International Journal of Automotive Technology, Vol. 16, No. 1, pp. 117−126 (2015) DOI 10.1007/s12239−015−0013−6
Copyright © 2015 KSAE/ 082−13 pISSN 1229−9138/ eISSN 1976−3832
NEW MOTION CUEING ALGORITHM FOR DRIVING SIMULATOR BASED ON VARIANT HARMONIC WAVELET X. M. GONG, X. H. LI* and S. A. WANG School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China (Received 25 March 2013; Revised 2 December 2013; Accepted 10 April 2014) ABSTRACT−As one of key technologies in movement perception simulation, motion cueing algorithm (MCA) is usually used for exploiting driving simulator within limited workspace and bounded dynamic characteristics. Several MCAs are investigated for movement perception simulation, however, the classical washout algorithm has shortage in time delay, the optimal washout algorithm completely depends on accurate vestibular model, while the adaptive washout algorithm needs long computational time. So the result of these defects is to reduce driving simulation fidelity. In order to meet the performances of high fidelity and real-time for driving simulator, this paper proposes a novel hybrid coordination motion cueing algorithm based on variant harmonic wavelet. The variant harmonic wavelet, mutating from traditional harmonic wavelet, has only three special wavelets. For its outstanding performances, box-shaped filter characteristics and zero phase shift, it would enhance driving sensation fidelity and real-time. Meanwhile, hybrid tilt and over-tilt coordination mechanism are introduced to design the new MCA for providing a special coordination strategy. Finally, the effectiveness and superiority of the new MCA are validated by simulation. KEY WORDS : Motion cueing algorithm, Variant harmonic wavelet, Hybrid coordination, Driving simulator
1. INTRODUCTION
al., 2010). Some improvements were achieved in optimal washout by introducing not only perception model but also human body model (Han et al., 2002). Improved adaptive method based on motion limits of single degree-offreedom calculates online and the parameters tune more “open” to improve motion cueing fidelity (Yang et al., 2011). Fang and Kemeny (2012) and Dagdelen et al. (2009) applied model predictive control technology into optimal washout algorithm to reduce accurate model-dependence. Romano (1999) proposed an optimal control algorithm based on over-tilt principle in large workspace simulator and its performances were superior to the traditional. Giordano et al. (2010) and Wang et al. (2008) separately applied classical washout algorithm to an anthropomorphic serial manipulator—the cybermotion simulator and locomotive driving simulator. The obtained performance and attained video were quite satisfactory in driving a Formula-a car along a lap on a virtual track. In view of the current studies, classical washout algorithm uses multi-order filter rather than box-shaped filter, it would cause the output signal with time delay, and high and low pass signals would overlap after corresponding filter, which would affect driving fidelity. The optimal washout algorithm is based on accurate vestibular model and reasonable optimization objective, namely linear quadratic cost function. Vestibular systems of different drivers, however, exist differences, so will the models of different drivers to be built. Thus, specific parameters
Driving simulator, having the main outstanding advantages in reducing training costs, risks and improving training efficiency, is of great significance in driving simulation. Motion Cueing Algorithm (MCA), as the key technology of driving simulator, could compensate for the defects of driving simulator to enhance fidelity in driving simulation. For the motion perception organ of humans is vestibular system, the mechanism of motion cueing algorithm is taking certain methods on it to produce a driving illusion just as in actual driving conditions. At present, the study on motion cueing algorithm mainly focuses on three typical MCAs, classical washout algorithm, optimal washout algorithm, adaptive washout algorithm, and the applications of three algorithms. Nahon and Reid (1990) and Nehaoua et al. (2006) compared the three washout algorithms from the perspective of theoretical analysis and experiments respectively. They found the same conclusion that the classical washout algorithm was the most desirable of the three MCAs. Kim et al. (2010), Han et al. (2002) and Yang et al. (2011) improved classical, optimal and adaptive washout algorithms respectively. Time delay and signal distortion were decreased by eliminating low pass filter and introducing partial range scaling method compared with classical washout (Kim et *Corresponding author. e-mail:
