Combined denoising method of acceleration signal during mobile robot collision

Collision safety of mobile robot is one of the important indexes of robot safety evaluation. The acceleration signal of the robot can completely feed-back the state of the collision process, but it is also vulnerable to noise interference such as vibration and impact, which is difficult to be used for direct analysis. In order to solve the problem of mixing acceleration signal with impact noise and periodic vibration noise during robot collision, a combined filtering noise reduction method based on empirical mode decomposition (EMD), improved wavelet threshold method and dynamic sliding window is proposed. And a wavelet adaptive threshold function is constructed. The wavelet coefficients are automatically adjusted using the information of decomposition degree and noise level, and a dynamic adjustment strategy of sliding window length is designed. The acceleration information of robot can be effectively extracted in the process of strong noise collision. The experimental results show that this method has better noise reduction effect than other methods.


Introduction
Mobile robots often work in a dynamic environment, with a high frequency of interaction between robots and environmental objects, and the motion safety of robots should be more fully verified [1][2][3].Collisions often occur when the safety functions of mobile robot are limited or invalid.Many standards of robot propose that the safety speed and force of robots need to be confirmed and evaluated [4].
Compared with the collision force measurement by collision plate detector, the accelerometer which installed on the robot can quickly feedback the motion state of the robot in the whole collision process [5,6].However, the accelerometer measurement results are easily affected by the vibration, impact and other signals generated by the robot movement process.Especially in the collision process, the robot state changes drastically will result in the acceleration signal shaking violently.Consequently, how to extract the effective acceleration signal from the strong noise is of great significance to the analysis of the robot collision process based on the accelerometer.
The methods, which are based on empirical mode decomposition (EMD) and wavelet decomposition, have good effects on filtering and denoising of nonlinear and non-stationary signals because of their dynamic adaptability.Cui et al. [7] improved the EMD threshold filtering method and applied to the drift signal denoising of FOG to obtain stable output.Dong et al. [8] proposed a wavelet adaptive threshold full-frequency denoising method, and it had good denoising effect for complex mixed noise scenes.Li et al. [9] comprehensively applied EMD and wavelet threshold method to the motor current signal filtering of rehabilitation robot, and achieved a good result.EMD and wavelet threshold method were comprehensively applied in paper [10] to denoise acceleration signal processing of vehicle shift, it provided a new idea for acceleration signal processing.In paper [11], wavelet transform denoising method was applied to the accelerometer calibration, and a denoising method based on sequence correlation and wavelet transform was proposed to effectively reduce the output noise of accelerometer.Zhao et al. [12] proposed an EMD/LPF hybrid denoising method, which effectively suppressed the high-frequency periodic signal in the gyro flywheel signal.Li et al.
[13] has constructed a wavelet continuous threshold function to make effective signal extraction more sufficient, and realized the extraction of safety valve emission signal under strong background noise interference.Fan et al. [14] proposed a joint noise reduction method of EMD and IIR filtering to reduce the signal noise aliasing in the high-frequency components of EMD, and improved the noise reduction level of the filter.
Traditional methods mostly consider how to effectively reduce impact noise or periodic vibration noise in the signal, while the acceleration signal of robot collision process has both of the above two noises and the problem of signal-noise aliasing is more prominent.Therefore, in this paper, we propose a combined denoising method based on EMD, wavelet threshold and dynamic sliding window.We construct a wavelet adaptive adjustment threshold function, that wavelet coefficients can be dynamically adjusted according to the decomposition degree and noise level.And a sliding window length adjustment strategy is designed to achieve the acceleration signal extraction in the collision process.The experiment shows that this method has better noise reduction effect than other methods.

Combined denoising method of collision acceleration signal
The general flow of the combined denoising method of collision acceleration signal based on EMD and improved wavelet threshold method is shown in Figure 1.First, EMD is used to decompose the raw signal into multi-level IMF components to realize the preliminary separation of high and low frequency signals.Then, the adaptive wavelet threshold method is used to de-noise the high-frequency noise components and extract the effective signals in the high-frequency noise.Finally, the signal is reconstructed using EMD and the adaptive dynamic sliding window are used for smoothing processing to highlight the robot status during the collision process.

