CN119645028A - Data driving switching gain estimation technology for bipedal walking race robot - Google Patents
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Abstract
本申请涉及一种双足竞走机器人数据驱动切换增益估计技术。所述技术利用线性系统的行为理论，构造了未知动态混合系统的数据解释系统，结合基于数据的线性矩阵不等式，建立了全局指数稳定性判据，在温和条件下，令双足机器人系统的全局指数稳定性得到了保证，使得双足竞走机器人不用依赖于模型就可以实现正常运行。同时，本申请提出的基于数据驱动的混杂估计方案，消除了系统模型识别步骤，减少了资源的消耗。
The present application relates to a data-driven switching gain estimation technology for a bipedal race walking robot. The technology uses the behavioral theory of linear systems to construct a data interpretation system for unknown dynamic hybrid systems, and combines data-based linear matrix inequalities to establish a global exponential stability criterion. Under mild conditions, the global exponential stability of the bipedal robot system is guaranteed, so that the bipedal race walking robot can operate normally without relying on the model. At the same time, the data-driven hybrid estimation scheme proposed in the present application eliminates the system model identification step and reduces resource consumption.
Description
Technical Field
The application relates to the technical field of robot control, in particular to a bipedal walking robot data driving switching gain estimation technology.
Background
With the deepening of control science, the innovation of sensor technology and the rapid development of the fields of artificial intelligence and machine learning, a robot system can effectively cope with uncertain factors and external disturbance in the walking process by means of an advanced self-adaptive algorithm. The bipedal walking robot is a mechanical device which is specially used for walking by two legs as a moving mode and aims at being integrated into the living space of human beings. Such robots demonstrate great environmental flexibility in terms of their unique unstructured and complex environmental walking capabilities. The biped heel-and-toe walking race robot has wide application potential in a plurality of key fields, and covers a plurality of aspects such as disaster relief, service industry, military safety, entertainment education and the like.
However, these application scenarios are often accompanied by complex and variable tasks and strong interference characteristics, which put higher demands on the bipedal walking robot, including system stability, flexibility and environmental adaptability. Therefore, ensuring the bipedal walking robot to stably execute the given tasks under various extreme conditions becomes a key point for promoting the technical development and practical application of the bipedal walking robot.
Disclosure of Invention
In view of the foregoing, it is desirable to provide a technology for estimating the data-driven switching gain of a bipedal walking robot, which makes the bipedal robot perform well in the face of diversified environments and task demands.
In a first aspect, the present application provides a bipedal walking robot data driven switching gain estimation technique. The technology comprises the following steps:
constructing a state space model of the biped robot system based on the model by utilizing the hybrid system framework, and constructing an equivalent system model of the biped robot system based on data according to the state space model, wherein the space state model and the equivalent system model both comprise unknown system matrixes;
constructing priori knowledge of noise in the bipedal walking race robot system;
acquiring a set of unknown system matrixes according to the prior knowledge of the equivalent system model and noise, wherein the expression of the set of the unknown system matrixes comprises stripping a first matrix of the unknown system matrixes;
Processing the set of the unknown system matrix by adopting the dual lemma to obtain a second matrix related to the first matrix;
Constructing a gain observer based on the state space model, and acquiring an augmentation system according to the gain observer and an equivalent system model;
Constructing a first model-based stability criterion of the bipedal robot system according to the augmentation system;
adopting S lemma to process the first stability criterion, substituting the first stability criterion into a second matrix, and obtaining a second stability criterion based on data;
Gain estimates are obtained based on a second stability criterion.
In one embodiment, the state space model is expressed as:
v=Cx,
Where x + is the time shift of x + (k) =x (k+1); Is the time derivative of state x, x (t, k) e R n represents the state of the bipedal robot system, y (t, k) e R s is the output of the bipedal robot system, κ (t, k) e [0, κ d ], the known constant κ d∈R＞0 is the periodic switching condition of the bipedal robot system, and A, D, C is an unknown system matrix.
In one embodiment, the equivalent system model is expressed as:
Y★＝CX★+V★,
Wherein, AndAre both hanker matrices represented by bipedal robot system data.
