Continuous signed distance computation for polygonal robots in 3D

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.