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Abstract

Differing from the commonly used spring loaded inverted pendulum model, this paper makes use of a two-mass spring model considering impact between the foot and ground which is closer to the real hopping robot. The height of upper mass which includes the upper leg and body is the main control objective. Then we develop a new kind of control algorithm acting on two levels: The upper level aims to achieve the desired velocity of the upper mass based on a stable limit cycle, where three different controllers are used to regulate the limit cycle; the target of the lower level is to drive the system to converge to the desired state and control the contact force between the foot and ground within an appropriate range based on the inner force control at the same time. Simulation results presented in this paper confirm the efficiency of this control algorithm.

Keywords

Two-mass hopping robot height control stable limit cycle force control

Introduction

The earliest complete research on a hopping robot can be traced back to 1980s when Raibert developed several hopping robot prototypes with his co-workers.¹ His hopping robot had a body hinged by one springy leg on which he experimentally realized a hopping gait including height control, forward velocity control and attitude control. Actually, he used a simple method to control the hopping height by delivering a fixed thrust to the leg. Though he declared the hopping height is monotonic to the thrust, the value and duration of the thrust were determined empirically. Saranli et al.² introduced the spring loaded inverted pendulum (SLIP) model, and demonstrated its equivalence to a more complex leg with hip, knee, and ankle. In spite of its simplicity, the SLIP model is still priceless in revealing the mechanism and dynamics of animal running.

The SLIP model attracts many scholars to study it because it can imply some specific high-level control hypotheses on the coordination between the joints and limbs of animal that produces perfect locomotion. M. Ahmadi et al. presented experimental implementation of an energy efficient “controlled passive dynamic running” strategy on a planar one-legged running robot “ARL monopod II” based on a SLIP model.³ This controller could reach a high energy coefficient of utilization. Later he demonstrated the stability of the limit cycle in the hopping robot.⁴ Akihiro Sato designed an experimental, planar, hopping robot platform based on SLIP model features and implemented a conceptual controller that reproduced the self-stability of the SLIP model.⁵ Ioannis Poulakakis et al. investigated the hybrid zero dynamic of a hopper with an asymmetric centre of mass and achieved the ASLIP (asymmetric spring loaded inverted Pendulum) model.⁶ It can stand for most kinds of robots in a hopping motion, thus the ASLIP model tends to possess some universal properties to some extent.

Although the SLIP model is simple and easy to analyse, it does not take the unsprung mass on the bottom of the leg into consideration and neglects the impact between the foot and the ground. To obtain more accurate dynamics of the hopping robot it is essential to take the lower leg into account. Y. Saitou et al. proposed a two-mass system and controlled the height of the hopping robot according to the optimal control method.⁷ Ishikawa et al. controlled the apex jumping height of a two-mass system by using a port-controlled Hamiltonian method in view of the system energy.⁸ In spite of taking the lower leg into consideration, they did not think about the impact between the leg and ground. Frank B. Mathis also used the two-mass model to describe a hopping robot,⁹ and modelled the impact instant alone. He designed a continuous controller and a discrete controller for the apex height control, but he did not control the impact force directly so that there was a relatively giant force.

In this paper we model a one-legged hopping robot as a tow-mass system, and model the ground as a springy damping system so that the contact force between the lower leg and the ground changes continuously in a very short time interval rather than changing instantly. What is more important is that we can make use of the interval to control the contact force tracing desired value. Next we use a kind of linear control method to drive the closed-loop system to converge to a stable limit cycle corresponding to a certain apex height of the upper leg. In Section ‘Model of the two-mass hopping robot’ we present the model of a two-mass hopping robot and its dynamical equations including the contact phase and flight phase. In Section ‘Control of the apex height of the upper leg’ we propose a kind of control algorithm based on the inner force loop in contact phase and a simple PD controller in flight phase. In Section ‘Stable limit cycle of the closed loop system’ we analyse the closed-loop system dynamics and the limit cycle of the closed-loop system, then present a simple but efficient controller. We show the simulation results in Section ‘Simulation’ to demonstrate its efficiency of the algorithm. At the end of the paper, there is some discussion in the last section.

