A three-link module for modular dynamics and control of high-dimensional humanoids

Modeling complicated dynamics of humanoids is considered in this paper. It is proposed that the three-link module is a pivotal element in formulation of high-dimensional humanoids. The equations of motion of the module are first derived by projection of the free body equations of motion onto the space of the translation of an arbitrary point and Bryant angles and angular velocities. It is then shown that the formulation can be used as a construction module for systems with a larger number of segments. Holonomic and nonholonomic constraints are included to show the feasibility and versatility for representing other parts of the humanoid system. Digital computer simulations are presented to test the module´s formulation and demonstrate its behavior in two maneuvers, jumping and sway.