技术领域technical field
本发明属于汽车技术领域。The invention belongs to the technical field of automobiles.
背景技术Background technique
由于汽车保有量迅速增加，道路交通问题日益严峻，交通环境逐渐恶化，交通拥堵情况不仅导致废气排放成为影响城市空气质量的重要因素，而且还造成了时间与资源的浪费。为了缓解城市道路交通压力，应付越来越严格的排放标准，提高汽车燃油经济性，一方面国内外一些汽车公司相继开发了发动机快速启/停系统。然而在频繁起步停车的城市交通中，发动机启停技术的应用虽然不仅带来明显的节油效果，对于减少尾气排放也起到了非常积极的作用，但是不可避免的会对发动机造成损害，而且自动启停系统养护成本较高。另外一方面先进的智能交通信号管理系统的应用，这为驾驶员节省了许多时间与资源，提高道路通行能力。但是在实际应用中对先进的智能交通系统的管理是十分昂贵的；而且即使应用了智能交通管理系统，也经常发生一种情况，即在自主驾驶车辆经过一个绿灯的路口时，交通信号灯会突然变红。这种由于缺少未来对一段时间内交通信号灯变化的了解，导致增加了车辆的燃油消耗，行驶时间以及发动机和刹车系统的磨损。为此本专利提出了基于交通信号灯的自主驾驶车辆轨迹预测控制方法，这样使得自主驾驶车辆可以根据交通信号灯的变化自动的来调节车辆的速度，使得自主驾驶车辆到达交通信号灯时正好是绿灯，以减少车辆等待时间和燃油消耗，提高交通路口的交通能力。Due to the rapid increase in car ownership, road traffic problems are becoming more and more serious, and the traffic environment is gradually deteriorating. Traffic congestion not only makes exhaust emissions become an important factor affecting urban air quality, but also causes waste of time and resources. In order to alleviate the pressure of urban road traffic, cope with increasingly stringent emission standards, and improve the fuel economy of automobiles, some automobile companies at home and abroad have successively developed engine quick start/stop systems. However, in urban traffic with frequent starts and stops, although the application of engine start-stop technology not only brings obvious fuel-saving effects, but also plays a very positive role in reducing exhaust emissions, it will inevitably cause damage to the engine, and the automatic The maintenance cost of the start-stop system is relatively high. On the other hand, the application of advanced intelligent traffic signal management system saves a lot of time and resources for drivers and improves road traffic capacity. However, the management of advanced intelligent traffic systems is very expensive in practice; turn red. This lack of future knowledge of traffic light changes over time results in increased vehicle fuel consumption, travel time, and wear on the engine and braking system. For this reason, this patent proposes an autonomous driving vehicle track prediction control method based on traffic lights, so that the autonomous driving vehicle can automatically adjust the speed of the vehicle according to the change of the traffic signal light, so that when the autonomous driving vehicle reaches the traffic signal light, it happens to be a green light. Reduce vehicle waiting time and fuel consumption, and improve traffic capacity at traffic intersections.
发明内容Contents of the invention
本发明的目的是实时的基于交通信号灯信息对自主驾驶车辆进行轨迹预测控制，最大限度减少停车次数，实现节能减排效果的基于交通信号灯的自主驾驶车辆轨迹预测控制方法。The object of the present invention is to carry out track prediction control on autonomous driving vehicles based on traffic signal light information in real time, minimize the number of stops, and realize the self-driving vehicle trajectory prediction control method based on traffic signal lights to achieve the effect of energy saving and emission reduction.
