arXiv subjects

Soulaimane Berkane

Publications and source records attributed to Soulaimane Berkane.

At least 37 records · Page 2Linked to original sources

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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arXiv2025

Attitude Estimation Using Scalar Measurements

This paper revisits the problem of orientation estimation for rigid bodies through a novel framework based on scalar measurements. Unlike traditional vector-based methods, the proposed approach enables selective utilization of only the reliable axes of vector measurements while seamlessly incorporating alternative scalar modalities such as Pitot tubes, barometers with range sensors, and landmark-based constraints. The estimation problem is reformulated within a linear time-varying (LTV) framework, allowing the application of a deterministic linear Kalman filter. This design guarantees Global Uniform Exponential Stability (GES) under the Uniform Observability (UO) condition. Simulation results demonstrate the effectiveness of the proposed approach in achieving robust and accurate attitude estimation, even with partial vector measurements that simulate sensor axis failure.

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arXiv2025

Nonlinear Observer Design for Landmark-Inertial Simultaneous Localization and Mapping

This paper addresses the problem of Simultaneous Localization and Mapping (SLAM) for rigid body systems in three-dimensional space. We introduce a new matrix Lie group SE_{3+n}(3), whose elements are composed of the pose, gravity, linear velocity and landmark positions, and propose an almost globally asymptotically stable nonlinear geometric observer that integrates Inertial Measurement Unit (IMU) data with landmark measurements. The proposed observer estimates the pose and map up to a constant position and a constant rotation about the gravity direction. Numerical simulations are provided to validate the performance and effectiveness of the proposed observer, demonstrating its potential for robust SLAM applications.

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arXiv2025

A Geometric Approach For Pose and Velocity Estimation Using IMU and Inertial/Body-Frame Measurements

This paper addresses accurate pose estimation (position, velocity, and orientation) for a rigid body using a combination of generic inertial-frame and/or body-frame measurements along with an Inertial Measurement Unit (IMU). By embedding the original state space, $\so \times \R^3 \times \R^3$, within the higher-dimensional Lie group $\sefive$, we reformulate the vehicle dynamics and outputs within a structured, geometric framework. In particular, this embedding enables a decoupling of the resulting geometric error dynamics: the translational error dynamics follow a structure similar to the error dynamics of a continuous-time Kalman filter, which allows for a time-varying gain design using the Riccati equation. Under the condition of uniform observability, we establish that the proposed observer design on $\sefive$ guarantees almost global asymptotic stability. We validate the approach in simulations for two practical scenarios: stereo-aided inertial navigation systems (INS) and GPS-aided INS. The proposed method significantly simplifies the design of nonlinear geometric observers for INS, providing a generalized and robust approach to state estimation.

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arXiv2025

Dissipative Avoidance Feedback for Reactive Navigation Under Second-Order Dynamics

This paper addresses the problem of autonomous robot navigation in unknown, obstacle-filled environments with second-order dynamics by proposing a Dissipative Avoidance Feedback (DAF). Compared to the Artificial Potential Field (APF), which primarily uses repulsive forces based on position, DAF employs a dissipative feedback mechanism that accounts for both position and velocity, contributing to smoother and more natural obstacle avoidance. The proposed continuously differentiable controller solves the motion-to-goal problem while guaranteeing collision-free navigation by using the robot's state and local obstacle distance information. We show that the controller guarantees safe navigation in generic $n$-dimensional environments and that all undesired $ω$-limit points are unstable under certain controlled curvature conditions. Designed for real-time implementation, DAF requires only locally measured data from limited-range sensors (e.g., LiDAR, depth cameras), making it particularly effective for robots navigating unknown workspaces. Simulations in 2D and 3D environments are conducted to validate the theoretical results and to showcase the effectiveness of our approach.

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arXiv2024

Safe and Quasi-Optimal Autonomous Navigation in Environments with Convex Obstacles

We propose a continuous feedback control strategy that steers a point-mass vehicle safely to a destination, in a quasi-optimal manner, in sphere worlds. The main idea consists in avoiding each obstacle via the shortest path on the cone's surface enclosing the obstacle and moving straight toward the target when the vehicle has a clear line of sight to the target location. In particular, almost global asymptotic stability of the target location is achieved in two-dimensional (2D) environments under a particular assumption on the obstacles configuration. We also propose a reactive (sensor-based) approach, suitable for real-time implementations in a priori unknown 2D environments with sufficiently curved convex obstacles, guaranteeing almost global asymptotic stability of the target location. Simulation results are presented to illustrate the effectiveness of the proposed approach.

