Jacobian inverse kinematics algorithms with variable steplength for mobile manipulators

We study Jacobian inverse kinematics algorithms for mobile manipulators composed of a nonholonomic mobile platform and a holonomic onboard manipulator. In general, the Jacobian algorithms converge locally, often producing weird end effector and platform trajectories. In the paper we use the existing theory of Newton algorithms in order to improve the quality of convergence of the Jacobian algorithms. Specifically, we examine a strategy of adjusting the steplength in the Jacobian pseudoinverse algorithm that results from the affine covariant Lipschitz condition imposed on the mobile manipulator's Jacobian. The affine covariant strategy is verified by extensive computer simulations and compared with the constant length step and a simple Armijo strategies.