Optimal Control of Differentially Flat Systems is Surprisingly Easy

This yields an equivalent flat system that is completely described by integrator dynamics. It There is an increasing demand to extend the boundaries is significantly easier to generate control trajectories in of autonomy in cyber-physical systems (CPS) using the flat space, wherein the trajectories can be exactly experimental testbeds (see: Rubenstein et al. (2012); mapped back to the original coordinate system. Differentially Jang et al. (2019); Beaver et al. (2020); Chalaki et al. flat systems have garnered significant interest (2022)) and outdoor experiments (see: Vásárhelyi et al. since their introduction by Fliess et al. (1995), and it has (2018); Mahbub and Malikopoulos (2020); Chalaki et al. been shown that generating trajectories in the flat space (2022)). As CPS achieve higher autonomy levels, they can reduce computational time by at least an order of will be forced into complicated interactions with other magnitude (e.g., see: Petit et al. (2001)). Differentially agents and the surrounding environment (Malikopoulos flat systems are closely related to feedback linearizable et al., 2021; Beaver and Malikopoulos, 2021; Oh et al., systems (Lévine, 2007); however, the standard control 2017). These autonomous agents must be able to react techniques for flat systems are distinct from feedback quickly to their environment and re-plan efficient trajectories.