[email protected] 117
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should be set for different drivers before driving simulation, which results in lacking of generality and adding inconvenience. As with classical washout algorithm, the optimal washout algorithm also yields fix-parameters filters, which would not exploit simulator capabilities very well. Nahon and Reid (1990) and Nehaoua et al. (2006) concluded that the optimal washout algorithm performed the worst among these three MCAs. Adaptive washout algorithm is based on minimization of cost function by the steepest descent method. Inappropriate convergence speed coefficient of adaptive washout algorithm, however, would result in value shock of cost function. Meanwhile, it is difficult to find the most relevant weighting of cost function and initial values of many parameters. What’s more, the performace of real-time is decrease because large numer of equations need to be solved. In order to improve driving fidelity, simplify motion cueing algorithm and enhance real-time performance, this paper presents a novel hybrid tilt and over-tilt hybrid coordination motion cueing algorithm based on variant harmonic wavelet. For variant harmonic wavelet filter’s outstanding performances, box-shaped filter characteristics and zero phase shift, the new motion cueing algorithm can achieve better driving fidelity and faster real-time. At the same time, adaptive filter mechanism is introduced, which instantaneously adjusts the filter parameters according to input signal in order to sufficiently exert the simulator platform. In addition, introducing hybrid tilt and over-tilt coordination mechanism into the novel motion cueing algorithm to provide a special coordination strategy for driving simulation in constraint of limited simulator workspace.
2. MECHANISM OF HYBRID COORDINATION 6-DOF parallel platform is mostly used as driving simulator and frames are established as shown in Figure 1. Origin OI of inertial frame FI locates in geometric center of the fixed platform when origin OV of body-axis frame FV locates in the center of driver’s vestibular system. Z-Y-X Euler angle is used to express rotation matrix LIV from FV to FI. cβcγ LIV = c βsγ sβ
–c αs γ – sαs βcγ sα sγ – cα sβc γ c αc γ – sαsβsγ –sαc γ – cα sβ sγ sαcβ cαcβ
Where, sα = sin α, cα = cos α.
(1)
Figure 2. Mechanism of hybrid coordination. Due to limited workspace and bounded dynamic characteristics of driving simulator, it is impossible to completely generate the real feelings in actual driving. Tilt coordination, however, could make driver have the continuous acceleration or deceleration feelings in corresponding acceleration or deceleration driving process by reasonably tilting the moving platform. It makes up the bad driving fidelity resulting from simulator defects. Here, hybrid tilt and over-tilt coordination are taken to provide a special coordination strategy. Its mechanism is shown in Figure 2. When the current position of moving platform does not exceed the set threshold, it switches to tilt coordination, while current position exceeds, it switches to over-tilt coordination. The set threshold δTH is a surface that inwardly offsets an appropriate distance di from the edge closed surface of platform workspace Sw(s, y, z) as expressed in equation (2).
δTH = Sw ( x, y, z ) – di
Moving platform will keep moving forward when decelerates or brakes because of moving inertia. Thus, when exceeds the set threshold, the moving platform has enough space to go back to initial set position not exceeding workspace range. The detailed realization will be demonstrated in the following paragraph. Humans perceive linear motion by detecting specific force defined as fIs = aI – gI in otolith system and perceive rotational motion by detecting angular acceleration in semicircular canal system in vestibular system (Greig, 1988). Here, gI = ( 0, 0, g )T and g stands for gravity acceleration. The otolith and vestibular systems are modeled in spring, mass and damper system by Young and Oman. Their transfer functions show in Figure 3 and Figure 4 respectively (Peter and Burnell, 1981). f and ω are the specific force and angular velocity respectively, they are in the center of driver’s otolith and vestibular systems respectively, while ˆf and ω are specific force and angular velocity respectively sensed by driver. k is gain factor. τa, τL and τs are otolith model parameters while
Figure 3. Model of otolith system.
Figure 1. Driving simulator.
(2)
Figure 4. Model of vestibular system.
