Incorporation of Rigid Body Dynamics into Indirect Hypersonic Trajectory Optimization

Abstract

This investigation demonstrates hypersonic trajectory optimization using planar rigid body dynamics within the indirect trajectory optimization framework. Employing rigid body dynamics captures the coupling between the optimal trajectory, the vehicle geometry, mass distribution, and control configuration. This provides trajectories that implicitly account for the maneuverability of the vehicle, wherein the vehicle is guaranteed to follow the angle-of-attack profile. This is unlike point-mass dynamics, wherein the angle-of-attack or angle-of-attack rate is directly used as the control variable, and maneuverability must be accounted for using bounds on these quantities. This is not straightforward because these bounds are dependent on flight conditions and are not constant for the entire trajectory. As a result, point-mass dynamics can produce infeasible solutions if these bounds are not properly handled. When using rigid body dynamics, these bounds are a consequence of the flight dynamics and are not required to be explicitly enforced, thereby circumventing the challenge with dynamic bounds on angle-of-attack and angle-of-attack rate altogether. Additionally, optimal trajectories calculated using rigid body dynamics more accurately reflect the drag penalties incurred when maneuvering the vehicle, such as when deflecting the aerodynamic control surfaces. The incurred drag penalties become critical in high-performance applications, wherein the terminal velocity is required to be maximized. Also, because the trajectory is coupled to the vehicle geometry, mass distribution, and control architecture, the optimal trajectory can be concurrently analyzed with the vehicle configuration, thereby enabling multidisciplinary design analysis. Despite these benefits offered by employing rigid body dynamics in trajectory optimization, there is limited literature in this regard, and none of them explored in this investigation employs indirect methods. This investigation fills this gap in the indirect trajectory optimization arena.