packing applications may have different objectives and constraints, they all share some common issues. These include CAD model preprocessing for packing purpose, data format translation during the packing process if performance evaluation and morphing use different representation methods, efficiency of collision detection methods, etc. These common issues are all brought together under the framework of a general methodology for layout design with shape morphing. Finally, practical examples of vehicle under-hood/underbody layout design with the mass-spring physical model based shape morphing are demonstrated to illustrate the proposed approach before concluding and proposing continuing work

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

Numerical methods for the modelling of chip formation

The modeling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. During the last few decades, there has been significant progress in the development of numerical methods for modeling machining operations. Furthermore, the most relevant techniques have been implemented in the the relevant commercial codes creating tools for the engineers working in the design of processes and cutting devices. This paper presents a review on the numerical modeling methods and techniques used for the simulation of machining processes. The main purpose is to identify the strengths and weaknesses of each method and strategy developed up-to-now. Moreover the review covers the classical Finite Element Method covering mesh-less methods, particle-based methods and different possibilities of Eulerian and Lagrangian approaches.Postprint (author's final draft