Harvesting wind energy is promising for extending long-endurance flights,which can be greatly facilitated by a flight technique called dynamic soaring.The presented study is concerned with generating model-based traje...Harvesting wind energy is promising for extending long-endurance flights,which can be greatly facilitated by a flight technique called dynamic soaring.The presented study is concerned with generating model-based trajectories with smooth control histories for dynamic soaring maneuvers exploiting wind gradients.The desired smoothness is achieved by introducing a trigonometric series parameterization for the controls,which are formulated with respect to the normalized time.Specifically,the periodicity of the trigonometric functions is leveraged to facilitate the connection of cycles and streamline the problem formulation.Without relying on a specified wind profile,a freefinal-time quadratic programming-based control strategy is developed for the online correction of the flight trajectory,which requires only the instant wind information.Offline and online numerical studies show the trade-off to achieve the smoothness and demonstrate the effectiveness of the proposed method in a varying wind field.展开更多
This study is dedicated to the development of a direct optimal control-based algorithm for trajectory optimization problems that accounts for the closed-loop stability of the trajectory tracking error dynamics already...This study is dedicated to the development of a direct optimal control-based algorithm for trajectory optimization problems that accounts for the closed-loop stability of the trajectory tracking error dynamics already during the optimization.Consequently,the trajectory is designed such that the Linear Time-Varying(LTV)dynamic system,describing the controller’s error dynamics,is stable,while additionally the desired optimality criterion is optimized and all enforced constraints on the trajectory are fulfilled.This is achieved by means of a Lyapunov stability analysis of the LTV dynamics within the optimization problem using a time-dependent,quadratic Lyapunov function candidate.Special care is taken with regard to ensuring the correct definiteness of the ensuing matrices within the Lyapunov stability analysis,specifically considering a numerically stable formulation of these in the numerical optimization.The developed algorithm is applied to a trajectory design problem for which the LTV system is part of the path-following error dynamics,which is required to be stable.The main benefit of the proposed scheme in this context is that the designed trajectory trades-off the required stability and robustness properties of the LTV dynamics with the optimality of the trajectory already at the design phase and thus,does not produce unstable optimal trajectories the system must follow in the real application.展开更多
基金supported in part by the TUM University Foundation Fellowshipin part by the German Federal Ministry for Economic Affairs and Energy(BMWi)within the Federal Aeronautical Research Program LuFo VI-1through Project“RAUDY”(No.20E1910B)。
文摘Harvesting wind energy is promising for extending long-endurance flights,which can be greatly facilitated by a flight technique called dynamic soaring.The presented study is concerned with generating model-based trajectories with smooth control histories for dynamic soaring maneuvers exploiting wind gradients.The desired smoothness is achieved by introducing a trigonometric series parameterization for the controls,which are formulated with respect to the normalized time.Specifically,the periodicity of the trigonometric functions is leveraged to facilitate the connection of cycles and streamline the problem formulation.Without relying on a specified wind profile,a freefinal-time quadratic programming-based control strategy is developed for the online correction of the flight trajectory,which requires only the instant wind information.Offline and online numerical studies show the trade-off to achieve the smoothness and demonstrate the effectiveness of the proposed method in a varying wind field.
基金supported in part by the TUM University Foundation Fellowshipin part by the German Federal Ministry for Economic Affairs and Energy(BMWi)within the Federal Aeronautical Research Program LuFo V-3 through Project“HOTRUN”(No.20E1720A)。
文摘This study is dedicated to the development of a direct optimal control-based algorithm for trajectory optimization problems that accounts for the closed-loop stability of the trajectory tracking error dynamics already during the optimization.Consequently,the trajectory is designed such that the Linear Time-Varying(LTV)dynamic system,describing the controller’s error dynamics,is stable,while additionally the desired optimality criterion is optimized and all enforced constraints on the trajectory are fulfilled.This is achieved by means of a Lyapunov stability analysis of the LTV dynamics within the optimization problem using a time-dependent,quadratic Lyapunov function candidate.Special care is taken with regard to ensuring the correct definiteness of the ensuing matrices within the Lyapunov stability analysis,specifically considering a numerically stable formulation of these in the numerical optimization.The developed algorithm is applied to a trajectory design problem for which the LTV system is part of the path-following error dynamics,which is required to be stable.The main benefit of the proposed scheme in this context is that the designed trajectory trades-off the required stability and robustness properties of the LTV dynamics with the optimality of the trajectory already at the design phase and thus,does not produce unstable optimal trajectories the system must follow in the real application.