Signal decomposition based on EMD
The principle of EMD is to decompose the signals into some IMF with frequencies arranged in order from high to low by the way of envelope fitting approximation according to the characteristics of the signals [14].Since the noise generally exists in the high frequency band, after the EMD decomposition is completed, the signal with lower frequency can be selected for reconstruction according to the need to remove the high frequency noise in the signal.After EMD decomposition, the original signal can be expressed as: ∑ where is the original signal, is the component of IMF obtained by decomposition, and is the residual term that reaches the decomposition stop condition.On the stop condition of EMD, the threshold judgment of the standard deviation (SD) of the continuous decomposition results adopted in this paper is expressed as: where and indicates two adjacent sequences of EMD decomposition, each sequence length is , for the selected threshold value, which can influence the number of decomposition levels, the accurate of the result and the calculation amount, is generally within the range of 0.2~0.3.
After the signal is decomposed, the low frequency IMF component and residual can be used to reconstruct the denoising signal: ∑ where is reconstructed signal, is the layering of high-frequency signal and low-frequency signal.
The collision of the robot is transient and abrupt, and the acceleration signal and noise in the collision process are in the high frequency range.After the collision acceleration signal is decomposed by EMD, the high frequency components of the first several layers contain have a lot of useful information.Therefore, in this paper, the signals of each layer decomposed by EMD are calculated the signal-to-noise ratio (SNR).The components with the SNR lower than the mean value are treated as high-frequency signals for further filtering, from which the effective information of the signal is extracted, and then the signal is reconstructed.The calculation formula is: where is the original signal, is the component of IMF.

High-frequency signal denoising based on wavelet threshold
In the high-frequency signal obtained by EMD, the effective signal is mixed with a lot of noise, which contains the information of acceleration sudden change at the time of collision.Therefore, it is necessary to grasp the filtering scale in the process of noise removal.Compared with Fourier transform, Wavelet transform has good local signal feature analysis ability, and has significant effect in the analysis of non-stationary signals.Wavelet threshold denoising method is based on the principle that the effective signal and noise energy are generally distributed in the low frequency and high frequency regions respectively.After the raw signal is transformed by wavelet, the wavelet coefficient and the set threshold value λ are divided, the effective signal will be set when its coefficient is greater than the threshold, and the interference signal will be set when its coefficient is less than the threshold.And then process the coefficients of the effective signal and the interference signal respectively [13].
The process of signal noise reduction is shown in Figure 2. The key parameters in wavelet threshold denoising are the threshold and the threshold function.In order to achieve better denoising effect, we select the threshold [10] dynamically determined by noise distribution, signal length and wavelet decomposition level, and its expression is: where is the threshold of layer j, is the standard deviation of noise at layer j, and N is the data length.
The threshold functions include hard threshold function and soft threshold function.The hard threshold function is discontinuous, which may cause oscillation during signal reconstruction.Although the soft threshold function remains continuous, there is a constant coefficient deviation from the original signal, which affects the accuracy of reconstruction.In addition, the above two threshold functions set the coefficient below the threshold to 0, which may cause excessive noise removal.Since the acceleration signal of the robot is subject to more interference during its operation and collision, and the useful signal still has partial distribution when it is lower than the threshold value, this paper improves the threshold function as: where , is the wavelet coefficient, ̅ , is the wavelet coefficient after threshold processing, is the threshold of layer j.When , , the effective value coefficient in the signal is larger, which means that the signal-to-noise ratio is higher, and the coefficient is not processed.When , , the coefficient value is smaller, the proportion of noise in the signal is larger.At this time, the exponential attenuation function is introduced.The coefficient decreases rapidly when it is far away from the threshold, and the attenuation speed is also related to the standard deviation of noise in this layer.When the noise standard deviation is large, the threshold is large, and the attenuation speed is slow.When the noise standard deviation is small, the threshold is small, and the attenuation speed is fast.
The improved threshold function characteristic curve is shown in Figure 3.When the absolute value of the coefficient is greater than the threshold value, the threshold function proposed in this paper will maintain the same value as the hard threshold function, and the accuracy of the soft threshold function will be improved.When the absolute value of the coefficient is less than the threshold, the processed coefficient decreases exponentially and still has a certain value near the