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Table 1. Human perception model parameters. (a) Specific force sensation model parameters
Parameters
Surge
Sway
Heave
τL
5.33
5.33
5.33
τS
0.66
0.66
0.66
τa
13.2
13.2
13.2
0.4
0.4
0.4
0.17
0.17
0.28
k
δTH (m/s ) 2
Figure 5. Mechanism of hybrid coordination.
(b) Rotational motion sensation model parameters
Parameters
Roll
Pitch
Yaw
TL
6.1
5.3
10.2
TS
0.1
0.1
0.1
Ta
30
30
30
δTH (°/s)
3.0
3.6
2.6
TL, TS and Ta are semicircular canal model ones. δTH is sensation threshold. The human perception model parameters are shown by Table 1 (Peter and Burnell, 1981). All of otolith and vestibularl systems have good perception in the band of 0.01~0.5Hz. In order to intuitively explain the mechanism of hybrid tilt and over-tilt coordination, suppose the driver has acceleration aV in body-axis frame and moving platform locating in initial pose described by rotation matrix as LIV0 . And then specific force in body-axis frame is fVs = aV – LTIV0 gI as shown in Figure 5 (a). Tilt coordination matches the Equation (3) conditions to make driver have the best continuous feeling of acceleration. ⎧ ˆfVs = –kLT LT g = f = a – LT g IV0 IV I Vs V IV0 I ⎪ ⎨ aV = 0 ⎪ ˆ ⎩ fVs = k fVs
Where, [ ⋅ ]x , [ ⋅ ]y and [ ⋅ ]z stand for frame component values. When moving platform exceeds the set threshold, it switches to over-tilt coordination. Its mechanism is similar to tilt coordination. The differences are that over-tilt coordination has return acceleration aVb = LTIV ab to drive the moving platform back to the initial set position and the specific force is disposed as fVs = aV – aVb – LTIV0gI . Then after over-tilt coordination, aV = 0 and return acceleration aVb remains as shown in Figure 5 (c).
3. DESIGN OF MOTIOIN CUEING ALGORITHM BASED ON VARIANT HARMONIC WAVELET ECTION TITLE 3.1. Variant Harmonic Wavelet Harmonic wavelet has extrusive advantages with boxshaped filter characteristics and zero phase shift. Hence,
(3)
Where, ˆfVs is specific force after tilt coordination. LIV is rotation matrix containing required coordination Euler angle. k is a scale coefficient. ⋅ represents 2-norm of a vector. The Equation (3) shows that tilt coordination is to make the directions of fVs consistent with fVs in body-axis frame and have no forward acceleration aV as shown in Figure 5 (b). Thus, it makes driver have the best continuous acceleration and do not need to exceed limited workspace of simulator. Then, from Equation (3), required coordination Euler angle θ = ( αc, βc, γc ) could be gained as: LIV0fVs ]-y⎞ ⎧ α = arctan ⎛ [-------------------⎪ c ⎝ [ LIV0 fVs ]z⎠ ⎪ ⎨ ⎛ [ LIV0 fVs ]-x⎞ ⎪ βc = –arcsin⎝ -------------------fs ⎠ ⎪ ⎩ γc = 0
(4) Figure 6. Variant harmonic wavelet.
