Proximity Queries for Absolutely Continuous Parametric Curves

In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is generally non-convex and serves as a significant computational bottleneck for motion planning algorithms. In this paper, we present methods for a general class of absolutely continuous parametric curves to compute: (i) the minimum separating distance, (ii) tolerance verification, and (iii) collision detection. Our methods efficiently compute bounds on obstacle proximity by bounding the curve in a convex region. This bound is based on an upper bound on the curve arc length that can be expressed in closed form for a useful class of parametric curves including curves with trigonometric or polynomial bases. We demonstrate the computational efficiency and accuracy of our approach through numerical simulations of several proximity problems.Comment: Proceedings of Robotics: Science and System

CFD-Simulations in the Early Product Development

AbstractA growing range of products shifts the product development in focus. Especially the early design phase defines the costs and quality. Thus, to ensure the quality of the products, different concepts are designed and evaluated. A tool for the evaluation of the different designs is simulation due to being fast and cost efficient. But simulation in the early phase still remains a problem. This results of the basic and fast changing concepts, which take too much effort to be converted into a simulation model. To get around these circumstances, we propose a method for an online modelling in the design process. Instead of defining the simulation model at once, the method modificates the simulation model during simulation run time. Furthermore, the functionality is shown in a CFD simulation using the meshless Smoothing Hydrodynamics method. Using the GPU to achieve real-time simulation, the method allows a WYSIWYG design-simulation development helping to raise the quality of products

Surface collision detection for virtual prototyping

This paper presents an efficient collision detection algorithm designed to support assembly and maintenance simulation of complex assemblies. This approach exploits the surface knowledge, available from CAD models, to determine intersecting surfaces. It proposes a novel combination of Overlapping Axis-Aligned Bounding Box (OAABB) and R-tree structures to gain considerable performance improvements. This paper also shows an efficient traversal algorithm based on the R-tree structure of Axis-Aligned Bounding Boxes to determine intersecting objects and intersecting surfaces between three-dimensional components, for supporting the recognition of constraints in assembly and disassembly operations in virtual prototyping environments. The implementation of the proposed collision detection algorithm performs well against moderately complex industrial case studies. Current experimental results show that this implementation is effective in determining intersecting surfaces at interactive rates with moderately complex real case studies.info:eu-repo/semantics/publishedVersio

Exact Minkowski sums of polyhedra and exact and efficient decomposition of polyhedra in convex pieces

We present the first exact and robust implementation of the 3D Minkowski sum of two non-convex polyhedra. Our implementation decomposes the two polyhedra into convex pieces, performs pairwise Minkowski sums on the convex pieces, and constructs their union. We achieve exactness and the handling of all degeneracies by building upon 3D Nef polyhedra as provided by Cgal. The implementation also supports open and closed polyhedra. This allows the handling of degenerate scenarios like the tight passage problem in robot motion planning. The bottleneck of our approach is the union step. We address efficiency by optimizing this step by two means: we implement an efficient decomposition that yields a small amount of convex pieces, and develop, test and optimize multiple strategies for uniting the partial sums by consecutive binary union operations. The decomposition that we implemented as part of the Minkowski sum is interesting in its own right. It is the first robust implementation of a decomposition of polyhedra into convex pieces that yields at most O(r 2) pieces, where r is the number of edges whose adjacent facets comprise an angle of more than 180 degrees with respect to the interior of the polyhedron

Sensory Steering for Sampling-Based Motion Planning

Sampling-based algorithms offer computationally efficient, practical solutions to the path finding problem in high-dimensional complex configuration spaces by approximately capturing the connectivity of the underlying space through a (dense) collection of sample configurations joined by simple local planners. In this paper, we address a long-standing bottleneck associated with the difficulty of finding paths through narrow passages. Whereas most prior work considers the narrow passage problem as a sampling issue (and the literature abounds with heuristic sampling strategies) very little attention has been paid to the design of new effective local planners. Here, we propose a novel sensory steering algorithm for sampling- based motion planning that can “feel” a configuration space locally and significantly improve the path planning performance near difficult regions such as narrow passages. We provide computational evidence for the effectiveness of the proposed local planner through a variety of simulations which suggest that our proposed sensory steering algorithm outperforms the standard straight-line planner by significantly increasing the connectivity of random motion planning graphs. For more information: Kod*la

Neural Bounding

Bounding volumes are an established concept in computer graphics and vision tasks but have seen little change since their early inception. In this work, we study the use of neural networks as bounding volumes. Our key observation is that bounding, which so far has primarily been considered a problem of computational geometry, can be redefined as a problem of learning to classify space into free or occupied. This learning-based approach is particularly advantageous in high-dimensional spaces, such as animated scenes with complex queries, where neural networks are known to excel. However, unlocking neural bounding requires a twist: allowing -- but also limiting -- false positives, while ensuring that the number of false negatives is strictly zero. We enable such tight and conservative results using a dynamically-weighted asymmetric loss function. Our results show that our neural bounding produces up to an order of magnitude fewer false positives than traditional methods