arXiv subjects

Soulaimane Berkane

Publications and source records attributed to Soulaimane Berkane.

48 records · Page 3Linked to original sources

arXiv2020

State Estimation for a Class of Linear Systems with Quadratic Output

This paper deals with the problem of state estimation for a class of linear time-invariant systems with quadratic output measurements. An immersion-type approach is presented that transforms the system into a state-affine system by adding a finite number of states to the original system. Under suitable persistence of excitation conditions on the input and its higher derivatives, global state estimation is exhibited by means of a Kalman-type observer. A numerical example is provided to illustrate the applicability of the proposed observer design for the problem of position and velocity estimation for a vehicle navigating in the $n-$dimensional Euclidean space using a single position range measurement.

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arXiv2020

Navigation in Unknown Environments Using Safety Velocity Cones

We rely on Nagumo's invariance theorem to develop a new approach for navigation in unknown environments of arbitrary dimension. The idea consists in projecting the nominal velocities (that would drive the robot to the target in the absence of obstacles) onto Bouligand's tangent cones (referred to as the safety velocity cones) when the robot is close to the boundary of the free space. The proposed projection-based controller is explicitly constructed to guarantee safety and convergence to a set of Lebesgue measure zero that contains the target. For specific free spaces such as Euclidean sphere worlds, the convergence to the target is guaranteed from almost all initial conditions in the free space. We provide a version of the controller (generating a continuous and piecewise smooth closed-loop vector field) relying on the robot's current position and local range measurements (e.g., from LiDAR or stereo vision) without global prior knowledge about the environment.

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arXiv2019

A Hybrid Controller for Obstacle Avoidance in an n-dimensional Euclidean Space

For a vehicle moving in an $n$-dimensional Euclidean space, we present a construction of a hybrid feedback that guarantees both global asymptotic stabilization of a reference position and avoidance of an obstacle corresponding to a bounded spherical region. The proposed hybrid control algorithm switches between two modes of operation: stabilization (motion-to-goal) and avoidance (boundary-following). The geometric construction of the flow and jump sets of the hybrid controller, exploiting a hysteresis region, guarantees robust switching (chattering-free) between the stabilization and avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for a 3-dimensional scenario.

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arXiv2018

A Survey on Output Feedback Control of Robot Manipulators with an Application to PHANToM 1.5A Haptic Device

This paper is aimed at presenting a short survey of velocity-free control schemes for robot manipulators. A salient feature of this work is the implementation of this control schemes on a simulation model of the 3-DOF industrial PHANToM 1.5 A robot. For both the regulation and tracking problems, two classes of control algorithms without velocity measurements are considered, namely, those based on observer-controller combination and those based on approximate derivation through an n-order filter. The latter was shown to be more advantageous from different aspects. First the controllers based on approximate derivation are very intuitive and easy to implement in practice. Moreover, these algorithms are proved to be globally asymptotically stable, while the observer-based controllers have only local stability results. We have also considered some algorithms that are robust to load disturbances and to unmodeled dynamics. Simulation results have confirmed the theoretical advantages and drawbacks of each algorithm.

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arXiv2017

Attitude and Gyro Bias Estimation Using GPS and IMU Measurements

We propose an attitude and gyro-bias estimation scheme for accelerated rigid body systems using an inertial measurement unit (IMU) and a global positioning system (GPS). The proposed scheme allows to obtain attitude estimates directly on the Special Orthogonal group $SO(3)$ while estimating the gyro bias and the unknown apparent acceleration of the vehicle. We prove semi-global exponential stability of the estimation errors. Furthermore, a new switching technique for the attitude state is introduced which results in a velocity-aided hybrid attitude observer with proven global exponential stability.

