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The first ever oscillation phenomenon of a copper wire embraced inside a self‐powered liquid metal machine is discovered. When contacting a copper wire to liquid metal machine, it would be swallowed inside and then reciprocally moves back and forth, just like a violin bow. Such oscillation could be easily regulated by touching a steel needle on the liquid metal surface.

The main objective of this paper is to revisit one of the key steps of immersion and invariance stabilizing controller design. Namely, the one that ensures attractivity of the manifold whose internal dynamics contains a copy of the desired system behavior. Towards this end we invoke contraction theory principles and propose two alternative procedures to carry out this step: (i) to replace attractivity of the manifold by virtual contraction of the off-themanifold coordinate and (ii) to ensure the attractivity of the manifold rendering it horizontally contractive. This makes more systematic the design with more explicit degrees of freedom to accomplish the task. Several examples, including the classical case of systems in feedback form, are used to illustrate the proposed design.

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The navigation accuracy of the rotational inertial navigation system (RINS) could be greatly improved by periodically rotating the inertial measurement unit (IMU) with gimbals. However, error parameters in RINS should be effectively calibrated and compensated. In this paper, a self-calibration method is proposed for tri-axis RINS using attitude errors and velocity errors as measurements. The proposed calibration scheme is designed as three separate steps, and a certain gimbal rotates continuously in each step. All the error parameters in the RINS are calibrated when the whole scheme finishes. The separate calibration steps reduce the correlations between error parameters, and the observability of errors in this method is clear to demonstrate according to the relations between navigation errors and error parameters when gimbals rotate. Each calibration step only lasts 12 min, thus gyro drifts and accelerometers biases could be regarded as constant. The proposed calibration scheme is tested in both simulation and actual tri-axis RINS, and simulation and experimental results show that all 23 error parameters could be well estimated in tri-axis RINS. A long-term vehicle navigation experiment results show that after calibration and compensation, the navigation performance has doubled approximately, and the velocity accuracy is less than 2 m s −1 while the position accuracy is less than 1500 m, fully illustrating the significance of the proposed self-calibration method in improving the navigation performance of RINS.

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