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We present a straightforward and efficient way to control unstable roboticsystems using an estimated dynamics model. Specifically, we show how to exploitthe differentiability of Gaussian Processes to create a state-dependentlinearized approximation of the true continuous dynamics that can be integratedwith model predictive control. Our approach is compatible with most Gaussianprocess approaches for system identification, and can learn an accurate modelusing modest amounts of training data. We validate our approach by learning thedynamics of an unstable system such as a segway with a 7-D state space and 2-Dinput space (using only one minute of data), and we show that the resultingcontroller is robust to unmodelled dynamics and disturbances, whilestate-of-the-art control methods based on nominal models can fail under smallperturbations. Code is open sourced athttps://github.com/learning-and-control/core .

Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control