Modeling and control of constrained dynamic systems with application to biped locomotion in the frontal plane

The general problem of control of state-space constrained dynamic systems is considered. Based on the derivation of the constraint forces as explicit functions of the state and the input, a general model is presented that encompasses both the constrained case and the corresponding unconstrained case. Stability and point-to-point motion of these systems in the vicinity of an operating point are considered under operating conditions which either maintain or deliberately violate the constraints. Algorithms for computation of the necessary feedback gains in the vicinity of the operating point are discussed. For a three-link biped model, several motions in the vicinity of the vertical stance are considered, and the necessary feedback gains are derived. Digital computer simulation of some biped motions are carried out to serve as examples and to demonstrate use of the theory. This work is to be regarded as an elementary step in better understanding of human motor control and in the design of robots and prosthetic devices.