  In the first part of this thesis, we present our efforts on experimental
validation of the predictive performance of mechanics-based mathematical models
on a physical one-legged hopping robot platform. We extend upon a recently
proposed approximate analytical solution developed for the lossy spring--mass
models for a real robotic system and perform a parametric system identification
to carefully identify the system parameters in the proposed model. We also
present our assessments on the predictive performance of the proposed
approximate analytical solution on our one-legged hopping robot data.
  The second part considers estimating state space models of legged locomotion
using input--output data. To accomplish this, we first propose a state space
identification method to estimate time periodic state and input matrices of a
hybrid LTP system under full state measurement assumption. We then release this
assumption and proceed with subspace identification methods to estimate LTP
state space realizations for unknown stable LTP systems. We utilize bilinear
(Tustin) transformation and frequency domain lifting methods to generalize our
solutions to different LTP system models. Our results provide a basis towards
identification of state space models for legged locomotion.
