基于可达集的自主车辆安全性验证方法
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摘要
针对自主车辆安全性验证在理论的完备性上无法得到保证的问题,提出一种使用哈密尔顿—雅克比(Hamilton-Jacobi)方程求解车辆运行安全状态空间方法。定义车辆运行不安全状态集合为目标集,逆时间求解目标集对应的车辆运行安全状态边界(可达集边界),并采用具有界面追踪和形状建模数值技术的水平集方法表示目标集和可达集。为了确定目标集在向量场作用下的后向可达集,提出采用求解Hamilton-Jacobi偏微分方程的粘性解的方法。自主车辆追逃安全预警范围验证结果表明,该方法能够提高自主车辆安全决策验证的置信水平,增强自主车辆安全性验证的可靠性。
Because safety verification of autonomous vehicle cannot be guaranteed in the completeness of the theory,a method to solve the safe state space of vehicle operation by using HamiltonJacobi partial equation is proposed. The set of unsafe states of vehicle operation is defined as the target set,and then the safe state boundary of vehicle operation( reachable set) corresponding to the target set is solved in inverse time. The target set and the reachable set are represented by level set method with the numerical techniques of interface tracking and shape modeling. In order to determine the backward reachable set which is obtained from the target set under the action of vector field,a method to solve the viscosity solution of Hamilton-Jacobi partial differential equation is presented. The verification results of safety warning range about two autonomous vehicles ' pursuitevasion games show that the proposed method can increase the confidence level of safety verification approach for autonomous vehicle decision and improve the reliability of the systemsafety verification.
Because safety verification of autonomous vehicle cannot be guaranteed in the completeness of the theory,a method to solve the safe state space of vehicle operation by using HamiltonJacobi partial equation is proposed. The set of unsafe states of vehicle operation is defined as the target set,and then the safe state boundary of vehicle operation( reachable set) corresponding to the target set is solved in inverse time. The target set and the reachable set are represented by level set method with the numerical techniques of interface tracking and shape modeling. In order to determine the backward reachable set which is obtained from the target set under the action of vector field,a method to solve the viscosity solution of Hamilton-Jacobi partial differential equation is presented. The verification results of safety warning range about two autonomous vehicles ' pursuitevasion games show that the proposed method can increase the confidence level of safety verification approach for autonomous vehicle decision and improve the reliability of the systemsafety verification.
引文
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[11]李治平.偏微分方程数值解讲义[M].北京:北京大学出版社,2010:94-97.
[2]刘秉政,曹凯.自主车辆行为决策的安全验证方法[J].山东理工大学学报(自然科学版),2011,25(6):6-12.
[3]方敏,张雅顺,李辉.混合系统的形式验证方法[J].系统仿真学报,2006,18(10):2921-2924.
[4]MITSHELL I M.A toolbox of level set methods[D].Columbia:University of British Columbia,2004.
[5]甘庭,夏壁灿.运用栅栏函数验证连续系统的有界时间安全性[J].软件学报,2016,27(3):645-654.
[6]罗来豹,方敏,刘震.形式验证中近似流管道的算法研究[J].合肥工业大学学报(自然科学版),2010,33(10):1506-1509.
[7]MOUSSA M,NACIM R,LOUISE T,et al.A CSP versus azonotope-based method for solving guard set intersection in nonlinear hybrid reachability[J].Mathematics in Computer Science,2014,8(3-4):407-423.
[8]NAZIN A V,NAZIN S A,POLYAK B T.On convergence of external ellipsoidal approximations of the reachability domains of discrete dynamic linear systems[J].Automation and Remote Control,2004,65(8):1210-1230.
[9]陈涛.等几何分析方法的本质边界条件处理研究[D].西安:西北工业大学航空学院,2016.
[10]ZHU P,ZHOU S Z.Relaxation Lax-friedrichs sweeping scheme for static Hamilton-Jacobi equations[J].Numerical Algorithms,2010,54(3):325-342.
[11]李治平.偏微分方程数值解讲义[M].北京:北京大学出版社,2010:94-97.