Removing Phase Variables from Biped Robot Parametric Gaits.

Area of Science:

• Robotics
• Control Theory
• Computer Algebra

Background:

• Hybrid zero dynamics (HZD) is a control framework for underactuated systems like biped robots and prosthetic legs.
• Stable walking gaits in HZD are encoded in polynomial output functions that are zeroed via feedback.
• Identifying a suitable mechanical phasing variable for gait progression can be challenging.

Purpose of the Study:

• To present a novel method for generating HZD output functions from parametric walking gaits.
• To eliminate the need for explicit knowledge of phase variables in the control design process.
• To leverage algebraic tools for simplifying HZD control design.

Main Methods:

• The proposed method utilizes the concept of resultants of polynomials from computer algebra.
• It computes the resultant to eliminate the phasing variable from the gait equations.
• This algebraic elimination generates the required output functions directly.

Main Results:

• Successfully generated output functions for bipedal locomotion without explicit phase variable definition.
• Demonstrated the effectiveness of using polynomial resultants for control function synthesis.
• Provided a systematic approach to HZD control design for legged robots.

Conclusions:

• The developed method offers a robust way to design HZD controllers for biped robots and prosthetic legs.
• Eliminating the need for explicit phase variable identification simplifies the control design workflow.
• This approach enhances the applicability of HZD control in legged robotics research and development.