Generating Smooth Near Time-Optimal Trajectories for Steering Drones

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 present a method to calculate the minimum-time control input to steer the drone between two waypoints based on a continuous-time problem formulation that is solved using Pontryagin's Minimum Principle. Subsequently, we use this two-point solution to find a minimum-time trajectory across multiple waypoints. We solve for the time-optimal trajectory across a 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 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.