CN104913787A - Novel path selection method under urban traffic control conditions - Google Patents
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Abstract
本发明涉及一种城区交通管制条件下的新型择径方法，其技术特点是：用二极管截止特性支路模型表示公路交通网络中受到交通管制的公路；并将二极管超越指数型V-A特性函数进行逐区间线性化，在此基础上，以二极管截止特性支路模型建立超越模拟电路网络,并采用改进型迭代法求解上述超越模拟电路网络模型的各个节点电压，进而得到从择径起点至择径终点的最优路径。本发明通过对非线性电子器件二极管的伏安特性进行分段线性化处理，并且改进迭代过程中的控制策略，使得路径规划方法的计算效率得到提高，并且复杂性分析与仿真实验证明了本方法的有效性与可行性。
The present invention relates to a new route selection method under traffic control conditions in urban areas. Its technical characteristics are: use the diode cut-off characteristic branch model to represent the roads subject to traffic control in the road traffic network; Interval linearization. On this basis, the transcendental analog circuit network is established with the diode cut-off characteristic branch model, and the improved iterative method is used to solve the voltages of each node of the above-mentioned transcendental analog circuit network model, and then the path selection starting point to the path selection end point is obtained. the optimal path. The present invention performs piecewise linearization processing on the volt-ampere characteristics of the nonlinear electronic device diode, and improves the control strategy in the iterative process, so that the calculation efficiency of the path planning method is improved, and the complexity analysis and simulation experiments prove the method effectiveness and feasibility.
Description
技术领域technical field
本发明涉及一种新型择径方法，特别涉及一种城区交通管制条件下的新型择径方法。The invention relates to a novel route selection method, in particular to a novel route selection method under urban traffic control conditions.
背景技术Background technique
随着北京、天津、上海、广州等一线重大城市的快速发展，道路交通网日趋复杂。现代城市复杂交通环境包含路段长度、车道数目、路面质量、实时车流密度、实时拥挤程度、单行道、禁止左转弯等属性。面对庞大的公路交通网络及日益增加的机动车保有量，交通管理部门多措并举治理交通拥堵，其中疏导车流、限路限行是其中一种有效措施。复杂交通网智能导航系统的最优路径规划是在满足基本道路约束(单行道)与响应实时道路信息的条件下，综合全交通网各路段属性，优化出满足用户要求的最佳路径。With the rapid development of major first-tier cities such as Beijing, Tianjin, Shanghai, and Guangzhou, the road traffic network is becoming increasingly complex. The complex traffic environment of modern cities includes attributes such as road section length, number of lanes, road surface quality, real-time traffic density, real-time congestion level, one-way street, and prohibition of left turns. Faced with the huge highway traffic network and the increasing number of motor vehicles, the traffic management department has taken various measures to control traffic congestion, among which traffic flow regulation and road restriction are one of the effective measures. The optimal route planning of the complex traffic network intelligent navigation system is to optimize the best route that meets the user's requirements by integrating the properties of each road section in the entire traffic network under the conditions of satisfying the basic road constraints (one-way street) and responding to real-time road information.
在智能交通导航系统的最优路径算法中，城市交通网络被映射为线性纯电阻电路网络。该电路网络与交通网络具有相同的拓扑结构，并且电路网络的支路电阻值表达路况信息，畅通、长度短、路况好的路段电阻小。电路网中小电阻支路有大电流通过的性质与交通网中短、宽路径较优的性质相互对应In the optimal routing algorithm of the intelligent traffic navigation system, the urban traffic network is mapped to a linear purely resistive circuit network. The circuit network has the same topological structure as the traffic network, and the branch resistance values of the circuit network express road condition information, and the road sections with smooth, short length and good road conditions have small resistance. The nature of small resistive branches with large currents in the circuit network corresponds to the nature of short and wide paths in the traffic network.
但现有技术中的非超越模拟电路没有对电气量-电流走向约束，故只可使用于无交通管制的中小城市简单公路网络。而现代城市城区交通管制下的方向限制条件无法用非超越模拟电路表达。However, the non-surpassing analog circuit in the prior art has no constraints on the electrical quantity-current direction, so it can only be used in simple road networks in small and medium-sized cities without traffic control. However, the directional constraints under traffic control in modern urban areas cannot be expressed by non-transcendent analog circuits.
