Energy-Efficiency in Legged Robots Locomotion: Open versus Closed Chains*

Quadrupedal gallop is one of the fastest and efficient forms of locomotion that can be found in nature. Engineers in the field of robotics use it as a source of inspiration to create legged robots. The most common model to describe galloping is the spring-loaded inverted pendulum, representing the body as a mass, while legs perform a spring-like bouncing movement. There are many design choices to implement a robotic system to get desirable bouncing dynamics. This paper compares two opposite ways to design a hopping robot in terms of energy-efficiency: algorithmically with an open chain or mechanically with a closed chain. The first way takes a relatively simple serial kinematic chain and, via impedance control algorithms, perform passive dynamic interaction with the ground. The second way takes SLIP-synthesized underactuated mechanism and via simple position and velocity control perform the same passive dynamic interaction with the ground. The paper contains a detailed description of the hoppers, analysis, and simulation results.