Inverse kinematics of redundant serial manipulators using interval method in handling uncertainties

The paper presents an application of Interval method to solve the inverse kinematics of a serially connected redundant manipulator, aiming its use in design optimization of manipulators. The article attempts to solve inverse kinematics, when the lengths of the links of the manipulator are not precisely known. The sources of uncertainties include manufacturing tolerances, approximations for complex link geometries, inaccuracies in joint angle measurements etc. The inverse kinematics is intended to produce solutions for joint variables in interval of tolerances for specified end effector accuracy range. The redundancy resolution is cast as an optimization problem with arm isotropy as performance metric. In solving for the inverse kinematics, two stage interval optimization method is implemented, where, in the first stage, bisection technique is applied and in the second stage interval discrete random variable method is used. As exemplar problem solving, two cases, namely a planar3-degrees-of-freedom and a spatial 5-degrees-of-freedom serial link manipulators are considered.