In one embodiment, the a priori knowledge of the noise is expressed as:
Wherein, Λ ij, i, j=1, 2 is a known matrix, Λ ij satisfies: I is an identity matrix.
In one embodiment, the set of unknown system matrices is represented as:
Wherein, Delta is the first matrix.
In one embodiment, the set of unknown system matrices that are treated by the dyadic processing is represented as:
Wherein, Θ is the second matrix.
In one embodiment, the gain observer is represented as:
Wherein, Is an estimate of x (t, k), L z∈Rn×s is the gain matrix, z represents the index of the gain observer;
the augmentation system is expressed as:
Wherein the error is
In one embodiment, the first stability criterion is expressed as:
P1≥(1-μ2)τP2,P2≥(1-μ1)τP1
And processing the first stability criterion by using the S lemma to obtain a second stability criterion, wherein the second stability criterion is expressed as:
P1≥(1-μ2)τP2,P2≥(1-μ1)τP1
wherein, kappa d＞0、τ＞0、γ、μ1、μ2, lambda is more than or equal to 0, delta is more than or equal to 0, rho >0 and theta >0 are all unknown constants, R n×n matrix And R n×p matrix F 1、F2 are both unknown matrices;
Solving a second stability criterion to obtain unknown matrixes P 1、P2、F1 and F 2;
The gain estimate is expressed as:
Lz＝Pz -1Fz,z∈[1,2]。
In a second aspect, the application also provides a data-driven switching gain estimation system of the bipedal walking race robot. The system comprises:
The system comprises a model construction module, a model analysis module and a model analysis module, wherein the model construction module is used for constructing a state space model of a biped robot system based on a model by utilizing a hybrid system framework and constructing an equivalent system model of the biped robot system based on data according to the state space model;
the noise constraint module is used for constructing priori knowledge of noise in the bipedal walking race robot system;
the first calculation module is used for acquiring a set of unknown system matrixes according to the equivalent system model and the priori knowledge of noise, wherein the expression of the set of the unknown system matrixes comprises stripping a first matrix of the unknown system matrixes;
the second calculation module is used for processing the set of the unknown system matrix by adopting the dual lemma to obtain a second matrix related to the first matrix;
the observer construction module is used for constructing a gain observer based on the state space model and acquiring an augmentation system according to the gain observer and the equivalent system model;
The stability design module is used for constructing a first stability criterion of the bipedal robot system based on the model according to the augmentation system;
The third calculation module is used for processing the first stability criterion by adopting the S lemma and substituting the first stability criterion into the second matrix to obtain a second stability criterion based on data;
And the gain estimation module is used for acquiring gain estimation according to the second stability criterion.
In a third aspect, the application also provides a bipedal walking race robot. The biped walking race robot comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps in the biped walking race robot data driving switching gain estimation technology when executing the computer program.
In a fourth aspect, the present application also provides a computer-readable storage medium. The computer readable storage medium has stored thereon a computer program which when executed by a processor implements the steps in a bipedal walking robot data driven switching gain estimation technique described above.
In a fifth aspect, the present application also provides a computer program product. A computer program product comprising a computer program which when executed by a processor implements the steps of a bipedal walking robot data driven switching gain estimation technique described above.
According to the biped walking race robot data driving switching gain estimation technology, the biped robot system is modeled as an unknown hybrid system and then is converted into a switching gain estimation method based on data driving, and a specific physical model is not required to be preset, so that the data driving method is very effective in the face of a highly complex and nonlinear system. Meanwhile, according to the driven hybrid estimation scheme, the system model identification step is eliminated, and the consumption of resources is reduced.
