The objective of this paper is to present the advantages of Model reference adaptive control (MRAC) motion cueing algorithm against the classical motion cueing algorithm in terms of biomechanical reactions of the participants during the critical maneuvers like chicane in driving simulator real-time. This study proposes a method and an experimental validation to analyze the vestibular and neuromuscular dynamics responses of the drivers with respect to the type of the control used at the hexapod driving simulator. For each situation, the EMG (electromyography) data were registered from arm muscles of the drivers (flexor carpi radialis, brachioradialis). In addition, the roll velocity perception thresholds (RVT) and roll velocities (RV) were computed from the real-time vestibular level measurements from the drivers via a motion-tracking sensor. In order to process the data of the EMG and RVT, Pearson’s correlation and a two-way ANOVA with a significance level of 0.05 were assigned. Moreover, the relationships of arm muscle power and roll velocity with vehicle CG (center of gravity) lateral displacement were analyzed in order to assess the agility/alertness level of the drivers as well as the vehicle loss of control characteristics with a confidence interval of 95%. The results showed that the MRAC algorithm avoided the loss of adhesion, loss of control (LOA, LOC) more reasonably compared to the classical motion cueing algorithm. According to our findings, the LOA avoidance decreased the neuromuscular-visual cues level conflict with MRAC algorithm. It also revealed that the neuromuscular-vehicle dynamics conflict has influence on visuo-vestibular conflict; however, the visuo-vestibular cue conflict does not influence the neuromuscular-vehicle dynamics interactions.
Multi-sensory datafusion: such as visual, auditory, haptic, inertial, vestibular, neuromuscular signals are of importance to represent a proper sensation (objectively) and so a perception (subjectively as cognition) in motion base driving simulators [
A use study of the physiological measurements (biofeedback methods) has been presented to estimate user interruptibility status by [
Motion sickness has been discussed when a moving visual surround induces the illusion of self-rotation in [
Motion cueing for a 2 DOF (degrees of freedom) driving simulator has been examined by [
Restituting the inertial cues on driving simulators play an important role to sustain a more proper functioning in proximity to the reality [
This research work was performed under the dynamic operations of the SAAM driving simulator as with a classical and a MRAC controlled tracking of the hexapod platform. The dynamic simulators’ utilization scope diversifies from driver training to research purposes such as vehicle dynamics control, advanced driver assistance systems (ADAS) [
This paper explores a comparative study between an open and a closed loop controlled platform to maintain the vehicle pursuing a chicane maneuver scenario (loss of control-LOC). For the evaluation and the validation procedure [
-Neuromuscular (EMGRMS total power) and vehicle dynamics (lateral displacement of the vehicle CG (center of gravity)) interaction indicates the limit of LOC in the driving simulation experiments.
If they are positively significant correlated, it means that an avoidance loss of control (LOC) is possible to occur.
If they are negatively significantly correlated, it shows that the drivers are prone to experience a loss of control (LOC) phenomenon.
-Vehicle dynamics approach (lateral displacement of the vehicle CG): Lateral displacement area decreases when the MRAC algorithm is used (avoidance of LOC).
-Vestibular (roll velocity perception threshold―RVT) and neuromuscular dynamics (EMGRMS mean total power and EMGRMS maximum total power) interaction gives the characteristics of the driver: If they are positively correlated; perception of agility, in other words alertness level of the drivers and avoidance of LOC increase when the MRAC motion cueing is used.
The proposed classical motion cueing algorithm’s sketch is indicated with continuous lines and arrows where the model reference controlled motion cueing algorithm’s sketch was drawn with discrete lines and arrows (
The proposed MRAC motion cueing algorithm here uses the same filters, gains (
Symbol | Longitudinal | Lateral | Roll | Pitch | Yaw |
---|---|---|---|---|---|
2nd order LP cut-off frequency (Hz) | 0.3 | 0.7 | |||
2nd order LP damping factor | 0.3 | 0.7 | |||
1st order LP time constant (s) | 0.1 | 0.1 | 0.1 | ||
2nd order HP cut-off frequency (Hz) | 0.5 | 0.5 | 2 | ||
2nd order HP damping factor | 1 | 1 | 1 | ||
1st order HP time constant (s) | 2 | 2 | 2 |
MRAS or Model Reference Adaptive System) is to build a closed-loop controller with parameters that can be updated to change the response of the system. The output of the system is compared to a desired response from a reference model. The control parameters are updated based on this error. The goal is for the parameters to converge to ideal values that cause the plant response to match the response of the reference model. It can focus on the continuous-time case and also on discrete-time design. A discrete-time MRAC was referred in this paper. The objective is to regulate the output minimized (platform-vehicle levels’ sensed acceleration difference minimization). The system (dynamic driving simulator) is subject to disturbances and is driven by controls [
The design step searches a state-feedback law that minimizes the cost function via applying this logic.
