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Demonstrating a Robust Walking Algorithm for Underactuated Bipedal Robots in Non-flat, Non-stationary Environments

Oluwami Dosunmu-Ogunbi, Aayushi Shrivastava, Jessy W Grizzle

Abstract

This work explores an innovative algorithm designed to enhance the mobility of underactuated bipedal robots across challenging terrains, especially when navigating through spaces with constrained opportunities for foot support, like steps or stairs. By combining ankle torque with a refined angular momentum-based linear inverted pendulum model (ALIP), our method allows variability in the robot's center of mass height. We employ a dual-strategy controller that merges virtual constraints for precise motion regulation across essential degrees of freedom with an ALIP-centric model predictive control (MPC) framework, aimed at enforcing gait stability. The effectiveness of our feedback design is demonstrated through its application on the Cassie bipedal robot, which features 20 degrees of freedom. Key to our implementation is the development of tailored nominal trajectories and an optimized MPC that reduces the execution time to under 500 microseconds--and, hence, is compatible with Cassie's controller update frequency. This paper not only showcases the successful hardware deployment but also demonstrates a new capability, a bipedal robot using a moving walkway.

Demonstrating a Robust Walking Algorithm for Underactuated Bipedal Robots in Non-flat, Non-stationary Environments

Abstract

This work explores an innovative algorithm designed to enhance the mobility of underactuated bipedal robots across challenging terrains, especially when navigating through spaces with constrained opportunities for foot support, like steps or stairs. By combining ankle torque with a refined angular momentum-based linear inverted pendulum model (ALIP), our method allows variability in the robot's center of mass height. We employ a dual-strategy controller that merges virtual constraints for precise motion regulation across essential degrees of freedom with an ALIP-centric model predictive control (MPC) framework, aimed at enforcing gait stability. The effectiveness of our feedback design is demonstrated through its application on the Cassie bipedal robot, which features 20 degrees of freedom. Key to our implementation is the development of tailored nominal trajectories and an optimized MPC that reduces the execution time to under 500 microseconds--and, hence, is compatible with Cassie's controller update frequency. This paper not only showcases the successful hardware deployment but also demonstrates a new capability, a bipedal robot using a moving walkway.
Paper Structure (18 sections, 12 equations, 8 figures)

This paper contains 18 sections, 12 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Contributions
  4. Review of the Control Philosophy
  5. Nominal Periodic Orbit
  6. Generating Nominal Trajectories with FROST
  7. Bézier Curves
  8. Lateral Stabilization of the Robot
  9. Euler Integration
  10. Impact Map for the New ALIP Model
  11. Linear Interpolation
  12. Navigating the sim-to-real Gap for Cassie Hardware
  13. Hardware Results and Discussion
  14. Maximum Walking Speed on Various Inclined Surfaces
  15. Continuous Walking on Changing Incline
  16. ...and 3 more sections

Figures (8)

  • Figure 1: Outtakes of a nominal trajectory for a non-flat terrain generated by FROST using a full-order model of the Cassie biped. The FROST animation is restricted to only showing a flat line at $y$=0. However, one can see that a non-flat trajectory is being followed by observing how the feet are placed with respect to the $y$=0 line.
  • Figure 2: Comparison of the nominal trajectory generated by FROST and ALIP model of angular momentum and CoM angle.
  • Figure 3: Graph of a Bézier Curve of Order 5 westerveltfeedback.
  • Figure 4: Schematic of the inverted pendulum to derive the impact map for the new variation on the ALIP model.
  • Figure 5: Plot of left and right ankle torque values for hardware experiment on the Cassie bipedal robot walking on an inclined moving treadmill moving at a constant speed of 0.9 m/s. The treadmill is gradually inclined from 0 degrees to its maximum incline of 20 degrees and back to 0 degrees.
  • ...and 3 more figures