Drawings
FIG. 1 is a schematic flow diagram of a bipedal walking robot data driven switching gain estimation technique in one embodiment;
FIG. 2 is a schematic diagram of a bipedal robotic system switching gain observation in one embodiment;
FIG. 3 is a data driven schematic diagram of a bipedal robotic system in one embodiment;
Fig. 4 is a block diagram of a data-driven switching gain estimation system of a bipedal walking robot in one embodiment.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
For ease of understanding, technical terms appearing in the present invention are explained as necessary. A hybrid system is a unique dynamic system that fuses a continuous dynamic system with a discrete dynamic system and handles the interaction between the two. The system model has wide application value in various academic and industrial fields, such as robotics, industrial automation, aviation flight control, power system management, traffic network optimization, bioengineering and the like. The concept of hybrid systems is particularly important in the operation of bipedal walking robots. The walking process of the robot not only involves continuous limb movements, but also contains a series of key discrete state transition events, particularly at the moment of contact and disengagement of the foot with the ground, which state changes have a large impact on the dynamic behaviour of the robot. The gait cycle of bipedal walking consists of a plurality of alternating successive phases of motion (e.g., single leg support, double leg support, leg swing, etc.), with transitions between the phases exhibiting significant discreteness. It is this nature of continuous motion interweaving with discrete events that makes the hybrid system an ideal framework for describing the dynamic behavior of bipedal robots. The method allows researchers to finely regulate and control continuous motion tracks of the robot in the same model and accurately capture and process key discrete state conversion points, so that comprehensive characterization of complex motion characteristics of the bipedal walking robot is realized. Therefore, the hybrid system theory occupies a core position in the modeling of the bipedal walking robot, and provides powerful theoretical support for realizing efficient and stable walking control.
In the precise control system of the bipedal walking robot, the noise suppression and the state observer are two indispensable elements, which are directly related to the stability, the accuracy and the robustness of the robot in complex and changeable environments. Noise is used as a main expression form of external interference, and challenges are presented to the robot to maintain balance, plan gait and accurately move. To address this challenge, bipedal robotic systems rely on efficient observers to accurately estimate the internal state of the system. The observer is used as an observation tool, and has the core value of indirectly calculating key state variables (such as accurate centroid positions, joint angles and the like) which are difficult to directly measure through a complex dynamic model and a feedback mechanism by using sensor data containing noise or errors. This capability is particularly critical for bipedal heel-and-toe walking race robots, because it is neither practical nor costly to directly measure all state variables in a comprehensive execution environment. In addition, the observer also plays an important role in system fault diagnosis and coping. The system can rapidly identify the fault source, quantify the fault degree, provide immediate and accurate fault information for maintenance personnel, greatly shorten the fault checking and repairing time, and ensure that the robot system rapidly recovers stable operation. Therefore, by optimizing the observer design and application, the bipedal walking race robot can exhibit more excellent control performance and adaptability in the face of noise interference and complex environments.
In the study of robotics, especially bipedal walking robots, there are two distinct strategic frameworks, model driven and data driven. The model driving method is rooted in the deep understanding of the physical mechanism of the system, and dynamic changes of the robot in the walking process are depicted through an accurate mathematical model, and the process emphasizes the rigors of theoretical deduction and system analysis. However, in the face of complex physical phenomena in real environments (such as variable friction, unpredictable collisions and compliant contacts, etc.), building a comprehensive and accurate model is challenging. In contrast, the data driving method exhibits unique advantages. The method utilizes advanced data science and technology such as machine learning, deep learning and the like to directly extract the mode and rule of robot behaviors from massive data without presetting a definite physical model. This feature makes the data driven approach very efficient in the face of highly complex and nonlinear systems, especially where the model is difficult to build accurately or there is a lot of uncertainty. Through continuous practice and feedback learning, the data driving model can autonomously optimize the control strategy, so that the robot adapts to diversified environment and task requirements. In view of the above advantages, the data driving method has become a research hotspot in the field of robot learning, and is widely applied to key tasks such as stability control and intelligent walking. The method not only promotes the progress of the bipedal walking race robot technology, but also provides powerful support for realizing a robot system with more intelligence, flexibility and strong adaptability. Therefore, the data driving method is expected to play a more central and key role in future robot research.
The embodiment of the application provides a biped heel-and-toe walking race robot data driving switching gain estimation technology, which is shown in fig. 1 and comprises the following steps:
Step 101, constructing a state space model of the biped robot system based on the model by utilizing a hybrid system framework, and constructing an equivalent system model of the biped robot system based on data according to the state space model, wherein the space state model and the equivalent system model both comprise unknown system matrixes.