Model of the two-mass hopping robot

As shown in Figure 1(a), the system includes two components whose masses are denoted by m₁ and m₂ respectively. m₁ means the upper leg actually including the upper leg and the body, while m₂ means the lower leg. Assuming that the coordinate of the ground in the vertical direction is zero, x₁ and x₂ represent the position of the COM (centre of mass) of the upper leg and the lower leg respectively. The position of the first mass relative to the second mass is $Δ x = x_{1} - x_{2}$ . The ground is modelled as a springy damping system, in which K means the elasticity coefficient, b means the viscous damping coefficient and the friction force in the normal direction is neglected. F_e is the contact force between the lower leg and ground, and its expression is $F_{e} = - K x_{2} - b {\dot{x}}_{2}$ , in which ${\dot{x}}_{2}$ means velocity of the lower leg. F is the only actuating force imposed by actuators such as electric motors, pneumatic actuators or hydraulic actuators which could change energy of the whole system. The leg expands when F > 0, while it shrinks when F < 0. On the basis of the model we can achieve the dynamics of the system divided into two parts just as follows.

Figure 1.

(a) The schematic diagram of the two-mass model, (b) forces acting on the masses.

Flight Phase

When the system stays in flight phase as shown in the right side of Figure 1(b), it is not in contact with the ground. F acts as the internal force and the motion of the COM of the whole system is affected only by gravity, meanwhile the contact force $F_{e} = 0$ . The dynamical equation is as follows

{\begin{matrix} m_{1} {\ddot{x}}_{1} = F - m_{1} g \\ m_{2} {\ddot{x}}_{2} = - F - m_{2} g \end{matrix}, x_{2} > 0

where g means gravity acceleration. The variables x₁ and x₂ are difficult to measure, while the relative position of the two masses is easier to measure in this phase, so that Δx is the key variable. Controlling Δx to converge to a desired value, for example a constant value, is what we will do in flight phase in fact. The dynamical equation about Δx can be concluded from equation (1)

Δ \ddot{x} = \frac{F}{m_{1}} + \frac{F}{m_{2}} - 2 g

Stance phase

Stance phase means the stage in which the second mass m₂ is in contact with the ground as shown in the left side of Figure 1(b). The contact force $F_{e} \neq 0$ , while the actuating force F and the contact force F_e acts on the lower leg at the same time. The dynamical equation is as follows

{\begin{matrix} m_{1} {\ddot{x}}_{1} = F - m_{1} g \\ m_{2} {\ddot{x}}_{2} = F_{e} - F - m_{2} g \\ F_{e} = - K x_{2} - b {\dot{x}}_{2} \end{matrix}

because in stance phase it is difficult to measure position and velocity of the second mass m₂, moreover the value of x₂ and ${\dot{x}}_{2}$ would be little enough to neglect under the condition that the elasticity coefficient is large enough. The value of the contact force F_e as feedback is actually measured by the force sensor equipped on the foot instead of being calculated according to the equation. On the other hand, $m_{2} < 0.1 m_{1}$ in our model. Thus we need not take x₂ and ${\dot{x}}_{2}$ into consideration when calculating the energy of the whole system in stance phase. So we put a reasonable assumption that $x_{2} = 0$ on the energy calculation in the stance phase. The length between the two masses and the position of the first mass is equal in stance phase according to the above assumption, that is to say $Δ x = x_{1}$ . Actually, what really attracts us in the stance phase is the state of the upper leg $(x_{1}, {\dot{x}}_{1})$ . If the length between the two masses is controlled to keep a constant value in the flight phase, the velocity of the two masses must be identical. So we can derive in terms of the system energy just as follows

(m_{1} + m_{2}) g h - m_{2} g Δ x = \frac{1}{2} m_{1} {\dot{x}}_{1 l o}^{2} + m_{1} g h_{l o}

where h means the apex height of the COM of the whole system, ${\dot{x}}_{1 l o}$ means the initial velocity of the upper leg in flight phase, and $h_{l o}$ means the initial height of the upper leg. In addition, we have

{\begin{matrix} h = \frac{m_{1} h_{1} + m_{2} h_{2}}{m_{1} + m_{2}} \\ a = h_{1} - h_{2} \end{matrix}

where h₁ and h₂ mean the apex height of the upper leg and lower leg respectively before lifting off, a is a constant. It could be concluded from equations (4) and (5) that a certain $({\dot{x}}_{1 l o}, h_{l o})$ corresponds to a certain h, h₁, and h₂ respectively. Therefore the control target converts from the apex height of the upper leg to the velocity and the height of the upper leg at lift off.