本发明的步骤是：The steps of the present invention are:
（1）信息采集：自主驾驶车辆采集当前车辆和前方车辆的速度信息；采集预测距离内道路情况，包括检测前方道路路口及前方交通灯位置以及道路交通限速情况；获取路口交通信号灯状态以及通行时间用以后续的优化求解；(1) Information collection: the self-driving vehicle collects the speed information of the current vehicle and the vehicle in front; collects the road conditions within the predicted distance, including detecting the intersection of the road ahead, the position of the traffic light ahead and the speed limit of the road traffic; obtains the status of the traffic signal light at the intersection and the passage The time is used for subsequent optimization solution;
（2）车辆动力学建模：以采集的当前车辆的速度信息为基础，以车辆驱动力和制动力为控制变量，车速和位移作为状态变量，根据汽车纵向动力学可以得到车辆的动力学方程：(2) Vehicle dynamics modeling: based on the collected speed information of the current vehicle Based on the vehicle driving force and braking force is the control variable, the vehicle speed and displacement As a state variable, the dynamic equation of the vehicle can be obtained according to the longitudinal dynamics of the vehicle:
（1） (1)
其中，为车重，为车辆行驶过程的阻力，包括空气阻力、滚动阻力和坡度阻力，有in, is the vehicle weight, The resistance of the vehicle running process, including air resistance, rolling resistance and slope resistance, has
(2) (2)
其中，为车辆迎风面积，为空气阻力系数，为重力加速度，为道路坡度；考虑目标车辆应减少制动以减少能量消耗，车辆燃油经济性和驾驶员期望综合指标为：in, frontal area of the vehicle , is the air resistance coefficient, is the acceleration of gravity , is the road slope; considering that the target vehicle should reduce braking to reduce energy consumption, the comprehensive index of vehicle fuel economy and driver expectation is:
(3) (3)
其中为权重系数，是采集的当前车辆的速度；in is the weight coefficient, is the speed of the current vehicle collected;
（3）自主驾驶车辆轨迹规划控制问题在线优化求解(3) Online optimization solution to the trajectory planning control problem of autonomous driving vehicles
将采集的预测距离内的道路信息，道路交通信号灯状态及可通行时间作为约束，以车辆的动力学模型为基础，综上所述，基于交通信号灯信息的自主驾驶车辆轨迹优化问题可以描述为：Taking the collected road information within the predicted distance, the state of road traffic lights and the available time as constraints, and based on the dynamic model of the vehicle, in summary, the trajectory optimization problem of autonomous driving vehicles based on traffic signal information can be described as:
（4） (4)
其中，为预测时域，为交通信号灯可通行时间，为驱动力，为制动力，为最大驱动力，为最大制动力，、分别是车辆当前的速度及位置，、分别是车辆时刻的速度及位置；in, For the prediction time domain, is the passing time of traffic lights, as the driving force, is the braking force, is the maximum driving force, is the maximum braking force, , are the current speed and position of the vehicle, respectively, , respectively vehicles The speed and position of the moment;
为保证系统的实时性能，在非限制性求解示例中，运用极大值原理求解两点边值问题，得到上述优化问题的显示解：In order to ensure the real-time performance of the system, in a non-restricted solution example, the maximum value principle is used to solve the two-point boundary value problem, and the explicit solution of the above optimization problem is obtained:
定义哈密顿方程：Define the Hamiltonian equation:
(5) (5)
其中；in ;
根据极大值原理，在预测时域内，协态变量在最优轨线上满足：According to the maximum value principle, in the prediction time domain, the co-state variables satisfy on the optimal trajectory:
(6) (6)
在最优轨线上，最优控制变量使哈密顿函数达到极小值，即On the optimal trajectory, the optimal control variable makes the Hamiltonian function reach the minimum value, that is,
(7) (7)
终端横截条件满足，函数在最优轨线终点满足；最终得到最优控制问题的显式解：The terminal transversal condition satisfies , The function satisfies at the end of the optimal trajectory ; Finally, an explicit solution to the optimal control problem is obtained:
(8) (8)
根据动力学方程和协态变量满足的方程组，在边界条件下，结合以上控制律，求出预测时域内的最优的车辆驱动力序列，提取车辆驱动力序列的第一个值给定车辆，下一个采样时刻重复上述步骤，从而实现滚动优化控制。According to the equations satisfied by the dynamic equations and co-state variables, under the boundary conditions, combined with the above control laws, the optimal vehicle driving force sequence in the prediction time domain is obtained, and the first value of the vehicle driving force sequence is extracted for a given vehicle , and repeat the above steps at the next sampling moment, so as to realize rolling optimization control.
