Studies that consider a legged machine walking with a statically unstable g
ait as a controlled system of solids with variable constraints are generali
zed. The motion of such a system is described by both differential and diff
erence equations. The method of optimization of periodic systems is used to
synthesize control algorithms for such systems. It is demonstrated that if
the dynamic processes due to constraint variation are taken into account i
n the synthesis of a control system, then it is possible to substantially i
ncrease the performances of control algorithms and to reduce loads on actua
ting mechanisms.