Trajectory generation for 3D fly-by transitions using analytically constrained Bézier curves

Abstract Conventional trajectory generation remains inadequate for high-accuracy aircraft guidance because Dubins- and clothoid-based turn transitions contain discontinuities in curvature or curvature derivative. As a result, even when high-order guidance laws are used to reduce tracking error, the reference trajectory itself does not provide suitable higher-order feedforward commands. Existing solutions are also unsatisfactory because they either recover higher-order smoothness only approximately through post-processing, rely on numerical optimization, which is unsuitable for deterministic airborne systems, or do not actively account for aircraft dynamic constraints. This paper closes these gaps with a closed-form method for generating three-dimensional turn trajectories as ninth-order Bézier curves. The curve is constructed analytically from smoothness requirements and aircraft dynamic constraints, yielding a high-order reference trajectory that is both dynamically consistent and deterministic. The methods presented are integrated into an operational trajectory generation system and validated analytically and through flight testing on a 700 kg medical evacuation eVTOL aircraft.