基于贝叶斯概率估计的智能电动车动态目标避障算法
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摘要
为了实现智能电动车在中汽中心智能网联示范基地内的动态避障,首先将直角坐标系与曲线坐标系进行转换,构建以参考路径的弧长s为横坐标,横向偏移距离q为纵坐标的曲线坐标系;其次,在曲线坐标系中利用三次多项式生成满足初始位姿与子目标点位姿的候选路径,同时对标准化常量的似然函数进行定义,在此基础上利用贝叶斯定理对每条候选路径的危险等级进行概率估计;在动态避障过程中,借鉴速度障碍法对碰撞威胁进行实时检测,并建立最短避障时间和安全距离的数学模型来实现高效的动态避障,最后对行人占用车道行走与横穿马路2种典型场景进行动态避障试验。研究结果表明:在曲线坐标系中,通过横向偏移距离能够便捷地建立起一系列候选路径,克服在直角坐标系中寻找移动子目标点这个难题;在寻找安全路径方面,由于智能电动车工作环境的不确定性,利用贝叶斯定理对候选路径危险等级进行概率计算的方法可靠性更高,速度障碍法与避障数学模型的结合满足碰撞危险检测的实时性和动态避障的高效性要求。试验结果表明:采用曲线坐标系中的动态避障算法对行人占用车道和横穿马路2种场景进行了有效的避障,在路径选择上符合实际驾驶习惯,达到了智能网联示范基地动态避障的要求。
In this study, a dynamic obstacle avoidance algorithm based on the Bayesian theory was proposed for an intelligent electric vehicle in the CATARC intelligent network demonstration base. Firstly, the Cartesian coordinate system and the curvilinear coordinate system were transformed, and an arc length with the reference path as the abscissa and the horizontal offset distance as the ordinate of the curvilinear coordinate system was thereby constructed. A cubic polynomial in the curvilinear coordinate system was then employed for generating candidate paths that satisfy the initial pose and the sub-target pose, and the likelihood function of the normalization constant was simultaneously defined. The Bayesian theory was thereby applied for estimating the probability of each candidate path. A mathematical model for the shortest obstacle avoidance time and corresponding safety distance was also established for realizing efficient dynamic obstacle avoidance. Furthermore, a dynamic obstacle avoidance experiment was conducted for two typical scenarios involving pedestrians occupying lanes and crossing roads. The obtained results indicate that a series of candidate paths can be established by incorporating the lateral offset distance in the curvilinear coordinate system, which in turn can overcome the difficulty of locating moving sub-targets in the Cartesian coordinate system. While searching safe paths, owing to the uncertainty of the operating environment of an intelligent electric vehicle, the Bayesian theory is found to be more reliable for probability calculation of candidate path hazards. Combining the velocity obstacle method with an obstacle avoidance mathematical model can help achieve real-time performance of collision risk detection and can meet the high efficiency requirements of dynamic obstacle avoidance. Hence, the proposed dynamic obstacle avoidance algorithm can be applied in the curvilinear coordinate system to effectively avoid obstacles for pedestrians occupying lanes and crossing roads. Furthermore, the proposed route selection process meets the requirements of actual driving habits, and the requirements of dynamic obstacle avoidance in the intelligent network demonstration base can thus be achieved.
