Minimum Waypoint Spacing for VTOL Rotorcraft Trajectory Guidance using B-Spline Midpoint Refinement

Given a cubic piecewise-polynomial spline representation of a Vertical Take-off and Landing (VTOL) rotorcraft guidance trajectory in the monomial basis, we propose a new method for defining the stopping criterion for midpoint refinement of its representation in the B-spline basis. This method incorporates a model of the rotorcraft flight dynamics, consisting of the wind-axes equations of motion for a point-mass particle under the assumptions of constant altitude, constant rotor speed, and negligible side force in the direction mutually perpendicular to the velocity vector and the thrust vector from the main rotor(s). Under such conditions, the rotorcraft’s ability to maneuver and change the ground track angle of the velocity vector is limited by its current speed and the available command accelerations along and normal to the velocity vector. The command acceleration limits are a function of available installed engine power, internal acceleration limiters in the vehicle control laws, and maximum allowable body-axis rates and Euler attitudes. Moreover, these acceleration limits constrain the rate of reorientation of the velocity vector. Our method defines the spline control points as the waypoints of the flight plan and iteratively refines these points until their spacing is too close for the vehicle to reorient its velocity vector to align with the bearing to the next waypoint. This stopping criterion permits a dense spacing of waypoints, since the vehicle is not required to fly through successive waypoints or along the legs connecting them. Five motion primitives were used to demonstrate the algorithm. The motion primitives were scaled in size and speed to match ADS-33/MIL-DTL-32742 Mission Task Elements (MTEs) such as the Slalom and Pirouette, as well as future proposed MTEs for VTOL uncrewed autonomous systems (UAS). We evaluated the tracking performance of a simulated single main-rotor tail-rotor helicopter for flight plans based on two of the MTEs, and we examined how closely the wind-axes flight dynamics model matches these high-fidelity simulations for turn maneuvers in different speed regimes. These investigations indicate directions for further development of our method in simulated scenarios and eventual flight tests. The benefit of this method is that it requires only minimal software changes to extend the capability of in-service autopilot and coupled flight director algorithms to fly generic trajectories that can be represented by cubic piecewise-polynomial splines.