Contributions to the estimation of rigid-body motion under sensor redundancy

Abstract

This thesis studies the estimation of the motion of a rigid-body from body-point motion data. This study is closely related to the direct kinematics problem in robotics, its solution being particularly challenging, at the displacement level, for parallel manipulators. The concept of measurement subspaces is used to characterize the motion of the end-point of three-degree-of-freedom serial manipulators of general geometry for any joint-sensor layout. Once the motion of a redundant set of body points is characterized by its measurement subspaces, the pose estimation problem reduces to a linear least-square problem subject to the nonlinear constraint of proper orthogonality over the orientation variables. Although the solution of this problem requires a nonlinear numerical procedure, we proposed two alternative linear least-square estimates for its solution. The polar least-square estimate (PLS) is based on the polar decomposition of the unconstrained least-square solution, while the decoupled polar least-square estimate (DPLS) uses the same approach, but solves a decoupled version of the kinematic relationships. A decoupling equation is derived for general combinations of measurement subspaces, for which sufficient conditions for isotropic decoupling are proposed and illustrated with an industrial parallel manipulator. Isotropic decoupling is defined in this thesis. The computational cost and estimation accuracy of the proposed procedures are analysed through simulation and experimental studies. Some procedures exhibit fair estimation accuracy and low computational cost, and hence, are well suited for the purpose of on-line implementation.