Vision-Aided Relative State Estimation for Approach and Landing on a Moving Platform with Inertial Measurements

TL;DR

The paper tackles estimating the UAV’s relative pose and velocity with respect to a moving planar landing target using dual IMUs and monocular vision that provides bearing and plane-normal data. It introduces a cascade observer: an SO(3) attitude estimator based on a complementary filter, followed by a linear Riccati observer for relative position and velocity, with convergence proven under persistent excitation and almost global asymptotic stability for attitude and local exponential stability for translation. An extension handles axis-only rotation by exploiting target acceleration to recover the remaining yaw angle, with sufficient conditions for local exponential convergence. Simulations demonstrate accurate attitude, normal, and translational state estimation across challenging maneuvers and validate the coupled-dynamics variant when excitation is limited.

Abstract

This paper tackles the problem of estimating the relative position, orientation, and velocity between a UAV and a planar platform undergoing arbitrary 3D motion during approach and landing. The estimation relies on measurements from Inertial Measurement Units (IMUs) mounted on both systems, assuming there is a suitable communication channel to exchange data, together with visual information provided by an onboard monocular camera, from which the bearing (line-of-sight direction) to the platform's center and the normal vector of its planar surface are extracted. We propose a cascade observer with a complementary filter on SO(3) to reconstruct the relative attitude, followed by a linear Riccati observer for relative position and velocity estimation. Convergence of both observers is established under persistently exciting conditions, and the cascade is shown to be almost globally asymptotically and locally exponentially stable. We further extend the design to the case where the platform's rotation is restricted to its normal axis and show that its measured linear acceleration can be exploited to recover the remaining unobservable rotation angle. A sufficient condition to ensure local exponential convergence in this setting is provided. The performance of the proposed observers is validated through extensive simulations.

Figures (4)

• Figure 1: Illustration of the relative extended pose $(R, \bm{\xi}, \bm{v})$ estimation problem, where both the UAV body frame $\{\mathcal{B}\}$ and the target frame $\{\mathcal{T}\}$ are moving with respect to the inertial frame $\{\mathcal{I}\}$.
• Figure 2: Diagram of the cascade observer architecture. The relative attitude $R$ is estimated via a complementary filter on $\mathbf{SO}(3)$ using the normal measurement $\bm{\eta}$, and then together with the bearing and UAV-target IMU measurements, is used in a Riccati observer to reconstruct the relative position and velocity $(\bm{\xi},\bm{v})$.
• Figure 3: Observer \ref{['R_observer']}-\ref{['pv_observer']}. (left) Time evolution of the reduced attitude (normal) and attitude errors. (right) Time evolution of the errors of position and velocity.
• Figure 4: Observer \ref{['eq:attitude_obs_theta']}. (left) Time evolution of the reduced attitude (normal) and attitude errors. (right) Time evolution of the errors of position and velocity.

Theorems & Definitions (12)

• Definition 1: Uniform Observability
• Definition 2: Almost global asymptotic stability
• Lemma 1
• Remark 1
• Lemma 2
• Theorem 1
• proof
• proof
• Lemma 3
• proof : Proof of Lemma \ref{['lemma_attitude_observer']}