title: Human Hopping Dynamics: From Biomechanical Analysis to Robotic Applications
Creators: name: Mohammadi Nejad Rashty, Aida
Publisher: name: UNSPECIFIED
Year: 2025

description: Legged locomotion is a complex interplay of three locomotor sub-functions, including stance (axial leg function), leg swinging, and balancing. These sub-functions are critical for achieving stable and efficient gaits in both humans and robots, facilitating advancements in biomechanical research and the development of more effective robotic systems and assistive devices. In this thesis, we select hopping to focus on the Stance subfunction, which involves the elastic rebounding of the stance leg, counteracts gravity, and provides vertical propulsion. Within a broader context of locomotion, hopping stands out as a particularly fundamental movement due to its simplicity while its biomechanical and control aligns with other forms of bipedal and quadrupedal locomotion, such as running. Hopping involves repeated, rhythmic movements primarily in one dimension (vertically), allowing researchers to isolate and examine the dynamics of vertical displacement. 
This simplification aids in modeling, simulating, and understanding the fundamental principles of dynamic legged locomotion.

Mechanical structure and motor control are the ingredients of locomotion generation. On one hand, actuator design, morphology (e.g., body segmentation), coupling between different mechanical elements, compliance, and passive dynamics role in facilitating movement generation are key aspects of the mechanical design of a locomotor system. On the other hand, appropriate motor control can complement well-designed mechanics to reach an efficient, robust, and agile motion. Human musculoskeletal and neural control can be used as a role model to design hopping robots. Therefore, investigating how human mechanics and motor control contribute to hopping in a variety of conditions and using these insights to design and control bioinspired hopping robots are the overlaying concepts of this thesis. 

To address the above mentioned research concepts, we first investigated human hopping to understand its variability and underlying mechanics. In our initial experiments, subjects hopped at various frequencies, choosing their own hopping characteristics such as frequency and height. We analyzed ground reaction forces, hopping times, and duty factors, observing significant variability both between subjects and within the same subject under different conditions. When subjects hopped to a metronome, intra-subject variability decreased, indicating that consistent rhythmic pacing stabilizes hopping behavior. We found minimal variability between 100 % and 150 % of the Preferred Hopping Frequency (PHF), but variability increased significantly at 75 % PHF.

The second study focused on the actuation and compliance role at different joints in the hopping experiment of first study. The kinematic and kinetic measurements were used to create a mechanical simulation model with Series Elastic Actuators (SEAs) to optimize joint stiffness for minimizing peak power and energy consumption. Our results showed that while fixed stiffness values were effective for the knee and ankle, adjustable stiffness could further reduce energy requirements. Optimal SEA stiffness reduced peak power demands by up to 73 % at the ankle and 66 % at the knee, particularly around the preferred hopping frequency, though no significant benefits were found for the hip at higher frequencies.

Further investigations focused on the roles of passive dynamics and active control properties at different leg joints during hopping. Our analysis suggested that distal joints, like the ankle, benefit more from passive elastic elements, while proximal joints, such as the knee and hip, require active control mechanisms for effective energy management. Using force-modulated compliance (FMC) alongside fixed springs, we accurately predicted knee torque-angle patterns across various frequencies.

In addition to studying human mechanical design and motor control in steady-state hopping, we investigated ground-level perturbation scenarios to understand human responses to unknown changes. We analyzed human leg reaction to perturbation in the stance phase using template models and their extensions using difference reflex pathways (e.g., force or length feedback). Criticality of perturbation timing in characterizing recovery scenes was shown in both data analysis and simulations. The importance of reflex signals and adaptation mechanisms to perturbation are highlighted when energy level changes due to perturbation is significant. 

To validate these concepts, we designed and controlled a bioinspired hopping robot based on our findings. This robot served as a testbed to implement passive and force-modulated springs, corroborating our human hopping observations. Experimental results demonstrated that incorporating compliant elements in distal joints significantly aids in energy management, with proximal joints benefiting from the stability provided by these passive elements.

Overall, this thesis enhances our understanding of human locomotion and its application to robotic systems. By focusing on the dynamics of hopping, we offer valuable insights into optimizing energy use and stability in legged locomotion. These findings have significant implications for the development of more efficient, versatile, and human-like robotic and assistive devices, bridging the gap between biological and mechanical systems.