The 2026 World Humanoid Robot Games saw run a 100-meter record at 8.64 seconds, showcasing dramatic advances in robotics, according to "Survivor" reality TV star Christian Hubicki.

In this paper, we present an energy-conservation based control architecture for stable dynamic motion in quadruped robots. We model the robot as a Spring-loaded Inverted Pendulum (SLIP), a model well-suited to represent the bouncing motion characteristic of running gaits observed in various biological quadrupeds and bio-inspired robotic systems. The model permits leg-orientation control during flight and leg-length control during stance, a design choice inspired by natural quadruped behaviors and prevalent in robotic quadruped systems. Our control algorithm uses the reduced-order SLIP dynamics of the quadruped to track a stable parabolic spline during stance, which is calculated using the principle of energy conservation. Through simulations based on the design specifications of an actual quadruped robot, Ghost Robotics Minitaur, we demonstrate that our control algorithm generates stable bouncing gaits. Additionally, we illustrate the robustness of our controller by showcasing its ability to maintain stable bouncing even when faced with up to a 10% error in sensor measurements.