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arXiv2024

Hybrid Feedback Control for Global and Optimal Safe Navigation

We propose a hybrid feedback control strategy that safely steers a point-mass robot to a target location optimally from all initial conditions in the n-dimensional Euclidean space with a single spherical obstacle. The robot moves straight to the target when it has a clear line-of-sight to the target location. Otherwise, it engages in an optimal obstacle avoidance maneuver via the shortest path inside the cone enclosing the obstacle and having the robot's position as a vertex. The switching strategy that avoids the undesired equilibria, leading to global asymptotic stability (GAS) of the target location, relies on using two appropriately designed virtual destinations, ensuring control continuity and shortest path generation. Simulation results illustrating the effectiveness of the proposed approach are presented.

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arXiv2024

State Estimation Using Single Body-Frame Bearing Measurements

This paper addresses the problem of simultaneous estimation of the position, linear velocity and orientation of a rigid body using single bearing measurements. We introduce a Riccati observer-based estimator that fuses measurements from a 3-axis accelerometer, a 3-axis gyroscope, a single body-frame vector observation (e.g., magnetometer), and a single bearing-to-landmark measurement to obtain the full vehicle's state (position, velocity, orientation). The proposed observer guarantees global exponential convergence under some persistency of excitation (PE) condition on the vehicle's motion. Simulation results are presented to show the effectiveness of the proposed approach.

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arXiv2024

Real-Time Sensor-Based Feedback Control for Obstacle Avoidance in Unknown Environments

We revisit the Safety Velocity Cones (SVCs) obstacle avoidance approach for real-time autonomous navigation in an unknown $n$-dimensional environment. We propose a locally Lipschitz continuous implementation of the SVC controller using the distance-to-the-obstacle function and its gradient. We then show that the proposed implementation guarantees safe navigation in generic environments and almost globally asymptotic stability (AGAS) of the desired destination when the workspace contains strongly convex obstacles. The proposed computationally efficient control algorithm can be implemented onboard vehicles equipped with limited range sensors (e.g., LiDAR, depth camera), allowing the controller to be locally evaluated without requiring prior knowledge of the environment.

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arXiv2023

State Estimation for Linear Systems with Quadratic Outputs

This letter deals with the problem of state estimation for a class of systems involving linear dynamics with multiple quadratic output measurements. We propose a systematic approach to immerse the original system into a linear time-varying (LTV) system of a higher dimension. The methodology extends the original system by incorporating a minimum number of auxiliary states, ensuring that the resulting extended system exhibits both linear dynamics and linear output. Consequently, any Kalman-type observer can showcase global state estimation, provided the system is uniformly observable.

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arXiv2023

Modeling of Four-Winged Micro Ornithopters Inspired by Dragonflies

In this paper, we present a full dynamical model of a four-winged micro ornithopter inspired by a dragonfly-type insect. The micro ornithopter is modeled as four articulated rigid body components (wings) connected to the main body via spherical joints. The dynamical model is derived using Lagrangian mechanics with intrinsic global coordinates, without relying on the common assumptions that neglect the wings-body interactions. Furthermore, the aerodynamic forces are modeled under the quasi-steady motion assumption without restricting the flapping frequency to be relatively high. This provides a full and elegant four-winged micro ornithopter model that captures the interaction between the body and the wings while avoiding the complexities and singularities associated with other coordinate representations (e.g., Euler angles). Simulation studies of the inertial effects of the relative motion between the different parts of the multibody system show the importance of considering the forces and torques, resulting from the wings-body interaction, in motion generation of these insects.

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arXiv2023

Safe and Quasi-Optimal Autonomous Navigation in Sphere Worlds

We propose a continuous feedback control strategy that steers a point-mass vehicle safely to a desired destination, in a quasi-optimal manner, from almost all initial conditions in an n-dimensional Euclidean space cluttered with spherical obstacles. The main idea consists in avoiding each obstacle via the shortest path within the cone enclosing the obstacle, and moving straight towards the target when the vehicle has a clear line of sight to the target location. The proposed control strategy ensures safe navigation with almost global asymptotic stability of the equilibrium point at the target location. Simulation results, illustrating the effectiveness of the proposed approach, are presented.

