Date of Award


Degree Name

MS in Mechanical Engineering


Mechanical Engineering


College of Engineering


Siyuan (Simon) Xing

Advisor Department

Mechanical Engineering

Advisor College

College of Engineering


Single degree-of-freedom hopping robots are typically modeled as spring loaded inverted pendulums (SLIPs). This simplified model, however, does not consider the overall leg geometry, consequently making it difficult to investigate the optimized inertial distribution of the leg for agile locomotion. To address this issue, the first part of this thesis establishes an accurate mathematical model of a DC-motor-driven, two-link hopping robot where the motors are modeled as torque sources. The equations of motion for the two distinct phases of locomotion (stance and flight) are derived using the Lagrangian approach for holonomic systems. A Simulink/Stateflow model is developed to numerically simulate the robot’s locomotion. The model is then validated with the simulation data from Simscape Multibody, which allows for accurate modeling of the environment and inertial properties for complex geometries. With the accurate model of the hopping robot, two distinct control strategies are adopted. The first strategy focuses on implementing position control while the robot is in flight to prepare for touchdown. The second control method explores implementing impedance control during stance, allowing the response to mimic that of a mass-spring-damper model. It was found that concentrating the mass of the robot in the hip allows the robot to attain larger apex heights as opposed to evenly distributing the mass throughout the leg. With plans to implement the leg on a quadruped robot, the mathematical model is easily expandable to 2 or 3 degrees-of-freedom. This allows for further stability analysis and development of control strategies of the leg.