Both of the motion control algorithms (classical and MRAC) were integrated at the dynamic driving simulator SAAM with a “dll plugin” which were created with Microsoft Visual 2008 C++ used in SCANeR studio version 1.1.
We considered adiscrete-time MIMO (multiple-input multiple-output) system described by [
with
The control objective is to design a state feedback control signal u(k) in Equation (1) such that all the closed- loop signals remain bounded and the system output signal y(k) tracks a given reference output
Wm(z) is an M ´ M transfer matrix, and r(k), an M-dimensional real array, is a bounded reference input signal [
To begin the real-time controller design which is implemented in driving simulator as “dll plugin”, we assume [
(A1) All zeros of
(A2)
DOF | Displacement | Velocity | Acceleration |
---|---|---|---|
Pitch | ±22 deg | ±30 deg/s | ±500 deg/s2 |
Roll | ±21 deg | ±30 deg/s | ±500 deg/s2 |
Yaw | ±22 deg | ±40 deg/s | ±400 deg/s2 |
Heave | ±0.18 m | ±0.30 m/s | ±0.5 g |
Surge | ±0.25 m | ±0.5 m/s | ±0.6 g |
Sway | ±0.25 m | ±0.5 m/s | ±0.6 g |
and the reference system transfer matrix
(A3) All leading minors
For a state feedback for state tracking design, the controller structure is
where
the plant state vector signal x(k) can asymptotically track a reference state vector signal xm(k) generated from a chosen reference system
where
where
Substituting the control law Equation (3) in Equation (1), we obtain
In view of the reference model Equation (2), matching equations Equation (5) and Equation (6), the output tracking error
where
In this section, we present the design and analysis of an adaptive scheme based on the LDS decomposition of the high frequency gain matrix KP.
To design an adaptive parameter update law, it is crucial to develop an error model in terms of some related parameter errors and the tracking error
Neglecting the term
To deal with the uncertainty of the high frequency gainmatrix KP, we use its LDS decomposition
where
such that
To parameterize the unknown Ls,
Then, it yields (17):
A filter was designed
where
Based on this parameterized error equation, we reach the estimation error signal
where
Within the estimation error model Equation (22), the chosen adaptive laws [
where the signal
is a standard normalization signal, where
We consider the dynamic model of the hexapod simulator described by Equation (28) which is a three state variable (x). The control inputs are (u) the pitch angle (θv), the roll angle (ϕv) and the yaw angle (ψv) of the vehicle model. Our MRAC model was given in Equation (29) (HP: high pass filtered motion, LP: low pass filtered motion) which was with a sampling interval of T = 1/60 seconds to obtain the discrete-time motion cueing algorithms implemented in our dll plugin.
Twenty-six healthy participants took place in the experiments (4 females, 22 males) with a mean age of 28.9 ± 5.8 years old and a driving license holding with a mean experience of 9.7 ± 6.6 years.
Vestibular level dynamics of the participants refer to the head movements of them (see
Multi-level data acquisition was performed at two levels as follows:
Such as the roll, pitch, yaw angles and rates as well as the accelerations in X,Y and Z. Quaternions have been used, since they are simpler to compose and to avoid singularity for angular calculations, so-called the problem of gimbal lock compared to Euler angles. The application domains of quaternions can be counted as computer graphics, computer vision, robotics, navigation, flight dynamics [
Electromyography (EMG) is an evaluation method of the electrical activity produced by musculoskeletal system. EMG is performed using an instrument called an electromyograph, to realize a record called an electromyogram. An electromyography detects the electrical potential generated by muscle cells [
By using the Biopac systems, several frequency and time domain techniques could be used for data reduction of EMG signals [
For this study, it was chosen to deal with the EMGRMS (root mean square: which is a product of longitudinal, lateral and vertical dynamics related dissipated power) power analysis (V2/Hz in unit) in time domain, in order to investigate their associations with RVT (˚/s in unit, which is an indicator of the conflict in dynamics).
