Time Distance: A Novel Collision Prediction and Path Planning Method

Motion planning is an active field of research in robot navigation and autonomous driving. There are plenty of classical and heuristic motion planning methods applicable to mobile robots and ground vehicles. This paper is dedicated to introducing a novel method for collision prediction and path planning. The method is called Time Distance (TD), and its basis returns to the swept volume idea. However, there are considerable differences between the TD method and existing methods associated with the swept volume concept. In this method, time is obtained as a dependent variable in TD functions. TD functions are functions of location, velocity, and geometry of objects, determining the TD of objects with respect to any location. Known as a relative concept, TD is defined as the time interval that must be spent in order for an object to reach a certain location. It is firstly defined for the one-dimensional case and then generalized to 2D space. The collision prediction algorithm consists of obtaining the TD of different points of an object (the vehicle) with respect to all objects of the environment using an explicit function which is a function of TD functions. The path planning algorithm uses TD functions and two other functions called Z-Infinity and Route Function to create the collision-free path in a dynamic environment. Both the collision prediction and the path planning algorithms are evaluated in simulations. Comparisons indicate the capability of the method to generate length optimal paths as the most effective methods do

Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions

AbstractAlgorithms are developed, based on topological principles, to evaluate the boundary and “internal structure” of the Minkowski sum of two planar curves. A graph isotopic to the envelope curve is constructed by computing its characteristic points. The edges of this graph are in one-to-one correspondence with a set of monotone envelope segments. A simple formula allows a degree to be assigned to each face defined by the graph, indicating the number of times its points are covered by the Minkowski sum. The boundary can then be identified with the set of edges that separate faces of zero and non-zero degree, and the boundary segments corresponding to these edges can be approximated to any desired geometrical accuracy. For applications that require only the Minkowski sum boundary, the algorithm minimizes geometrical computations on the “internal” envelope edges, that do not contribute to the final boundary. In other applications, this internal structure is of interest, and the algorithm provides comprehensive information on the covering degree for different regions within the Minkowski sum. Extensions of the algorithm to the computation of Minkowski sums in R3, and other forms of geometrical convolution, are briefly discussed

Kinetic collision detection between two simple polygons

AbstractWe design a kinetic data structure for detecting collisions between two simple polygons in motion. In order to do so, we create a planar subdivision of the free space between the two polygons, called the external relative geodesic triangulation, which certifies their disjointness. We show how this subdivision can be maintained as a kinetic data structure when the polygons are moving, and analyze its performance in the kinetic setting

Collision-free automatic dimensional inspection using coordinate measuring machines

This research presents an inspection plan that generates automatic dimensional measurement process for inspecting workpiece surface with Coordinate Measuring Machines. The inspection plan is broken down into two phases: accessibility analysis and collision-free path generation. For accessibility analysis, a visibility map(VMAP) with respect to a point on a general surface is constructed. Based on the information of VMAPs, the collection of workpiece setups and probe orientations associated with the workpiece geometry are computed using the multi-echelon simulated annealing method. The safe and locally shortest inspection path can automatically be generated. This is made possible by appropriate probe abstractions and their swept volumes, collision detections, and heuristic modifications for the collide path segments. The hierarchical collision detection method based on the sweeping operation is presented. For each collide path segments, the interference-free detour is generated heuristically according to the components of probe model to be made collision. The tangent graph method is applied in case of collision against the probe tip and stylus, while the heuristic method is applied in case of collision against the probe column

Ambiente de desenvolvimento de manufatura virtual

The demand for foreign equipments in teaching institutions is well-know. To properly train an engineer, a lot of hours in several equipments are required. This is a problem if the equipments are expensive. The problem increases if manufacturing automation and control are focus. The number of equipments needed to simulate real industrial problems is enormous and even if considering the unlikable possibility that founds are not the problem, the physical space would be. To overcome this problem, the present work introduces a robotic and manufacturing framework. Based on the virtual reality present on games this framewo rk enables one to generate any desirable rigid-body scenario raging from manufacturing process to robot, manipulators, pneumatic engines and others. The graphics quality as well its physical behaviors enables an operator to live a realistic immersion in the virtual environment.A demanda por equipamentos importados em instituições de ensino é um fato conhecido. Este problema se agrava quando a área envolvida é o controle e automação da manufatura, onde os equipamentos utilizados possuem um alto custo. Para que um treinamento de controle destes equipamentos seja tido como satisfatório é necessário que um aluno, além do estudo teórico, faça diversas simulações e observe as respostas dos diversos equipamentos e das formas de programação e ajuste. Para contornar esta situação este projeto propõe a montagem de um ambiente virtual para treinamento em robótica e manufatura integrada. Utilizando técnicas semelhantes às dos tão conhecidos jogos em realidade virtual será construído um ambiente onde será possível a visualização, montagem e programação de quaisquer processos de manufatura, como robôs, mesas pneumáticas, esteiras, etc. A qualidade gráfica da simulação, bem como seu comportamento físico coerente e sua flexibilidade permitem uma imersão realística no ambiente virtual

Collision response analysis and fracture simulation of deformable objects for computer graphics

Computer Animation is a sub-field of computer graphics with an emphasis on the time-dependent description of interested events. It has been used in many disciplines such as entertainment, scientific visualization, industrial design, multimedia, etc. Modeling of deformable objects in a dynamic interaction and/or fracture process has been an active research topic in the past decade. The main objective of this thesis is to provide a new effective approach to address the dynamic interaction and fracture simulation. With respect to the dynamic interaction between deformable objects, this thesis proposes a new semi-explicit local collision response analysis (CRA) algorithm which is better than most of previous approaches in three aspects: computational efficiency, accuracy mid generality. The computational cost of the semi-explicit local CRA algorithm is guaranteed to be O('n') for each time step, which is especially desirable for the collision response analysis of complex systems. With the use of the Lagrange multiplier method, the send-explicit local CPA algorithm avoids shortcomings associated with the penalty method and provides an accurate description of detailed local deformation during a collision process. The generic geometric constraint and the Gauss-Seidel iteration for enforcing the loading constraint such as Coulomb friction law make the semi-explicit local CRA algorithm to be general enough to handle arbitrary oblique collisions. The experimental results indicate that the semi-explicit local CRA approach is capable of capturing all the key features during collision of deformable objects and matches closely with the theoretical solution of a classic collision problem in solid mechanics. In the fracture simulation, a new element-split method is proposed, which has a sounder mechanical basis than previous approaches in computer graphics and is more flexible to accommodate different material fracture criteria such that different failure patterns are obtained accordingly. Quantitative simulation results show that the element-split approach is consistent with the theoretical Mohr's circle analysis and the slip-line theory in plasticity, while qualitative results indicate its visual effectiveness