this paper employs nonlinear disturbance observer (ndo) for robust trajectory-free nonlinear model predictive control (nmpc) of biped robots. the ndo is used to reject the additive disturbances caused by parameter uncertainties, unmodeled dynamics, joints friction, and external slow-varying forces acting on the biped robots. in contrary to the slow-varying disturbances, handling sudden pushing ...

Given a free product of groups G=⁎j∈JAj and natural number n, what is the minimal possible commutator length an element gn∈G not conjugate to elements factors? We give exhaustive answer this question.