Stability Principle Inherent in Wheel Gait of Planar X-Shaped Walker Generated Using Constant Torque Drive and Mechanical Stoppers
Fumihiko Asano, Cong Yan
AI summary
Problem
Theoretical understanding of how mechanical stoppers enhance gait stability in passive-dynamic walkers remains insufficient, particularly for complex wheel gaits where kinetic energy loss is difficult to model analytically.
Approach
The authors derive nonlinear equations of motion and collision dynamics for a 2-DOF X-shaped walker, then linearize the model to compute state error transition matrices across four distinct walking phases to assess overall stability.
Key results
- Derivation of phase-specific state error transition matrices
- Proof that two stable phases overcome two unstable phases for asymptotic stability
- Numerical demonstration of torque-dependent walking speed and convergence
- Development of a reduced scalar Poincaré map for efficient stability evaluation
Why it matters
Provides a rigorous mathematical foundation for designing stable, torque-driven bipedal robots using simple mechanical constraints, guiding future robotic locomotion research.
Abstract
Since the late 19th century when the first walking toys were developed, it has been known that mechanical stoppers at the hip joint are crucial for generating stable passive dynamic walking. Recent research on passive-dynamic and limit-cycle walkers has also confirmed that mechanical stoppers at the hip and knee joints are effective for gener- ating stable walking motion, but theoretical research on how this mechanical constraint enhances the overall gait stability remains insufficient. This paper introduces a planar X-shaped walker equipped with mechanical stoppers at the hip joint, and investigates the effect of the mechanical constraint on the stability of the wheel gait generated by constant torque drive on a downslope. By simply falling forward while using the stoppers to constrain itself to the target impact posture, the robot can generate a highly stable wheel gait. We divide the motion of one step into four phases, derive approximate analytical solutions for the state error transition function matrix in each phase using a linearized model, and analyze the increase or decrease in the state error norm using metrics such as its maximum singular value. Numerical simulations demonstrate that while two phases are unstable in terms of the increase in the state error norm, the remaining two phases are stable, resulting in overall asymptotic stability.