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In monocular visual-inertial navigation, it is desirable to initialize the system as quickly and robustly as possible. A state-of-the-art initialization method typically constructs a linear system to find a closed-form solution using the image features and inertial measurements and then refines the states with a nonlinear optimization. These methods generally require a few seconds of data, which however can be expedited (less than a second) by adding constraints from a robust but only up-to-scale monocular depth network in the nonlinear optimization. To further accelerate this process, in this work, we leverage the scale-less depth measurements instead in the linear initialization step that is performed prior to the nonlinear one, which only requires a single depth image for the first frame. Importantly, we show that the typical estimation of all feature states independently in the closed-form solution can be modeled as estimating only the scale and bias parameters of the learned depth map. As such, our formulation enables building a smaller minimal problem than the state of the art, which can be seamlessly integrated into RANSAC for robust estimation. Experiments show that our method has state-of-the-art initialization performance in simulation as well as on popular real-world datasets (TUM-VI, and EuRoC MAV). For the TUM-VI dataset in simulation as well as real-world, we demonstrate the superior initialization performance with only a 0.3 s window of data, which is the smallest ever reported, and validate that our method can initialize more often, robustly, and accurately in different challenging scenarios. 

This paper outlines a methodology for the construction of vector fields that can enable a multi-robot system moving on the plane to generate multiple dynamical behaviors by adjusting a single scalar parameter. This parameter essentially triggers a Hopf bifurcation in an underlying time-varying dynamical system that steers a robotic swarm. This way, the swarm can exhibit a variety of behaviors that arise from the same set of continuous differential equations. Other approaches to bifurcation-based swarm coordination rely on agent interaction which cannot be realized if the swarm members cannot sense or communicate with one another. The contribution of this paper is to offer an alternative method for steering minimally instrumented multi-robot collectives with a control strategy that can realize a multitude of dynamical behaviors without switching their constituent equations. Through this approach, analytical solutions for the bifurcation parameter are provided, even for more complex cases that are described in the literature, along with the process to apply this theory in a multi-agent setup. The theoretical predictions are confirmed via simulation and experimental results with the latter also demonstrating real-world applicability.