本发明带来的有益效果是：Thebeneficial effects brought by the present invention are:
1.自主驾驶车辆能够根据交通信号灯的信息，优化出预测距离内的速度轨迹，使车辆顺利通过交通路口，减少车辆停车次数。1. Autonomous driving vehicles can optimize the speed trajectory within the predicted distance according to the information of traffic lights, so that the vehicle can pass through the traffic intersection smoothly and reduce the number of vehicle parking.
2.能够大幅减少自主驾驶车辆由于交通灯而频繁启停的情况，减少车辆在路口等车时间，提高车辆在交通路口的通过能力。2. It can greatly reduce the frequent start and stop of self-driving vehicles due to traffic lights, reduce the waiting time of vehicles at intersections, and improve the passing ability of vehicles at traffic intersections.
3.在保证安全的情况下，能够减少自主驾驶车辆在路口的燃油消耗，提高车辆在通过交通路口时的燃油经济性。3. Under the condition of ensuring safety, it can reduce the fuel consumption of self-driving vehicles at intersections and improve the fuel economy of vehicles passing through traffic intersections.
附图说明Description of drawings
图1为本发明的结构框图；Fig. 1 is a block diagram of the present invention;
图2为本发明的流程图；Fig. 2 is a flowchart of the present invention;
图3为本发明轨迹规划描述图；Fig. 3 is a description diagram of trajectory planning of the present invention;
图4为本发明轨迹规划断点描述图；Fig. 4 is a description diagram of a trajectory planning breakpoint in the present invention;
图5为本发明轨迹规划约束描述图。Fig. 5 is a description diagram of trajectory planning constraints in the present invention.
具体实施方式Detailed ways
本发明的步骤是：The steps of the present invention are:
（1）信息采集：自主驾驶车辆采集当前车辆和前方车辆的速度信息；采集预测距离内道路情况，包括检测前方道路路口及前方交通灯位置以及道路交通限速情况；获取路口交通信号灯状态以及通行时间用以后续的优化求解；(1) Information collection: the self-driving vehicle collects the speed information of the current vehicle and the vehicle in front; collects the road conditions within the predicted distance, including detecting the intersection of the road ahead, the position of the traffic light ahead and the speed limit of the road traffic; obtains the status of the traffic signal light at the intersection and the passage The time is used for subsequent optimization solution;
（2）车辆动力学建模：以采集的当前车辆的速度信息为基础，以车辆驱动力和制动力为控制变量，车速和位移作为状态变量，根据汽车纵向动力学可以得到车辆的动力学方程：(2) Vehicle dynamics modeling: based on the collected speed information of the current vehicle Based on the vehicle driving force and braking force is the control variable, the vehicle speed and displacement As a state variable, the dynamic equation of the vehicle can be obtained according to the longitudinal dynamics of the vehicle:
（1） (1)
其中，为车重，为车辆行驶过程的阻力，包括空气阻力、滚动阻力和坡度阻力，有in, is the vehicle weight, The resistance of the vehicle running process, including air resistance, rolling resistance and slope resistance, has
(2) (2)
其中，为车辆迎风面积，为空气阻力系数，为重力加速度，为道路坡度；考虑目标车辆应减少制动以减少能量消耗，车辆燃油经济性和驾驶员期望综合指标为：in, frontal area of the vehicle , is the air resistance coefficient, is the acceleration of gravity , is the road slope; considering that the target vehicle should reduce braking to reduce energy consumption, the comprehensive index of vehicle fuel economy and driver expectation is:
(3) (3)
其中为权重系数，是采集的当前车辆的速度；in is the weight coefficient, is the speed of the current vehicle collected;
（3）自主驾驶车辆轨迹规划控制问题在线优化求解(3) Online optimization solution to the trajectory planning control problem of autonomous driving vehicles
