Applicability analysis of generalized inverse kinematics algorithms with respect to manipulator geometric uncertainties

Abstract

Accurate kinematic models and measurements are needed in many robotic applications. However uncertainties related to joint angle measurements and manipulator geometry are unavoidable, especially when grasping and using different tools or when we do not have access to an accurate robot model, e.g. when we construct a robotic system by hand. The generalized inverse kinematics methods are not applicable when a manipulator stay inside its singular region. We derive the upper bounds on the joint measurement errors and geometric uncertainties, in order to guarantee that the open-chain serial manipulators stay outside the singular region. These bounds in other words enable en effective execution of generalized inverse kinematics methods for a robotic system which is prone to geometric uncertainties. In addition to the analytic derivation, We validate the proposed bounds through a trajectory tracing task performed by a PR2 robot simulator.