而且，现有技术中针对非超越模拟电路常用的最优路径规划算法有改进型Dijkstra算法、遗传算法、神经网络算法、电路地图算法等。而在面对交通网中单行道的局部约束问题(即超越模拟电路)时，上述方法无法解决。或是理论上通过广义牛顿-拉弗逊迭代方法、广义阻尼牛顿-拉弗逊方法虽可得出上述超越模拟电路网络的各个模拟电位。但此类连续型超越模拟电路方程组是非线性方程组，上述算法在计算求解过程中普遍存在对初始值设定敏感、收敛域较小、复杂性过高、收敛速度慢等问题。Moreover, the optimal path planning algorithms commonly used for non-transcendent analog circuits in the prior art include improved Dijkstra algorithm, genetic algorithm, neural network algorithm, circuit map algorithm, and the like. However, when faced with the local constraint problem of one-way streets in the traffic network (ie, beyond the analog circuit), the above methods cannot be solved. Or theoretically, the above-mentioned analog potentials beyond the analog circuit network can be obtained through the generalized Newton-Raphson iterative method and the generalized damped Newton-Raphson method. However, such continuous transcendental analog circuit equations are nonlinear equations, and the above-mentioned algorithms generally have problems such as sensitivity to initial value setting, small convergence domain, high complexity, and slow convergence speed in the calculation and solution process.
发明内容Contents of the invention
本发明的目的在于克服现有技术的不足，提供一种设计合理、可行有效且计算求解过程简易的城区交通管制条件下的新型择径方法。The purpose of the present invention is to overcome the deficiencies of the prior art and provide a new route selection method under urban traffic control conditions with reasonable design, feasible and effective calculation and solution process.
本发明解决其技术问题是采取以下技术方案实现的：The present invention solves its technical problem and realizes by taking the following technical solutions:
一种城区交通管制条件下的新型择径方法，包括以下步骤：A new route selection method under urban traffic control conditions, comprising the following steps:
步骤1、用二极管截止特性支路模型表示公路交通网络中受到交通管制的公路；并将二极管超越指数型V-A特性函数进行逐区间线性化，在此基础上，以二极管截止特性支路模型建立超越模拟电路网络,转化后的二极管截止特性支路模型的逻辑判断非超越方程为：Step 1. Use the diode cut-off characteristic branch model to represent the roads subject to traffic control in the highway traffic network; and linearize the diode transcendence exponential V-A characteristic function interval by interval. On this basis, use the diode cut-off characteristic branch model to establish the transcendence To simulate the circuit network, the logic judgment non-transcendental equation of the converted diode cut-off characteristic branch model is:
其中,v为模拟电路中该段电压，G为模拟电路中该段电导，f为电导函数，a、b、c为决定此路段所花费时间的因素；Among them, v is the voltage of this section in the analog circuit, G is the conductance of this section in the analog circuit, f is the conductance function, and a, b, and c are factors that determine the time spent on this section;
步骤2、求解上述超越模拟电路网络模型的节点电压,具体方法包括以下步骤：Step 2, solving the above-mentioned node voltage beyond the analog circuit network model, the specific method includes the following steps:
(1)判断整个公路交通网络中受到交通管制而限行的公路的数量；(1) Determine the number of roads restricted by traffic control in the entire road traffic network;
(2)若整个公路交通网络中只有一条公路受到交通管制而限行，则首先将该交通管制而限行的公路以外的公路交通网络转化为具有若干内部节点和对外接口的非超越模拟电路；通过解决纯电阻电路的方法求得该非超越模拟电路中各个节点电压；并根据戴维南等效原理进一步确定从该条因受到交通管制而限行公路向整个公路交通网络观察的设有外部激励的非超越模拟电路网络的等效电路；然后，在上述等效电路基础上，判断是否将二极管截止特性支路加进上述非超越模拟电路,进而构造新的非超越模拟电路网络；最后，应用解决纯电导电路的方法，得到新的非超越模拟电路网络节点电压；(2) If only one road in the entire road traffic network is restricted by traffic control, the road traffic network other than the road restricted by traffic control is first transformed into a non-transcendent analog circuit with several internal nodes and external interfaces; by solving The method of pure resistance circuit is used to obtain the voltage of each node in the non-transcendent analog circuit; and according to Thevenin's equivalent principle, it is further determined that the non-transcendent analog circuit with external excitation is observed from the road restricted by traffic control to the entire road traffic network. The equivalent circuit of the circuit network; then, on the basis of the above equivalent circuit, judge whether to add the diode cut-off characteristic branch into the above non-transcendence analog circuit, and then construct a new non-transcendence analog circuit network; finally, apply the solution to the pure conductance circuit method to obtain new non-transcendent analog circuit network node voltages;
(3)若整个公路交通网络中有多条公路受到交通管制而限行，则超越模拟电路网络中包含有多个二极管截止特性支路，采用改进型迭代法求解超越模拟电路节点电压。(3) If there are multiple roads in the entire highway traffic network that are restricted by traffic control, the transcendence analog circuit network contains multiple diode cut-off characteristic branches, and the improved iterative method is used to solve the node voltage of the transcendence analog circuit.
