We consider the problem of flagging all collisions between a large number of dynamic objects. Because the number of possible collisions grows quadratically with the number of objects, a brute force approach is not applicable with finite computational resources.Hence, we propose a scheduling mechanism that reduces the computational load by exploiting the coherence of the world throughout time. This mechanism has a very simple structure and easily lends itself to distributed processing. It considers all pairwise interactions between objects and maintains a structure that reflects the imminence, or urgency, of collision for each pair. Bounds on the urgency of collisions can be computed given minimal knowledge of the system dynamics. For example, we represent physical objects by their positions and by bounds on their relative speeds and accelerations. These are assumed to be available at all times. If the environment does not change too rapidly, the mechanism flags all collisions. False alarms may also be generated but can be eliminated with a specialized exact collision post-processor.We address the question of how often to perform the collision checks while guaranteeing that all collisions will be caught. Given the large number of possible environments and motions, no general optimal answer can be provided. Yet the soundness and efficiency of the proposed algorithm is eaperimentally verified in the case of a simple world consisting of many spheres moving simultaneously and randomly.

We consider a world made up of a collection of objects which are all moving with respect to each other. We wish to design a system capable to report and to predict all possible object collisions; given that, all relevant information is available in due time. Previous approaches are based on the notion of a distance function that reflects the closest distance between objects in the world at any given instant in time. By explicitly including time in the representation, we describe an algorithm based on the shortest possible time before the next possible collision. The algorithm deals with all pairwise interactions between objects, sorts the pairs with respect to their predicted collision time, and maintains the most likelyto-collide pairs at the top of a stack. A new kind of hierarchy in the representation of the world is thus introduced. To find the shortest possible time before a collision, we constrain the trajectory of objects by imposing bounds on the objects' acceleration and velocity. All interacting pairs are classified into buckets that reflect the imminence of the collision. The computing cost is kept constant by reclassifying only one pair from each bucket at each time sample.

The programming and execution environments of advanced robotic systems are esamples of complex software environments which deal with a variety of distributed mechanical and computer subsystems. Traditional software design methodologies have been shown t o have drawbacks in designing and implementing such software systems for robotics. A novel dual-hierarchical object-oriented design (DHOOD) methodology is presented, which is well suited to problems of this type. A practical example of the application of this methodology is presented, utilizing CLOS as the implementation vehicle. The methodology developed is shown to facilitate the programming and planning of complex robot tasks, and the provision of generic recovery procedures for exception handling.

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