The construction of a data-driven state space model of a biped heel-and-toe walking race robot system specifically models an unknown hybrid system description biped robot as follows:
y=Cx,
where x + is the time shift of x + (k) =x (k+1), k is a positive integer; Is the time t derivative of state x, specifically expressed as: x (t, k) e R n represents the state of the bipedal robot system, y (t, k) e R s is the output of the bipedal robot system, k (t, k) e [0, k d ], the known constant k d∈R＞0 is the periodic switching condition of the bipedal robot system, A e R n×n、D∈Rn×n and C e R s×n are unknown system matrices, A is a continuous time dynamic state matrix, D is a discrete time dynamic state matrix, and C is the output matrix of the system.
On the basis of the state space model, a data driving equivalent system model in the bipedal walking robot system is constructed, and the model is as follows:
Y★＝CX★+V★,
Wherein, Where w and v are process noise and measurement noise, respectively;
And A hanker matrix represented as bipedal robot system data in the continuous time domain or in the discrete time domain, where u represents the system output.
Step 102, constructing prior knowledge of noise in the bipedal walking robot system.
Wherein, Λ ij, i, j=1, 2 is a known matrix, Λ ij satisfies: The prior knowledge of the noise constrains the maximum value of the noise.
And 103, acquiring a set of unknown system matrixes according to the equivalent system model and the priori knowledge of noise, wherein the expression of the set of the unknown system matrixes comprises stripping a first matrix of the unknown system matrixes.
In this embodiment, a set of system matrices based on data driving in a bipedal robot system is designed, and the form thereof is as follows:
Wherein, Delta is the first matrix.
Step 104, processing the set of unknown system matrixes by adopting the dual lemma to obtain a second matrix related to the first matrix.
In dual priming, if Δ is reversible, the following set holds:
Wherein, Θ is the second matrix.
And 105, constructing a gain observer based on the state space model, and acquiring an augmentation system according to the gain observer and the equivalent system model.
The data-driven gain observer in the bipedal walking race robot system is as follows:
Wherein, Is an estimate of x (t, k), and L z∈Rn×s is the gain matrix. If an error occursFor all (t, K) ∈K, convergence is 0. Fig. 2 shows a hybrid switching gain observation framework. Let the observer gain for the area 1 design be L 1 and the observer gain for the area 2 design be L 2, where y s is the switching point between area 1 and area 2 and ψ is the minimum dwell time.
The data-driven augmentation system of the bipedal walking race robot system is established according to the gain observer, and the form is as follows:
And step 106, constructing a first stability criterion of the bipedal robot system based on the model according to the augmentation system.
The first stability criterion is a global exponential stability criterion.
The mixing system in step 101 defines each solution in the mixing time domain as:
K:={(t,k),t∈[tk,tk+1],k∈N},
Where t k：＝kκd and t k+1：＝(k+1)κd represent transition periods of motion switching in a bipedal robot. The system solution in step 101 is a local absolute continuous function of the mapping (t, K) ∈k, as is well known. Let ζ (t, K, x 0) be the solution of the equation set of step 101 to (t, K) ∈K, where x 0 is the initial condition.
For the state space model in step 101, the definition of stability is described as:
Enclosed collection Is globally exponentially stable, if constants a, b >0 and c are present, such that
||ζ(t0,k0,x0)||H<a,
||ζ(t,k,x0)||H≤b||ζ(t0,k0,x0)||He-c(t+k),
For any initial condition x 0, the initial times t 0＝0,k0 =0 and (t, K) ∈k are true, and the bipedal robot system is stable.
Thus, the first model-based stability criterion is expressed using a linear matrix inequality as follows:
if a constant kappa d＞0,τ＞0,γ,μ1,μ2,Rn×n matrix is present The R n×p matrices F 1 and F 2 are such that:
P1≥(1-μ2)τP2,P2≥(1-μ1)rP1 (6)
and if the time (t, K) epsilon K is true, the bipedal robot system is stable.
In another embodiment, since the uncertainty term in conditions (1) and (2) in the first stability criterion is only the unknown system matrix a, a data set containing only a is needed. From steps 102 to 104, the unknown system matrix a is included in the noise data W ★, and it is not difficult to conclude that the noise data W ★ satisfies the following conditions:
Wherein, Γ ij, i, j=1, 2 is a known matrix, Γ ij satisfies: And And (3) stripping the unknown system matrix A in the noise data W ★ by adopting a technology similar to the step 103 to obtain:
Wherein, In this embodiment Ω is a first matrix. According to the dual lemma, this condition is equivalent to:
Wherein, In this embodiment Y is a second matrix.
