Global Attitude Estimation using Uncertainty Ellipsoids
Authors: Taeyoung Lee, Amit K. Sanyal, Melvin Leok, N. Harris McClamroch
AI-generated Key Points
- The paper explores the problem of attitude estimation for mechanical systems.
- Attitude estimation is a crucial step in controlling the orientation or attitude of such systems.
- Current algorithms use coordinate representations, which have associated problems.
- This paper proposes a deterministic attitude estimation algorithm that globally minimizes the attitude estimation error.
- The algorithm assumes that the initial attitude, initial angular velocity and measurement noise lie within given ellipsoidal bounds.
- An uncertainty ellipsoid that bounds the attitude and angular velocity of the rigid body is obtained from these assumptions.
- A Lie group variational integrator and its linearization are used to propagate point estimates and uncertainty ellipsoids over time.
- This approach ensures that the resulting attitude estimation is optimal in terms of minimizing both the attitude estimation error and the size of the uncertainty ellipsoid.
Abstract: Attitude estimation is often a prerequisite for control of the attitude or orientation of mechanical systems. Current attitude estimation algorithms use coordinate representations for the group of rigid body orientations. All coordinate representations of the group of orientations have associated problems. While minimal coordinate representations exhibit kinematic singularities for large rotations, non-minimal coordinates like quaternions require satisfaction of extra constraints. A deterministic attitude estimation problem for a rigid body with bounded measurement errors is considered here. An attitude estimation algorithm that globally minimizes the attitide estimation error, is obtained. Assuming that the initial attitude, the initial angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and the size of the uncertainty ellipsoid measures the accuracy of the estimates. The point estimates, and the uncertainty ellipsoids are propagated using a Lie group variational integrator, and its linearization, respectively. The attitude estimation is optimal in the sense that the attitude estimation error and the size of the uncertainty ellipsoid is minimized.
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