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Figure 7. Frequency distributions of variant harmonic wavelets. variant harmonic wavelets are constructed to realize essential and better filters in motion cueing algorithm. It only has three special wavelets defined as low-pass wavelet j2πf t wl( t ) = ( e lc – 1 ) ⁄ j2πflct , band-pass wavelet wb(t) = j2πflc t j2 π fhc t ( ej2πf –t e j2πf )t⁄ j2π ( fhc – flc )t and high-pass wavelet wh(t) = ( e max – e hc ) ⁄ j2π ( fmax – fhc )t . flc, fhc and fmax correspond to low-pass wavelet cut-off frequency, high-pass wavelet cut-off frequency and maximum frequency of input signal. All of the three wavelets have the similar shape as Figure 6 shows. Thus, their frequencies Wl ( ω ), Wb( ω ) and Wh ( ω ) after Fourier transform are distributed as Equation (5), Equation (6) and Equation (7). Figure 7 gives their frequency distributions. ⎧ 1 ⁄ 2π flc 0 ≤ ω < 2π flc Wl ( ω ) = ⎨ ⎩ 0 others ⎧ 1 ⁄ 2π( fhc – flc ) Wb ( ω ) = ⎨ ⎩ 0 others ⎧ 1 ⁄ 2π( fmax – fhc ) Wh ( ω ) = ⎨ ⎩ 0 others
2π flc ≤ ω < 2 πfhc
2π fhc ≤ ω ≤ fmax
(5)
(6)
(7)
(8)
–∞
Where, wl ( x ) and w*b( x ) express in inverse Fourier transform as: wl( t ) = ∫ Wl ( ω )ejωtdt
(9)
–∞ ∞
w*b( t ) = ∫ W*b( –ω )e jωt dt –∞
∞
*
∞
ya
∞
*
j ( ω 1 + ω2 )t
dt
(11)
From the theory of generalized functions, the Fourier transform of the function δ ( t – t0 ) is
∫
∞ –∞
δ ( t – t0 )e–jωtdt = e
– j ω t0
(12)
So that, by the inverse Fourier transform,
∫ ∫
∞
e
j ω ( t – t0 )
–∞
dω = 2 πδ ( t – t0 )
(13)
(10)
∞
e
jt (ω1 + ω2 )
–∞
dt = 2 πδ( ω1 + ω2 )
(14)
On substituting Equation (14) into Equation (11) and integrating over ω2, the result can be gained below:
∫
〈 wl( t), wb ( t )〉 = ∫ wl ( t )w*b ( t )dt
∞
∞
∫–∞ wl ( t )wb ( t ) dt = ∫–∞ ∫–∞ dω1 ∫–∞ Wl ( ω1 )Wb ( –ω2 )e
Using above result, the integral over t in Equation (11) is
As can be known from Equation (5) ~ (7), these three frequency distributions do not overlap each other and they are complementary each other at the same time. Any of two in these three harmonic wavelets meet orthogonally. The proof is shown as follows. Proof: Firstly, low-pass and band-pass wavelets will be selected to study their orthogonality. Then we can extend to other wavelet groups. Inner product of low-pass and bandpass wavelets is +∞
Then
∞ –∞
∞
wl( t)w*b ( t )dt = 2π∫ Wl( ω )W*b ( ω )dω
(15)
–∞
While, the frequency of Wl( ω ) and W*b ( ω ) are occupy different frequency bands so that their inner product is always zero, namely 〈 wl ( t ), wb ( t )〉 = 2 π 〈 Wl( ω ), Wb ( ω )〉 = 0 .
(16)
Thus, the low-pass and band-pass wavelets are orthogonal. Similarly, low-pass and high-pass wavelets, band-pass and high-pass wavelets are also orthogonal. Therefore, the three variant harmonic wavelets satisfy orthogonally. The three variant harmonic wavelets are orthogonal and complementary each other. So every certain signal could be expressed as linear weighted sum of low-pass, band-pass and high-pass wavelets: x( t) =
∑
akwk( t).
(17)
k = l, b, h
Where, ak = 〈 x( ( t ), wk ( t ) )〉 ( k = l, b, h ) are defined as wavelet coefficients. The realization of variant harmonic wavelet filter is shown in Figure 8. Where, Wx( ω ) stands for Wl( ω ), Wb ( ω ) or Wh ( ω ) . Modular FFT and IFFT stand for Fourier transform and inverse Fourier transform respectively. The purpose of modular gain is to restore
NEW MOTION CUEING ALGORITHM FOR DRIVING SIMULATOR BASED
121
Figure 8. Realization of variant harmonic wavelet filter.
