arXiv subjects

Soulaimane Berkane

Publications and source records attributed to Soulaimane Berkane.

At least 19 recordsLinked to original sources

arXiv2026

Attitude Estimation Using Inertial and Barometric Measurements

Accurate and robust attitude estimation is a key challenge for autonomous vehicles, particularly in GNSS-denied conditions and during highly accelerated flight. In such conditions, Inertial Measurement Units (IMUs) alone are insufficient for reliable tilt estimation due to the ambiguity between gravitational and inertial accelerations. Although auxiliary velocity sensors such as GNSS, Pitot tubes, Doppler radar, or Visual Inertial Odometry are commonly used, they may be unavailable, intermittent, or costly. This paper introduces a barometer-aided attitude estimation architecture that exploits barometric altitude measurements to provide complementary information on the vehicle's vertical motion, thereby enhancing attitude estimation within nonlinear observers on SO(3). The contributions are twofold. First, we design a deterministic Riccati observer cascaded with a complementary filter, ensuring almost-global asymptotic stability (AGAS) under a uniform observability (UO) condition while preserving the geometric structure of the attitude dynamics. Second, we propose a nonlinear observer evolving on SO(3)xR2, which integrates IMU measurements as inputs and barometer and magnetometer measurements as outputs within a unified framework, guaranteeing local exponential stability (LES) under relaxed uniform observability conditions. The proposed approaches are validated using both simulated and real flight data. The results demonstrate that barometer-aided estimation provides a lightweight, reliable, and effective complementary sensing modality for attitude estimation in minimal-sensing configurations, offering a practical alternative when conventional velocity measurements are unavailable or degraded.

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arXiv2026

Relative Pose-Velocity Estimation Using Dual IMU Measurements and Relative Position Sensing

This paper addresses the problem of estimating the relative pose (position and orientation) and velocity of a vehicle with respect to a moving target, where both are equipped with Inertial Measurement Units (IMUs), assuming the availability of relative position or bearing measurements. The body-target relative dynamics are formulated on $\mathbf{SE}_2(3)$ and recast into a linear time-varying (LTV) model in the ambient space $\mathbb{R}^{15}$, on which a deterministic Riccati observer is designed. We analyze the uniform observability (UO) conditions required to guarantee global exponential convergence of the estimation error in the ambient space for both measurement cases. In the case of relative position measurements, UO requires only a persistence-of-excitation condition on the target acceleration, whereas for bearing measurements, additional conditions are required. Building on this, a nonlinear complementary filter on $\mathbf{SO}(3)$ is designed to provide a smooth estimate of the orientation component of the state with almost global asymptotic stability. Finally, simulation results are provided to validate the proposed solution.

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arXiv2026

Complementary Filtering on SO(3) for Attitude Estimation with Scalar Measurements

Attitude estimation using scalar measurements, corresponding to partial vectorial observations, arises naturally when inertial vectors are not fully observed but only measured along specific body-frame vectors. Such measurements arise in problems involving incomplete vector measurements or attitude constraints derived from heterogeneous sensor information. Building on the classical complementary filter on SO(3), we propose an observer with a modified innovation term tailored to this scalar-output structure. The main result shows that almost-global asymptotic stability is recovered, under suitable persistence of excitation conditions, when at least three inertial vectors are measured along a common body-frame vector, which is consistent with the three-dimensional structure of SO(3). For two-scalar configurations - corresponding either to one inertial vector measured along two body-frame vectors, or to two inertial vectors measured along a common body-frame vector - we further derive sufficient conditions guaranteeing convergence within a reduced basin of attraction. Different examples and numerical results demonstrate the effectiveness of the proposed scalar-based complementary filter for attitude estimation in challenging scenarios involving reduced sensing and/or novel sensing modalities.

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arXiv2026

Attitude Synchronization on SO(3) for Heterogeneous Multi-Agent Systems Using Vector Measurements

This paper addresses the distributed attitude synchronization problem for a network of rigid-body systems on the special orthogonal group SO(3). Each agent measures, in its body frame, its own angular velocity and a set of vectors whose corresponding directions in the inertial frame are unknown. Under an undirected, connected, and acyclic interaction graph topology, we develop four distributed synchronization schemes relying solely on local vector measurements, without the need for attitude estimation and attitude exchange between agents. Specifically, two leaderless schemes are proposed at the kinematic and dynamic levels to achieve synchronization to a common unknown orientation. In addition, two leader-follower schemes are proposed to align all agents with a prescribed constant orientation defined by reference vector measurements available only to a designated leader. All control laws are formulated directly on SO(3), preserving the geometric structure of the attitude dynamics. A rigorous stability analysis is provided showing that the closed-loop systems achieve almost global asymptotic stability, which is the strongest stability property one can achieve on SO(3) with smooth controllers. %Compared with existing vector-measurement-based approaches that provide only local stability or convergence results, the proposed methods significantly strengthen the theoretical guarantees while maintaining a fully distributed architecture. Numerical simulations are provided to illustrate the effectiveness and performance of the proposed distributed control schemes.