Signal smoothing based on sliding window filtering
After the combined filtering and noise reduction of 2.1 and 2.2, the reconstructed signal noise is significantly reduced, but the timing of the signal is not well correlated.Before and after the collision, the acceleration signal of the robot is kept in a relatively stable range.At the time of collision, the acceleration signal mutation will occur due to the drastic change of the robot speed.When the acceleration analysis of the collision process is carried out, the noise needs to be suppressed in the stable stage, and the signal needs to be tracked in time at the time of change.One of the key factors affecting sliding window filtering is the selection of window length.The long window contains more data, which can fully consider the global characteristics of data, but also lose the sensitivity to transient signals; The response performance of short window to transient signal is good, but the global characteristics of signal are lost due to the lack of time series data.When processing signals with both change and stability, if a single window length is used, its value is difficult to determine and lacks flexibility.Therefore, this paper proposes an adaptive sliding window method by dynamically adjusting the window length according to the instantaneous and timing characteristics of the signal [15].The expression is: where and represents the lower limit and upper limit of the sliding window, and is the size of the previous window and the current window, and is the mean and standard deviation of the data in the previous window, is the data at the current time, is a constant used to determine the change threshold of the sliding window, sign(•) represents the positive and negative sign, and round(•) represents the integer.When the difference between the mean value of the current signal and the previous batch of data is greater than the set threshold, it is considered that the signal has a sudden change and the window length is reduced.When the current signal is close to the average of the previous batch of data, it is considered that the data is still in a stable stage, and the window length is increased.Therefore, the window length changes with the change of signal characteristics.After determining the window length, the data in the window is processed as follows: where is the current time data after processing, and is the mean and variance of the current batch data.After sliding window filtering, the relatively stable acceleration signal is smoothed, while the abrupt acceleration signal is still retained, which makes the acceleration signal characteristics of the whole collision process more prominent.

Simulation of impulse signal based on MATLAB
In order to verify the effect of the acceleration combined denoising method proposed in this paper, the impulse signal is generated by MATLAB and processed by the 10-order Butterworth filter to simulate the acceleration signal mutation as the raw signal [11].The Butterworth filter cut-off frequency is 100Hz, and the sampling frequency is 1kHz (shown in Figure 4).Gaussian noise is added to the original signal to generate noisy signal as the signal to be processed (shown in Figure 5).EMD denoising method, combined denoising method based on hard threshold function, combined denoising method based on soft threshold function, combined denoising method based on threshold function proposed in Literature [13], and our denoising method are used to processing respectively.The wavelet basis function is uniformly sym6, and the number of decomposition layers is 3.The signal-tonoise ratio (SNR) and root mean square error (RMSE) of the processed signal are used to evaluate the noise reduction effect of the algorithm.If the SNR is greater and the RMSE is smaller, the noise reduction energy of the algorithm is stronger.The expressions of SNR and RMSE are [14]: is the raw signal, is the signal after denoising, and is the length of the time domain signal.
Table 1 shows the SNR and RMSE of the denoised signals of each algorithm.Compared with the EMD method, the SNR after the combined denoising method is significantly improved, and the RMSE is significantly decreased, so the combined denoising method is better.Compared with the combined denoising methods of four different threshold functions, our method has significantly improved performance compared with the hard threshold function and soft threshold function methods, and is better than the threshold function method proposed in Literature [13].Compared with the threshold function method proposed in Literature [13], the threshold function proposed in this paper does not require additional adjustment of super parameters, and has better adaptability.The effect of the combined denoising method proposed in this paper is shown in Figure 6.Compared with the raw signal, the noisy signal and the filtered signal, our method can effectively remove the noise while preserving the peak and detail trend of the signal.

