  In this paper, we perform safety and performance analysis of an autonomous
vehicle that implements reactive planner and controller for navigating a race
lap. Unlike traditional planning algorithms that have access to a map of the
environment, reactive planner generates the plan purely based on the current
input from sensors. Our reactive planner selects a waypoint on the local
Voronoi diagram and we use a pure-pursuit controller to navigate towards the
waypoint. Our safety and performance analysis has two parts. The first part
demonstrates that the reactive planner computes a plan that is locally
consistent with the Voronoi plan computed with full map. The second part
involves modeling of the evolution of vehicle navigating along the Voronoi
diagram as a hybrid automata. For proving the safety and performance
specification, we compute the reachable set of this hybrid automata and employ
some enhancements that make this computation easier. We demonstrate that an
autonomous vehicle implementing our reactive planner and controller is safe and
successfully completes a lap for five different circuits. In addition, we have
implemented our planner and controller in a simulation environment as well as a
scaled down autonomous vehicle and demonstrate that our planner works well for
a wide variety of circuits.
