Hough transform for distance computation and collision avoidance

Abstract

A new technique for collision detection based on the application of the Hough transform is presented in this paper. As a consequence of applying this technique, a method for computing the minimum translational distance (MTD) between two spherically extended polytopes is introduced. This distance algorithm is based on the Gilbert-Johnson-Keerthi (GJK) algorithm. Parameters returned by the MTD algorithm hold collision-free configurations that avoid a predicted collision.Index Terms-Gilbert-Johnson-Keerthi (GJK) algorithm, Hough transform, minimum translational distance, spherically extended polytope.

Predictive and Multirate Sensor-Based Planning Under Uncertainty

“…The MTD is defined in [34] as the shortest relative translation of two objects to bring them in contact. It is the separation distance between them if MTD>0 or the penetration distance if MTD<0 (objects colliding).…”

“…3 depicts the MTD between ellipsoids obtained from the trajectory prediction at different instants of time within the prediction horizon, for an omnidirectional vehicle and a pedestrian obstacle. In this case, where linear and decoupled kinematic models are used, MTD can be quickly computed by the method in [34], because the uncertainty ellipsoids turn into spheres and the uncertainty volumes are spherical volumes. Hence, the MTD computation is reduced to a Euclidean distance calculus between spheres.…”

“…For the calculation of U rep,i , a circular model with center in G (gravity center) is used enlarged with the uncertainty ellipsoid in i (not shown in Fig. 5), which is approximated by a sphere for fast distance computation with [34]. 4.…”

Grasp modelling with a biomechanical model of the hand

“…This graphical representation has been successfully used previously in robotics (Bernabeu and Tornero 2002), allowing a fast and efficient collision detection between the grasping hand and the grasped object while showing a sufficient level of realism (Fig. 4).…”

Kinematics-Based Characterization of the Collision Course

“…Collision detection using the notion of a distance function is widely discussed [18][19][20][21][22][23]. The aim is to detect the pair of the closest features between two objects.…”