而且，所述改进型迭代法求解超越模拟电路节点电压的具体步骤包括：Moreover, the specific steps for solving the node voltage beyond the analog circuit by the improved iterative method include:
步骤(1)求解初始内外节点电压；Step (1) Solve the initial internal and external node voltages;
步骤(2)确定方程初始状态；Step (2) determines the initial state of the equation;
步骤(3)系统电压状态迭代求解节点电压；Step (3) system voltage state iteratively solves the node voltage;
步骤(4)判断二极管截止特性支路电流是否存在误差，若存在误差，则返回步骤(3)继续迭代；若不存在误差，则输出结果。Step (4) Judging whether there is an error in the current of the diode cut-off characteristic branch, if there is an error, return to step (3) to continue the iteration; if there is no error, output the result.
而且，所述求解初始内外节点电压的具体方法包括以下步骤：Moreover, the specific method for solving the initial internal and external node voltages includes the following steps:
(1)将因受交通管制而限行的d条公路移除，则剩余的非超越模拟电路网络变为具有d个端口的设有外部激励并且具有若干内部节点和对外接口非超越模拟电路网络。(1) Remove the d roads that are restricted by traffic control, and then the remaining non-surpassing analog circuit network becomes a non-transcending analog circuit network with d ports that is provided with external excitation and has several internal nodes and external interfaces.
(2)编制该具有外部激励的非超越模拟电路网络的非超越模拟电路方程，求解出该设有外部激励的非超越模拟电路网络内部电位与外部端口电位；(2) Compile the non-transcendence analog circuit equation of the non-transcendence analog circuit network with external excitation, and solve the internal potential and external port potential of the non-transcendence analog circuit network with external excitation;
而且，所述确定方程初始状态的具体步骤为：Moreover, the specific steps for determining the initial state of the equation are:
检验外部端口电位与所有二极管截止特性支路的适配情况，将正极端口要接高电位的二极管截止特性支路全部以纯电导支路的形式加进到d端口，其他二极管截止特性支路不加进，进而构造新的非超越模拟电路网络，并确定方程的初始状态。Check the adaptability of the external port potential to all diode cut-off characteristic branches, and add all the diode cut-off characteristic branches connected to the positive port to the high potential in the form of pure conductance branches to the d port, and other diode cut-off characteristic branches are not added. Then, a new non-transcendence analog circuit network is constructed, and the initial state of the equation is determined.
