Vertical Takeoff Vertical Landing Spacecraft Trajectory Optimization via Direct Collocation and Nonlinear Programming

Open Access
Policelli, Michael J
Graduate Program:
Aerospace Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • Dr David Spencer, Thesis Advisor
  • Direct
  • Collocation
  • Nonlinear Programming
  • Vertical
  • Takeoff
  • Landing
  • VTVL
  • moon
  • lunar
  • trajectory
  • optimization
  • spacecraft
Rocket-powered translational Vertical Takeoff Vertical Landing (VTVL) maneuvers are a promising lander spacecraft mobility method as compared with or in addition to rovers for certain mission profiles. Such a VTVL vehicle would take off vertically under rocket propulsion, translate a specified horizontal distance, and vertically return softly to the surface. Previous literature suggested that the propellant required to perform such a maneuver could be estimated via an impulsive-ballistic trajectory using the “ideal” rocket equation. This analysis was found to be inadequate. Any feasible trajectories will always require additional propellant to compensate for gravity losses while lifting off and landing. Additionally, there is an asymmetry between the takeoff and landing phases of the maneuver due to the propellant mass used over the course of the flight. Lastly, various potential spacecraft propulsion systems architectures impose a number of possible constraints on the allowable path and boundary conditions. An adaptable Optimal Control Problem (OCP) was developed instead to model the basic dynamics and required propellant consumption of various VTVL spacecraft trajectory profiles for a range of constraints, spacecraft parameters, and translation distances. The model was discretized into a Nonlinear Programming (NLP) problem and a Direct Collocation (DC) method utilizing implicit Simpson-Hermite integration was used to ensure the feasibility of solutions with sufficient accuracy. MATLAB’s Nonlinear Programming fmincon routine with the sequential quadratic programming solver was able to converge on the optimal VTVL trajectory in terms of minimizing the required propellant use within the spacecraft and mission constraints. Trades were performed to determine the impact of various parameters on the required propellant including thrust to initial weight ratios, propellant specific impulse, the allowable range and angular rate of change of the spacecraft thrust vector, translation distances, maximum altitude, flight times, and boundary conditions. The VTVL trajectory optimization model developed was found to be robust and able to handle a wide range of various spacecraft and mission parameters. Results were compared against the required propellant use and nominal time of flight determined via the ballistic-impulse burn-coast-burn analysis. For the finite model developed herein, the required propellant use and optimal flight times exceeded the ideal impulsive case by 5-30% depending on the specific spacecraft and mission parameters and constraints implemented. These results can help guide future mission planners in deciding whether to utilize VTVL as a mobility method.