Figure 9. Schematic diagram for MCA based on variant harmonic wavelet. signal amplitude, i.e. signal energy, so there is no signal energy loss after variant harmonic wavelet filter. Certain input signal x( t), 0 ≤ t ≤ ∞ , can be expressed in discrete form as x( nT ) , n = 0, 1, 2, …, ∞ . T stands for the sampling period. According to variant harmonic wavelet filter characteristics, assumed that certain filtering moment is kT, the data group for real-time filtering has N moments which contains the frontal N−1 moments and the kT moment itself. So data group is x [ ( k – N + 1 )T ], x[ ( k – N + 2 )T ], …, x ( kT ) . After processed by variant harmonic wavelet filter, data series wx ( T ), wx( 2T ), …, wx( NT ) is gained and wx ( NT ) is extracted as filtering signal at the moment x( kT ) . In order to sufficiently exert the function of simulator platform and attain the best combination namely balanceable point between transient dynamic motion and tilt or over-tilt coordination for any changeable input signal, adaptive filter mechanism is applied. flc and fhc in variant harmonic wavelet non-adaptive filter is changeless in filtering process while in variant harmonic wavelet non-adaptive filter is changeable. They change based on Equation (18)-(19). ρl and ρh are defined as low-pass filter coefficient and highpass coefficient respectively. According to specific simulator capabilities, ρl and ρh are set to fixed values. So the cut-off frequencies flc and fhc continuously vary in different realtime data groups of input signal. flc
∫
Amp ( f ) df
0 ρl = ---------------------------------fmax
∫
∫
(18)
Amp ( f ) df
4. SIMULATION ANALYSES
0 fmax f
Amp( f )df
hc ρh = ---------------------------------fmax
∫
f df
0
3.2. Novel Hybrid Coordination Motion Cueing Algorithm Based on Variant Harmonic Wavelet The basic process of motion cueing algorithm is that extracting the high frequency component of specific force to enable driver to generate transient dynamic acceleration or deceleration feeling. The low frequency component is coordinated by tilt or over-tilt coordination mechanism to enable driver to keep continuous feelings of acceleration or deceleration. The high and low frequency components are obtained by corresponding high-pass and low-pass filters. It is also similar to angular velocity. The schematic diagram of novel hybrid coordination motion cueing algorithm based on variant harmonic wavelet is shown in Figure 9. According to pre-setting driving simulation scene terrain and the pose of vehicle, the acceleration aV and angular velocity ωV of origin OV in body-axis frame could be easily gained by sensors in actual driving or computation in driving simulation, which are regarded as input signals. The linear displacement could be obtained after two integrating the VHW(Variant Harmonic Wavelet) high-pass filtered specific force plus the possible return acceleration ab from hybrid coordination. The angular displacement could be obtained by integrating the sum of required coordinated angles and VHW low-pass filtered angular velocity and direct-current (DC) component of angles standing for pavement pose. All the acceleration and angular velocity values are limited due to bounded dynamic characteristics.
(19)
In order to judge the effectiveness and superiority of motion cueing algorithm, valuation indexes, i.e. specific force sensation average error EIf and angular velocity sensation
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average error EIω , are established as: T
1 EIf = --- ∫ ˆfd( t ) – ˆf( t ) dt T 0
(20)
1 T ˆ ˆ (21) EIω = --- ∫ ω d ( t ) – ω ( t ) dt T 0 Where, ˆfd ( t ) and ˆf( t ) are the desired and actual output ˆ ( t ) are the ˆ d( t ) and ω of specific force sensation while ω desired and actual output of angular velocity sensation, respectively.
