Balancing and Hopping Motion Control Algorithms for an Under-actuated Robot

Abstract

The main contribution of this thesis is a new and simple angular momentum based control algorithm for balancing an under-actuated planar robot. The proposed controller is able to stabilize the robot at any unstable balanced configuration and to control the robot to follow motion trajectory commands. This controller is also capable of balancing the robot on a rolling contact. A modified version of the controller is used to control the robot during a single hop motion. The proposed planar controller is then used as a part of a 3D balancing controller for a spatial under-actuated robot. The 3D control algorithm, which is based on the angular momentum of the robot, can balance the robot within any vertical plane and also rotate the robot from a vertical plane to any other one. Performance of the control algorithm in planar balancing, spatial balancing and planar hopping motions is demonstrated by simulation results. Although hopping motion of a spatial under-actuated robot is not considered in this thesis, it is shown in simulations that, starting from an upright configuration, the 3D controller is able to move the robot within any arbitrary vertical plane. Therefore, by confining the robot’s motion to a vertical plane, the robot is potentially able to perform hopping motion in 3D using the same algorithm that is proposed for planar hopping motion. Another major contribution of this thesis is a new nonlinear model for the contact normal force. This new model accurately predicts the measured values of the coefficient of restitution between spheres and plates of various materials. The new contact model is used in this thesis to model the contact between the robot’s foot and the ground during a hopping motion.