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Robots with Attitude: Singularity-Free Quaternion-Based Model-Predictive Control for Agile Legged Robots

Zixin Zhang, John Z. Zhang, Shuo Yang, Zachary Manchester

TL;DR

This work parameterizes the robot's attitude with singularity-free unit quaternions and makes modifications to the iterative linear-quadratic regulator (iLQR) algorithm to deal with the resulting geometry.

Abstract

We present a model-predictive control (MPC) framework for legged robots that avoids the singularities associated with common three-parameter attitude representations like Euler angles during large-angle rotations. Our method parameterizes the robot's attitude with singularity-free unit quaternions and makes modifications to the iterative linear-quadratic regulator (iLQR) algorithm to deal with the resulting geometry. The derivation of our algorithm requires only elementary calculus and linear algebra, deliberately avoiding the abstraction and notation of Lie groups. We demonstrate the performance and computational efficiency of quaternion MPC in several experiments on quadruped and humanoid robots.

Robots with Attitude: Singularity-Free Quaternion-Based Model-Predictive Control for Agile Legged Robots

TL;DR

This work parameterizes the robot's attitude with singularity-free unit quaternions and makes modifications to the iterative linear-quadratic regulator (iLQR) algorithm to deal with the resulting geometry.

Abstract

We present a model-predictive control (MPC) framework for legged robots that avoids the singularities associated with common three-parameter attitude representations like Euler angles during large-angle rotations. Our method parameterizes the robot's attitude with singularity-free unit quaternions and makes modifications to the iterative linear-quadratic regulator (iLQR) algorithm to deal with the resulting geometry. The derivation of our algorithm requires only elementary calculus and linear algebra, deliberately avoiding the abstraction and notation of Lie groups. We demonstrate the performance and computational efficiency of quaternion MPC in several experiments on quadruped and humanoid robots.
Paper Structure (19 sections, 26 equations, 10 figures)

This paper contains 19 sections, 26 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Related Works
  3. Background
  4. Unit Quaternions
  5. Quaternion Differential Calculus
  6. Model-Predictive Control for Legged Robots
  7. Quaternion MPC
  8. MPC Architecture
  9. Coordinate Systems
  10. SRB Dynamics
  11. Modification to AL-iLQR
  12. Objective Function
  13. Experiments and Results
  14. Experiments Setup
  15. Dynamic Quadruped Walking with Attitude Control
  16. ...and 4 more sections

Figures (10)

  • Figure 1: A Unitree Go1 robot standing vertically between two walls using quaternion MPC (right) similar to a human climber human_climber (left).
  • Figure 2: Quaternion MPC control architecture. The green component operates at 140 Hz, while the blue and yellow elements function at 1000 Hz.
  • Figure 3: Coordinate systems
  • Figure 4: SRB dynamics
  • Figure 5: Unitree Go1 position and attitude data on hardware. Quaternion MPC tracks a sinusoidal desired attitude trajectory during dynamic locomotion.
  • ...and 5 more figures