- EMGRMS mean total power yields the average power of the power spectrum within the epoch [
- EMGRMS total power is equal to the sum of power at all frequencies of the power spectrum within the epoch [
- Epoch corresponds to how many time steps (∆t) a whole time series signal is divided into [
For the calibration of the electromyography, a gain of 1000 was used. And the
Electrodes in black circle were connected to flexor carpi radialis muscle where the electrodes in red circle were connected to brachioradialis muscles. We measured and saved the electrical activity changes on the brachioradialis and flexor carpi radialis muscles. In this paper, we explained the results which were taken from the muscle ‘flexor carpi radialis’ (at right hand side,
If
It can be seen that the discrepancy has been decreased between the EMGRMS total power and the roll velocity at vestibular level by using MRAC motion cueing (see
According to
Classical motion cueing Correlation of vestibular roll velocity-vehicle CG lateral displacement | Classical motion cueing Correlation of EMG RMS total power for arm muscles-vehicle CG lateral displacement | |||
---|---|---|---|---|
r | p | r | p | |
Subject 1 | −0.0252 | 0.6025 | −0.7730 | 0.0000*** |
Subject 2 | −0.5375 | 0.0000*** | 0.4004 | 0.0000*** |
Subject 3 | −0.5815 | 0.0000*** | −0.1068 | 0.0244* |
Subject 4 | −0.2872 | 0.0000*** | 0.1714 | 0.0003*** |
Subject 5 | −0.6761 | 0.0000*** | 0.5870 | 0.0000*** |
Subject 6 | 0.3348 | 0.0000*** | 0.4380 | 0.0000*** |
Subject 7 | −0.4486 | 0.0000*** | −0.2023 | 0.0000*** |
Subject 8 | −0.3638 | 0.0000*** | −0.1652 | 0.0007*** |
Subject 9 | −0.1770 | 0.0003*** | 0.1994 | 0.0000*** |
Subject 10 | −0.6624 | 0.0000*** | 0.1413 | 0.0051** |
Subject 11 | −0.6265 | 0.0000*** | 0.1931 | 0.0001*** |
Subject 12 | −0.7544 | 0.0000*** | 0.2197 | 0.0000*** |
Subject 13 | −0.0691 | 0.1448 | −0.1083 | 0.0220* |
*Means one zero after the point “.”, **means two zeros after the point “.”, ***means three and more than three zeros after the point “.”.
MRAC motion cueing Correlation of vestibular roll velocity-vehicle CG lateral displacement | MRAC motion cueing Correlation of EMG RMS total power for arm muscles-vehicle CG lateral displacement | ||||
---|---|---|---|---|---|
r | p | r | p | ||
Subject 1 | −0.2241 | 0.0000*** | 0.3925 | 0.0000*** | |
Subject 2 | −0.6283 | 0.0000*** | 0.3586 | 0.0000*** | |
Subject 3 | 0.4826 | 0.0000*** | 0.0896 | 0.0618 | |
Subject 4 | −0.5073 | 0.0000*** | −0.3667 | 0.0000*** | |
Subject 5 | −0.4519 | 0.0000*** | 0.0969 | 0.0182* | |
Subject 6 | 0.1222 | 0.0155* | 0.4443 | 0.0000*** | |
Subject 7 | −0.1934 | 0.0001*** | 0.1651 | 0.0008*** | |
Subject 8 | 0.0368 | 0.4506 | 0.1650 | 0.0007*** | |
Subject 9 | −0.1310 | 0.0063** | 0.0667 | 0.1658 | |
Subject 10 | −0.5408 | 0.0000*** | 0.1386 | 0.0064** | |
Subject 11 | −0.1222 | 0.0198* | 0.0036 | 0.9456 | |
Subject 12 | −0.6599 | 0.0000*** | 0.3367 | 0.0000*** | |
Subject 13 | −0.4904 | 0.0000*** | 0.3724 | 0.0000*** | |
*Means one zero after the point “.”, **means two zeros after the point “.”, ***means three and more than three zeros after the point “.”.
According to
From
According to
rest of the subjects (9 subjects out of 13 subjects), the MRAC motion cueing algorithm brought a more controllable vehicle in the dynamic simulator as operated in real-time. This shows that the MRAC motion cueing algorithm (closed loop control) provides a less LOA and LOC comparing to the classical motion cueing algorithm (open loop control).
