Analysis and Control of a Body-Attached Spring-Mass Runner Based on Central Pivot Point Approach

The Spring-Loaded Inverted Pendulum (SLIP) template and its extensions have long been used as benchmark models for analyzing the dynamics of legged systems in biology and robotics. The fundamental SLIP model is composed of single point mass attached to the ground (during stance phase) via an ideal lossless spring. Many researchers introduced various extensions to this fundamental model, such as damping & torque actuation, to handle critical physical phenomena that are unavoidable in real systems. Another crucial missing concept in SLIP template is the effect of the upper body in humans and humanoid robotic systems on the closed-loop system dynamics. Even though the SLIP template can effectively capture COM behavior, it cannot provide a framework for describing fullbody stabilization and control. In this paper, 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. Firstly, we analyze the characteristics and stability of the periodic solutions of the CPP model. Then, we develop a PD controller for pitch dynamics and an LQR (Linear Quadratic Regulator) 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 examples of how the model behaves under disturbances. The results show that the purposed model and associated control policy could be beneficial in the design and control of humanoid robotic systems.