Research Article
An enhanced anti-disturbance guidance scheme for powered descent phase of Mars landing under actuator fault
International Journal of Advanced Robotic Systems January-February 2018: 1–9 ª The Author(s) 2018 DOI: 10.1177/1729881418759889 journals.sagepub.com/home/arx
Jianwei Xu1, Jianzhong Qiao1,2 and Lei Guo1,2
Abstract As a class of autonomous deep-space exploration robots, Mars lander is simultaneously affected by wind disturbance and actuator fault, which hinders precise landing on Mars. In this article, we propose a composite guidance approach by combining disturbance observer and iterative learning observer together. The Mars wind disturbance is dealt by the disturbance observer providing wind estimation which is rejected through feed-forward channel. Meanwhile, the iterative learning observer is used to estimate the deficiency of actuators. The proposed guidance scheme ensures not only the precision but also the reliability of the Mars guidance system. The stability of the closed-loop system is analyzed. Simulations made in different situations demonstrate the performance of the proposed approach. Keywords Powered descent phase, precise landing on Mars, iterative learning observer, disturbance observer, enhanced anti-disturbance guidance Date received: 5 July 2017; accepted: 22 January 2018 Topic: Special Issue—Intelligent Control Methods in Advanced Robotics and Automation Topic Editor: Andrey V Savkin Associate Editor: Junzhi Yu
Introduction Powered descent phase is the final regulation phase in Mars landing tasks.1,2 Unfortunately, landers will inevitably face Mars wind disturbance, which may result in far range away from the prespecified landing point, sometimes it even causes a crush into the ground.3–5 Besides, the Mars landing mission needs to endure a long stage including launching from the earth, in-orbit flying, and landing. Therefore, landers will probably occur fault which leads to the safety problem of landers.6,7 Reviewing the past 46 Mars exploration missions since 1960, only eight landing missions were successfully achieved due to the strong impact of disturbance and fault during the Mars landing process.8,9 Overall, improving the precision and reliability of Mars landers is a key issue that needs to be addressed.
Considering dynamics and constraints of the spacecraft guidance system, Apollo guidance approach gives a comprehensive reference trajectory satisfying mission requirements. A simple guidance framework is then set up to cancel the tracking error preserving the nominal performance. With the advantage of low calculation cost and
1
School of Automation Science and Electrical Engineering, Beihang University, Beijing, China 2 Beijing Advanced Innovation Center for Big Data-based Precision Medicine, Beihang University, Beijing, China Corresponding authors: Jianzhong Qiao and Lei Guo, School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, 100191, Beijing, China. Emails:
[email protected];
[email protected]
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage).
2 parameters preassigned, the guidance technique of Apollo has been successfully applied in Lunar and Mars space exploration missions since 1970s.10–12 Gradually, based on the Apollo method and its extension, a great deal of attention has been focused on the guidance problem using zero-effort-miss/zero-effort-velocity theory, optimal nonlinear feedback guidance algorithm, and sliding mode guidance approach during Mars landing process. 13–17 Nevertheless, most studies ignore the effect of disturbances or just regard the disturbance as a norm bounded vector. Abandoning the prior information or not using measurable signals will bring great conservativeness to the system. Consequently, landers may consume extra energy when coming into unexpected disturbances during the landing process. Recently, anti-disturbance control theory is widely applied due to its advantage of achieving a better performance by fully making use of attainable disturbance information.18–21 The essential virtue of the anti-disturbance control has been introduced into the Mars landing problem to improve the anti-disturbance performance of landing system.22,23 Although guidance command is calculated to improve the precision of landers, unresolved actuator fault or deficiency issues still limit the ability of safely delivering the Mars lander to the prescribed landing point. Until now, some effective active and passive tolerant control methods have been provided to solve fault problems like partial loss of actuator effectiveness, saturation constraints, control allocation, and controller degradation.24–29 Recently, intelligent methods including adaptive-proportional integral derivative (PID) control, fuzzy control, and iterative learning observer (ILO)-based control have gradually come into attention.30–33 Benefiting from its “smart” construction, intelligent methods achieve a desirable performance of ensuring the reliability of spacecraft. However, when disturbance and fault coexist, it is not enough to just handle one aspect of the problem by using traditional methods. Meanwhile, few literatures consider the additive wind disturbance and multiplicative actuator fault problem on Mars precision landing. Motivated by this problem, a novel anti-disturbance guidance method integrating disturbance observer (DO) with ILO is proposed to simultaneously improve the landing accuracy and ensure the performance of reliability. The main contributions of this article can be summarized as follows: (1) the powered descent guidance model has been established, considering the concurrence of wind disturbance and actuator fault problem; (2) compensating the effect of wind disturbance and autonomously healing actuators fault, DO and ILO are combined to achieve a high precision and safe landing; and (3) the closed-loop landing guidance system has been analyzed to guarantee the stability of the proposed approach. This article is organized as follows. In the “Problem description” section, the guidance system model is given and the problem is formulated. In the “Composite guidance scheme
International Journal of Advanced Robotic Systems design” section, ILO is designed under disturbance affecting to deal with the time-varying actuators inefficiency; DO is constructed for the purpose of rejecting the effect of Mars wind; the Apollo-based guidance law combining the estimation of ILO and DO is then described. The closed-loop system stability is analyzed in the “Stability analysis” section. In the “Illustrative examples” section, the proposed approach is simulated on Mars lander guidance system and, in addition, comparisons are made between different situations. Finally, the “Conclusion” section gives a total conclusion to this article.
Problem description Consider the following Mars lander system during powered descent phase r_L ¼ vL ð1Þ v_L ¼ f 1 ðvL ðtÞ; tÞ þ H 0 ðua þ dðtÞÞ where rL 2 R 3 and vL 2 R 3 represent lander’s positions and velocities, respectively, H 0 2 R 33 is given system matrix, ua 2 R 3 is the control input, dðtÞ 2 R 3 is the disturbance acceleration from Mars wind,3–5,22 and f1 ðvL ðtÞ; tÞ is nonlinear function corresponding to the Mars angle rotating velocity which is supposed to be known and satisfies bounded condition described in Assumption A.1. Here, f 1 ðvL ðtÞ; tÞ ¼ 2o vL þ o o rL þ gðrL Þ, where o denotes the rotation angular velocity of the Mars, vL and rL denote the velocity and position of the Mars lander, respectively, and gðvL Þ denotes the gravity vector. Assumption A.1. For any vL 2 R 3 , nonlinear function f 1 ðvL ðtÞ; tÞ satisfies jjf1 ðvL ðt 1 Þ; t 1 Þ f 1 ðvL ðt 2 Þ; t2 Þjj jjU1 ðvL ðt1 Þ vL ðt 2 ÞÞjj ð2Þ where U1 is given constant weighting matrix. The lander guidance system is fully operated in the condition that all actuators perform well. However, considering long-time flying and fiercely conflicting with atmosphere, actuators usually work with loss of effectiveness, representing by constant or time-varying loss of the command signal. FðtÞ 2 R 3 3 is adopted to represent the deficiency of each actuator. It needs to be pointed out that 0 < FðtÞ 1 not including actuators totally broken issue. Then the actual input signal can be described as ua ¼ FðtÞu
ð3Þ
The control input considered here also has its saturation action ability, representing by juj u max . Here, the unknown disturbance dðtÞ has to be noticed. Considering the collected information of Mars surface, the Mars wind is a crucial affecting factor during the powered descent phase. Here, the wind disturbance is supposed to be generated by an external generated system. Then the formulation below is adopted22
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Figure 1. Composite guidance scheme structure.
_ ¼ WwðtÞ wðtÞ dðtÞ ¼ VwðtÞ
ð4Þ
where wðtÞ 2 R 2 is the disturbance state and W 2 R 2 2 and V 2 R 3 2 are given known matrices. Because of the unknown initial values of equation (4), the disturbance is unpredictable to the guidance system. Then converting equation (1) into state-space representation with equation (3), we can get _ ¼ AxðtÞ þ Bf 1 ðx; tÞ þ HðFðtÞu þ dðtÞÞ xðtÞ ð5Þ 0 1 0 where xðtÞ ¼ ½ rL vL T , A ¼ , B¼ , and 0 0 1 0 H¼ . H0 Remark 1. Different from the previous works,22,33 there are both additive modeled uncertainty dðtÞ and multiplicative one FðtÞ in the established model. Therefore, traditional approaches give single consideration to either additive term or multiplicative variable, which is not suitable for the wind disturbance and actuators fault coexisting problem.
