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Stochastic processes and feedback-linearisation for online identification and Bayesian adaptive control of fully-actuated mechanical systems

This work proposes a new method for simultaneous probabilistic identification and control of an observable, fully-actuated mechanical system. Identification is achieved by conditioning stochastic process priors on observations of configurations and noisy estimates of configuration derivatives. In contrast to previous work that has used stochastic processes for identification, we leverage the structural knowledge afforded by Lagrangian mechanics and learn the drift and control input matrix functions of the control-affine system separately. We utilise feedback-linearisation to reduce, in expectation, the uncertain nonlinear control problem to one that is easy to regulate in a desired manner. Thereby, our method combines the flexibility of nonparametric Bayesian learning with epistemological guarantees on the expected closed-loop trajectory. We illustrate our method in the context of torque-actuated pendula where the dynamics are learned with a combination of normal and log-normal processes.

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