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

TL;DR

This paper introduces a quaternion-based model-predictive control framework for legged robots that avoids attitude singularities, enabling more reliable and efficient large-angle rotations in agile robotic movements.

Contribution

The paper develops a singularity-free quaternion-based MPC for legged robots, modifying the iLQR algorithm without complex Lie group notation.

Findings

Effective large-angle rotation handling demonstrated on quadruped robots

Improved computational efficiency over traditional methods

Robust attitude control without singularities

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.