Atmospheric vehicle trajectory optimization with minimum dynamic pressure constraint

Abstract

In this work, a trajectory optimization formulation for hypersonic boost-glide class vehicles to achieve maximum range under various in-flight and terminal constraints is proposed. While most of the published literature has considered maximum dynamic pressure as a constraint, the requirement of a certain minimum dynamic pressure has been addressed in this formulation to ensure aerodynamic controllability throughout the flight envelope for various ranges. The minimum dynamic pressure constraint is imposed as an in-flight inequality constraint and is achieved through a penalty function approach by casting it as a differential equation. Simulations are carried out, and the results are analyzed and presented to demonstrate the efficacy of the proposed formulation.

Dynamic pressure based mid-course guidance scheme for hypersonic boost-glide vehicle

“…The γ d -profile is optimized for minimum structural loads subjecting to minimum dynamic pressure and other constraints. 16 Hence, the constraint on minimum dynamic pressure is a soft constraint and is achieved by shaping the ascend phase trajectory till apogee. The desired dynamic pressure starts after apogee, i.e.…”

“…With this motivation and extending the work presented in Kumar et al. 16,17 further, a mid-course guidance scheme to track the dynamic pressure in real time while suppressing the phugoid oscillations is proposed in this work. Efficacy of the proposed guidance scheme in tracking the dynamic pressure as well as in suppression of phugoid oscillations has been illustrated through simulations by using a two-dimensional point mass model.…”

“…In gliding flight, thrust is absent and the vehicle fly a near zero flight path angle trajectory and therefore, such vehicles can achieve longer ranges using the aerodynamic lift. Since the gliding phase influences maximum range capability of the vehicle, offline trajectory optimization for this section from burnout till the impact including the dive phase has been carried out using gradient approach 16 with minimum dynamic pressure as a constraint. Trajectory optimization is also carried out with population (pattern search) 17 -based approach using lift-to-drag ( L / D ) ratio as a control variable under various path and terminal constraints.…”

“…Addressing this issue, trajectory optimization formulations for HBGV to achieve maximum range under various in-flight, including the constraint on minimum dynamics pressure and terminal constraints have been proposed by the authors in Kumar et al. 16 and Kumar et al. 17 Since the trajectories that meet the minimum dynamic pressure constraint cannot be optimized in real time because of being computationally intensive exercise, a guidance scheme that employs the optimum glide dynamic pressure at maximum L / D at given flight altitude as reference becomes essential.…”

“…Addressing this issue, trajectory optimization formulations for HBGV to achieve maximum range under various in-flight, including the constraint on minimum dynamics pressure and terminal constraints have been proposed by the authors in Kumar et al 16 and Kumar et al 17 Since the trajectories that meet the minimum dynamic pressure constraint cannot be optimized in real time because of being computationally intensive exercise, a guidance scheme that employs the optimum glide dynamic pressure at maximum L/D at given flight altitude as reference becomes essential. With this motivation and extending the work presented in Kumar et al 16,17 further, a mid-course guidance scheme to track the dynamic pressure in real time while suppressing the phugoid oscillations is proposed in this work. Efficacy of the proposed guidance scheme in tracking the dynamic pressure as well as in suppression of phugoid oscillations has been illustrated through simulations by using a two-dimensional point mass model.…”