Model tabanlı ve veri güdümlü yöntemlerle bacaklı hareketlilik için sistem tanılaması

Robotics is one of the core areas where the bioinspiration is frequently used to design various engineered morphologies and to develop novel behavioral controllers comparable to the humans and animals. Biopinspiration requires a solid understanding of the functions and concepts in nature and developing practical engineering applications. However, understanding these concepts, especially from a human or animal point of view, requires the significant use of mathematical modeling and system identification methods. In this thesis, we focus on developing new system identification methods for understanding legged locomotion models towards building better legged robot platforms that can locomote effectively as their animal counterparts do in nature. 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. Experiments with different leg springs and cross validation of results yield that our approximate analytical solutions provide a sufficiently accurate representation of the physical robot platform. In the second part, we adopt a data-driven approach to obtain an input--output representation of legged locomotion models around a stable periodic orbit (a.k.a. limit cycle). To this end, we first linearize the hybrid dynamics of legged locomotor systems around a limit cycle to obtain a linear time periodic (LTP) system representation. Hence, we utilize the frequency domain analysis and identification methods for LTP systems towards the identification of input--output models (harmonic transfer functions) of legged locomotion. We propose simulation experiments on simple legged locomotion models to illustrate the prediction performance of the estimated input--output models. Finally, the third 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.