定义向量N＝[Ni]d×1，描述d个二极管截止特性支路的状态：Define vector N=[N i ] d×1 to describe the states of d diode cut-off characteristic branches:
而且，所述系统电压状态迭代求解节点电压的具体步骤为：Moreover, the specific steps for iteratively solving the node voltage in the system voltage state are as follows:
定义并计算二极管截止特性支路误差电流列向量E＝[Ei]d×1：则进而得出E的最小元素Em和其所在支路号m；Define and calculate the error current column vector E=[E i ] d×1 of the diode cut-off characteristic branch: then Then get the minimum element E m of E and its branch number m;
其中，Ei为第i条支路的误差电流、Ni为第i条支路的状态量、为d个二极管截止特性支路中第i条支路的电导、为第i条支路正极电压、为第i条支路负极电压；Among them, E i is the error current of the i-th branch, N i is the state quantity of the i-th branch, is the conductance of the i-th branch in the d diode cut-off characteristic branches, is the anode voltage of the ith branch, is the negative pole voltage of the i-th branch;
若Em＜0，则存在二极管截止特性支路不满足二极管约束条件的情况，改变第m条二极管截止特性支路的状态；If E m <0, there is a situation that the diode cut-off characteristic branch does not satisfy the diode constraint condition, and the state of the mth diode cut-off characteristic branch is changed;
若Em≥0，则所有二极管截止特性支路满足二极管截止特性支路的约束条件，从而确定等效线性电路的拓扑结构；确定电路的拓扑结构后，将含多条二极管截止特性支路的电路网络转化成为线性纯电导电路网络，应用解决纯电导电路的方法，得到新的非超越模拟电路网络的节点电压。If E m ≥ 0, all the diode cut-off characteristic branches meet the constraints of the diode cut-off characteristic branch, so as to determine the topology of the equivalent linear circuit; after determining the topology of the circuit, the The circuit network is converted into a linear pure conductance circuit network, and the method for solving the pure conductance circuit is applied to obtain a new node voltage that does not exceed the analog circuit network.
而且，所述改变第m条二极管截止特性支路的状态的具体方法为：若Nm＝1，则将其从d端口中切除；若Nm＝-1，说明电流存在误差，则将其投入d端口，继续迭代。Moreover, the specific method for changing the state of the mth diode cut-off characteristic branch is: if N m =1, then cut it off from the d port; if N m =-1, it means that there is an error in the current, then cut it Put in the d port and continue to iterate.
而且，判断是否将二极管截止特性支路加进上述非超越模拟电路的具体步骤是：判断将二极管截止特性支路加进前的两端电压的电压关系，若二极管截止特性支路正极接高电位，则将含相同电导的线性支路加进非超越模拟电路网络中，若二极管截止特性支路负极接高电位，则不将其加进非超越模拟电路网络。Moreover, the specific steps for judging whether to add the diode cut-off characteristic branch to the above-mentioned non-surpassing analog circuit are: to judge the voltage relationship between the voltages at both ends before adding the diode cut-off characteristic branch, if the positive pole of the diode cut-off characteristic branch is connected to a high potential , then add the linear branch with the same conductance into the non-transcendence analog circuit network. If the negative pole of the diode cut-off characteristic branch is connected to a high potential, it will not be added to the non-transcendence analog circuit network.
本发明的优点和积极效果是：Advantage and positive effect of the present invention are:
1、本发明比较了因交通管制而限行公路与非线性二极管单向导电之间的类似特性，在电路地图基础上建立了城市交通网的电路网络模型，并提出一种基于二极管截止特性支路模型的车辆最优路径规划方法；该方法通过对二极管截止特性电子器件二极管的伏安特性进行分段线性化处理，并且改进迭代过程中的控制策略，使得路径规划方法的计算效率得到提高，并且复杂性分析与仿真实验证明了本方法的有效性与可行性。1. The present invention compares the similar characteristics between restricted roads and non-linear diode one-way conduction due to traffic control, establishes a circuit network model of urban traffic network on the basis of circuit maps, and proposes a branch based on diode cut-off characteristics The vehicle optimal path planning method of the model; this method performs piecewise linearization on the volt-ampere characteristics of the diode cut-off characteristic electronic device, and improves the control strategy in the iterative process, so that the calculation efficiency of the path planning method is improved, and Complexity analysis and simulation experiments prove the validity and feasibility of this method.