And 107, processing the first stability criterion by adopting the S lemma, substituting the first stability criterion into a second matrix, and acquiring a second stability criterion based on data.
Wherein the S lements are that the R (s+h)×(s+h) matrix is assumedAndIs symmetrical. If R s×h matrix N is present, the Slater condition is such that:
R s×h、S22≤0、Q22 is less than or equal to 0 and for all N If and only if the following constants sigma >0 and p >0 exist,
This is true. Meanwhile, the observable assumptions are given as:
If the data (X, Y ★) is observable, if and only if So that
The second stability criterion can be obtained by processing the first stability criterion using S-theorem, under the assumption that the constants lambda >0, delta >0, rho >0, theta >0, kappa d＞0、τ＞0、γ、μ1、μ2 and R n×n matrix existAnd R n×p matrix F 1、F2 such that
P1≥(1-μ2)τP2,P2≥(1-μ1)τP1 (6)
And if so, the bipedal robot system is stable.
In this embodiment, the conditions (1) and (2) with the unknown system matrix a in step 106 are converted into the conditions (1) and (2) in step 107 with only the second matrix Y, and the conditions (3) and (4) with the unknown system matrices C and D in step 106 are converted into the conditions (1) and (2) in step 107 with only the second matrix Θ, so as to realize the conversion from the first stability criterion based on the model to the second stability criterion based on the data of the bipedal robot system.
And step 108, obtaining gain estimation according to the second stability criterion.
By solving the second stability criterion, the unknown matrices P 1、P2、F1 and F 2 are obtained through calculation, and then the switching gain estimation based on the data is as follows:
Lz＝Pz -1Fz,z∈[1,2]。
In order to verify the stability process of the data-driven switching gain estimation in the bipedal walking race robot system, it is assumed that the data-driven switching gain estimation in the bipedal walking race robot system given in step 107 is feasible, and the verification steps are as follows:
S1, conditions (1) and (2) in step 107 are given using S lemma:
s2, multiplying the left side and the right side of the S1 formula by (I, A) and transposition thereof respectively to obtain the following formula:
Thus, the first and second light sources are connected,
This means that conditions (1) and (2) in step 107 can ensure that conditions (1) and (2) in step 106 are satisfied.
S3, the same thing is done, and the conditions (3) and (4) in the 107 can be obtained by adopting S quotients:
substituting the data-based switching gain estimate L z in step 108 into the above equation:
S4, definition The expression is:
By aligning Multiplying the left and right sides of (C) by (I, D, C) and its transpose, respectively, to obtain
It is clear that conditions (3) and (4) in step 106 are true.
Fig. 3 is a schematic diagram of the data driving of the bipedal robot system of the present application. In the figure, a sensor acquires input state data, output state data and the like of the bipedal robot system and transmits the input state data, the output state data and the like to an unknown hybrid system, the sensor also acquires noise data, a data gain observer carries out switching gain estimation according to the data acquired by the sensor by using the switching gain estimation technology provided by the application, the data gain observer outputs the switching gain estimation and transmits the switching gain estimation to an executor of the bipedal robot system for execution, and an execution result is fed back to the observer. The state change of the bipedal robot caused by the execution of the actuator can also be reflected in unknown hybrid systems and noise data.
The invention provides a data driving estimation technology aiming at a bipedal walking race robot with an unknown hybrid system with cycle hopping. By designing the state observer, a global index stability criterion is established by utilizing a linear matrix inequality, so that the bipedal walking race robot system is in a relatively stable state, and the bipedal walking race robot system is ensured to normally execute tasks without depending on a model.
It should be understood that, although the steps in the flowcharts related to the embodiments described above are sequentially shown as indicated by arrows, these steps are not necessarily sequentially performed in the order indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least some of the steps in the flowcharts described in the above embodiments may include a plurality of steps or a plurality of stages, which are not necessarily performed at the same time, but may be performed at different times, and the order of the steps or stages is not necessarily performed sequentially, but may be performed alternately or alternately with at least some of the other steps or stages.
