Range of Motion Hull: An approach for detecting collision and self-collision for dynamic objects based on hierarchical sphere trees. Diploma Thesis

Collision Detection must choose a trade-off between approximative complexity, tightness of approximative fit, and cost of overlap test and distance computation. The collision detection system must be robust, efficient, and capable to deal with any kind of object. Therefore, hierarchical data structures are used to deal with complex objects. An algorithm for computing compact sphere tree hierarchies over general 3D polygonal meshes for the purposes of efficient collision detection and minimum distance computations is presented. A sphere tree construction method is developed to optimize the location of the sphere centers and radii at each level of the hierarchy to compactly contain the underlying geometry. An enhanced and partly new developed algorithm for collision detection with additional distance information is presented. During the query phase, the algorithm incrementally updates both the lower bound and the upper bound on the value of the global minimum distance separating two meshes, enabling more efficient tree traversals compared to previous methods. This avoids unnecessary distance computations, leading to a faster algorithm that performs particularly well on collections of multiple mesh objects. In addition, the developed algorithm is well-suited to time-critical applications because it can always return a valid upper and lower bound on the true minimum distance at any time during the computation. Independent of the algorithm an improvement is developed by caching sphere transformations. An approach is introduced to expand hierarchical data structures for dynamic objects like manipulators. In this context the term “Range of Motion Hull” is introduced, which describes the enhancement of the hierarchical data structure by approximating the valid motion of all rigid parts of the kinematic subchain. Algorithms for efficient collision detection are accordingly adjusted to the enhanced hierarchical data structure. This enables fast and efficient collision detection for dynamic objects, due to the fact that unnecessary distance computation between the rigid parts of a dynamic object are 3 4 avoided. An general algorithm for self-collision detection of dynamic objects is developed. The algorithm offers additional distance information to guaranty self-collision free regions in the configuration space of the dynamic object. For efficency improvements and distance information suitability the use of look up tables is introduced. This enables faster and more efficient selfcollision detection, due to the fact that no attention is payed to pairs of never colliding rigid parts. The look up tables are automatically computed in a precomputation step and can be stored as well as the hierarchical data structure on external memory.