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arXiv2026

Tutorial on Aided Inertial Navigation Systems: A Modern Treatment Using Lie-Group Theoretical Methods

This tutorial presents a control-oriented introduction to aided inertial navigation systems using a Lie-group formulation centered on the extended Special Euclidean group SE_2(3). The focus is on developing a clear and implementation-oriented geometric framework for fusing inertial measurements with aiding information, while making the role of invariance and symmetry explicit. Recent extensions, including higher-order state representations, synchronous observer designs, and equivariant filtering methods, are discussed as natural continuations of the same underlying principles. The goal is to provide readers with a coherent system-theoretic perspective that supports both understanding and practical use of modern aided inertial navigation methods.

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arXiv2026

Scalar-Measurement Attitude Estimation on $\mathbf{SO}(3)$ with Bias Compensation

Attitude estimation methods typically rely on full vector measurements from inertial sensors such as accelerometers and magnetometers. This paper shows that reliable estimation can also be achieved using only scalar measurements, which naturally arise either as components of vector readings or as independent constraints from other sensing modalities. We propose nonlinear deterministic observers on $\mathbf{SO}(3)$ that incorporate gyroscope bias compensation and guarantee uniform local exponential stability under suitable observability conditions. A key feature of the framework is its robustness to partial sensing: accurate estimation is maintained even when only a subset of vector components is available. Experimental validation on the BROAD dataset confirms consistent performance across progressively reduced measurement configurations, with estimation errors remaining small even under severe information loss. To the best of our knowledge, this is the first work to establish fundamental observability results showing that two scalar measurements under suitable excitation suffice for attitude estimation, and that three are enough in the static case. These results position scalar-measurement-based observers as a practical and reliable alternative to conventional vector-based approaches.

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arXiv2026

A General Nonlinear Observer Design for Inertial Navigation Systems with Almost Global Stability Guarantees

This paper studies nonlinear observer design for rigid-body extended pose estimation using inertial measurements and generic exteroceptive sensing. The estimation problem is formulated as a cascade architecture that separates translational dynamics from rotational kinematics while preserving the geometric constraint of attitude evolution on $SO(3)$. By embedding the inertial navigation model into a Linear Time-Varying (LTV) representation, we construct an observer composed of a Kalman-Bucy-type estimator for translational states and an auxiliary unconstrained attitude variable, coupled with a nonlinear geometric reconstruction filter evolving on $SO(3)$. The cascade interconnection is analyzed within a nonlinear systems framework. We prove that uniform observability of the LTV subsystem guarantees almost global asymptotic stability of the overall nonlinear observer. For a benchmark GPS landmark aided configuration, explicit sufficient conditions on admissible trajectories are derived to ensure uniform observability. Simulation results illustrate the effectiveness of the proposed estimation framework.

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arXiv2026

Pitot-Aided Attitude and Air Velocity Estimation with Almost Global Asymptotic Stability Guarantees

This paper investigates the problem of attitude and air velocity estimation for fixed-wing unmanned aerial vehicles (UAVs) using IMU measurements and at least one Pitot tube measurement, with almost global asymptotic stability (AGAS) guarantees. A cascade observer architecture is developed, in which a Riccati/Kalman-type filter estimates the body-fixed frame air velocity and the vehicle's tilt using IMU data as inputs and Pitot measurements as outputs. Under mild excitation conditions, the resulting air velocity and tilt estimation error dynamics are shown to be uniformly observable. The estimated tilt is then combined with magnetometer measurements in a nonlinear observer on SO(3) to recover the full attitude. Rigorous analysis establishes AGAS of the overall cascade structure under the uniform observability (UO) condition. The effectiveness of the proposed approach is demonstrated through validation on real flight data.