4.1. Comparison of Filters in Novel Motion Cueing Algorithm and Classical Washout Algorithm Traditional filters are generally used in Classical Washout Algorithm (CWA) (Nehaoua et al., 2006; Giordano et al., 2010; Wang et al., 2008; Grant and Reid, 1997; Grant et al., 2009).Three-order filter is for high-pass filter of acceleration, and two-order filter is for low-pass filter of acceleration and high-pass for angular velocity. Those are partly listed as below. Three-order high-pass filter for acceleration is s2 s - ⋅ -----------HPf ( s ) = -----------------------------------------. 2 s + 2ζfhωnfhs + ω2nfh s + ωb
Table 2. Simulation parameters. (a) VHW parameters VHW VHW adaptive
VHW non-adaptive
ρl
ρH
N
0.3
0.7
64
flc (Hz) fhc (Hz) 2
2
N 64
(b) CWA parameters CWA
ωnfh
ωb
(rad/s)
(rad/s)
2π × 2
2π × 2
ζfh 0.7
ωnfl
(rad/s) 2π × 2
ζfl 0.7
(22)
Two-order low-pass filter for angular velocity is
ω2
nfl -. LPf( s ) = --------------------------------------------s2 + 2ζfl + ωnfl s + ω2nfl
(23)
Where, ωnfh, ωb and ωnfl are corresponding cut-off frequencies, ζfh and ζfl are corresponding damping ratios. The purpose of this comparison: one is to compare the filters’ performances in three MCAs and to have an intuitive knowing of high-pass and low-pass signals in the case; the other is to express the phenomenon that high-pass and low-pass signals after filtered are similar but results vary considerably after different MCAs. It has three members: filters in Motion Cueing Algorithm based on Variant Harmonic Wavelet adaptive (VHW adaptive), filters in Motion Cueing Algorithm based on Variant Harmonic Wavelet non-adaptive (VHW nonadaptive) and filters in CWA. VHW adaptive and VHW nonadaptive belong to the novel motion cueing algorithm. Both of them apply variant harmonic wavelet while the difference of them is that one uses adaptive filter mechanism and the other does not. For comparison, only surge acceleration signal ax ( t ) is given as Equation (24) shows. ⎧ 2.5 ( t – 0.5 ) 0.5 ≤ t < 0.6 ⎪ 0.6 ≤ t < 1.4 ⎪ 2.5 ⎪ –25( t – 1.5 ) 1.4 ≤ t < 1.5 ⎪ – 25 ( t – 2 ) 2 ≤ t < 2.1 ⎪ ⎪ –2.5 2.1 ≤ t < 2.9 ax ( t ) = ⎨ (24) 2.9 ≤ t < 3 ⎪ 25 ( t – 3 ) ⎪ ( 2 + sin2πω1t )sin [2 πω2 ( t – 3.5 ) + 2πω3 ( t – 3.5 ) ] ⎪ ⎪ + ( 2sin2 πω4 t )sin[ 2πω5( t – 3.5 )+2πω6( t – 3.5 + φ ) ⎪ 3.5 ≤ t < 10 ⎪0 others ⎩
Figure 10. High-pass & low-pass signals by filters in three MCAs.
NEW MOTION CUEING ALGORITHM FOR DRIVING SIMULATOR BASED
Where, ω1 = ω2 = 0.08(t+1), ω3 = 0.05(2t+1), ω4 = ω5 = 0.2(t+1), ω6 = 0.2[t+1+0.5rand()], φ = 0.2(t−3.5). According to this specific acceleration signal, suitable parameters are set in Table 2. The sampling frequency fs = 64Hz. Results of signal decomposition, i.e. high-pass and lowpass components, and signal reconstruction for validating filter superior performances in novel motion cueing algorithm are shown in Figure 10 ~ 11.
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The reconstructed errors reconstructing by high-pass and low-pass signals by filters in VHW adaptive and nonadaptive are 10−15 order of magnitude while reconstructed error in CWA is quite larger reaching to 100 order of magnitude and the maximum error is to 4.52 m/s2. Meanwhile, there is almost no time delay in reconstructed signal by filters in VHW adaptive and non-adaptive while obvious time delay appears in reconstructed signal in CWA. Therefore, we draw a conclusion that the filters VHW adaptive and nonadaptive are superior to traditional filters in CWA. 4.2. Comparisons of the Three MCAs: VHW Adaptive, VHW Non-adaptive and CWA Furthermore, we comprehensively compared these three MCAs’ performances. Results contain 2-norm of specific force sensation and error, surge sensation and error, heave sensation and error are shown in Figure 12 ~ 17. Table 3 above shows the average and max values of 2norm of specific force sensation error, surge sensation error and heave sensation error by the three MCAs. From the statistical data, we can conclude that VHW adaptive and VHW non-adaptive are superior to CWA. Meanwhile, in Figure 14, time delay obviously appears by CWA but no obvious phenomenon in VHW adaptive and VHW non-
Figure 12. 2-norm of specific force sensation without washout & by three MCAs.
