On Calculus of Variations in Aircraft and Spacecraft Formation Flying Path Planning
Andrea L’Afflitto, Cornel Sultan · 2010
*† The optimal trajectory for formations of aerospace vehicles in terms of energy consumption and fuel consumption is addressed by mean of Calculus of Variations. Accounting for environmental models of increasing complexity, mission scenarios examined require each vehicle to leave from unspecified positions, pass through assigned waypoints, avoid static obstacles, and intercept allotted surfaces. Tasks are modularly optimized to be effortlessly recombined by varying a finite amount of coefficients. Compactness of the formation as well as collision avoidance is always guaranteed. Nomenclature a = acceleration of the vehicle ac = acceleration of the vehicle due to control forces f = generic integrand of the cost function fx = derivative of f with respect to x fr = derivative of f with respect to x ’ fr2