Papers › Learning Flatness-Preserving Residuals for Pure-Feedback Systems
Learning Flatness-Preserving Residuals for Pure-Feedback Systems
Fengjun Yang, Jake Welde, Nikolai Matni
We study residual dynamics learning for differentially flat systems, where a nominal model is augmented with a learned correction term from data. A key challenge is that generic residual parameterizations may destroy flatness, limiting the applicability of flatness-based planning and control methods. To address this, we propose a framework for learning flatness-preserving residual dynamics in systems whose nominal model admits a pure-feedback form. We show that residuals with a lower-triangular structure preserve both the flatness of the system and the original flat outputs. Moreover, we provide a constructive procedure to recover the flatness diffeomorphism of the augmented system from that of the nominal model. We then introduce a learning algorithm that fits such residuals from trajectory data using smooth function approximators. Our approach is validated in simulation on a 2D quadrotor subject to unmodeled aerodynamic effects. We demonstrate that the resulting learned flat model enables tracking performance comparable to nonlinear model predictive control (5× lower tracking error than the nominal flat model) while also achieving over a 20× speedup in computation.
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