New AI Trick Makes Drones and Robots Easier to Steer

Feedback linearization is a powerful tool in nonlinear control, but finding the linearizing coordinate transform remains challenging. The transforms are governed by well-established partial differential equations whose well-posedness rests on the Lie-algebraic Frobenius theorem — but solving those PDEs becomes computationally intractable for large system dimensions. To address this, the authors propose a cascaded physics-informed neural network (PINN) framework that approximately solves the PDEs. By separately parameterizing terms of different Lie derivative orders, they mitigate the compounding errors inherent in fitting high-order Lie derivatives of neural networks. They then use the learned transform to design a tracking controller and establish theoretical bounds on its error with respect to inaccuracies in the learned feedback-linearizing representation. They validate the method on a broad class of feedback linearizable systems, including a multi-input, multi-output planar quadrotor and synthetic examples for which analytical approaches are impractical, demonstrating that their approach can computationally discover effective feedback-linearizing representations of nonlinear systems for control tasks.