In this study, a dynamic obstacle avoidance algorithm based on the Bayesian theory was proposed for an intelligent electric vehicle in the CATARC intelligent network demonstration base. Firstly, the Cartesian coordinate system and the curvilinear coordinate system were transformed, and an arc length with the reference path as the abscissa and the horizontal offset distance as the ordinate of the curvilinear coordinate system was thereby constructed. A cubic polynomial in the curvilinear coordinate system was then employed for generating candidate paths that satisfy the initial pose and the sub-target pose, and the likelihood function of the normalization constant was simultaneously defined. The Bayesian theory was thereby applied for estimating the probability of each candidate path. A mathematical model for the shortest obstacle avoidance time and corresponding safety distance was also established for realizing efficient dynamic obstacle avoidance. Furthermore, a dynamic obstacle avoidance experiment was conducted for two typical scenarios involving pedestrians occupying lanes and crossing roads. The obtained results indicate that a series of candidate paths can be established by incorporating the lateral offset distance in the curvilinear coordinate system, which in turn can overcome the difficulty of locating moving sub-targets in the Cartesian coordinate system. While searching safe paths, owing to the uncertainty of the operating environment of an intelligent electric vehicle, the Bayesian theory is found to be more reliable for probability calculation of candidate path hazards. Combining the velocity obstacle method with an obstacle avoidance mathematical model can help achieve real-time performance of collision risk detection and can meet the high efficiency requirements of dynamic obstacle avoidance. Hence, the proposed dynamic obstacle avoidance algorithm can be applied in the curvilinear coordinate system to effectively avoid obstacles for pedestrians occupying lanes and crossing roads. Furthermore, the proposed route selection process meets the requirements of actual driving habits, and the requirements of dynamic obstacle avoidance in the intelligent network demonstration base can thus be achieved.
引文
[1] GONZALEZ D,PEREZ J,MILANES V,et al.A Review of Motion Planning Techniques for Automated Vehicles [J].IEEE Transactions on Intelligent Transportation Systems,2015,17 (4):1-11.
[2] KRISHNAN J,RAJEEV U P,JAYABALAN J,et al.Optimal Motion Planning Based on Path Length Minimisation [J].Robotics & Autonomous Systems,2017,94:245-263.
[3] DAS P K,BEHERA H S,PANIGRAHI B K.A Hybridization of an Improved Particle Swarm Optimization and Gravitational Search Algorithm for Multi-robot Path Planning [J].Swarm & Evolutionary Computation,2016,28:14-28.
[4] CHU K,LEE M,SUNWOO M.Local Path Planning for Off-road Autonomous Driving with Avoidance of Static Obstacles [J].IEEE Transactions on Intelligent Transportation Systems,2012,13 (4):1599-1616.
[5] 宋晓琳,潘鲁彬,曹昊天.基于改进智能水滴算法的汽车避障局部路径规划[J].汽车工程,2016,38(2):185-191.SONG Xiao-lin,PAN Lu-bin,CAO Hao-tian.Local Path Planning for Vehicle Obstacle Avoidance Based on Improved Intelligent Water Drops Algorithm [J].Automotive Engineering,2016,38 (2):185-191.
[6] CHEN J,ZHAO P,MEI T,et al.Lane Change Path Planning Based on Piecewise Bezier Curve for Autonomous Vehicle [C] // IEEE.Proceedings of 2013 IEEE International Conference on Vehicular Electronics and Safety.New York:IEEE,2013:17-22.
[7] 黄如林,梁华为,陈佳佳,等.基于激光雷达的无人驾驶汽车动态障碍物检测、跟踪与识别方法[J].机器人,2016,38(4):437-443.HUANG Ru-lin,LIANG Hua-wei,CHEN Jia-jia,et al.Lidar Based Dynamic Obstacle Detection,Tracking and Recognition Method for Driverless Cars [J].Robot,2016,38 (4):437-443.
[8] FERGUSON D,DARMS M,URMSON C,et al.Detection,Prediction,and Avoidance of Dynamic Obstacles in Urban Environments [C] // IEEE.Intelligent Vehicles Symposium Conference.New York:IEEE,2008:1149-1154.
[9] 张嘉琦.基于移动子目标的复合式路径规划算法[J].中国公路学报,2017,30(11):138-146.ZHANG Jia-qi.Compound Path Planning Algorithm Based on Sliding Subtarget [J].China Journal of Highway and Transport,2017,30 (11):138-146.
[10] 祁若龙,周维佳,刘金国,等.基于概率论的机器人高斯运动避障轨迹规划方法[J].机械工程学报,2017,53(5):93-100.QI Ruo-long,ZHOU Wei-jia,LIU Jin-guo,et al.Obstacle Avoidance Trajectory Planning for Gaussian Motion of Robot Based on Probability Theory [J].Journal of Mechanical Engineering,2017,53 (5):93-100.