将采集的预测距离内的道路信息，道路交通信号灯状态及可通行时间作为约束，以车辆的动力学模型为基础，综上所述，基于交通信号灯信息的自主驾驶车辆轨迹优化问题可以描述为：Taking the collected road information within the predicted distance, the state of road traffic lights and the available time as constraints, and based on the dynamic model of the vehicle, in summary, the trajectory optimization problem of autonomous driving vehicles based on traffic signal information can be described as:
（4） (4)
其中，为预测时域，为交通信号灯可通行时间，为驱动力，为制动力，为最大驱动力，为最大制动力，、分别是车辆当前的速度及位置，、分别是车辆时刻的速度及位置；in, For the prediction time domain, is the passing time of traffic lights, as the driving force, is the braking force, is the maximum driving force, is the maximum braking force, , are the current speed and position of the vehicle, respectively, , respectively vehicles The speed and position of the moment;
为保证系统的实时性能，在非限制性求解示例中，运用极大值原理求解两点边值问题，得到上述优化问题的显示解：In order to ensure the real-time performance of the system, in a non-restricted solution example, the maximum value principle is used to solve the two-point boundary value problem, and the explicit solution of the above optimization problem is obtained:
定义哈密顿方程：Define the Hamiltonian equation:
(5) (5)
其中；in ;
根据极大值原理，在预测时域内，协态变量在最优轨线上满足：According to the maximum value principle, in the prediction time domain, the co-state variables satisfy on the optimal trajectory:
(6) (6)
在最优轨线上，最优控制变量使哈密顿函数达到极小值，即On the optimal trajectory, the optimal control variable makes the Hamiltonian function reach the minimum value, that is,
(7) (7)
终端横截条件满足，函数在最优轨线终点满足；最终得到最优控制问题的显式解：The terminal transversal condition satisfies , The function satisfies at the end of the optimal trajectory ; Finally, an explicit solution to the optimal control problem is obtained:
(8) (8)
根据动力学方程和协态变量满足的方程组，在边界条件下，结合以上控制律，求出预测时域内的最优的车辆驱动力序列，提取车辆驱动力序列的第一个值给定车辆，下一个采样时刻重复上述步骤，从而实现滚动优化控制。According to the equations satisfied by the dynamic equations and co-state variables, under the boundary conditions, combined with the above control laws, the optimal vehicle driving force sequence in the prediction time domain is obtained, and the first value of the vehicle driving force sequence is extracted for a given vehicle , and repeat the above steps at the next sampling moment, so as to realize rolling optimization control.
以下结合技术方案和附图详细阐述本发明的具体实施方式。The specific implementation manners of the present invention will be described in detail below in conjunction with the technical solutions and accompanying drawings.
本发明的结构框图如图1所示，主要包括信息采集单元、车辆建模单元、滚动时域优化计算单元；信息采集单元主要用于同时采集自车的行驶状态信息以及道路交通信息，并将有效信息传递给车辆建模单元，车辆建模单元根据采集的信息确定优化计算所需要的各种参数，建立车辆模型并设定求解目标函数，优化计算车辆的速度轨迹；滚动时域优化计算单元将得到的速度轨迹的第一个值给定车辆，实现滚动优化。The structural block diagram of the present invention is as shown in Figure 1, mainly comprises information collection unit, vehicle modeling unit, rolling time-domain optimization calculation unit; Effective information is transmitted to the vehicle modeling unit, and the vehicle modeling unit determines various parameters required for optimization calculation according to the collected information, establishes the vehicle model and sets the solution objective function, and optimizes the calculation of the vehicle's speed trajectory; the rolling time domain optimization calculation unit The first value of the obtained velocity trajectory is given to the vehicle to achieve rolling optimization.