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arXiv2026

Nonlinear Observer Design for Visual-Inertial Odometry

This paper addresses the problem of Visual-Inertial Odometry (VIO) for rigid body systems evolving in three-dimensional space. We introduce a novel matrix Lie group structure, denoted SE_{3+n}(3), that unifies the pose, gravity, linear velocity, and landmark positions within a consistent geometric framework tailored to the VIO problem. Building upon this formulation, we design an almost globally asymptotically stable nonlinear geometric observer that tightly integrates data from an Inertial Measurement Unit (IMU) and visual sensors. Unlike conventional Extended Kalman Filter (EKF)-based estimators that rely on local linearization and thus ensure only local convergence, the proposed observer achieves almost global stability through the decoupling of the rotational and translational dynamics. A globally exponentially stable Riccati-based translational observer along with an almost global input-to-state stable attitude observer are designed such that the overall cascaded observer enjoys almost global asymptotic stability. This cascaded architecture guarantees robust and consistent estimation of the extended state, including orientation, position, velocity, gravity, and landmark positions, up to the VIO unobservable directions (i.e., a global translation and rotation about gravity). The effectiveness of the proposed scheme is demonstrated through numerical simulations as well as experimental validation on the EuRoC MAV dataset, highlighting its robustness and suitability for real-world VIO applications.

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arXiv2025

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

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 $\mathbf{SO}(3)$ 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 for local exponential convergence in this setting is provided. The proposed observers are validated through extensive simulations.

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arXiv2025

Perception-Limited Smooth Safety Filtering

This paper develops a smooth safety-filtering framework for nonlinear control-affine systems under limited perception. Classical Control Barrier Function (CBF) filters assume global availability of the safety function - its value and gradient must be known everywhere - an assumption incompatible with sensing-limited settings, and the resulting filters often exhibit nonsmooth switching when constraints activate. We propose two complementary perception-aware safety filters applicable to general control-invariant safety sets. The first introduces a smooth perception gate that modulates barrier constraints based on sensing range, yielding a closed-form Lipschitz-safe controller with forward-invariance guarantees. The second replaces the hard CBF constraint with a differentiable penalty term, leading to a smooth unconstrained optimization-based safety filter consistent with CBF principles. For both designs, we establish existence, uniqueness, and forward invariance of the closed-loop trajectories. Numerical results demonstrate that the proposed smooth filters enable the synthesis of higher-order tracking controllers for systems such as drones and second-order ground robots, offering substantially smoother and more robust safety-critical behaviors than classical CBF-based filters.

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arXiv2025

A Nonlinear Observer for Air-Velocity and Attitude Estimation Using Pitot and Barometric Measurements

This paper addresses the problem of estimating air velocity and full attitude for unmanned aerial vehicles (UAVs) in GNSS-denied environments using minimal onboard sensing-an interesting and practically relevant challenge for UAV navigation. The contribution of the paper is twofold: (i) an observability analysis establishing the conditions for uniform observability, which are useful for trajectory planning and motion control of the UAV; and (ii) the design of a nonlinear observer on SO3R3R that incorporates pitot-tube, barometric altitude, and magnetometer measurements as outputs, with IMU data used as inputs, within a unified framework. Simulation results are presented to confirm the convergence and robustness of the proposed design, including under minimally excited trajectories.

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arXiv2025

Cascaded Tightly-Coupled Observer Design for Single-Range-Aided Inertial Navigation

This work introduces a single-range-aided navigation observer that reconstructs the full state of a rigid body using only an Inertial Measurement Unit (IMU), a body-frame vector measurement (e.g., magnetometer), and a distance measurement from a fixed anchor point. The design first formulates an extended linear time-varying (LTV) system to estimate body-frame position, body-frame velocity, and the gravity direction. The recovered gravity direction, combined with the body-frame vector measurement, is then used to reconstruct the full orientation on $\mathrm{SO}(3)$, resulting in a cascaded observer architecture. Almost Global Asymptotic Stability (AGAS) of the cascaded design is established under a uniform observability condition, ensuring robustness to sensor noise and trajectory variations. Simulation studies on three-dimensional trajectories demonstrate accurate estimation of position, velocity, and orientation, highlighting single-range aiding as a lightweight and effective modality for autonomous navigation.