Control of the apex height of the upper leg

To control the apex height of the upper leg, we still divide the controller into two parts, flight phase and contact phase. The controller is presented next.

Flight phase

In order to keep the velocity of the two masses identical, the relative position Δx should be kept constant. According to equation (2) a simple PD controller, as given below, can satisfy the requirement

F = \frac{m_{1} m_{2}}{m_{1} + m_{2}} [K_{p f} (Δ x_{d} - Δ x) - K_{d f} Δ \dot{x} + 2 g]

where $K_{p f}$ and $K_{d f}$ are the feedback gain coefficients, $Δ x_{d}$ is the desired length between the two masses, the third term is a gravity compensation. Substituting equation (6) into equation (2) we could obtain the dynamics of the closed loop system in flight phase as shown below

Δ \ddot{x} + K_{d f} Δ \dot{x} + K_{p f} (Δ x - Δ x_{d}) = 0

We can conclude from equation (7) that Δx asymptotically converges to the equilibrium $(Δ x, Δ \dot{x}) = (Δ x_{d},0)$ .

Contact phase

On the basis of the analysis in Section ‘Model of the two-mass hopping robot’, we realise that the main control target could be described as “ensure the upper leg is speeding up to the desired velocity at the desired height before lifting off”. On the other hand the contact force is another factor which needs to be considered because a lesser impact force is significant to avoid damaging the robot. In view of the above thought, a kind of control algorithm based on the inner force loop is applied in the contact phase. The structure of the controller is shown in Figure 2.

Figure 2.

The control block diagram of contact phase.

Actually, the analysis of the system dynamics in contact phase and this control algorithm were presented in our other paper and we rewrite the control law below.¹⁰ The Force Controller shown in Figure 2 is as follows

u = F_{d} + K_{F} (F_{d} - F_{e}) - K_{d F} {\dot{F}}_{e} - m_{2} g

where u is the actuating force, that is to say u = F. F_d is the desired contact force and K_F and $K_{d F}$ are the feedback gain. The position controller is as follows

F d = \frac{K_{p c} m_{1}}{m_{1} + m_{2}} (x_{1 d} - x_{1}) - \frac{K_{d c} m_{1}}{m_{1} + m_{2}} {\dot{x}}_{1} + (m_{1} + m_{2}) g

where $x_{1} d$ is the desired position of the upper leg in contact phase, $K_{p c}$ and $K_{d c}$ are feedback gain.

The control frequency of the inner force loop is about ten times of the outer position loop. When the system is well controlled, the real contact force is equal to the desired value, that is to say $F_{e} = F_{d}$ , so that we install a virtual spring and a damping oscillator between the upper leg and lower leg by controlling the actuating force F. Supplying a certain energy equal to the amount that the system needs to reach the desired apex height, subtracts the current value and loss of energy due to system damping and in addition could form an ideal spring oscillator that moves up-and-down along a stable periodic orbit. How to achieve the desired velocity and position of the upper leg and keep a stable periodic motion will be discussed in the next section.

Stable limit cycle of the closed loop system

Dynamics of the closed-form system

Flight phase dynamics of the closed-form system is presented in Section ‘Control of the apex height of the upper leg’, that is to say equation (7). When the system reaches a steady state, the dynamics of the upper leg becomes

{\ddot{x}}_{1} = - g

At the beginning of flight, the leg shrinks and the dynamics of the upper leg does not obey equation (7), but the system energy is preserved as constant once the robot lifts off, so that it could be supposed that the two masses lift off with the same velocity and a constant leg length, then the equivalent initial velocity of the upper leg is

v_{l o} = \sqrt{\frac{m_{1}}{m_{1} + m_{2}}} {\dot{x}}_{1 l o}

besides $h_{l o}$ is the initial height of the upper leg and the desired leg length in flight phase. Solving equation (11) results in flight motion

\begin{array}{l} x_{1} = h_{l o} + v_{l o} t - \frac{1}{2} g t^{2} \\ {\dot{x}}_{1} = v_{l o} - g t \end{array}

We can obtain the trajectory of the upper leg in the $(x_{1}, {\dot{x}}_{1})$ -plane as a parabolic form

{\dot{x}}_{1}^{2} + 2 g x_{1} = v_{l o}^{2} + 2 g h_{l o}

Because gravity is the only external force acting on the system, the height of the upper leg has even symmetry about the apex height h, while the velocity has odd symmetry about the highest point. Then we can conclude that the state of the upper leg at touch down is $(h_{l o}, - v_{l o})$ .

