  In this paper, disturbance reconstruction and robust trajectory tracking
control of biped robots with hybrid dynamics in the port-Hamiltonian form is
investigated. A new type of Hamiltonian function is introduced, which ensures
the finite-time stability of the closed-loop system. The proposed control
system consists of two loops: an inner and an outer loop. A fractional
proportional-integral-derivative filter is used to achieve finite-time
convergence for position tracking errors at the outer loop. A fractional-order
sliding mode controller acts as a centralized controller at the inner-loop,
ensuring the finite-time stability of the velocity tracking error. In this
loop, the undesired effects of unknown external disturbance and parameter
uncertainties are compensated using estimators. Two disturbance estimators are
envisioned. The former is designed using fractional calculus. The latter is an
adaptive estimator, and it is constructed using the general dynamic of biped
robots. Stability analysis shows that the closed-loop system is finite-time
stable in both contact-less and impact phases. Simulation studies on two types
of biped robots (i.e., two-link walker and RABBIT biped robot) demonstrate the
proposed controller's tracking performance and disturbance rejection
capability.