Classical motion cueing Lateral displacement area (m∙s) | MRAC motion cueing Lateral displacement area (m∙s) | LOA change (%) from Classical to MRAC algorithm | |
---|---|---|---|
Subject 1 | 3.2166×104 | 1.6569 × 104 | 48.4% of decrease |
Subject 2 | 1.5717 × 104 | 1.4588 × 104 | 7.1% of decrease |
Subject 3 | 2.1987 × 104 | 1.7697 × 104 | 19.5% of decrease |
Subject 4 | 1.6291 × 104 | 1.5022 × 104 | 7.8% of decrease |
Subject 5 | 1.3508 × 104 | 1.2317 × 104 | 8.8% of decrease |
Subject 6 | 1.0828 × 104 | 1.3160 × 104 | 21.5% of increase |
Subject 7 | 1.3432 × 104 | 1.3630 × 104 | 1.4% of increase |
Subject 8 | 1.4279 × 104 | 1.4479 × 104 | 1.4% of increase |
Subject 9 | 1.3804 × 104 | 1.5422 × 104 | 11.7% of increase |
Subject 10 | 1.2864 × 104 | 1.2560 × 104 | 2.36% of decrease |
Subject 11 | 1.4529 × 104 | 1.1474 × 104 | 21% of decrease |
Subject 12 | 1.2642 × 104 | 1.1966 × 104 | 5.35% of decrease |
Subject 13 | 1.7150 × 104 | 1.5708 × 104 | 8.4% of decrease |
After having completed the data evaluation by individual as above, the overall data analysis has been studied for the thirteen subject group for each motion cueing (both for the classical and the MRAC motion cueing algorithms).
The overall data analysis was done by using a two-way ANOVA (Analysis of Variance) and Pearson’s correlation with an α = 0.05. In order to accomplish the statistical analysis, we took
- the vestibular roll velocity into account, which were measured from the right ear level of the participants during the real-time simulator experiments through the motion tracking sensor.
- the EMGRMS total power from the muscle ‘flexor carpi radialis’.
The two-way ANOVA was applied to identify the level of significance as between subjects’ principle test. The Pearson’s correlation was computed to clarify the correlation of the vestibular level roll velocity threshold with the EMGRMS power dissipation of the arm muscles.
The two-way ANOVA tests were used to check the influence of one type of response dynamics (spent power from the arms) of the drivers on the other type of response dynamics (vestibular roll velocity) of them as an interaction metrics.
By studying the output of the two-way ANOVA for the proposed classical motion cueing algorithm, we see that there is no evidence of a significant interaction effect (F = 3.74, p = 0.085 > 0.05) between those two types of response dynamics of the drivers. We therefore can conclude that no interaction was obtained between the EMGRMS mean power and the vestibular roll velocity threshold. The test for the main effect of the vestibular roll velocity perception threshold (F = 45.17, p < 0.0001) shows a significant roll velocity perception threshold effect on the EMGRMS maximum power level. Finally, the test for the main effect of the EMGRMS mean power (F = 1360.89, p < 10−9) tells us there is an evidence to conclude that the EMGRMS mean power has a significant effect on the EMGRMS maximum power level.
By investigating the output of the two-way ANOVA for the proposed model reference adaptive control motion cueing algorithm, we see that there is no evidence of a significant interaction effect (F = 0.43, p = 0.528 > 0.05) between those two types of response dynamics of the drivers. We therefore cannot conclude that an interactionis found between the EMGRMS mean power and the roll velocity threshold. The test for the main effect of the vestibular roll velocity perception threshold (F = 9.22, p = 0.01412 < 0.05) shows a significant roll velocity perception threshold effect on the EMGRMS maximum power level. Finally, the test for the main effect of the EMGRMS mean power (F = 232.44, p < 10−6) tells us there is an evidence to conclude that the EMGRMS mean power has a significant effect on the EMGRMS maximum power level.
Having searched the relationships of the roll velocity thresholds with the EMGRMS mean and maximum total power, we recognized that if we drive the same scenario with the MRAC, it shows a more alerted (agile) mode compared to the classical motion cueing algorithm. Because, the correlation coefficients (r) between the roll velocity thresholds and the EMGRMS mean/maximum total power are positive for the MRAC and negative for the classical motion cueing algorithm.
