Core Concepts
Novel hybrid path-lifting algorithm ensures stability in MRP-based control strategies.
Abstract
The article discusses the use of Modified Rodrigues Parameters (MRP) in attitude control strategies. It introduces a hybrid dynamic path-lifting mechanism to extract MRP from the attitude space, ensuring stability properties. The paper explores equivalence of stability results between spaces and exemplifies with an MRP-based controller for unmanned aerial vehicles.
I. Abstract:
- Introduces MRP as a non-singular attitude description.
- Proposes a hybrid dynamic path-lifting mechanism for robustly extracting MRP.
- Demonstrates equivalence of stability results between spaces.
II. Introduction:
- Attitude control significance in aerospace and robotics.
- Challenges in stabilizing equilibrium points using continuous feedback.
III. Background and Motivation:
- SO(3) as configuration manifold for attitude dynamics.
- Topological obstructions to global stabilization discussed.
IV. Hybrid Dynamic Path-Lifting Algorithm:
- Introduces a novel algorithm for extracting MRP from attitude space.
- Incorporates stereographic projection and memory state for robustness.
V. Equivalence of Stability Results:
- Compares stability results between base space SO(3) and covering space ¯R3.
- Demonstrates that controllers designed in covering space yield equivalent stability results in base space.
Stats
The modified Rodrigues parameters (MRP) are two numerically different triplets that yield a minimal globally non-singular attitude description by switching between them.
The unit quaternion representation is an example of multiple covering manifold of SO(3).
The modified Rodrigues parameters (MRP) stem from the stereographic projection of the unit quaternion representation comprising two numerically different triplets.
Quotes
"The design renders the attitude space tracking dynamics robustly globally exponentially stable."
"Proposes a novel hybrid dynamic path-lifting algorithm for MRP extraction."