Trajectory planning of differentially flat systems with dynamics and inequalities

Trajectory planning of dynamic systems, in near real time, is important for aerospace systems, especially uncrewed air vehicles and launched munitions. Trajectory plans that do not consider the governing dynamic equations, applicable path, and actuator constraints may be unrealizable during execution. A trajectory planning scheme is proposed for a class of dynamic systems, referred to as differentially hat systems. The planner is motivated from online computations and is aimed to satisfy the state equations, path and actuator constraints, and given initial and terminal constraints. The essence of the approach is demonstrated by two examples: 1) a hardware implementation on a spring-mass-damper system to demonstrate real-time capabilities during pursuit and 2) trajectory planning of a planar vertical takeoff and landing aircraft to illustrate the application to nonlinear problems.