Chained formulation of 3D path following for nonholonomic autonomous robots in a Serret-Frenet frame

Abstract

The problem of 3D path following of nonholonomic systems in closed-loop is addressed. The kinematic model in a local coordinate system using a Serret-Frenet frame with sideslip and attack angles is used to express the motion of the robot. A new derivation of the chained form with five states and three inputs is developed to linearize the kinematic model of the robot in order to design a decoupled stable controller. The 3D path following is validated experimentally using a magnetic helical swimmer with visual servo control by following first a helix trajectory then an inclined sinusoidal trajectory. The results show the accuracy and robustness of the controller.