2、本发明提出基于二极管截止特性电路的最优路径规划算法，通过对线性电路在特殊局部进行以二极管截止特性电子元件为基础的建模与变构，解决了因交通管制而限行公路的最优路径规划问题。本发明在分析了因交通管制而限行的公路局部最优化的基础上，将二极管截止特性电路求解过程离散线性化，克服了由传统泰勒级数建立的二极管截止特性方程迭代过程过于繁琐的缺陷，并且运算过程更广泛适用计算机控制，在保证精度的前提下简化了规划方法，对快速发展的复杂交通智能导航系统具有重要意义。2. The present invention proposes an optimal path planning algorithm based on the diode cut-off characteristic circuit, and solves the optimal path planning algorithm based on the diode cut-off characteristic electronic component in a special part of the linear circuit, which solves the problem of the road being restricted due to traffic control. Optimal path planning problem. On the basis of analyzing the local optimization of roads restricted by traffic control, the present invention discretely linearizes the solution process of the diode cut-off characteristic circuit, and overcomes the too cumbersome defect of the iterative process of the diode cut-off characteristic equation established by the traditional Taylor series. And the calculation process is more widely applicable to computer control, which simplifies the planning method under the premise of ensuring accuracy, which is of great significance to the rapid development of complex traffic intelligent navigation systems.
附图说明Description of drawings
图1是本发明的二极管截止特性支路电路模型图；Fig. 1 is a diode cut-off characteristic branch circuit model diagram of the present invention;
图2是本发明的二极管截止特性支路正极接高电位的戴维宁等效电路模型图；Fig. 2 is the Thevenin equivalent circuit model figure that the anode of the diode cut-off characteristic branch of the present invention connects high potential;
图3是本发明的二极管截止特性支路负极接高电位的戴维宁等效电路模型图；Fig. 3 is the Thevenin equivalent circuit model figure that the cathode of the diode cut-off characteristic branch of the present invention is connected to a high potential;
图4是本发明的d端口及其二极管截止特性支路模型图；Fig. 4 is a d port and a diode cut-off characteristic branch model diagram of the present invention;
图5是本发明的改进型迭代法求解节点电压的计算流程图；Fig. 5 is the calculation flowchart of solving node voltage by improved iterative method of the present invention;
图6是本发明交通管制条件下的超越电路网络模型图Fig. 6 is the beyond circuit network model diagram under the traffic control condition of the present invention
具体实施方式Detailed ways
以下结合附图对本发明实施例做进一步详述：Embodiments of the present invention are described in further detail below in conjunction with the accompanying drawings:
一种城区交通管制条件下的新型择径方法，包括以下步骤：A new route selection method under urban traffic control conditions, comprising the following steps:
步骤1、用图1所示的二极管截止特性支路模型表示公路交通网络中受到交通管制的公路；并将二极管超越指数型V-A特性函数进行逐区间线性化，在此基础上，以图1所示的二极管截止特性支路模型建立超越模拟电路网络模型；Step 1. Use the diode cut-off characteristic branch model shown in Fig. 1 to represent the roads subject to traffic control in the road traffic network; and linearize the diode transcendental V-A characteristic function interval by interval. On this basis, use Fig. 1 The shown diode cut-off characteristic branch model is established beyond the analog circuit network model;
转化后的二极管截止特性支路的逻辑判断非超越方程变为：The logic judgment non-transcendence equation of the converted diode cut-off characteristic branch becomes:
其中v为模拟电路中该段电压，G为模拟电路中该段电导，f为电导函数，a、b、c为决定此路段所花费时间的因素，例如：公路长度、车道数量、车流密度等。Among them, v is the voltage of this section in the analog circuit, G is the conductance of this section in the analog circuit, f is the conductance function, a, b, and c are factors that determine the time spent on this section, such as: road length, number of lanes, traffic density, etc. .
