Sanal sarkaç kavramına dayalı dik gövde ile koşan yay-kütle modelinin analizi ve kontrolü

Spring-Loaded Inverted Pendulum (SLIP) is widely used in locomotion community to analyze the running behavior of legged animals and design controllers by embedding its dynamics as a template model. It is a conceptual model composed of a mass-less ideal compliant leg attached to a point mass. Although the SLIP model can adequately explain the center of mass trajectories of legged animals, there have been some cases where this model remains insufficient while embedding into real platforms because of its over-simplified structure. Over the years, researchers have proposed various extensions to the SLIP model, such as torque actuation and damping, to adopt SLIP for physical platforms. In addition to these, another critical extension to the SLIP model is a rigid trunk that stands for upper body dynamics, which are unavoidable in systems that have body mass far from the hip joint like humanoid robots. In this context, researchers have developed several methods and algorithms to stabilize and regulate the trunk extended SLIP like systems. One of these control schemes is called the Virtual Pivot Point (VPP) concept, and it will be one of the focal points of this thesis. In this thesis, we present a comprehensive analysis of the VPP concept. We systematically analyze the periodic solutions of this concept for running behavior. We extract periodic solutions for different states and parameters of the system using numeric analysis tools. And then, we compare the characteristic of periodic solutions among themselves based on metrics such as energy efficiency and stability. Finally, we develop a new controller to stabilize the system dynamics. We compare this new control policy with an extended version of a controller introduced by Sharbafi et al. (2013) for the VPP framework. We demonstrate the effectiveness of both controllers and find that the proposed controller can create a larger basin of attractions for different periodic solutions without compromising from the convergence speed performance. After all, this thesis shows that the VPP concept, in conjunction with the proposed controller, could be beneficial in the design and control of legged robots targeting running behavior with non-trivial upper body dynamics.