A new approach for orientation determination

In some modeling and control problems, especially in robotics, determination of orientation of a rotating body or frame requires slow and time taking numerical calculations. In some cases, such as for continuum robots, these time-taking calculations are an impediment to real-time control. The common approaches for orientation determination, such as Euler angles or Euler parameters, are beneficial when generalized coordinates are needed. Otherwise, these approaches require some time-taking equations for calculation of the rotation matrix (direction cosine matrix). Another method is to calculate the rotation matrix directly, based on the angular velocity. Although this method is very fast, it is numerically unstable, because of accumulation of some numerical errors. In this paper, an approach is introduced that cancels these errors with the least numerical efforts, and provides high accuracies. The application and importance of this approach is studied and discussed in the case of modeling and control of continuum robotic arms, as an instance. The proposed methods are used to model a spring, as a case study. The obtained results are validated by analytic data, and are compared to the results obtained by other methods.