步骤2、求解上述超越模拟电路网络模型Step 2. Solve the above-mentioned transcendental analog circuit network model
其中，步骤2的具体步骤为：Among them, the specific steps of step 2 are:
(1)判断整个公路交通网络中受到交通管制而限行的公路的数量；(1) Determine the number of roads restricted by traffic control in the entire road traffic network;
(2)若整个公路交通网络中只有一条公路K受到交通管制而限行，则首先将该K公路以外的公路交通网络转化为非超越模拟电路，通过解决纯电阻电路的方法求得该非超越模拟电路中各个节点电压；并根据戴维南等效原理进一步确定从K公路向整个公路交通网络观察的设有外部激励的非超越模拟电路网络的等效电路，所述等效电路，如图2、图3所示；然后，在上述等效电路基础上，判断是否将表示因受交通管制而限行的公路的二极管截止特性支路模型加入上述非超越模拟电路网络中，其具体判断方法为：首先、判断将二极管截止特性支路加进前的i、j两端节点电压的电压关系，如图2所示，若二极管截止特性支路正极接高电位，则二极管导通且影响整个网络电流分布。但此时i、j节点电压依然满足投入前的关系，与仅含电导的线性支路形式投入网络一样，不会影响k支路的局部约束条件，因此，将含相同电导的线性支路加进非超越模拟电路网络中；若二极管截止特性支路负极接高电位，如图3所示，则二极管截止特性支路截止而不影响原网络电流分布，因此不将其加进非超越模拟电路网络，进而构造新的非超越模拟电路网络；最后，应用解决纯电导电路的方法，得到新的非超越模拟电路网络节点电压；(2) If there is only one road K in the entire road traffic network that is restricted by traffic control, first convert the road traffic network other than the K road into a non-transcendence analog circuit, and obtain the non-transcendence analog circuit by solving the pure resistance circuit Each node voltage in the circuit; And according to Thevenin's equivalent principle, further determine the equivalent circuit of the non-surpassing analog circuit network that is provided with external excitation from the K highway to the whole highway traffic network observation, described equivalent circuit, as Fig. 2, Fig. 3; then, on the basis of the above-mentioned equivalent circuit, it is judged whether to add the diode cut-off characteristic branch model of the highway restricted by traffic control into the above-mentioned non-surpassing analog circuit network, and its specific judgment method is: first, Judging the voltage relationship between the node voltages of i and j before adding the diode cut-off characteristic branch, as shown in Figure 2, if the anode of the diode cut-off characteristic branch is connected to a high potential, the diode will be turned on and affect the current distribution of the entire network. But at this time, the voltages of nodes i and j still satisfy the relationship before the input, which is the same as the input of the linear branch with only conductance into the network, and will not affect the local constraints of the k branch. Therefore, adding the linear branch with the same conductance to Into the non-surpassing analog circuit network; if the negative pole of the diode cut-off characteristic branch is connected to a high potential, as shown in Figure 3, the diode cut-off characteristic branch will be cut off without affecting the current distribution of the original network, so it will not be added to the non-surpassing analog circuit network, and then construct a new non-transcendence analog circuit network; finally, apply the method to solve the pure conductance circuit, and obtain a new non-transcendence analog circuit network node voltage;
(3)若整个公路交通网络中有d条(多条)公路受到交通管制而限行，投入(或切除)一条二极管截止特性支路会影响其他端口电压而改变其他二极管导通情况和网络拓扑结构，因此，采用改进型迭代法求解超越模拟电路节点电压，其具体步骤如图5所示：(3) If there are d (multiple) roads in the entire road traffic network that are restricted by traffic control, switching on (or cutting off) a branch with a diode cut-off characteristic will affect the voltage of other ports and change the conduction of other diodes and the network topology , therefore, using the improved iterative method to solve the node voltage beyond the analog circuit, the specific steps are shown in Figure 5:
①求解初始内外节点电压① Solve the initial internal and external node voltage
如图6所示，将因受交通管制而限行的公路4移除，则除去d条二极管截止特性支路的超越模拟电路网络视为具有d个端口的设有外部激励8的非超越模拟电路网络，简称d端口。列写d端口内部非超越模拟电路的方程式，解得上述非超越模拟电路的内节点2电压列向量U与d端口5的电压。As shown in Figure 6, the road 4 restricted by traffic control is removed, and the transcendental analog circuit network that removes d diode cut-off characteristic branches is regarded as a non-transcendental analog circuit with d ports provided with external excitation 8 Network, referred to as d-port. Write down the equation of the non-transcendence analog circuit inside the d-port, and solve the above-mentioned non-transcendence analog circuit's internal node 2 voltage column vector U and the voltage of the d-port 5.