In contact phase, it is mentioned in Section ‘Control of the apex height of the upper leg’ that $F e = F d$ , then combining equations (3), (8) and (9), in addition to the COM of the system $x_{c} = m_{1} x_{1} / (m_{1} x_{1} + m_{2} x_{2})$ because of $x_{2} = 0$ , we could conclude the dynamics of the closed loop system as

{\ddot{x}}_{1} + \frac{K_{d c}}{m_{1} + m_{2}} {\dot{x}}_{1} + \frac{K_{p c}}{m_{1} + m_{2}} (x_{1} - x_{1 d}) = 0

If the system damping is compensated completely through controlling and there is no other artificial damping, that is to say $K_{d c} = 0$ , the system becomes an ideal spring oscillator, whose motion obeys periodic orbits. Based on the above assumption, equation (14) degenerates as

{\ddot{x}}_{1} + \frac{K_{p c}}{m_{1} + m_{2}} (x_{1} - x_{1 d}) = 0

The initial condition of equation (15) is $x_{1} (t_{t d}) = x_{1 d} = h_{l o}$ and ${\dot{x}}_{1} (t_{t d}) = - v_{l o}$ , in which $t_{t d}$ means the time of touching down. Solving equation (15) leads to the stance motion

\begin{matrix} x_{1} = \frac{v_{l o}}{\sqrt{A}} sin (\sqrt{A} (t - t_{t d})) + h_{l o} \\ {\dot{x}}_{1} = v_{l o} \cos (\sqrt{A} (t - t_{t d})) \end{matrix}

where $A = K_{p c} / (m_{1} + m_{2})$ . The trajectory of the upper leg on the phase plane could be derived from equation (16) so that

{(x_{1} - h_{l o})}^{2} + \frac{{\dot{x}}_{1}^{2}}{A} = \frac{v_{l o}^{2}}{A}

It is obvious that the trajectory is a set of elliptical orbits. $h_{l o}$ is constant, while a $v_{l o}$ corresponds to a certain apex height h, so that $v_{l o}$ is the only variable that determines the characteristic and shape of the elliptical orbit.

In summary, if given a desired apex height of the upper leg h or the initial velocity $v_{l o}$ when lifting off, the cycle motion of upper leg could be expressed as given below

L_{c} ≜ {\begin{matrix} {\dot{x}}_{1}^{2} + 2 g x_{1} = v_{l o}^{2} + 2 g h_{l o} & x_{1} > h_{l o} \\ {(x_{1} - h_{l o})}^{2} + \frac{{\dot{x}}_{1}^{2}}{A} = \frac{v_{l o}^{2}}{A} & x_{1} < h_{l o} \end{matrix}

Note that when $x_{1} = h_{l o}$ , the solution of the two equalities in equation (18) both are ${\dot{x}}_{1} = \pm v_{lo}$ , whose sign indicates the state is lifting off or touching down. Of course the trajectory is smooth and continuous. Figure 3 shows a few limit cycles with different desired apex heights of the upper leg.

Figure 3.

The ideal limit cycles corresponding to different lift-off velocities.

After the analysis above, we realize that the upper leg moves along periodic orbits if controlled well. The desired position of upper leg x _1d in stance phase is calculated online. How to obtain value of x _1d and switch between different limit cycles will be discussed next.

Control of limit cycle

As the upper level controller, it calculates the desired height and the velocity of the upper leg in stance phase by regulating its acceleration. We use three kinds of controller here.

Open-loop controller

This is the simplest controller, setting the acceleration as constant

{\ddot{x}}_{1} = {\begin{matrix} α g & {\dot{x}}_{1} < {\dot{x}}_{1 l o} \\ 0 & {\dot{x}}_{1} \geq {\dot{x}}_{1 l o} \end{matrix}

where α is a positive constant and ${\dot{x}}_{1 l o}$ is the desired velocity at lifting off presented in equation (4).