[11] SCHUBERT R,WANIELIK G.A Unified Bayesian Approach for Object and Situation Assessment [J].IEEE Intelligent Transportation Systems Magazine,2011,3 (2):6-19.
[12] KIM J,JO K,LIM W,et al.Curvilinear-coordinate-based Object and Situation Assessment for Highly Automated Vehicles [J].IEEE Transactions on Intelligent Transportation Systems,2015,16 (3):1559-1575.
[13] JO K,LEE M,KIM J,et al.Tracking and Behavior Reasoning of Moving Vehicles Based on Roadway Geometry Constraints [J].IEEE Transactions on Intelligent Transportation Systems,2017,18 (2):1-17.
[14] 杨秀霞,周硙硙,张毅.基于速度障碍圆弧法的UAV自主避障规划研究[J].系统工程与电子技术,2017,39(1):168-176.YANG Xiu-xia,ZHOU Kai-kai,ZHANG Yi.Obstacle Avoidance Planning for UAV Based on Velocity Obstacle Arc Method [J].Systems Engineering and Electronics,2017,39 (1):168-176.
[15] 蒲华燕,丁峰,李小毛,等.基于椭圆碰撞锥的无人艇动态避障方法[J].仪器仪表学报,2017,38(7):1756-1762.PU Hua-yan,DING Feng,LI Xiao-mao,et al.Maritime Autonomous Obstacle Avoidance in a Dynamic Environment Based on Collision Cone of Ellipse [J].Chinese Journal of Scientific Instrument,2017,38 (7):1756-1762.
[16] WALTON D J,MEEK D S,ALI J M.Planar G2 Transition Curves Compose of Cubic Bezier Spiral Segments [J].Journal of Computational and Applied Mathematics,2003,157 (2):453-476.
[17] 陈成,何玉庆,卜春光,等.基于四阶贝塞尔曲线的无人车可行轨迹规划[J].自动化学报,2015,41(3):486-496.CHEN Cheng,HE Yu-qing,BU Chun-guang,et al.Feasible Trajectory Generation for Autonomous Vehicles Based on Quartic Bezier Curve [J].Acta Automatica Sinica,2015,41 (3):486-496.
[18] WANG H,KEARNEY J,ATKINSON K.Arc-length Parameterized Spline Curves for Real-time Simulation [C] // HAGEN H.Proceedings of the Fifth International Conference:Curve and Surface Design.Brentwood:Nashboro Press,2003:387-396.
[19] GUENTER B,PARENT R.Computing the Arc Length of Parametric Curves [J].IEEE Computer Graphics & Applications,1990,10 (3):72-78.
[20] 许小勇,钟太勇.三次样条插值函数的构造与MATLAB实现[J].兵工自动化,2006,25(11):76-78.XU Xiao-yong,ZHONG Tai-yong.Construction and Realization of Cubic Spline Interpolation Function [J].Ordnance Industry Automation,2006,25 (11):76-78.
[21] KALMAN RE.A New Approach to Linear Filtering and Prediction Problems [J].Journal of Basic Engineering Transactions,1960,82:35-44.
[2] KRISHNAN J,RAJEEV U P,JAYABALAN J,et al.Optimal Motion Planning Based on Path Length Minimisation [J].Robotics & Autonomous Systems,2017,94:245-263.
[3] DAS P K,BEHERA H S,PANIGRAHI B K.A Hybridization of an Improved Particle Swarm Optimization and Gravitational Search Algorithm for Multi-robot Path Planning [J].Swarm & Evolutionary Computation,2016,28:14-28.
[4] CHU K,LEE M,SUNWOO M.Local Path Planning for Off-road Autonomous Driving with Avoidance of Static Obstacles [J].IEEE Transactions on Intelligent Transportation Systems,2012,13 (4):1599-1616.
