  In this paper, we address a minimum-time steering problem for a drone modeled
as point mass with bounded acceleration, across a set of desired waypoints in
the presence of gravity. We first provide a method to solve for the
minimum-time control input that will steer the point mass between two waypoints
based on a continuous-time problem formulation which we address by using
Pontryagin's Minimum Principle. Subsequently, we solve for the time-optimal
trajectory across the given set of waypoints by discretizing in the time domain
and formulating the minimum-time problem as a nonlinear program (NLP). The
velocities at each waypoint obtained from solving the NLP in the discretized
domain are then used as boundary conditions to extend our two-point solution
across those multiple waypoints. We apply this planning methodology to execute
a surveying task that minimizes the time taken to completely explore a target
area or volume. Numerical simulations and theoretical analyses of this new
planning methodology are presented. The results from our approach are also
compared to traditional polynomial trajectories like minimum snap planning.