Composite guidance scheme design The purpose of the proposed composite guidance scheme is to simultaneously compensate the loss of the efficiency in actuators and cancel the effect of the wind disturbance. The composite guidance scheme contains two layers: The inner layer includes the DO estimating wind disturbance, ILO estimating loss of the efficiency, and the compensator in the feed-forward path; the outer layer includes the nominal guidance method with disturbance attenuation and precision requirement. The structure of the composite guidance scheme is shown in Figure 1. It needs to be pointed out that the minus sign in Figure 1 represents that the composite guidance scheme simultaneously rejects wind disturbance and compensates the loss of actuators in the feed-forward path. Therefore, both the ILO and the DO are designed at
the same time. The ILO is first introduced followed by the DO. During powered descent phase of Mars landing, engine propelling is the major power whose precision directly decides the flight performance of landers. Because of the iterative updating law, the ILO costs less online computing power than other algorithms, which makes it a potential technique of engineering application prospect.34 The objective of ILO design is to improve the reliability of guidance system by estimating the deficiency value of actuators which can be reconstructed by its estimation into dynamic equations. At first, for calculation convenience, a transition can be made as follows31 FðtÞu ¼ FðtÞ
ð6Þ
where ¼ diagðu1 ; u 2 ; . . . ; un Þ and F ¼ ½p1 ; p2 ; . . . ; pn T (n ¼ 3). The ILO is constructed as ^ x; tÞ þ H FðtÞ x^_ðtÞ ¼ A^ xðtÞ þ Bf 1 ð^ ^ Gð^ þ HV wðtÞ xðtÞ xðtÞÞ ^ ^ ¼ g 1 Fðt tÞ þ g 2 ð^ FðtÞ xðtÞ xðtÞÞ
ð7Þ
^ and wðtÞ and wðtÞ, ^ are the estimations of FðtÞ where FðtÞ ^ is called the ILO input, t is the sampling respectively, FðtÞ time, G is a positive-definite observer gain matrix, and g 1 and g 2 are positive gains. The observer updates the fault estimation value to achieve accurately estimation by iterating the state estimated error and previous fault information. The state estimation error ex ðtÞ ¼ xðtÞ x^ðtÞ is defined and actuator defi^ FðtÞ ciency value estimation error is defined as eFðtÞ ¼ FðtÞ to later evaluate the performance of ILO, then ^ tÞ g ð^ g 1 Fðt eFðtÞ ¼ FðtÞ 2 xðtÞ xðtÞÞ tÞ þ FðtÞ ¼ g 1 eFðt tÞ þ g 2 ex ðtÞ þ g 1 Fðt ð8Þ
4
International Journal of Advanced Robotic Systems The derivative of state estimation error can be also obtained _ x^_ðtÞ e_x ðtÞ ¼ xðtÞ ¼ ðA GÞex ðtÞ þ H eFðtÞ þ HVew ðtÞ þ Bð f1 ðx; tÞ f 1 ð^ x; tÞÞ
ð9Þ u¼
33
the estimation of deficiency value ^ 1:5 which is guar FðtÞ is between the interval 0 < FðtÞ anteed by amplitude restriction function. Here, we do not consider the situation that actuator is totally broken, which ^ ¼ 0 represents. FðtÞ Followed by dealing with actuators fault, the wind disturbance is then handled through DO methodology. According to the wind disturbance modeled as equation (4), the DO can be constructed as ( ^_ ¼ W wðtÞ ^ þ LHV ðwðtÞ wðtÞÞ ^ wðtÞ ð10Þ ^ ^ dðtÞ ¼ V wðtÞ As in Zhang et al.,
disturbance estimation into the Apollo guidance law. The reference trajectory is not designed in this article using nominal condition curve instead. Therefore, the total guidance law applied to the system is given by
where L 2 R 2 6 is the DO gain to be calculated. In order to ensure all states can be obtained, we use ^ LxðtÞ, then the realized form is given as qðtÞ ¼ wðtÞ _ ¼ ðW LHV ÞðqðtÞ þ LxðtÞÞ qðtÞ ^ þ L AxðtÞ Bf 1 ðx; tÞ H FðtÞ
ð11Þ
For the purpose of proving estimated value can track actual disturbance, the estimation error is defined as ^ Similar to the ILO, the performance of DO ew ¼ w w. has to consider the effect of actuators fault. Therefore, the derivative is deduced as
ð13Þ
Substituting equation (12) into equation (4), we have _ ¼ AxðtÞ þ Bf 1 ðx; tÞ þ HðKxðtÞ þ Vew ðtÞ þ eF ðtÞuÞ xðtÞ ð14Þ Considering the entire system equation (14) with ILO estimation error equation (8), state estimation error equation (9), and DO estimation error equation (12), the state can converge to a small set containing the origin by the analysis in the following section.