On the basis of equation (15), it is natural to think about adding derivation of the velocity from the desired value to regulate the acceleration. Therefore, we have proposed a simple linear controller

{\ddot{x}}_{1} = - A (x_{1} - x_{1 d}) + K_{d l} ({\dot{x}}_{1 l o} - {\dot{x}}_{1}) + a_{0}

where $K_{d l}$ is the feedback gain and a₀ is a positive constant for compensating insufficient acceleration at the beginning. This controller takes the velocity error into consideration so that it ensures asymptotic stability.

Because the linear controller has its shortcomings, such as overshoot and neglecting some internal dynamics, a kind of nonlinear controller was proposed in the literature as given below⁴

{\ddot{x}}_{1} = - A (x_{1} - x_{1 d}) - β {\dot{x}}_{1} (x_{1} - h_{l o}) ((x_{1} - h_{l o})^{2} + \frac{{\dot{x}}_{1}^{2}}{A} - \frac{x_{1 l o}^{2}}{A}) + a_{0}

where β is a positive constant and a₀ is a positive constant as well for compensating insufficient acceleration at the beginning. This controller has been proved to be asymptotically stable in which β affects the rate of convergence in the literature.

Given the acceleration that is used for shifting between different limit cycles, the desired velocity and position of the upper leg in stance phase can be obtained from the time integral in the control period.

{\dot{x}}_{1 d} ((k + 1) T) = {\dot{x}}_{1} (k T) + \int_{k T}^{(k + 1) T} {\ddot{x}}_{1} (k T) d t

\begin{array}{l} x_{1 d} ((k + 1) T) = x_{1} (k T) + \int_{k T}^{(k + 1) T} {\dot{x}}_{1} (k T) d t \\ + \iint_{k T}^{(k + 1) T} {\ddot{x}}_{1} (k T) d t \end{array}

where k is a positive integer and T means the duration of a control period.

The controller above can achieve a stable limit cycle that not only drives the upper leg to reach a constant height, but also traces a desired curve. The simulation results will be shown in next section.

Simulation

We simulated the two-level control algorithm proposed in this paper on a two-mass platform in Matlab. Simulation results of such a two-mass hopping robot confirm efficiency of this control algorithm. Some parameters of the robot are listed in Table 1. The springy coefficient and damping coefficient are identical with the values presented by Raibert in terms of the order of magnitude.¹¹ Our target is to drive the robot’s apex height, that is its velocity when lifting off, to trace a sinusoidal function. The function is described as equation (24)

{\dot{x}}_{1 l o} (t) = 2 | sin (\frac{π}{10} t) |

Table 1.

Parameters of the two-mass hopping robot.

Parameter	Value	Unit
m ₁	10	kg
m ₂	1	kg
K	10⁵	N/m
b	150	N/(m/s)

where t means simulation time. The desired relative position of the two masses in flight phase is 0.5 m. We use three kinds of controllers presented in equations (19) to (21), in which the parameters are listed in Table 2. One point that needs to be explained is that the group of controller parameters is not only non-unique, but also non-optimal. As a group of practicable parameters, it sufficiently achieves a preferable performance as the simulation results show.

Table 2.

Parameters of the three controllers.

Parameter	Value
α	1
$K_{d l}$	1/10
β	1/5
a ₀	g

Given the following parameters, the desired lift-off velocity of the upper leg presented in equation (24), the velocity calculated from equation (22) and the real velocity of the upper leg are shown in Figure 4.

Figure 4.

(a) The desired lift-off velocity of the upper leg, (b) the desired velocity and real velocity of the upper leg with three different controllers.

Accelerations obtained from equations (19) to (21) are shown in Figure 5.

Figure 5.

Accelerations obtained from three controllers.

The height of the upper leg and its deviation from the desired value are presented in Figure 6. It can be seen from Figures 4 and 6 that the robot traces the desired trajectory well with some acceptable error. Actually the algorithm proposed in this paper works well with all of the three controllers. Figure 5 shows that accelerations produced by the controllers differ from each other. As mentioned before, as a group of practicable controller parameters, it is hard to say which controller is the best one or what parameters are optimal. We just want to illustrate that all of the three controllers could acquire a relatively good performance, and that it is indicated in Figure 5 that the accelerations produced by different controllers are approximate to each other.

Figure 6.

