Magnetometers measure the local magnetic field and are present in most modern inertial measurement units (IMUs). Readings from magnetometers are used to identify Earth’s Magnetic North outdoors, but are often ignored during indoor experiments since the magnetic field does not behave how most expect. This paper presents methods to create, validate, and visualize three-dimensional magnetic field maps to expand the use of magnetic fields as a sensing modality for navigation. The utility of these maps is measured in their ability to accurately represent the magnetic field and to enable dynamic attitude estimation. In experiments with motion capture truth data, a small multicopter with three-axis inertial measurements, including magnetometer, traversed five flight profiles distinctly exciting roll, pitch, and yaw motion to provide interesting trajectories for attitude estimation. Indoor experimental results were compared to those outdoors to emphasize how spatial variation in the magnetic field drives the need for our mapping techniques. Our work presents a new way of visualizing 3D magnetic fields, which allows users to better reason about the magnetic field in their workspace. Next, we show that magnetic field maps generated from coverage patterns are generally more accurate, but training such maps using observations from desired flight paths is sufficient in the vicinity of these paths. All training sets were interpolated using Gaussian process regression (GPR), which yielded maps with <1 μT of error when interpolating between and extrapolating outside of observed locations. Finally, we validated the utility of our GPR-based maps in enabling attitude estimates in regions of high magnetic field spatial variation with experimental data.

This paper experimentally evaluates continuum deformation cooperative control for the first time. Theoretical results are expanded to place a bounding triangle on the leader-follower system such that the team is contained despite nontrivial tracking error. Flight tests were conducted with custom quadrotors running a modified version of ArduPilot on a BeagleBone Blue in M-Air, an outdoor netted flight facility. Motion capture and an onboard inertial measurement unit were used for state estimation. Position error was characterized in single vehicle tests using quintic spline trajectories and different reference velocities. Five-quadrotor leader trajectories were generated, and followers executed the continuum deformation control law in-flight. Flight tests successfully demonstrated continuum deformation; future work in characterizing error propagation from leaders to followers is discussed.

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This study presents a comprehensive approach to mapping local magnetic field anomalies with robustness to magnetic noise from an unmanned aerial vehicle (UAV). The UAV collects magnetic field measurements, which are used to generate a local magnetic field map through Gaussian process regression (GPR). The research identifies two categories of magnetic noise originating from the UAV’s electronics, adversely affecting map precision. First, this paper delineates a zero-mean noise arising from high-frequency motor commands issued by the UAV’s flight controller. To mitigate this noise, the study proposes adjusting a specific gain in the vehicle’s PID controller. Next, our research reveals that the UAV generates a time-varying magnetic bias that fluctuates throughout experimental trials. To address this issue, a novel compromise mapping technique is introduced, enabling the map to learn these time-varying biases with data collected from multiple flights. The compromise map circumvents excessive computational demands without sacrificing mapping accuracy by constraining the number of prediction points used for regression. A comparative analysis of the magnetic field maps’ accuracy and the spatial density of observations employed in map construction is then conducted. This examination serves as a guideline for best practices when designing trajectories for local magnetic field mapping. Furthermore, the study presents a novel consistency metric intended to determine whether predictions from a GPR magnetic field map should be retained or discarded during state estimation. Empirical evidence from over 120 flight tests substantiates the efficacy of the proposed methodologies. The data are made publicly accessible to facilitate future research endeavors.