Motion transformation solutions based on Euler angle perturbation model

Abstract

This paper presents two novel solutions to compute motion transformation by effectively addressing the nonlinear constraints formed by observational data. These solutions have broad applicability in algorithms involving rotation calculation, such as autonomous positioning systems. Instead of the commonly used Lie algebra-based solutions, the two novel solutions are based on the Euler angle perturbation model, which circumvent the problem arising from the singularity of Euler angles. The first solution is a forward compositional algorithm, which emphasizes accelerated iterative processes. The second solution is an inverse compositional algorithm that aims to minimize computational complexity. Both algorithms offer accelerated iteration by employing efficient Jacobian computation and parameter updates. Furthermore, we have developed an odometry algorithm and a point cloud alignment program to assess the performance of these different solutions. The experimental results demonstrate that the two novel solutions achieve an equivalent global minimum while also reducing computational load.