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arXiv2022

Hybrid Feedback for Autonomous Navigation in Environments with Arbitrary Convex Obstacles

We develop an autonomous navigation algorithm for a robot operating in two-dimensional environments cluttered with obstacles having arbitrary convex shapes. The proposed navigation approach relies on a hybrid feedback to guarantee global asymptotic stabilization of the robot towards a predefined target location while ensuring the forward invariance of the obstacle-free workspace. The main idea consists in designing an appropriate switching strategy between the move-to-target mode and the obstacle-avoidance mode based on the proximity of the robot with respect to the nearest obstacle. The proposed hybrid controller generates continuous velocity input trajectories when the robot is initialized away from the boundaries of the unsafe regions. Finally, we provide an algorithmic procedure for the sensor-based implementation of the proposed hybrid controller and validate its effectiveness through some simulation results.

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arXiv2021

Nonlinear Observers Design for Vision-Aided Inertial Navigation Systems

This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)\times \mathbb{R}^{15}$ relying on body-frame acceleration, angular velocity and (stereo or monocular) bearing measurements of some landmarks that are constant and known in the inertial frame. Unlike the existing local Kalman-type observers, our proposed nonlinear observer guarantees almost global asymptotic stability and local exponential stability. A detailed uniform observability analysis has been conducted and sufficient conditions are derived. Moreover, a hybrid version of the proposed observer is provided to handle the intermittent nature of the measurements in practical applications. Simulation and experimental results are provided to illustrate the effectiveness of the proposed state observer.

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arXiv2021

Nonlinear Estimation for Position-Aided Inertial Navigation Systems

In this work we solve the position-aided 3D navigation problem using a nonlinear estimation scheme. More precisely, we propose a nonlinear observer to estimate the full state of the vehicle (position, velocity, orientation and gyro bias) from IMU and position measurements. The proposed observer does not introduce additional auxiliary states and is shown to guarantee semi-global exponential stability without any assumption on the acceleration of the vehicle. The performance of the observer is shown, through simulation, to overcome the state-of-the-art approach that assumes negligible accelerations.

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arXiv2021

Obstacle Avoidance via Hybrid Feedback

In this paper we present a hybrid feedback approach to solve the navigation problem of a point mass in the n-dimensional space containing an arbitrary number of ellipsoidal shape obstacles. The proposed hybrid control algorithm guarantees both global asymptotic stabilization to a reference and avoidance of the obstacles. The intuitive idea of the proposed hybrid feedback is to switch between two modes of control: stabilization and avoidance. The geometric construction of the flow and jump sets of the proposed hybrid controller, exploiting hysteresis regions, guarantees Zeno-free switching between the stabilization and the avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for 2-dimensional and 3-dimensional scenarios.

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arXiv2021

A Nonlinear Navigation Observer Using IMU and Generic Position Information

This paper deals with the problem of full state estimation for vehicles navigating in a three dimensional space. We assume that the vehicle is equipped with an Inertial Measurement Unit (IMU) providing body-frame measurements of the angular velocity, the specific force, and the Earth's magnetic field. Moreover, we consider available sensors that provide partial or full information about the position of the vehicle. Examples of such sensors are those which provide full position measurements (e.g., GPS), range measurements (e.g., Ultra-Wide Band (UWB) sensors), inertial-frame bearing measurements (e.g., motion capture cameras), or altitude measurements (altimeter). We propose a generic semi-globally exponentially stable nonlinear observer that estimates the position, linear velocity, linear acceleration, and attitude of the vehicle, as well as the gyro bias. We also provide a detailed observability analysis for different types of measurements. Simulation and experimental results are provided to demonstrate the effectiveness of the proposed estimation scheme.

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arXiv2020

Constrained Stabilization on the n-Sphere

We solve the stabilization problem on the $n-$sphere in the presence of conic constraints. We use the stereographic projection to map this problem to the classical navigation problem on $\mathbb{R}^n$ in the presence of spherical obstacles. As a consequence, any obstacle avoidance algorithm for navigation in the Euclidean space can be used to solve the given problem on the $n-$sphere. We illustrate the effectiveness of the approach using the kinematics of the reduced attitude model on the $2-$sphere.

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