②确定方程初始状态② Determine the initial state of the equation
检验d个端口电压与所有二极管截止特性支路的适配情况，如图4中虚线所示，将阳极端口要接高电位的二极管支路全部以纯电导支路1的形式投入到d端口，其他二极管截止特性支路不投入，构造如图6所示的新的非超越模拟网络，其中设定择径起点6、择径终点7以及交通网络的等效拓扑连接3；Check the adaptation of d port voltages to all diode cut-off characteristic branches, as shown by the dotted line in Figure 4, put all the diode branches whose anode ports are connected to high potentials into the d port in the form of pure conductance branch 1, and other The diode cut-off characteristic branch is not put into use, and a new non-surpassing analog network as shown in Figure 6 is constructed, in which the starting point 6 of routing, the ending point of routing 7, and the equivalent topological connection 3 of the traffic network are set;
定义向量N＝[Ni]d×1，描述d个二极管截止特性支路的状态：Define vector N=[N i ] d×1 to describe the states of d diode cut-off characteristic branches:
③系统电压状态迭代求解节点电压③The system voltage state iteratively solves the node voltage
定义并计算非超越模拟电路的误差电流列向量E＝[Ei]d×1：则进而得出E的最小元素Em和其所在支路号m；Define and calculate the error current column vector E=[E i ] d×1 of the non-transcendence analog circuit: then Then get the minimum element E m of E and its branch number m;
其中，Ei为第i条支路的误差电流、Ni为第i条支路的状态量、为d个二极管截止特性支路中第i条支路的电导、为第i条支路正极电压、为第i条支路负极电压。Among them, E i is the error current of the i-th branch, N i is the state quantity of the i-th branch, is the conductance of the i-th branch in the d diode cut-off characteristic branches, is the anode voltage of the ith branch, is the negative pole voltage of the i-th branch.
④判断二极管截止特性支路电流是否存在误差，若存在误差，则返回步骤③继续迭代；若不存在误差，则输出结果。④ Judging whether there is an error in the current of the diode cut-off characteristic branch, if there is an error, return to step ③ to continue the iteration; if there is no error, output the result.
若Em＜0，则存在二极管截止特性支路不满足二极管约束条件的情况(E的负值元素所对应的二极管截止特性支路均不满足约束条件)。改变第m条二极管截止特性支路的状态，即若第m条支路状态为Nm＝1，则将其从d端口中切除；若Nm＝-1，说明电流存在误差，则将其投入d端口，继续迭代。If E m <0, there is a case that the diode cut-off characteristic branch does not satisfy the diode constraint condition (the diode cut-off characteristic branch corresponding to the negative element of E does not satisfy the constraint condition). Change the state of the mth diode cut-off characteristic branch, that is, if the state of the mth branch is N m =1, then cut it from the d port; if N m =-1, it means that there is an error in the current, then cut it Put in the d port and continue to iterate.
若Em≥0，则E所有元素非负，即所有二极管截止特性支路满足二极管约束条件的情况，此时的N描述了d条二极管截止特性支路的状态，从而确定了等效线性电路的拓扑结构，输出结果；再将含d条二极管截止特性支路的电路网络转化成为线性纯电导电路网络，应用解决纯电导电路的方法，得到新的非超越模拟电路网络节点电压。If E m ≥ 0, then all elements of E are non-negative, that is, all diode cut-off characteristic branches satisfy the diode constraint condition. At this time, N describes the state of d diode cut-off characteristic branches, thus determining the equivalent linear circuit The topological structure and the output result; then transform the circuit network containing d diode cut-off characteristic branches into a linear pure conductance circuit network, apply the method to solve the pure conductance circuit, and obtain a new non-transcendent analog circuit network node voltage.
需要说明的是：因为一条支路电流的改变对整个网络其他支路电流的影响程度，与投入(或切除)该支路前后电流的变化量正相关，所以每次迭代时都是对投入(或切除)前后电流变化最大的支路进行处理。随着迭代过程的进行，不满足二极管截止特性支路电压电流约束条件的程度越来越小，结果不断接近于真值。并且所有二极管通断状态组合的有限性和真值的存在性，所以迭代结果一定收敛并使所有二极管截止特性支路同时满足约束条件。上述改进型迭代算法的复杂性分析。What needs to be explained is: because the influence degree of the change of a branch current on the current of other branches in the whole network is positively related to the change of the current before and after the branch is put in (or cut off), so each iteration is an input ( or cutting off) the branch with the largest current change before and after processing. With the progress of the iterative process, the degree of the branch voltage and current constraints that do not meet the diode cut-off characteristics is getting smaller and smaller, and the result is constantly approaching the true value. And the finiteness of all diode on-off state combinations and the existence of true value, so the iterative result must converge and make all diode cut-off characteristic branches meet the constraint conditions at the same time. The complexity analysis of the improved iterative algorithm mentioned above.
