Least squares methods and applications in robotics

Sammanfattning: This thesis consider the least squares problems and various applications to the inverse kinematic problem in robotics. Two main linear least squares results are given; new backward perturbation bounds and an adaptive algorithm for rank-I regularization for rank deficient linear least squares problems. The inverse kinematic problem, i.e. the problem of finding the joint angles of a robot so that a given position and orientation condition is satisfied, is here formulated as a set of nonlinear equations. A general solver using Gauss-Newton's method is implemented on a fast signal processor. Methods to handle kinematic singularities are discussed, and the regularization algorithm proposed is used. Finally we consider redundant robots, where the number of joints is 7 or more. The extra degrees of freedom are here used for obstacle avoidance, a practical implementation strategy is proposed where the obstacles are assumed to be convex.