Trajectory Planning and Optimization for Minimizing Uncertainty in Persistent Monitoring Applications

This paper considers persistent monitoring of environmental phenomena using unmanned aerial vehicles (UAVs). The objective is to generate periodic dynamically feasible UAV trajectories that minimize the estimation uncertainty at a set of points of interest in the environment. We develop an optimization algorithm that iterates between determining the observation periods for a set of ordered points of interest and optimizing a continuous UAV trajectory to meet the required observation periods and UAV dynamics constraints. The interest-point visitation order is determined using a Traveling Salesman Problem (TSP), followed by a greedy optimization algorithm to determine the number of observations that minimizes the maximum steady-state eigenvalue of a Kalman filter estimator. Given the interest-point observation periods and visitation order, a minimum-jerk trajectory is generated from a bi-level optimization, formulated as a convex quadratically constrained quadratic program. The resulting B-spline trajectory is guaranteed to be feasible, meeting the observation duration, maximum velocity and acceleration, region enter and exit constraints. The feasible trajectories outperform existing methods by achieving comparable observability at up to 47% higher travel speeds, resulting in lower maximum estimation uncertainty.