Relative Angular Measurements Research Articles

Quaternion-based attitude synchronisation for multiple rigid bodies in the presence of actuator saturation

ABSTRACTThis paper concentrates on the quaternion-based attitude synchronisation problems of networked rigid bodies under fixed and undirected communication topology without relative angular measurements in the presence of actuator saturation. We first consider the leaderless attitude synchronisation problem with zero final angular velocity. In this case, we not only discuss the performance under the acyclic communication topology with the proposed bounded control algorithm, but also analyse that if there exist cycles in the topology, the proposed bounded algorithm guarantees that all equilibrium points are unstable except that the attitudes of networked rigid bodies achieve synchronisation. We also expand the result to the case of attitude tracking synchronisation with a static leader in the presence of actuator saturation. Next, the tracking synchronisation problem with the desired time-varying attitude is addressed in the presence of actuator saturation. Numerical examples are provided to validate the effectiveness of the proposed bounded schemes and illustrate the performances of multiple rigid bodies.

A numerical method for solving the horizontal resection problem in Surveying

A numerical method for solving the horizontal resection problem in SurveyingThe three-point resection problem, i.e., the problem of obtaining the position of an unknown point from relative angular measurements to three known stations is a basic operation in surveying engineering. In the last centuries, a number of approaches to solve this problem have been developed. In this note, a new numerical approach to solve this problem is presented. The method uses only basic formulae from coordinate geometry. We present also numerical simulations that show the good performance and accuracy of this approach.

New Method That Solves the Three-Point Resection Problem Using Straight Lines Intersection

The three-point resection problem, i.e., the problem of obtaining the position of an unknown point from relative angular measurements to three known stations is a basic operation in surveying engineering. Several approaches to solve this problem, graphically or analytically, have been developed in the last centuries. In this paper, a new analytical approach to solve this problem is presented. The method determines the coordinates of the unknown point by intersecting straight lines through the three stations. The required azimuths of these lines are obtained from the geometric relationship between two similar triangles. Numerical simulations that show the good performance and accuracy of this approach are also reported.