Date of Award


Document Type


Degree Name

Master of Science (MS)


Mechanical Engineering

Committee Chair/Advisor

Dr. Umesh Vaidya

Committee Member

Dr. Ardalan Vahidi

Committee Member

Dr. Yue Wang


The existence of nonlinearities and the lack of sufficient equations are fundamental challenges in modeling, analyzing, and controlling complex systems. However, recent developments revolutionizing the study of dynamical systems. An emerging method in nonlinear dynamical systems is the Koopman operator theory, which provides us with key advantages in performing the modeling, prediction, and control of nonlinear systems. The linear system representation allows us to leverage linear stability analysis. The first section of this thesis briefly covers the construction of a quadrupedal robot, a sufficiently complex nonlinear dynamical system, for the use of analyzing data-driven modeling techniques. The second section details the physics based dynamic model of this quadruped, using linearized single rigid body dynamics and then we provide the data-driven Koopman models using DMDc. We are able to show that the physics-based model fails to capture the dynamics of the system, whereas the Koopman model can accurately forecast the nonlinear response of the system. Lastly, we propose an experimental framework to obtain a data-driven Koopman model of a quadrupeds leg dynamics over deformable terrains as a switched system. Results show that the Koopman generator has a unique spectrum associated with each terrain, making terrain classification possible, using only proprioceptive sensors. Through the methods presented in this thesis, we are able to show that the data-driven models of dynamical systems using Koopman operator theory can sufficiently approximate the nonlinearities of the system and can accurately predict future trajectories of the system.



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