Almost Global Three-Dimensional Path-Following Guidance Law for Arbitrary Curved Paths

Motivated by aircraft applications, we revisit the path-following guidance problem in three dimensions. First, by formulating the path-following error directly in the inertial frame, we propose a class of guidance laws for regular parameterized paths that, unlike most approaches existing in the literature, do not require the explicit construction of a path frame. Based on an inner-outer loop control paradigm, the guidance law generates a normal acceleration command that is normal to the flow-relative velocity vector (as the lift force). This allows for a natural decomposition of the desired vehicle acceleration for aerial vehicles in coordinated turns: tangential acceleration for airspeed control and normal acceleration for guidance generated through bank-to-turn maneuvers, i.e., by tilting the lift vector. By using cascade arguments, we show that the proposed design leads to almost global stability results and thus relaxes the set of feasible initial conditions compared to existing methods. The efficacy of the proposed guidance law is demonstrated in a simulation study.