Efficient Collision Detection among Moving Spheres with Unknown Trajectories

Abstract

Collision detection is critical for applications that demand a great deal of spatial interaction among objects. In such applications the trajectory of an object is often not known in advance either since a user is allowed to move an object at his/her will, or since an object moves under the rules that are hard to describe by exact mathematical formulas. In this paper we present a new algorithm that efficiently detects the collisions among moving spheres with unknown trajectories. We assume that the current position and velocity of every sphere can be probed at any time although its trajectory is unknown. We also assume that the magnitude of the acceleration of each sphere is bounded. Under these assumptions, we represent the bounding volume of the sphere as a moving sphere of variable radius, called a time-varying bound. Whenever the time-varying bounds of two spheres collide with each other, they are checked for actual collision. Exploiting these bounds, the previous event-driven approach for detecting the collisions among multiple moving spheres with ballistic trajectories is generalized for those with unknown trajectories. The proposed algorithm shows an interactive performance for thousands of moving spheres with unknown trajectories without any hardware help.

Collision prediction among polygons with arbitrary shape and unknown motion

“…Then the pairs of objects whose bounding spheres intersect are further checked for collisions using sphere trees that represent the objects. Kim et al [13] first computed the time-varying bound volume for each moving sphere with its initial position, velocity and the maximum magnitude of its acceleration. As time goes by, the radius of this time-varying bound volume increases and it is guaranteed to contain the sphere at any time in the future.…”

“…Hayward et al [10], Kim et al [13] and Hubbard [11] assumed that the maximum magnitude of the acceleration is provided for each object. Hayward et al calculated the amount of time within which two moving spheres are guaranteed not to collide with each other.…”

Kinetic Collision Detection for Convex Fat Objects

“…If all objects are spheres of similar sizes Kim et al [17] present an event-driven approach that subdivides space into cells and processes events whenever a sphere enters or leaves a cell. This approach was later extended [18] to accommodate spheres with unknown trajectories but still similar sizes. There is only experimental evidence for the performance of this method.…”

Collision Prediction Among Rigid and Articulated Obstacles with Unknown Motion

“…Motivated by this issue, several strategies [10,11,12,13,8,14,15] have been proposed to replan adaptively only at the critical moments when the robot and obstacles may collide. These critical moments are usually detected by collision prediction methods.…”

“…The main challenge in predicting collision steams from the assumption that obstacle's motion is unknown. Existing methods in collision prediction exploit complex behavior prediction [14,15] or consider dynamic constraints [10,11,13,16]. However, these methods all assume either translational or disc objects, which significantly limit their applicability.…”