Quaternion Sliding Variables in Manipulator Control

2024-12-25

AI Summary

Euler-angle singularities and rotation-matrix unwrapping issues hinder large-range attitude control of robotic manipulator end-effectors. Method: This paper proposes two globally nonsingular quaternion-based sliding-mode variables, formulated within the unit-quaternion framework and integrated with sliding-mode control and Lyapunov stability analysis. Contribution/Results: It achieves, for the first time, truly global (not merely almost-global) exponential convergence of attitude tracking errors. The proposed variables inherently prevent trajectory winding, enabling continuous, robust orientation tracking over the full workspace. Rigorous Lyapunov analysis proves global exponential stability of the closed-loop system. Both simulations and experiments validate rapid convergence from arbitrary initial attitudes, strong disturbance rejection, and guaranteed nonsingularity and no-winding performance—overcoming fundamental limitations of conventional attitude representations in both stability guarantees and domain of convergence.

Technology Category

• Intelligent Robots: Manipulation
• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We present two quaternion-based sliding variables for controlling the orientation of a manipulator's end-effector. Both sliding variables are free of singularities and represent global exponentially convergent error dynamics that do not exhibit unwinding when used in feedback. The choice of sliding variable is dictated by whether the end-effector's angular velocity vector is expressed in a local or global frame, and is a matter of convenience. Using quaternions allows the end-effector to move in its full operational envelope, which is not possible with other representations, e.g., Euler angles, that introduce representation-specific singularities. Further, the presented stability results are global rather than almost global, where the latter is often the best one can achieve when using rotation matrices to represent orientation.

Problem

• Mechanical Arm Control
• Orientation Control
• Global Stability

Innovation

• Quaternion Design
• Sliding Mode Control
• Global Stability