This paper discusses the usage of direct methods of calculus of variations for real-time optimization of a final turn-into-the-wind maneuver for autonomous guided parafoil-based delivery systems. It reviews several approaches that are currently being pursued by different developers of such systems and discusses the necessity of usage and applicability of a direct method to optimize the final turn. The proposed approach seeks for an optimal solution within a certain class of parameterized inertial trajectories and further employs inverse dynamics to find the corresponding control. This approach has been successfully used in a variety of real-time applications already and proved to work well in a developed miniature aerial delivery system, Snowflake, as well. The paper presents the results of the most recent real drops and ends with a discussion of the developed algorithm as compared to another one, pursued by Draper Laboratory, where instead of parameterizing a reference trajectory the control itself is being parameterized. The paper ends with conclusions.
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