In this paper, a new camera calibration method based on the image of the absolute quadratic curve (IAC) is proposed, and a new target is designed for this method, which is both convenient and flexible. It first extracts the characteristic points and the characteristic lines of the target and finds out the vanishing point and the vanishing line. The radial and tangential distortion coefficients are obtained by using the cross ratio invariance to correct the target image distortion. Then, the four internal parameters of the camera are obtained by IAC. The influence of the skew parameters is ignored. The rotation matrix is then calculated by the orthogonal characteristic of the coordinate system, and the translation vector is calculated by the center coordinates of the camera. In this way, the internal and external parameters of the camera can be obtained. The internal and external parameters are taken as initial values, and the optimal results are obtained by nonlinear optimization using the reprojection method. Finally, the relative position between different target images can be obtained by using the fundamental matrix, namely, the rotation angle. In the process of solving, the normalization method is used to improve the accuracy of data processing. Not requiring any prior information of the camera, the method has a wide range of applications. INDEX TERMS Camera calibration, image of the absolute quadratic curve (IAC), fundamental matrix, cross ratio invariance, vanishing point, vanishing line, distortion correction.
This paper is concerned with the time-varying formation tracking issue for high-order multiagent systems based on event-triggered mechanism and adaptive control strategy. The time-varying formation configuration involved in our work is expressed as a bounded piecewise continuously differentiable vector function. The follower agents are required to achieve a pre-specified time-varying formation while tracking the state trajectory of the leader. First of all, in the light of event-triggered schema, we constructed an adaptive control protocol with adjustable time-variant parameters for achieving time-varying formation tracking. Meanwhile, the corresponding triggering conditions were designed to avoid continuous communication. Then, a four-step algorithm and feasible conditions have been provided to determine protocol parameters. Additionally, theoretically proof reveals that the specified formation tracking could be realized while excluding Zeno behavior. Two simulation examples were finally provided to illustrate the effectiveness of the obtained results. INDEX TERMS Time-varying formation tracking, adaptive control, event-triggered communication, multiagent systems (MASs).
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