A model of a humanoid biped and a locomotion control system for it are developed. Dynamics formulations are presented to model multi-limb systems using a form of Lagrange's equations in terms of quasi-coordinates. The formulation method can be applied to systems where the kinetic and potential energies are explicit functions of angular velocities and coordinate transformations. The ground contact is modeled using springs, viscous damping, and Coulomb friction. Therefore the system can be treated as an open mechanism with a tree structure even when it contacts the ground at multiple locations. This dynamic formulation is applied to a humanoid biped, which is modeled as a trunk with two legs and 20 joint degrees of freedom. An algorithm for controlling the locomotion of the simulated biped is also presented. The algorithm is hierarchical with local Joint Space Control (JSC) and global Virtual Model Control (VMC). VMC plays an important role in the stance phase of the legs and provides postural stability during locomotion. JSC is essential during the swing phase and for placement of the foot to obtain or change the speed of the robot. Simulations of various body motions and walking of a three dimensional humanoid biped are achieved through the superposition of these two control schemes.
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