Robot collision simulation based on Gazebo
In order to verify the effectiveness of the combined denoising method proposed in this paper in the acceleration signal processing of the robot collision process, the robot collision simulation is carried out in Gazebo to obtain the acceleration signal of the collision process.Gazebo is a robot simulation software.Users can build robot models, environment models, sensor models, and actuator models as needed in the workspace [16].It can simulate the real physical characteristics of robots and environments.Gazebo has been widely used in robot research because of its good compatibility with ROS.
A simplified model of two-wheel differential mobile robot was constructed in the experiment, with wheel track L=0.4m, wheel diameter D=0.15m and friction coefficient μ= 0.3, the vehicle body is a rectangular rigid body of 0.5x0.3x0.2m, and the overall weight of the robot is 16kg.An IMU sensor is added at the center of the robot body to measure the acceleration and angular velocity.The sensor data acquisition frequency is 100Hz, and two-wheel differential motion actuators are added to publish the position and velocity information of the robot at 100Hz.The collision object is a 2x1.5x1m rectangular rigid body with a weight of 500kg, which is fixed on the floor.In the experiment, the control robot accelerates from the static state to the speed of 1 m/s and collides with the object in the center.After the contact collision, the control speed of 1 m/s is continuously issued for not less than 5 seconds, and then the stop speed of 0 m/s is issued, and the IMU sensor information of the whole process is recorded.Since the robot only moves along the direction of the body, the linear acceleration in the direction of IMU is used as the acceleration information of the robot collision process for analysis.
Figure 7 shows the speed information of the robot collision process.In combination with the acceleration signal of the robot collision process shown in Figure 8, the acceleration signal of the robot is relatively stable when there is no collision, and there is certain high-frequency noise.During the collision, due to the reaction force exerted by the collision object, the acceleration signal has a maximum value, and then attenuates.At this time, the control speed is still 1m/s, so the robot continues to collide and contact, However, the contact force is greatly reduced compared with the first collision, and the acceleration signal continues to oscillate.After receiving the stop speed, the acceleration value returns to 0. The velocity information of the robot collision process feedback in Figure 7 is consistent with the acceleration signal.As shown in Figure 9, after the combined denoising method proposed in this paper, the acceleration mutation signal is completely retained, while the vibration signal noise after smooth motion and collision is significantly reduced, and the acceleration change process of the robot is highlighted.2. It can be seen from Table 2 that the SNR of our method is significantly increased and RMSE is significantly decreased compared with the other four methods.The experimental result can indicate that the method in this paper has better performance under strong interference signals.

Conclusions
This paper aims at the problem that the acceleration information of robot is greatly affected by strong noise during collision.A combined denoising method is proposed, which comprehensively uses EMD, wavelet threshold method and sliding window method to carry out multi-level denoising for the signal.An adaptive and dynamic adjustment wavelet threshold function is proposed to enable the filter to extract effective signals from signal-to-noise aliasing.A dynamic adjustment strategy of sliding window length is designed to smooth the whole process signal while preserving the abrupt acceleration value.According to the impulse signal simulation experiment and robot collision simulation experiment, the results show that this method has better noise reduction effect than other methods.It can provide better conditions for the research of robot collision safety based on acceleration.

Figure 1 .
Figure 1.The flow of combined denoising method.

Figure 2 .
Figure 2. The flow of wavelet threshold denoising method.
threshold.Comparison | | 2 and | | 3 , the attenuation rate is slower and more effective information is extracted when | | 2.

Figure 7 .
Figure 7. Velocity of the robot collision process.

Figure 8 .
Figure 8. Acceleration of the robot collision process.

Figure 9 .
Figure 9. Denoising results of acceleration.Similar to 3.1, five methods are used to process the acceleration signal, and the results are shown in Table2.It can be seen from Table2that the SNR of our method is significantly increased and RMSE is significantly decreased compared with the other four methods.The experimental result can indicate that the method in this paper has better performance under strong interference signals.

Table 1 .
Denoising results of impulse signal by different algorithms.

Table 2 .
Denoising results of collision acceleration signal by different algorithms.