Soulaimane Berkane

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 to generate a central 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.

Global hybrid attitude estimation on the Special Orthogonal group SO(3)

This paper presents a hybrid attitude and gyro-bias observer, on the Special Orthogonal group SO(3), leading to global exponential stability results. The proposed observer relies on a hysteresis-based switching between different configurations. Each observer configuration is derived from a non-differentiable potential function on SO(3). The proposed hybrid observer can be, explicitly, expressed in terms of inertial vector measurements. Simulation results are given to illustrate the effectiveness of the proposed attitude observer.

On the design of synergistic potential functions on SO(3)

This paper deals with the design of synergistic potential functions which are instrumental in hybrid control design on SO(3). We propose a systematic procedure for the construction of central synergistic families of potential functions on SO(3) via angular warping. A new map on SO(3) is introduced allowing for an explicit computation of the critical points of the potential functions as well as the synergistic gap. Some optimization results on the synergistic gap are also provided.

A globally exponentially stable hybrid attitude and gyro-bias observer

We propose a hybrid attitude and gyro-bias observer designed directly on the Special Orthogonal group SO(3). The proposed hybrid observer guarantees global exponential stability using biased angular velocity measurements and inertial vector observations. Simulation results are provided to illustrate the effectiveness of the proposed observer.

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) × ℝ3. 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.

Velocity-free hybrid attitude stabilization using inertial vector measurements

This paper deals with the design of a velocity-free hybrid attitude stabilization scheme relying solely on inertial vector measurements. The proposed control approach, relying on the concept of synergistic potential functions, leads to global asymptotic stability results. Comparative simulation results between the proposed global hybrid control scheme and an existing almost global smooth control scheme have been carried out.

Disordered speech quality estimation using linear prediction

Tracheoesophageal (TE) speech is generated by patients who have undergone a total laryngectomy where the larynx (voice box) is removed and replaced by a tracheoesophageal puncture. This work presents a novel low complexity algorithm to estimate the degree of severity of disordered TE speech. The proposed algorithm uses features which are computed from 32-ms voiced frames of the speech signal. A 21-st order LPC analysis is performed on each voiced frame of the speech and high order statistics (central moments: mean, standard deviation, skewness and kurtosis) are extracted from the LPC coefficients, Cepstral coefficients and the LPC residual signal. The averages of each of these moments are computed along with the pitch average over all voiced frames yielding a total of 14 quality features. Experimental results with two sets of databases (20 and 35 TE speakers) showed that the proposed speech quality estimation approach performs well with a correlation with subjective scores in the range between 0.81 and 0.86.

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 time-explicit solutions of the norm of the attitude estimation error dynamics. One constant-gain and two state-dependent-gain attitude observers are considered. The stability and performance properties of these attitude observers can be easily deduced from the obtained closed-form solutions. We show that the traditional (constant-gain) complementary attitude filter, previously proposed in the literature, is not Input-to-State-Stable (ISS) with respect to bounded measurement disturbances, while the state-dependent-gain versions are. We also show that the state-dependent-gain versions of the attitude complementary filter exhibit better convergence rates. Simulation results are provided to illustrate our results.