Angular Momentum based Stabilizing Control of Underactuated Multi-Link Planar Robots with Last Active Joint

摘要

For multi-link planar robots moving in the vertical plane with a last active joint, this paper studies how to design angular momentum based stabilizing controllers with a large region of attraction for the upright equilibrium point (UEP) of the robots, where all the links are upright. First, for ann$n$n-link planar robot, the presented stabilizing control in this paper contains a term compensating the gravitational term related to the last joint and a linear feedback ofn$2n$nvariables, which are the angular momentum of the robot about the first joint, its first-time derivative, its second-time derivative, and the othern$(2n-3$n) variables to be designed such that the Jacobian matrix of thesen$2n$nvariables is nonsingular at the UEP. Second, as an application, regarding the three-link case, this paper proves that the Jacobian matrix is nonsingular at the UEP regardless of all the mechanical parameters if the three variables to be designed are chosen to be one of the nine combinations of any two joint angles from three joint angles and any one joint angular velocity from three joint angular velocities of the robot. Finally, the simulation results of a three-link robot are presented to show that the regions of attraction of the obtained nine controllers are bigger than that of the conventional linear state-feedback controller with the state variables being the angles and angular velocities of the robot. The new results obtained in this paper include the existing results for the two-link case as a special case.