1，首先检测当前目标车辆和前方车辆及道路环境的状态，包括预测距离内道路情况，道路路口1. First detect the state of the current target vehicle, the vehicle in front and the road environment, including the road conditions within the predicted distance, road intersections
及前方交通灯位置，路口交通灯实时信息、道路交通要求如限速等；And the position of traffic lights ahead, real-time information of traffic lights at intersections, road traffic requirements such as speed limit, etc.;
图3揭示了本发明的示例性实施例，自主驾驶车辆10其沿着道路200行驶，车辆10对应在道路200上的该车辆的当前位置，该车辆以当前速度行驶，图中用210表示；图中220表示道路交通灯的位置，230为道路速度限速，车辆10前方距离内没有路口及其他车辆干扰，此时选定车辆10到下一个交通信号灯的位置之间的距离作为预测距离，图中用20表示。当车辆的控制单元判断汽车在驾驶员给出的期望车速210下不能通过下一个路口220时，下一个交通灯路口220作为终端约束设置为停车，在此期间车辆以低于期望车速的速度进行经济性驾驶，减少燃油消耗。当车辆的控制单元判断在驾驶员给出的期望车速210下能够通过下一个路口220时，车辆以高于驾驶员期望车速的速度运行，通过给出适当的终端约束，保证车辆顺利通过路口。综上，假设在当前时刻，下一个交通灯可通行时间（绿灯的时间）为，则交通灯对预测时域和终端约束的影响可以表达成以下形式：Figure 3 discloses an exemplary embodiment of the invention, an autonomously driven vehicle 10 traveling along a road 200, the vehicle 10 corresponding to the vehicle's current position on the road 200, the vehicle traveling at a current speed Driving, represented by 210 in the figure; 220 represents the position of road traffic lights in the figure, 230 is the speed limit of the road, there is no intersection and other vehicles interference in the distance ahead of vehicle 10, at this time, select the position of vehicle 10 to the next traffic signal light The distance between is used as the predicted distance , represented by 20 in the figure. When the control unit of the vehicle judges that the car cannot pass the next intersection 220 under the expected speed 210 given by the driver, the next traffic light intersection 220 is set as a terminal constraint to stop, during which the vehicle proceeds at a speed lower than the expected speed. Drive economically and reduce fuel consumption. When the control unit of the vehicle judges that the next intersection 220 can be passed at the expected speed 210 given by the driver, the vehicle runs at a speed higher than the driver's expected speed, and by giving appropriate terminal constraints, the vehicle can pass through the intersection smoothly. To sum up, assuming that at the current moment, the next traffic light time (the time of green light) is , then the impact of traffic lights on the prediction time domain and terminal constraints can be expressed in the following form:
1.当车辆以期望车速的平均车速不能通过下一个交通灯，此时车辆以略低于期望车速的速度行驶，增大汽车滑行距离，减少车量的能量损耗。此时车辆在下一个交通灯前停车；1. When The vehicle cannot pass the next traffic light at the average speed of the expected speed. At this time, the vehicle travels at a speed slightly lower than the expected speed, which increases the sliding distance of the car and reduces the energy loss of the vehicle. At this time, the vehicle stops before the next traffic light;
2.当车辆以期望车速的平均车速能通过下一个交通灯，此时车辆以略高于期望车速的速度行驶，此时车辆在交通灯变成红色前通过交通灯。2. When The vehicle can pass the next traffic light at an average speed of the expected speed, when the vehicle is traveling at a speed slightly higher than the expected speed, and when the vehicle passes the traffic light before it turns red.
