We propose a novel method adaptive subdivision (AS) to evaluate the distance function for moving general polygonal models. The distance function can have a positive and a negative value, each of which corresponds to the Euclidean distance and penetration depth, respectively. In our approach, the distance between a pair of objects can be evaluated along any time interval of the object's trajectory; therefore it is called “continuous”, and a minimum of the continuous distance (MCD) is determined for collision avoidance. In order to compute a MCD for general polygonal models, we calculate the upper and lower bounds of the distance in the time interval and abandons the time intervals that cannot realize the MCD. We have implemented our distance evaluation method, and have experimentally validated the proposed methods to effectively and accurately find the MCDs to generate a collision-free motion for the HRP-2 humanoid robot.

We present a novel algorithm to compute a gradient-continuous penetration depth (PhongPD) between two interpenetrated polygonal models. Our penetration depth (PD) formulation ensures separating the intersected models by translation, and the amount of such translation is close to an optimal motion to resolve interpenetration in most cases. In order to achieve the gradient-continuity in our algorithm, we interpolate tangent planes continuously over the contact space and then perform a projection along a normal direction defined by the interpolated tangent planes; this projection scheme is known as Phong projection. We have implemented our PhongPD algorithm and certifies its continuity using three benchmarks consisting of diverse combinatorial complexities, and show that our algorithm shows smoother PD results than a conventional Euclidean-projection-based PD method.

We propose three novel methods to evaluate a distance function for robotic motion planning based on semiinfinite programming (SIP) framework; these methods include golden section search (GSS), conservative advancement (CA) and a hybrid of GSS and CA. The distance function can have a positive and a negative value, each of which corresponds to the Euclidean distance and penetration depth, respectively. In our approach, each robot's link is approximated and bounded by a capsule shape, and the distance between some selected link pairs is continuously evaluated along the joint's trajectory, provided by the SIP solver, and the global minimum distance is found. This distance is fed into the SIP solver, which subsequently suggests a new trajectory. This process is iterated until no negative distance is found anywhere in the links of the robot.We have implemented the three distance evaluation methods, and experimentally validated that the proposed methods effectively and accurately find the global minimum distances to generate a self-collision-free motion for the HRP-2 humanoid robot. Moreover, we demonstrate that the hybrid method outperforms other two methods in terms of computational speed and reliability.

We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid difference, maximally clear configuration, motion coherence, random configuration, and sampling-based search. We project this configuration on to a local contact space using a variant of continuous collision detection algorithm and construct a linear convex cone around the projected configuration. We then formulate a new projection of the in-collision configuration onto the convex cone as a Linear Complementarity Problem (LCP), which we solve using a type of Gauss-Seidel iterative algorithm. We repeat this procedure until a locally optimal PD is obtained. Our algorithm can process complicated models consisting of tens of thousands triangles at interactive rates.

Abstract We present simple and fast parallel proximity algorithms for rigid polygonal models. Given two polygon‐soup models in space, if they overlap, our algorithm can find all the intersected primitives between them; otherwise, it reports their Euclidean minimum distance. Our algorithm is performed in a parallel fashion and shows scalable performance in terms of the number of available computing cores. The key ingredient of our algorithm is a simple load‐balancing metric based on the penetration depth (PD) (for collision detection) and approximate Euclidean distance (for Euclidean distance computation) between bounding volumes. To compute the PD between oriented bounding boxes (OBBs), we present a novel algorithm based on the well‐known separating axis theorem (SAT) and also shows that the PD can be trivially obtained as a byproduct of SAT. We have implemented these algorithms on a commodity PC with eight cores and benchmarked their performance on complicated geometric models. In practice, the performance of our algorithm shows up to 5 and 9.7 times improvement for collision and distance queries, respectively, compared to single core computation. Copyright © 2010 John Wiley & Sons, Ltd.

We cull collisions between very large numbers of moving bodies using graphics processing units (GPUs). To perform massively parallel sweep-and-prune (SaP), we mitigate the great density of intervals along the axis of sweep by using principal component analysis to choose the best sweep direction, together with spatial subdivisions to further reduce the number of false positive overlaps. Our algorithm implemented entirely on GPUs using the CUDA framework can handle a million moving objects at interactive rates. As application of our algorithm, we demonstrate the real-time simulation of very large numbers of particles and rigid-body dynamics.