Date

2022-2-10

Author

Sever Gökmen, İzel

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One of the benchmark models for analyzing legged systems in biology and robotics is the Spring-Loaded Inverted Pendulum (SLIP) template and its extensions. The basic SLIP model consists of a single point mass with an ideal spring connecting it to the ground during the stance phase. After its introduction, this model has received numerous extensions to handle physical constraints that exist in practical configurations, such as the upper body's effect on the system dynamics. Although the SLIP template can describe COM behavior in its primary form, it fails to provide a framework for describing full-body stabilization and control. In the first part of the thesis, we present a new control policy called the Central Pivot Point (CPP) for the body-attached spring-mass runners. In the stance phase, CPP directs ground reaction forces through the center of mass and cancels the torque created by these forces on the body. In this way, the CPP model makes it possible to develop different controllers for both the body's rotational and euclidean dynamics. Moreover, we analyze the characteristics and stability of the periodic solutions of the CPP model. Then, we develop a Proportional-Derivative (PD) controller for pitch dynamics and a Linear Quadratic Regulator (LQR) for gait-level apex-to-apex discrete dynamics to stabilize the system's periodic solutions. We compute the basin of attraction of the proposed control scheme and show how the model behaves under disturbances. Although our model has a compact mathematical form for its dynamics, there is no qualifying analytical expression due to its nonlinear nature. In the second part, we present a precise analytical approximation to the stance dynamics of the model in the case of no damping and non-symmetric trajectories. Our approach is based on radial actuation and the partial feedback linearization that embeds a simple template to linearize the radial dynamics and approximate the angular dynamics for handling the nontrivial body dynamics of TSLIP. The next step is simulating the model under different gravity correction methods to study their prediction performance for a comprehensive set of trajectories, including non-symmetric ones. Finally, we analyze the extended model in terms of the characteristics and stability of the periodic solutions. Results obtained throughout the analysis of the TSLIP model and the proposed control scheme substantiate the model's prospect to ease the design and control of humanoid systems.

Subject Keywords

Legged Locomotion, Spring-Mass Hopper, Periodic Solution Analysis, Template Model Embedding, Analytic Approximate Solutions

URI

https://hdl.handle.net/11511/96364

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Graduate School of Natural and Applied Sciences, Thesis