Based on the same inventive concept, the embodiment of the application also provides a data-driven switching gain estimation system of the bipedal walking robot for realizing the data-driven switching gain estimation technology of the bipedal walking robot. The implementation of the system for solving the problem is similar to that described in the above technology, so the specific limitation in the embodiments of the data-driven switching gain estimation system for one or more bipedal walking robots provided below can be referred to above for the limitation of the data-driven switching gain estimation technology for a bipedal walking robot, which is not described herein.
In one embodiment, as shown in fig. 4, there is provided a bipedal walking race robot data-driven switching gain estimation system, comprising:
the model construction module 401 is configured to construct a state space model of the model-based biped robot system by using the hybrid system framework, and construct an equivalent system model of the data-based biped robot system according to the state space model, where the space state model and the equivalent system model both include an unknown system matrix;
A noise constraint module 402, configured to construct a priori knowledge of noise in the bipedal walking robot system;
A first calculation module 403, configured to obtain a set of unknown system matrices according to the equivalent system model and a priori knowledge of noise, where an expression of the set of unknown system matrices includes stripping a first matrix of the unknown system matrices;
A second calculation module 404, configured to process the set of unknown system matrices using the dual lemma, and obtain a second matrix related to the first matrix;
An observer construction module 405, configured to construct a gain observer based on the state space model, and obtain an augmentation system according to the gain observer and an equivalent system model;
A stability design module 406, configured to construct a first model-based stability criterion for the bipedal robotic system according to the augmentation system;
a third calculation module 407, configured to process the first stability criterion by using the S lemma, and substitute the first stability criterion into a second matrix to obtain a second stability criterion based on data;
the gain estimation module 408 is configured to obtain a gain estimation according to the second stability criterion.
The modules in the data-driven switching gain estimation system of the bipedal walking race robot can be fully or partially realized by software, hardware and a combination thereof. The modules can be embedded in or independent of a processor in the bipedal walking race robot in a hardware mode, and can also be stored in a memory in the bipedal walking race robot in a software mode, so that the processor can conveniently call and execute operations corresponding to the modules.
In one embodiment, a bipedal walking robot is provided, comprising a memory and a processor, the memory having stored therein a computer program, the processor implementing the steps of all technical embodiments described above when executing the computer program.
In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored which, when executed by a processor, implements the steps of all the technical embodiments described above.
In one embodiment, a computer program product is provided, comprising a computer program which, when executed by a processor, implements the steps of all technical embodiments described above.
It should be noted that, the user information (including but not limited to user equipment information, user personal information, etc.) and the data (including but not limited to data for analysis, stored data, presented data, etc.) related to the present application are information and data authorized by the user or sufficiently authorized by each party, and the collection, use and processing of the related data need to comply with the related laws and regulations and standards of the related country and region.
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, database, or other medium used in embodiments provided herein may include at least one of non-volatile and volatile memory. The nonvolatile Memory may include Read-Only Memory (ROM), magnetic tape, floppy disk, flash Memory, optical Memory, high density embedded nonvolatile Memory, resistive random access Memory (ReRAM), magneto-resistive random access Memory (Magnetoresistive Random Access Memory, MRAM), ferroelectric Memory (Ferroelectric Random Access Memory, FRAM), phase change Memory (PHASE CHANGE Memory, PCM), graphene Memory, and the like. Volatile memory can include random access memory (Random Access Memory, RAM) or external cache memory, and the like. By way of illustration, and not limitation, RAM can be in various forms such as static random access memory (Static Random Access Memory, SRAM) or dynamic random access memory (Dynamic Random Access Memory, DRAM), etc. The databases referred to in the embodiments provided herein may include at least one of a relational database and a non-relational database. The non-relational database may include, but is not limited to, a blockchain-based distributed database, and the like. The processor referred to in the embodiments provided in the present application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic unit, a data processing logic unit based on quantum computing, or the like, but is not limited thereto.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The foregoing examples illustrate only a few embodiments of the application and are described in detail herein without thereby limiting the scope of the application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of the application should be assessed as that of the appended claims.
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