An extended Jacobian inverse kinematics algorithm for doubly nonholonomic mobile manipulators

Based on the concept of endogenous configuration space we derive an extended Jacobian inverse kinematics algorithm for doubly nonholonomic mobile manipulators, i.e. mobile manipulators built of a nonholonomic manipulator and a nonholonomic mobile platform. A key step in the derivation consists in defining a local diffeomorphism between the endogenous configuration space and the suitably augmented (extended) taskspace of the mobile manipulator. This has been achieved by decomposing the Fourier series representation of control functions driving the mobile manipulator into a finite dimensional part isomorphic to the taskspace, and a complementary infinite dimensional part augmenting the taskspace. By definition, our algorithm has the property of repeatability. Theoretical considerations are illustrated with computer simulations accomplished for a 3 d.o.f. planar nonholonomic manipulator mounted on a kinematic car-type platform.