A new approach to trajectory optimization based on direct transcription and differential flatness

• Solving a constrained problem via direct transcription formulation.
• Lowering problem dimensions by use of flatness theory.
• Approximating flat variables via integrating linear function of acceleration profile.
• Trajectory optimization; TAEM phase of a reusable launch vehicle.
• Lower computational efforts; number of iterations and function evaluations.

The objective of the present paper is to introduce a reliable method to produce an optimal trajectory in the presence of all limitations and constraints. Direct transcription, has been employed to convert the trajectory optimization problem into nonlinear programming problem via discretizing the profile of state and control parameters and solving for a constrained problem. Differential flatness as a complementary theory leads to model the optimization problem in a lowered dimensional space through defining flat variables. Several curvilinear functions have been used to approximate flat variables and have their own benefits and disadvantages. Accuracy, complexity and number of needed points are examples of related issues. A new approach is developed based on an indirect approximation of flat variables, which leads to decrease the optimization variables and computational costs while preserving the needed accuracy. The proposed method deals with a 3rd order approximation of flat variables via integrating linear function of the acceleration profile. The new method is implemented on the terminal area energy management phase of a reusable launch vehicle. Test results show that the suggested method, as compared with other conventional methods, requires lower computational efforts in cases of the number of iterations and function evaluations, while providing a more accurate optimal solution.