Point-Cloud Processing Using Modified Rodrigues Parameters for Relative Navigation

Point-cloud registration pertains to the computation of point pairs between a source and a destination point cloud, followed by the calculation of the rigid transform minimizing a relative distance (such as the iterative closest point-to-plane distance criterion) between the set of point pairs. The work described in this paper presents an alternative parametrization of the rotational component of the rigid transform using modified Rodrigues parameters. The performance of this formulation is compared with that of Euler angles-based algorithms over random and structured point clouds, using additive and multiplicative formulations. Monte Carlo results assuming perfect point-pair matching show a better performance for the new modified Rodrigues parameter formulation in terms of accuracy and speed, with convergence achieved on average 30% faster than the baseline algorithm. Relying on a realistic pair-matching procedure degrades the convergence basin of all methods, but the modified Rodrigues parameter formulation still retains the best performance.