Jacobian motion planning of nonholonomic robots: The Lagrangian Jacobian algorithm

For nonholonomic robots whose kinematics are described by a driftless control system with outputs a new Jacobian inverse and a Jacobian motion planning algorithm are proposed. This inverse is based on solving a Lagrange-type constrained optimization problem, generalizing the usual Jacobian pseudoinverse. A case study illustrates a potential applicability of the new algorithm to shaping the system´s motion.