Asymptotically Stable Optimal Multi-rate Rigid Body Attitude Estimation based on Lagrange-d'Alembert Principle
The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states.
Code (0)
등록된 구현이 없습니다.
Tasks
RelationSimilar Papers 제목 키워드 기반
Rigid-Body Attitude Control on $\mathsf{SO(3)}$ using Nonlinear Dynamic Inversion
This paper presents a cascaded control architecture, based on nonlinear dynamic inversion (NDI), for rigid body attitude control. The proposed controller works directly with the rotation matrix parameterization, that is,…
A Dynamical Perspective on Point Cloud Registration
We provide a dynamical perspective on the classical problem of 3D point cloud registration with correspondences. A point cloud is considered as a rigid body consisting of particles. The problem of registering two point c…
Point Cloud RegistrationBeyond Compromise: Pareto-Lenient Consensus for Efficient Multi-Preference LLM Alignment
Transcending the single-preference paradigm, aligning LLMs with diverse human values is pivotal for robust deployment. Contemporary Multi-Objective Preference Alignment (MPA) approaches predominantly rely on static linea…
Optimism Stabilizes Thompson Sampling for Adaptive Inference
Thompson sampling (TS) is widely used for stochastic multi-armed bandits, yet its inferential properties under adaptive data collection are subtle. Classical asymptotic theory for sample means can fail because arm-specif…
Multi-Armed BanditsThompson sampling: Precise arm-pull dynamics and adaptive inference
Adaptive sampling schemes are well known to create complex dependence that may invalidate conventional inference methods. A recent line of work shows that this need not be the case for UCB-type algorithms in multi-armed …
Multi-Armed Bandits