Toward Step-by-Step Synthesis of Stable Gaits for Underactuated Compliant Legged Robots

Many control policies developed for legged robots are based on control of an underlying, simplified version of the dynamics of the robot. A good example is the Linear Inverted Pendulum Model (LIPM) which has become the standard control template for ZMP-based rigid robots. For compliant robots, this reduced order model is naturally the Spring-Loaded Inverted Pendulum (SLIP), which has proven to have many interesting traits that are potentially useful for control of full order robots. The methods proposed so far for this purpose are mainly focused on either matching the dynamics of the robot to those of SLIP, or following a SLIP-produced trajectory. These methods can be problematic, especially for underactuated systems. In the present work, we explore an opposite approach, by starting from SLIP and step-by-step constructing toward the full order robot. The goal is to detect and capture the essential stabilizing variables in the reduced order model that can potentially maintain their stabilizing effect in the full order robot, as well. Our initial investigations show that the proposed method provides excellent potentials for synthesizing stable gaits for underactuated compliant robots by use of a much simpler and more robust approach compared to the ones previously presented in the literature.