We described the RV (roll velocity) at “vestibular” level [
Root-mean square (RMS) of EMG (EMGRMS) (mV) values were computed based on a total range of motion during the driving phase of the simulator experiments [
where t is the onset of signal time and Tis the duration of RMS averaging [
For the frequency domain analysis used in this study to determine the spent power/energy by the arm muscles of the drivers, a Fast Fourier Transformation algorithm was used to calculate the power spectrum of EMG signals (mV) [
where xn is a set of consecutive EMG signals with the specific number of epochs, PSD is power spectral density in mV2/Hz [
In this article:
- EMGRMS total power indicates the dissipated power (times series data) during the driving simulation experiments (Equation (31) and Equation (32)). It yields the sum of the power at all frequencies of the power spectrum within the epoch.
- EMGRMS maximum total power refers to the peak values (one value point) obtained from the dissipated energy during the driving simulation experiments (Equation (31) and Equation (32)).
- EMGRMS mean total power indicates the mean of the sum of the dissipated power (one value point) at all frequencies during the driving simulation experiments (Equation (31) and Equation (32)).
- Roll velocity perception threshold gives maximum vestibular level roll velocityat low frequent motion independent from the direction: Those signals were conditioned with a 1st order Butterworth low-pass filter at 5 Hz.
Due to
According to Pearson’s correlation, it is shown that the RVT and the EMGRMS mean power are positively correlated (r = 0.228, p = 0.453) for the MRAC algorithm and they are negatively correlated (r = −0.167, p = 0.586) for the classical algorithm.
According to Pearson’s correlation, it is shown that the RVT and the EMGRMS maximum power are positively
correlated (r = 0.192, p = 0.531) for the MRAC motion cueing algorithm and they are negatively correlated (r = −0.178, p = 0.560) for the classical motion cueing algorithm. (
Head roll velocity, arm muscle and vehicle dynamics interaction were investigated. For the classical motion cueing the discrepancy of the curves (vestibular-arm muscle dynamics) has increased (see
We also investigated the vestibular sensed roll velocity perception threshold (impulse effect dynamics: high frequent motion) with the total power spent by the arm muscles. It gave an idea about the driver’s behaviours as “alertness (agility)”.
Having a closed loop control of the hexapod platform (a MRAC motion cueing strategy) supplied more alertness (39.5% increase in agility: r = 0.228, p = 0.453 for the MRAC algorithm and r = −0.167, p = 0.586 for the classical algorithm in terms of RVT-EMGRMS mean total power. And also 37% increase in agility: r = 0.192, p = 0.531 for the MRAC algorithm and r = −0.178, p = 0.560 for the classical algorithm in terms of RVT-EMGRMS maximum total power), that helps the dynamic simulator be driven more controllably, compared to an open loop control of the hexapod platform (a classic motion cueing strategy) with the same filters and gains (
We thus cannot conclude that there is an interaction between the EMGRMS means power and the roll velocity threshold. The test for the main influence of the vestibular roll velocity perception threshold indicates a significant roll velocity perception threshold influence on the EMGRMS maximum power level. Eventually, the test for the main effect of the EMGRMS mean power gives us an evidence to conclude that there is a significant EMGRMS mean power effect on the EMGRMS maximum power level for both classical and MRAC motion cueing algorithms.
As a conclusion, the MRAC motion cueing strategy optimized the dynamic simulator condition with respect to the classical motion cueing strategy, so that it resulted as an improved situation for the drivers in terms of the “avoidance of LOA” and improving the “motion sickness” depending on sensory conflict theory between neuromuscular-vehicle (visual) cues, between vestibular-vehicle (visual) cues.
It also proved that the neuromuscular-vehicle dynamics conflict has influence on visuo-vestibular conflict; however, the visuo-vestibular cue conflict does not influence the neuromuscular-vehicle dynamics interactions.
As prospective work, we would like to evaluate the sickness regarding the pitch velocity/acceleration perception threshold as well as the neuromuscular-vestibular reaction time relationships of the drivers on various road scenarios, under different controls of the hexapod platform with correlations in inertial, vestibular, neuromuscular cues.
Arts et Métiers Paris Tech built up the SAAM driving simulator with the partnership of Renault.
B.Aykent,D.Paillot,F.Merienne,C.Guillet,A.Kemeny, (2015) The Role of a Novel Discrete-Time MRAC Based Motion Cueing on Loss of Control at a Hexapod Driving Simulator. Intelligent Control and Automation,06,84-102. doi: 10.4236/ica.2015.61010