Smooth time optimal trajectory generation for drones
This work addresses faster and more efficient drone navigation for tasks like surveying, though it is incremental as it builds on existing optimal control methods.
The paper tackles the problem of generating time-optimal trajectories for drones moving through waypoints with gravity, by solving a minimum-time control problem using Pontryagin's Minimum Principle and nonlinear programming. It demonstrates improved performance over traditional methods like minimum snap planning in simulations.
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.