Survivability: Measuring and ensuring path diversity

A novel criterion is introduced for assessing the diversity of a collection of paths or trajectories. The main idea is the notion of survivability, which measures the likelihood that numerous paths are obstructed by the same obstacle. This helps to improve robustness with respect to collision, which is an important challenge in the design of real-time planning algorithms. Efficient algorithms are presented for computing the survivability criterion and for selecting a subset of paths that optimize survivability from a larger collection. The algorithms are implemented and solutions are illustrated for two different systems. Chi-square tests are used to show uniform coverage obtained by using the computed paths in a simple breadth-first search. Random obstacle placement is used to show superior robustness of these primitives compared to uniform sampling of the control space.