Trajectory Optimization of a Subsonic Unpowered Gliding Vehicle Using Control Vector Parameterization

In many aero gliding vehicles, achieving the maximum gliding range is a challenging task. A frequent example is the breakdown of an engine during flight or the use of unpowered stand-off weapons. When an unpowered stand-off weapon begins gliding at a given height, it eventually strikes the ground after some distance, and height is considered a stopping constraint in this general condition. To avoid the time-scaling approach for the free time optimal problem, the maximum stoppable time with a stopping constraint is addressed to attain the maximum glide range. This problem can be chosen as an optimal gliding range problem which can be solved by direct or indirect methods. In this paper, the inverted Y-tail joint stand-off weapon is selected as the subsonic unpowered gliding vehicle (SUGV). After being released from dispersion points, the SUGV has to face fluctuating gliding flight because of flight phase transition that causes gliding range reduction. To achieve a damped and steady gliding flight while maximizing the gliding range, we propose a non-uniform control vector parameterization (CVP) approach that uses the notion of exponential spacing for the time vector. When compared with the maximum step input and conventional uniform CVP approach, simulations of the proposed non-uniform CVP approach demonstrate that the SUGV exhibits superior damping and steady gliding flight, with a maximum gliding range of 121.278 km and a maximum horizontal range of 120.856 km