Figure 11. Original signal and reconstructed signal & Reconstructed error by filters in three MCAs.
Figure 13. Errors of 2-norm of specific force sensation by three MCAs.
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Figure 14. Surge sensation without washout & by three MCAs.
Figure 16. Heave sensation without washout & by three MCAs.
Figure 15. Errors of surge sensation by three MCAs. Figure 17. Errors of heave sensation by three MCAs. adaptive. VHW adaptive performances are a little worse than VHW non-adaptive in this case, but it provides a balanced mechanism. When the cut-off frequencies flc and fhc in VHW non-adaptive are set inappropriate, it easily goes to extreme case, such as under-exerting or overexerting the tilt coordination of moving platform. The less moving platform exerts the tilt coordination, the higher driving fidelity and more intensive transient dynamic motion it will have, but higher performance requirements driving simulator will need. In this case, cut-off frequencies flc = 2Hz and fhc = 2Hz in VHW non-adaptive are set appropriate. They are the same values compared with cut-
off frequencies in CWA in order to fairly compare their performances between VHW non-adaptive and CWA. If inappropriate cut-off frequencies flc = 1Hz and fhc = 1Hz in VHW non-adaptive are set, the results are listed as following: average of error of 2-norm of special force sensation is 2.39 and its max value is 0.13; average of error of surge sensation is 0.30 and its max value is 0.02; average of error of heave sensation is 2.37 and its max value is 0.13. Obviously, it’s worse than VHM adaptive. It’s difficult to set appropriate cut-off frequencies because the input signal is unknown or hard to be estimated. Therefore,
Table 3. Comparison of three MCAs. VHW Error of 2-norm of specific force sensation Error of surge sensation Error of heave sensation
CWA
VHW adaptive
VHW non-adaptive
Average EIf
2.16
1.97
15.02
Max
0.13
0.10
0.62
Average
0.31
0.22
13.69
Max
0.02
0.02
0.62
Average
2.14
1.96
4.29
Max
0.13
0.10
0.20
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input signals so as to acquire the best balanceable point between tilt or over-tilt coordination and transient dynamic motion. Meanwhile, an special coordination strategy for driving simulation in constraint of limited workspace of driving simulator is provided by introducing hybrid tilt and over-tilt coordination into the novel motion cueing algorithm.
Figure 18. Euler angle needed to be coordinated.
ACKNOWLEDGEMENT−This work is supported in part by National Natural Science Foundation of China under Grant #51105297, and we also thank editor and referees’ sincere comments and suggestions.
REFERENCES
Figure 19. Cut-frequency in VHW adaptive. adaptive mechanism should be introduced to adjust cut-off frequencies flexibly according to the changeable input signal. So the best balanceable point between tilt or overtilt coordination and transient dynamic motion will be achieved. Figure 18 shows the Euler angle βc needed to be coordinated by three MCAs while the other two αc and γc always equal to zero in this case. All the Euler angle αc, βc and γc are gained from mechanism of coordination. Figure 19 shows the cut-frequency fhc (fhc = flc) adaptively adjusts in VHM adaptive.
5. CONCLUSION This paper proposes a new hybrid coordination motion cueing algorithm based on variant harmonic wavelet. Mutating from traditional harmonic wavelet, variant harmonic wavelet only has three special wavelets. With box-shaped filter characteristics, zero phase shift, variant harmonic wavelet filter is better than traditional filter in CWA in filter performance from theoretical analyses. Certain signal decomposition and reconstruction simulation experiments validate VHW filter superiority again. After comparison of the three MCAs, VHW adaptive, VHW non-adaptive and CWA, the former two that we proposed are superior to CWA. VHW adaptive performs a little worse than VHW non-adaptive which uses appropriate parameters in this case, but adaptive mechanism should be introduced to improve algorithm adaptability for different
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