设计以下三点前提以消除执行方法下机器速率与示例特殊性的影响：The following three assumptions are designed to eliminate the effect of machine speed and instance specificity under the execution method:
1.定义执行该方法进行一次加减乘除及比较等基本验算均需要相同时间，该时间为单位时间；1. Define that it takes the same time to execute the method to perform basic calculations such as addition, subtraction, multiplication, division, and comparison, and this time is the unit time;
2.方法的复杂性定义为该择径方案的效果，即将固定规模的实例需要被执行基本验算次数的上限；2. The complexity of the method is defined as the effect of the path selection scheme, that is, the upper limit of the number of basic checking calculations that need to be performed for a fixed-scale instance;
3.定义F1(x)与F2(x)为正整数集上的两个正实数函数，若有一个大于零的常数D，使得当x足够大时有F1(x)≤DF2(x)，记F1(x)＝O[F2(x)]。3. Define F 1 (x) and F 2 (x) as two positive real number functions on the set of positive integers, if there is a constant D greater than zero, so that when x is large enough, F 1 (x)≤DF 2 (x), denote F 1 (x)=O[F 2 (x)].
以节点数为x，支路数为b的复杂交通网为例，研究分析该方法的复杂性。该x-1阶非超越模拟电路网络并搜索最大电流通路的验算次数最多为：Taking the complex traffic network with node number x and branch road number b as an example, the complexity of this method is studied and analyzed. The x-1 order non-transcendence analog circuit network and the maximum number of checks to search for the maximum current path are:
其次，假设在最坏情况时所有b个方向限制模型需要全部进行迭代。由于该方法的优化性，每次调整最大电流变化的方向限制模型极性，出现一个、两个或多于两个的方向限制模型极性由符合条件变为不符合条件情况的概率，会随着电路网络规模的增大而趋于0。略去两个或多于两个的情况，并按一个方向限制模型的最坏情况分析。迭代方向限制模型支路的验算次数：Second, assume that in the worst case all b direction-limited models need to be iterated. Due to the optimization of this method, each time the polarity of the direction-limited model of the maximum current change is adjusted, the probability that one, two or more than two direction-limited model polarities will change from meeting the conditions to not meeting the conditions will vary with tends to 0 as the scale of the circuit network increases. Omit two or more cases and limit the worst-case analysis of the model in one direction. The iteration direction limits the number of checks for model branches:
F2＝[b2+(b-1)2+…+22+12]＝O(b3)F 2 =[b 2 +(b-1) 2 +...+2 2 +1 2 ]=O(b 3 )
最后，整个方法的复杂性为F＝F1F2＝O(x4b3)，故该方法有多项式界，即该方法是有效的。Finally, the complexity of the whole method is F=F 1 F 2 =O(x 4 b 3 ), so the method has a polynomial bound, ie the method is efficient.
本发明所提出的路径规划方法还可以扩展应用于有特殊行为要求的机器人控制系统，只要对行为约束条件建立二极管截止特性电子元件模型，应用离散线性化的迭代方法即可求解。The path planning method proposed by the present invention can also be extended and applied to robot control systems with special behavior requirements, as long as the diode cut-off characteristic electronic component model is established for the behavior constraints, and the discrete linearization iteration method can be used to solve the problem.
需要强调的是，本发明所述的实施例是说明性的，而不是限定性的，因此本发明包括并不限于具体实施方式中所述的实施例，凡是由本领域技术人员根据本发明的技术方案得出的其他实施方式，同样属于本发明保护的范围。It should be emphasized that the embodiments described in the present invention are illustrative rather than restrictive, so the present invention includes and is not limited to the embodiments described in the specific implementation, and those skilled in the art according to the technology of the present invention Other implementations derived from the scheme also belong to the protection scope of the present invention.
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