(a) The real and desired height of upper leg, (b) the error between the real and desired height of upper leg.

Motion trajectories of the upper leg in the $(x_{1}, {\dot{x}}_{1})$ -plane using different controllers are shown in Figure 7. Because the desired height of the upper leg is not constant but a continuous changeable curve, the motion trajectory is a spiral line. Note that the upper leg touches down at about 0.55 m, because we set the COM of the lower leg is 0.05 m when it lies on the ground. While the upper leg lifts off at about 0.6 m, because we set the switch condition so that it lifts off when $x_{1} = 0.6$ m. On the other hand, the velocity of the upper leg changes suddenly when touching down, because the impact affects the system momentum as in equation (25)

$(m_{1} + m_{2}) {\dot{x}}_{1} (t_{t d}^{-}) = m_{1} {\dot{x}}_{1} (t_{t d}^{+}) + m_{2} {\dot{x}}_{2} (t_{t d}^{+}) + F_{e} δ t$ 25

Figure 7.

Upper leg motion trajectory in phase plane with (a) an open-loop controller, (b) a linear controller, (c) a nonlinear controller and (d) a SLIP model.

where

{\dot{x}}_{1} (t_{t d}^{-})

is the velocity of the upper leg at the time before touching down while

{\dot{x}}_{1} (t_{t d}^{+})

means the velocity of the upper leg after touching down,

{\dot{x}}_{2} (t_{t d}^{+})

means the velocity of the lower leg after touching down and δt is the duration of the impact.

{\dot{x}}_{2} (t_{t d}^{+})

decreases close to zero in δt. Though it is difficult to estimate or measure F_e and δt, δt is an extremely short duration that leads to the sudden change of

{\dot{x}}_{1}

. Figure 7 also shows that at the beginning of lifting off the trajectory sinks when the relative position Δx is controlled to the desired value. Because the velocity of the upper leg is larger than the lower leg, Acceleration of upper leg

{\ddot{x}}_{1} < - g

in the part of sunken curve actually before the velocity of the two masses becomes identical.

Figures 7(a) to (c) illustrates the limit cycle of the upper leg with three different controllers, and Figure 7(d) presents the limit cycle of the body with the SLIP model. The limit cycles shown in Figures 7(a) to (c) are close to each other in spite of little differences. It can be seen that the stiffness of the linear controller is larger than the other controllers and that of the SLIP model is the smallest. The precision of the velocity and the position of the upper leg with the linear controller is also the highest. Figure 7(d) shows that the precision of the SLIP model is the smallest and its distance of the run in stance phase is the longest. It is obvious that the frequency of hopping of the SLIP model is the smallest.

The contact forces are shown in Figure 8. We can learn from Figure 8(a) that contact forces between the foot and the ground with the linear controller is larger than the others except several peak points. Figure 8(b) shows the contact force between the foot and the ground of the SLIP model which indicates that the contact force is close to 350 N, while others are less than 300 N, except several peak points.

Figure 8.

(a) Contact force between the lower leg and the ground of the two-mass model. (b) Contact force between the foot and the ground of the SLIP model.

Conclusion

We use three kinds of controllers to regulate the upper leg between different limit cycles in this paper, but it cannot be affirmed which controller is better compared to the others from the simulation results, and they have their own merits and drawbacks. The open-loop controller is the simplest but its anti-interference ability is weak; the linear controller is also simple and brings in state feedback of the upper leg, but the output of this controller is non-smooth; while the nonlinear controller is more complicated than the other two, but it produces smooth acceleration and has an excellent anti-interference ability. In fact, when the output of the upper level controller maintains a reasonable range there are not apparent differences among these controllers. In other words, for the three different controllers, the hopping height error and stance duration are harmonious if the accelerations of the upper leg in stance phase are close to each other produced by no matter which controller.

The SLIP model as the traditional hopping robot model has its advantages, but we also could learn from the simulation results that its contact force is larger than the two-mass model except several peaks because the SLIP model neglects the impact without controlling when touching down. The two-mass spring model is closer to the real hopping robot. Our future work will centre on controlling the real robot to bounce and extending this method to control 2D and 3D hopping. The experimental performance will be presented in the next paper in the near future.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship and/or publication of this article: This research received grant from National Hi-tech Research and Development Program of China(Grant No. 2015AA042202).

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