Stability analysis The stability of the guidance system under the proposed composite scheme is guaranteed by Theorem 1, which is described as follows. Theorem 1. Consider system equation (14) together with equations (9) and (12), if there exists positive matrices P > 0, Q > 0, M, N , and R > 0 satisfying 2 3 Y1 0 PHV 6 7 ð15Þ 4 Y2 QHV 5 < 0
Y3
where
_ wðtÞ ^_ e_w ðtÞ ¼ wðtÞ _ þ LxðtÞÞ _ ¼ WwðtÞ ðqðtÞ
Y1 ¼ PA þ AT P þ PBBT P þ U 1 T U1 þ M
¼ WwðtÞ ½ðW LHV ÞðqðtÞ þ LxðtÞÞ ^ þ ½LðAxðtÞ Bf ðx; tÞ H FðtÞÞ
þ M T þ PHH T P Y2 ¼ QðA GÞ þ ðA GÞT Q þ QBBT Q þ U 2 T U2 þ QHH T Q
1
þ HVwÞ þ LðAxðtÞ þ Bf 1 ðx; tÞ þ H FðtÞ ¼ WwðtÞ ½ðW LHV ÞðqðtÞ þ LxðtÞÞ þ LH eFðtÞ þ LHVw ¼ ðW LHV Þew ðtÞ LH eFðtÞ
1 ^ KxðtÞ dðtÞ ^ FðtÞ
Y 3 ¼ RW NV þ W T R V T N T þ NN T ð12Þ
Remark 2. Different from previous studies,33,34 the ILO equation (7) is constructed together with wind disturbance estimation provided by the DO due to the direct effect of wind disturbance. The import of disturbance estimation reduces the conservation of traditional ILOs. Similarly, the DO equation (11) takes actuators fault estimation into account which is different from the DO utilized by Guo and Wen21. The combination of ILO and DO simultaneously causes coupling problem of estimation performance, which is analyzed in the following section. Finally, the composite guidance scheme is designed by infusing the reconstructed information of fault and
then the closed-loop system with gain LH ¼ R1 N and HK ¼ P1 M such that equation (14) together with equations (8), (9), and (12) is bounded stable. Proof. We choose a Lyapunov function as V ¼ V1 þ V2 þ V3 þ V4
ð16Þ
where T
V 1 ¼ xðtÞ PxðtÞ þ
ðt h
i jjU1 xðtÞjj 2 jjf 1 ðx; tÞjj 2 dt
0 T
V 2 ¼ ex ðtÞ Qex ðtÞ þ
ðt
jjU 2 ex ðtÞjj 2
0
jjf 1 ðx; tÞ f 1 ð^ x; tÞjj 2 dt
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5 Table 1. Mars lander initial and terminal simulation parameters.