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arXiv2025

A Smooth Penalty-Based Feedback Law for Reactive Obstacle Avoidance with Convergence Guarantees

This paper addresses the problem of safe autonomous navigation in unknown obstacle-filled environments using only local sensory information. We propose a smooth feedback controller derived from an unconstrained penalty-based formulation that guarantees safety by construction. The controller modifies an arbitrary nominal input through a closed-form expression. The resulting closed-form feedback has a projection structure that interpolates between the nominal control and its orthogonal projection onto the obstacle boundary, ensuring forward invariance of a user-defined safety margin. The control law depends only on the distance and bearing to obstacles and requires no map, switching, or set construction. When the nominal input is a gradient descent of a navigation potential, we prove that the closed-loop system achieves almost global asymptotic stability (AGAS) to the goal. Undesired equilibria are shown to be unstable under a mild geometric curvature condition, which compares the normal curvature of the obstacle boundary with that of the potential level sets. We refer to the proposed method as SPF (Safe Penalty-based Feedback), which ensures safe and smooth navigation with minimal computational overhead, as demonstrated through simulations in complex 2D and 3D environments.

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arXiv2025

Global Attitude Synchronization for Heterogeneous Multi-agent Systems on SO(3)

In this paper, we address the problem of attitude synchronization for a group of rigid body systems evolving on SO(3). The interaction among these systems is modeled through an undirected, connected, and acyclic graph topology. First, we present an almost global continuous distributed attitude synchronization scheme with rigorously proven stability guarantees. Thereafter, we propose two global distributed hybrid attitude synchronization schemes on SO(3). The first scheme is a hybrid control law that leverages angular velocities and relative orientations to achieve global alignment to a common orientation. The second scheme eliminates the dependence on angular velocities by introducing dynamic auxiliary variables, while ensuring global asymptotic attitude synchronization. This velocity-free control scheme relies exclusively on attitude information. The proposed schemes are applicable to heterogeneous multi-agent systems, where agents may have distinct inertia matrices. Simulation results are provided to illustrate the effectiveness of the proposed distributed attitude synchronization schemes.

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arXiv2025

Hybrid Feedback Control for Global Navigation with Locally Optimal Obstacle Avoidance in n-Dimensional Spaces

We present a hybrid feedback control framework for autonomous robot navigation in n-dimensional Euclidean spaces cluttered with spherical obstacles. The proposed approach ensures safe and global navigation towards a target location by dynamically switching between two operational modes: motion-to-destination and locally optimal obstacle-avoidance. It produces continuous velocity inputs, ensures collision-free trajectories and generates locally optimal obstacle avoidance maneuvers. Unlike existing methods, the proposed framework is compatible with range sensors, enabling navigation in both a priori known and unknown environments. Extensive simulations in 2D and 3D settings, complemented by experimental validation on a TurtleBot 4 platform, confirm the efficacy and robustness of the approach. Our results demonstrate shorter paths and smoother trajectories compared to state-of-the-art methods, while maintaining computational efficiency and real-world feasibility.

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arXiv2025

Barometer-Aided Attitude Estimation

Accurate and robust attitude estimation is a central challenge for autonomous vehicles operating in GNSS-denied or highly dynamic environments. In such cases, Inertial Measurement Units (IMUs) alone are insufficient for reliable tilt estimation due to the ambiguity between gravitational and inertial accelerations. While auxiliary velocity sensors, such as GNSS, Pitot tubes, Doppler radar, or visual odometry, are often used, they can be unavailable, intermittent, or costly. This work introduces a barometer-aided attitude estimation architecture that leverages barometric altitude measurements to infer vertical velocity and attitude within a nonlinear observer on SO(3). The design cascades a deterministic Riccati observer with a complementary filter, ensuring Almost Global Asymptotic Stability (AGAS) under a uniform observability condition while maintaining geometric consistency. The analysis highlights barometer-aided estimation as a lightweight and effective complementary modality.

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arXiv2025

Observer Design for Optical Flow-Based Visual-Inertial Odometry with Almost-Global Convergence

This paper presents a novel cascaded observer architecture that combines optical flow and IMU measurements to perform continuous monocular visual-inertial odometry (VIO). The proposed solution estimates body-frame velocity and gravity direction simultaneously by fusing velocity direction information from optical flow measurements with gyro and accelerometer data. This fusion is achieved using a globally exponentially stable Riccati observer, which operates under persistently exciting translational motion conditions. The estimated gravity direction in the body frame is then employed, along with an optional magnetometer measurement, to design a complementary observer on $\mathbf{SO}(3)$ for attitude estimation. The resulting interconnected observer architecture is shown to be almost globally asymptotically stable. To extract the velocity direction from sparse optical flow data, a gradient descent algorithm is developed to solve a constrained minimization problem on the unit sphere. The effectiveness of the proposed algorithms is validated through simulation results.

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