Differential-Geometric Optimal Guidance with Embedded Obstacle Avoidance for UAVs: Simulations and Experimental Validation

This work proposes a guidance strategy for unmanned aerial vehicles (UAVs) that is built on differential-geometric modeling and optimal control, enabling the vehicle to pass through a prescribed sequence of waypoints while keeping a safe distance from known static obstacles. The overall task is cast as a global optimization problem defined over the complete waypoint list so that path design and guidance command generation are handled within a single analytical framework. For a given set of waypoints and obstacle locations, the method produces explicit acceleration commands. The derivation relies on an arc-length–based differential-geometric kinematic description together with a curvature-related performance index, which reduce the overall guidance effort and exhibit limited sensitivity to changes in vehicle speed. The effectiveness and practicality of the method are verified using nonlinear numerical simulations and real UAV flight tests. The results demonstrate robust waypoint traversal with explicit avoidance of specified obstacles and show that the generated trajectories are smooth and efficient while demanding reduced control effort.