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arXiv2017

On the Design of Attitude Observers on the Special Orthogonal Group $SO(3)$

We revisit the nonlinear complimentary filter on $SO(3)$, previously proposed in the literature, and provide the (time-explicit) solution to the matrix ODE governing the attitude estimation error in the absence of measurement errors. The stability and performance properties of this filter can be easily deduced from the obtained closed-from solution. Thereafter, we consider two nonlinear complimentary filters (with state-dependent gains) which are shown to exhibit improved stability and performance proprieties compared to the traditional filter. We perform robustness analysis for the three discussed attitude filters on $SO(3)$ with respect to attitude and angular velocity measurement errors. Specifically, we show that the state-dependent-gain filters may exhibit improved robustness to gyro measurement disturbances and a better disturbance attenuation levels. Simulation results are performed to confirm the obtained theoretical results.

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arXiv2017

On the Design of Globally Exponentially Stable Hybrid Attitude and Gyro-bias Observers

This paper presents hybrid attitude and gyro-bias observers designed directly on the Special Orthogonal group SO(3). The proposed hybrid observers, enjoying global exponential stability, rely on a hysteresis-based switching between different configurations derived from a set of potential functions on SO(3). Different sets of potential functions have been designed via an appropriate angular warping transformation applied to some smooth and non-smooth potential functions on SO(3). We show that the proposed hybrid observers can be expressed solely in terms of inertial vector measurements and biased angular velocity readings. Simulation results are given to illustrate the effectiveness of the proposed attitude estimation approach.

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arXiv2016

A Central Synergistic Hybrid Approach for Global Exponential Stabilization on SO(3)

We propose a new central synergistic hybrid approach for global exponential stabilization on the Special Orthogonal group SO(3). We introduce a new switching concept relying on a central family of (possibly) non-differentiable potential functions that enjoy (as well as their gradients) the following properties: 1) being quadratic with respect to the Euclidean attitude distance, and 2) being synergistic with respect to the gradient's singular and/or critical points. The proposed approach is used to solve the attitude tracking problem, leading to global exponential stability results.

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arXiv2016

A Globally Exponentially Stable Hybrid Attitude and Gyro-bias Observer

This paper presents a hybrid attitude and gyro-bias observer designed directly on the Special Orthogonal group SO(3). The proposed hybrid observer, relying on a hysteresis-based switching between two configurations, guarantees global exponential stability using biased angular velocity and inertial vector measurements. Simulation results are given to illustrate the effectiveness of the proposed observer.

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arXiv2016

On Deterministic Attitude Observers on the Special Orthogonal Group SO(3)

We revisit the gradient based nonlinear attitude complementary filters (observers) on the Special Orthogonal group SO(3) and provide explicit solutions of the norm of the attitude estimation error dynamics. One smooth and two non-smooth attitude observers are considered. The stability and performance properties of theses attitude observers can be easily deduced from the obtained explicit solutions. We show that the smooth complementary attitude filter, previously proposed in the literature, is not Input-to-State-Stable (ISS) with respect to bounded measurement disturbances while the non-smooth versions are. We also show that the non-smooth versions of the attitude complementary filter exhibit better convergence rates. Some simulations are provided to illustrate our results.

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arXiv2016

Global Exponential Angular Velocity Observer for Rigid Body Systems

We present a uniformly globally exponentially stable hybrid angular velocity observer for rigid body systems designed directly on $SO(3)\times\mathbb{R}^3$. The global exponential stability result makes this observer a good candidate for a controller-observer combination with a guaranteed separation property. Simulation results are provided to demonstrate the effectiveness of the proposed hybrid observer as a part of an attitude stabilization scheme.

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arXiv2016

Construction of Synergistic Potential Functions on SO(3) with Application to Velocity-Free Hybrid Attitude Stabilization

We propose a systematic and comprehensive procedure for the construction of synergistic potential functions, which are instrumental in hybrid control design on SO(3). A new map via angular warping on SO(3) is introduced for the construction of such a family of potential functions allowing an explicit determination of the critical points and the synergistic gap. Some optimization results on the synergistic gap are also provided. The proposed synergistic potential functions are used for the design of a global velocity-free hybrid attitude stabilization scheme relying solely on inertial vector measurements. Comparative simulation results between the proposed global hybrid control scheme and the almost global smooth control scheme have been carried out.

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