当车辆的安全距离内出现路口或者其他车辆超车并道的情况，我们称这种情况为断点。图4中车辆10在道路200上行驶。行驶过程中，在前方安全距离内检测前方出现路口240，此时车辆以当前位置到此路口的距离30为新的预测距离，重新进行经济性优化，终端约束适当减少车辆在路口的速度，以保证车辆通过路口时的安全。When there is an intersection or other vehicles overtaking and merging within the safe distance of the vehicle, we call this situation a breakpoint. In FIG. 4 a vehicle 10 is traveling on a road 200 . During the driving process, an intersection 240 is detected in front of the safe distance ahead, and at this time, the vehicle uses the distance 30 from the current position to the intersection as the new predicted distance , re-optimize the economy, and reduce the speed of the vehicle at the intersection appropriately to ensure the safety of the vehicle when passing the intersection.
图5中自主驾驶车辆10在道路200上行驶，行驶过程中，车辆110以速度120超车并在230处并道，自主驾驶车辆10至交通信号灯的距离为，用40表示，速度为，用210表示，车辆110到交通灯的距离为，用50表示，速度为，用120表示，自主驾驶车辆10通过确定前方车辆速度和自主驾驶车辆的期望车速判断自主驾驶模式：In Fig. 5 , the self-driving vehicle 10 is driving on the road 200. During the driving process, the vehicle 110 overtakes at a speed of 120 and merges at 230. The distance from the self-driving vehicle 10 to the traffic light is , represented by 40, the speed is , denoted by 210, the distance from the vehicle 110 to the traffic light is , represented by 50, the speed is , denoted by 120 , the autonomous vehicle 10 determines the speed of the vehicle ahead by and the expected speed of the autonomous vehicle Judging the autonomous driving mode:
1)当前车的速度以高于自主驾驶车辆的期望车速行驶时，判断出前方车辆对目标车辆轨迹规划没有约束，此时采集前端车辆的加速度和速度来预测未来一段时间内前车的速度轨迹，确定出车辆10在整个轨迹规划过程中的最高车速，并以此作为车辆10在优化问题中的约束。保证自主驾驶中车辆10与前车110的安全距离。1) When the speed of the front vehicle is higher than the expected speed of the self-driving vehicle, it is judged that the vehicle in front has no constraints on the trajectory planning of the target vehicle. At this time, the acceleration and speed of the front vehicle are collected to predict the speed trajectory of the front vehicle in the future , determine the maximum vehicle speed of the vehicle 10 in the entire trajectory planning process, and use it as a constraint of the vehicle 10 in the optimization problem. Ensure the safe distance between the vehicle 10 and the preceding vehicle 110 during autonomous driving.
2)当前车的速度以低于自主驾驶车辆的期望车速行驶时，判断前方车辆对目标车辆通过交通灯造成影响。当时，判断前方车辆对目标车辆通过交通灯造成影响，此时汽车转入自适应巡航模式，采取自适应跟车策略。2) When the speed of the front vehicle is lower than the expected speed of the self-driving vehicle, it is judged that the front vehicle has an impact on the target vehicle passing the traffic light. when At this time, it is judged that the vehicle in front has an impact on the target vehicle passing through the traffic lights. At this time, the car switches to the adaptive cruise mode and adopts an adaptive car following strategy.
2，建立自主驾驶车辆行驶过程中的车辆模型，并确定出自主驾驶过程中轨迹规划的目标函数。2. Establish the vehicle model during the driving process of the autonomous driving vehicle, and determine the objective function of the trajectory planning during the autonomous driving process.
以车辆驱动力和制动力为控制变量，车速和位移作为状态变量，根据汽车纵向动力学可以得到车辆的动力学方程：drive by vehicle and braking force is the control variable, the vehicle speed and displacement As a state variable, the dynamic equation of the vehicle can be obtained according to the longitudinal dynamics of the vehicle:
(1) (1)
其中，为车重，为车辆行驶过程的阻力，包括空气阻力、滚动阻力和坡度阻力，有in, is the vehicle weight, The resistance of the vehicle running process, including air resistance, rolling resistance and slope resistance, has
(2) (2)
其中，为车辆迎风面积，为空气阻力系数，为重力加速度，为道路坡度。in, frontal area of the vehicle , is the air resistance coefficient, is the acceleration of gravity , is the road slope.
