  Biologically inspired strategies have long been adapted to swarm robotic
systems, including biased random walks, reaction to chemotactic cues and
long-range coordination. In this paper we apply analysis tools developed for
modeling biological systems, such as continuum descriptions, to the efficient
quantitative characterization of robot swarms. As an illustration, both
Brownian and L\'{e}vy strategies with a characteristic long-range movement are
discussed. As a result we obtain computationally fast methods for the
optimization of robot movement laws to achieve a prescribed collective
behavior. We show how to compute performance metrics like coverage and hitting
times, and illustrate the accuracy and efficiency of our approach for area
coverage and search problems. Comparisons between the continuum model and
robotic simulations confirm the quantitative agreement and speed up of our
approach. Results confirm and quantify the advantage of L\'{e}vy strategies
over Brownian motion for search and area coverage problems in swarm robotics.