V 3 ¼ ew ðtÞT Rew ðtÞ ðt V4 ¼ eFðsÞT eFðsÞds
Parameter
tt
According to equations (8), (12), and (14), the derivative of equation (13) can be deduced as follows V_ ðtÞ ¼ 2xðtÞT P½AxðtÞ þ Bf1 ðx; tÞ þ HðKxðtÞ þ Vew ðtÞ þ eF ðtÞuÞ
rx (m) ry (m) rz (m) vx (m/s) vy (m/s) vz (m/s)
Initial value
Final value
100 150 1100 40 20 50
0 0 0 0 0 0
x; tÞÞ þ H eFðtÞ þ 2ex ðtÞT Q½ðA GÞex þ Bðf1 ðx; tÞ f1 ð^ þ HVew þ ew ðtÞT R½ðW LHV Þew LH eFðtÞ T
T
T
T
þ eFðtÞ eFðtÞ eFðt tÞ eFðt tÞ þ xðtÞ U 1 U1 xðtÞ jjf 1 ðx; tÞjj2 þ ex ðtÞT U2 T U 2 ex ðtÞ jjf1 ðx; tÞ f1 ð^ x; tÞjj 2
ð17Þ let EF ðtÞu ¼ s, then we can show that V_ ðtÞ ¼ xðtÞT ðPA þ AT P þ PBBT P þ U 1 T U 1 þ PHK þ K T H T P þ PHH T PÞxðtÞ þ 2xðtÞT PHVew ðtÞ þ ex ðtÞT ðQðA GÞ þ ðA GÞT Q þ QBBT Q þ U 2 T U 2 Þex ðtÞ þ 2ex ðtÞT QH eFðtÞ þ 2ex ðtÞT QHVew ðtÞ þ 2ew ðtÞT RðW LHV Þew ðtÞ 2ew ðtÞT RLH eFðtÞ þ eFðtÞT eFðtÞ eFðt tÞT eFðt tÞ þ jjsjj2
ð18Þ Let u max represents the max value of control input, then we can have V_ ðtÞ xðtÞT ðPA þ AT P þ PBBT P þ U 1 T U 1 þ PHK þ K T H T P þ PHH T PÞxðtÞ þ xðtÞT ðPHV þ V T H T PÞew ðtÞ þ ex ðtÞT ðQðA GÞ þ ðA GÞT Q þ QBBT Q þ U 2 T U 2 þ QHH T QÞex ðtÞ þ ex ðtÞT ðQHV þ V T H T QÞew ðtÞ ew ðtÞT ðRðW LHV Þ þ ðW LHV ÞT R þ RLHH T LT RÞew ðtÞ þ ð1 þ 2u 2 max ÞeFðtÞT eFðtÞ eFðt tÞT eFðt tÞ þ jjsjj2 3T 2 3 32 2 xðtÞ xðtÞ Y1 0 PHV 7 6 7 76 6 7 6 7 76 ¼6 4 ex ðtÞ 5 4 Y2 QHV 54 ex ðtÞ 5 þ d ew ðtÞ Y3 ew ðtÞ
ð19Þ where d ¼ ð1 þ 2u 2 max ÞeFðtÞT eFðtÞ eFðt tÞT eFðt tÞ þ jjsjj2
^ both and FðtÞ It can be seen that eFðtÞ is bounded as FðtÞ varying inside ð0; 1, so does eFðt tÞ. According to preceding contents, s is also norm bounded. By introducing equation (15), the conclusion is formulated. Then the proof is completed.
Illustrative examples In this article, the powered descent guidance model used in the simulations is similar to those in other studies16,35 and is
representative of the Mars Science Laboratory lander. The simulation parameters adopted are shown in Table 1. The mass of Mars lander is approximately 1905 kg. The wind disturbance functioning on Mars lander is considered to be about 380–760 N and is transformed to 0.2–0.4 m/s acceleration disturbance dðtÞ in the channel of control input. The control input is constructed by eight power engines symmetrically installed around the lander with maximum propelling of 3000 N for each power engine, which representing by u max ¼ 10:4 m/s2. As the lander is approaching near enough to the Mars surface, the Mars angle rotating velocity here is ignored. Due to the requirement of pinpoint soft landing, the Mars lander needs to touch the surface of Mars with the vertical velocity < 0.75 m/s. Meanwhile, under the precondition of safety, the lander is better to be sent nearer to the target point. The performance of the proposed guidance method is verified by comparing the Apollo guidance method which is already applied in the previous Mars landing missions together with Apollo guidance combined with DO (ApolloþDO) and Apollo guidance combined with ILO (ApolloþILO). Simulations are driven by different occasions that fault simultaneously occurring combined with wind disturbance cases. In simulation, the three-axis fault scenario 1 0 s t < 30 s Fx ðtÞ ¼ 0:6 30 s t 120 s 8 1 0 s t < 30 s; 60 s t < 70 s > > > > > 0:8 30 s t < 50 s > < Fy ðtÞ ¼ 08 þ 02 sinð01tÞ 50 s t < 60 s > > > signalðtÞ 70 s t < 100 s > > > : 0:8 100 s t 120 s 8 1 0 s t < 35 s > < Fz ðtÞ ¼ 0:7 35 s t < 50 s > : 09 þ 01 sinð01tÞ 50 s t < 120 s is introduced to the power engine propelling and the signalðtÞ is an aperiodic signal. G ¼ 250I3 , g 1 ¼ 1, and g 2 ¼ 20 are parameters for the iterative observer equation (7) 8:12 10:43 10:68 13:78 15:32 16:43 L¼ 8:08 10:60 11:36 14:60 14:53 15:60 ð20Þ
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International Journal of Advanced Robotic Systems
Figure 2. Deficiency histories for different methods.