考虑目标车辆应减少制动量以减少能耗，车辆燃油经济性和驾驶员期望综合指标为Considering that the target vehicle should reduce the amount of braking to reduce energy consumption, the comprehensive index of vehicle fuel economy and driver expectation is
(3) (3)
其中（）为权重系数。针对上述目的，综合考虑道路信号灯信息等环境因素，以车辆燃油消耗为目标函数进行优化控制。综上所述，基于道路信号灯信息的自主驾驶轨迹优化问题可以描述为：in ( ) is the weight coefficient. For the above purpose, the environmental factors such as road signal light information are considered comprehensively, and the vehicle fuel consumption is used as the objective function to carry out optimal control. In summary, the autonomous driving trajectory optimization problem based on road signal information can be described as:
(4) (4)
其中，为预测时域，是交通信号灯可通行时间，为驱动力，为制动力，为最大驱动力，为最大制动力。in, For the prediction time domain, is the passable time of traffic lights, as the driving force, is the braking force, is the maximum driving force, is the maximum braking force.
3，建立优化控制模型并在线求解，得到未来一断时间内的需求驱动力和制动力；将预测时域分成N段，将第一段的控制量作为目标车辆的执行指令，实现自主驾驶车辆的滚动优化；在下一个采样时刻重复控制过程，实现反馈控制。3. Establish an optimized control model and solve it online to obtain the demanded driving force and braking force in the future; divide the forecast time domain into N segments, and use the control amount of the first segment as the execution command of the target vehicle to realize autonomous driving vehicles The rolling optimization of ; repeat the control process at the next sampling time to realize feedback control.
为保证系统的实时性能，在非限制性求解示例中，本发明运用极大值原理求解两点边值问题，得到上述优化问题的显示解：In order to ensure the real-time performance of the system, in a non-restrictive solution example, the present invention uses the maximum value principle to solve the two-point boundary value problem, and obtains the explicit solution of the above-mentioned optimization problem:
定义哈密顿方程：Define the Hamiltonian equation:
(5) (5)
其中。in .
根据极大值原理，在预测时域内，协态变量在最优轨线上满足：According to the maximum value principle, in the prediction time domain, the co-state variables satisfy on the optimal trajectory:
(6) (6)
在最优轨线上，最优控制变量使哈密顿函数达到极小值，即On the optimal trajectory, the optimal control variable makes the Hamiltonian function reach the minimum value, that is,
(7) (7)
终端横截条件满足，函数在最优轨线终点满足。最终得到最优控制问题的显式解：The terminal transversal condition satisfies , The function satisfies at the end of the optimal trajectory . Finally, an explicit solution to the optimal control problem is obtained:
(8) (8)
根据统动力学方程和协态变量满足的方程组，在边界条件下，结合以上控制律，可以求出预测时域内的最优控制量，提取出第一个控制量给定车辆，实现滚动优化控制。According to the equations satisfied by the statistic dynamics equation and the co-state variable, under the boundary conditions, combined with the above control laws, the optimal control quantity in the forecast time domain can be obtained, and the first control quantity can be extracted to specify the vehicle to realize the rolling optimization control.
| Application Number | Priority Date | Filing Date | Title |
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| CN201510302819.8ACN105035090B (en) | 2015-06-06 | 2015-06-06 | Autonomous land vehicle trajectory predictions control method based on traffic lights |
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| CN201510302819.8ACN105035090B (en) | 2015-06-06 | 2015-06-06 | Autonomous land vehicle trajectory predictions control method based on traffic lights |
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| CN105035090Atrue CN105035090A (en) | 2015-11-11 |
| CN105035090B CN105035090B (en) | 2017-10-13 |
| Application Number | Title | Priority Date | Filing Date |
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| CN201510302819.8AActiveCN105035090B (en) | 2015-06-06 | 2015-06-06 | Autonomous land vehicle trajectory predictions control method based on traffic lights |
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