Learning-based algorithms have demonstrated impressive performance in agile locomotion of legged robots. However, learned policies are often complex and opaque due to the black-box nature of learning algorithms, which hinders predictability and precludes guarantees on performance or safety. In this work, we develop a novel safe navigation framework that combines Koopman operators and model-predictive control (MPC) frameworks. Our method adopts Koopman operator theory to learn the linear evolution of dynamics of the underlying locomotion policy, which can be effectively learned with Dynamic Mode Decomposition (DMD). Given that our learned model is linear, we can readily leverage the standard MPC algorithm. Our framework is easy to implement with less prior knowledge because it does not require access to the underlying dynamical systems or control-theoretic techniques. We demonstrate that the learned linear dynamics can better predict the trajectories of legged robots than baselines. In addition, we showcase that the proposed navigation framework can achieve better safety with less collisions in challenging and dense environments with narrow passages.
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