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Trajectory representation using sequenced linear dynamical systems

In this paper we present a novel approach for representing trajectories using sequenced linear dynamical systems. This method uses a closed-form least-squares procedure to fit a single linear dynamical system (LDS) to a simple trajectory. These LDS estimates form the elemental building blocks used to describe complicated trajectories through an automatic segmentation procedure that can represent complicated trajectories with high accuracy. Each estimated LDS induces a control law, mapping current state to desired state, that encodes the target trajectory in a generative manner. We provide a proof of stability of the control law and show how multiple trajectories can be incorporated to improve the generalization ability of the system.