2
0:17
6 K¼4 0 0
2:80
0
0
0
0 0
0:82 0
3:15 0
0 1:12
0
Figure 3. Wind disturbance histories for different methods.
affected. Figure 3 shows the wind disturbance estimation performance is also inaccurate by just using DO.
3
7 0 5 5:23
ð21Þ
The DO and controller gains are using parameters in equations (20) and (21). Figure 2 shows the fault estimation in ApolloþILO and proposed method. It can easily be seen that without the function of DO, the fault estimation has been
Remark 3. The simulation result in Figure 3 indicates that the performance of single observer approach is worse than that of the baseline Apollo guidance method. The reason is that the estimation is bigger than the actual disturbance, which causes a heavier damage to the system. Figure 4 shows the height and the vertical velocity of the lander under. As can be seen from the pink line, as the fault
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Figure 6. Y-axis position histories for different methods. Table 2. The terminal precision (rz ¼ 0 m) of Mars lander using different methods with the condition. Apollo ApolloþDO ApolloþILO ApolloþILOþDO rx (m) ry (m) vx (m/s) vy (m/s) vz (m/s)
35.3 37.5 40 20 1.9
22.0 22.6 2.1 1.8 8.9
36.1 40.2 0.8 0.7 1.9
0.1 0.2 0.0 0.1 0.0
DO: disturbance observer; ILO: iterative learning observer.
Figure 4. Z-axis position and velocity histories for different methods.
case 1, using the Apollo guidance method the lander touches surface at t 1 and the velocity is > 0.75 m/s which is not satisfying the requirement of pinpoint soft landing. Horizontal position and velocity of lander are shown in Figures 5 and 6. It also can be seen that the final position is not satisfiable. The final precision of different methods is demonstrated in Table. 2; it can be seen that the proposed guidance scheme is effectiveness dealing with wind disturbance and loss of efficiency. The sign of parameters here is set to be negative according to the landing descent mission as height and velocity are decreasing.
Conclusion
Figure 5. X-axis position histories for different methods.
estimation is bigger than actual fault value, the lander gives less propulsion than it actually requires, which leads to an early touch with high velocity. Similarly, the lander cannot satisfy the demand for touching the Mars surface. As can be seen from Figure 2(a) that, under
This article has proposed a novel composite guidance method for powered decent phase of precise landing on Mars subject to wind disturbance and deficiency of actuators. The adoption of the learning mechanism promotes the ILO dealing with multiplicative time-varying fault formations more than constant ones. The DO is utilized to estimate and reject the additive influence of the wind disturbance. The combination of two techniques provides the solution to resolve disturbance term and actuators fault coexisting problem. The results show that with the proposed method, the guidance system can achieve a better performance against the disturbance and time-varying
8 actuator faults. The technique developed in this article has the potential to be an intelligent (learning ability) guidance method for future high-precision and highreliability Mars lander. Declaration of conflicting interests
International Journal of Advanced Robotic Systems
11.
12.
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. 13.
Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (grant numbers 61627810, 61320106010, 61633003, 61661136007 and 61603021), the Program for Changjiang Scholars and Innovative Research Team (grant number IRT 16R03) and Innovative Research Team of National Natural Science Foundation of China (grant number 61421063).
14.
15.
16.
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