Repeatable, extended Jacobian inverse kinematics algorithm for mobile manipulators

An inverse kinematics algorithm for a robotic system is called repeatable, if it transforms closed paths in the task space into closed paths in the configuration space. In this paper we assume the endogenous configuration space approach and define a repeatable inverse kinematics algorithm for mobile manipulators, patterned on the extended Jacobian scheme. An examination of a dynamic system associated with this algorithm gives new insight into the mechanism of repeatability. As an illustration of the general design strategy an exemplary extended Jacobian algorithm is applied to a kinematic cartype platform carrying the POLYCRANK, 7 DOF on-board manipulator.