[5] 宋晓琳,潘鲁彬,曹昊天.基于改进智能水滴算法的汽车避障局部路径规划[J].汽车工程,2016,38(2):185-191.SONG Xiao-lin,PAN Lu-bin,CAO Hao-tian.Local Path Planning for Vehicle Obstacle Avoidance Based on Improved Intelligent Water Drops Algorithm [J].Automotive Engineering,2016,38 (2):185-191.
[6] CHEN J,ZHAO P,MEI T,et al.Lane Change Path Planning Based on Piecewise Bezier Curve for Autonomous Vehicle [C] // IEEE.Proceedings of 2013 IEEE International Conference on Vehicular Electronics and Safety.New York:IEEE,2013:17-22.
[7] 黄如林,梁华为,陈佳佳,等.基于激光雷达的无人驾驶汽车动态障碍物检测、跟踪与识别方法[J].机器人,2016,38(4):437-443.HUANG Ru-lin,LIANG Hua-wei,CHEN Jia-jia,et al.Lidar Based Dynamic Obstacle Detection,Tracking and Recognition Method for Driverless Cars [J].Robot,2016,38 (4):437-443.
[8] FERGUSON D,DARMS M,URMSON C,et al.Detection,Prediction,and Avoidance of Dynamic Obstacles in Urban Environments [C] // IEEE.Intelligent Vehicles Symposium Conference.New York:IEEE,2008:1149-1154.
[9] 张嘉琦.基于移动子目标的复合式路径规划算法[J].中国公路学报,2017,30(11):138-146.ZHANG Jia-qi.Compound Path Planning Algorithm Based on Sliding Subtarget [J].China Journal of Highway and Transport,2017,30 (11):138-146.
[10] 祁若龙,周维佳,刘金国,等.基于概率论的机器人高斯运动避障轨迹规划方法[J].机械工程学报,2017,53(5):93-100.QI Ruo-long,ZHOU Wei-jia,LIU Jin-guo,et al.Obstacle Avoidance Trajectory Planning for Gaussian Motion of Robot Based on Probability Theory [J].Journal of Mechanical Engineering,2017,53 (5):93-100.
[11] SCHUBERT R,WANIELIK G.A Unified Bayesian Approach for Object and Situation Assessment [J].IEEE Intelligent Transportation Systems Magazine,2011,3 (2):6-19.
[12] KIM J,JO K,LIM W,et al.Curvilinear-coordinate-based Object and Situation Assessment for Highly Automated Vehicles [J].IEEE Transactions on Intelligent Transportation Systems,2015,16 (3):1559-1575.
[13] JO K,LEE M,KIM J,et al.Tracking and Behavior Reasoning of Moving Vehicles Based on Roadway Geometry Constraints [J].IEEE Transactions on Intelligent Transportation Systems,2017,18 (2):1-17.
[14] 杨秀霞,周硙硙,张毅.基于速度障碍圆弧法的UAV自主避障规划研究[J].系统工程与电子技术,2017,39(1):168-176.YANG Xiu-xia,ZHOU Kai-kai,ZHANG Yi.Obstacle Avoidance Planning for UAV Based on Velocity Obstacle Arc Method [J].Systems Engineering and Electronics,2017,39 (1):168-176.
[15] 蒲华燕,丁峰,李小毛,等.基于椭圆碰撞锥的无人艇动态避障方法[J].仪器仪表学报,2017,38(7):1756-1762.PU Hua-yan,DING Feng,LI Xiao-mao,et al.Maritime Autonomous Obstacle Avoidance in a Dynamic Environment Based on Collision Cone of Ellipse [J].Chinese Journal of Scientific Instrument,2017,38 (7):1756-1762.
[16] WALTON D J,MEEK D S,ALI J M.Planar G2 Transition Curves Compose of Cubic Bezier Spiral Segments [J].Journal of Computational and Applied Mathematics,2003,157 (2):453-476.
[17] 陈成,何玉庆,卜春光,等.基于四阶贝塞尔曲线的无人车可行轨迹规划[J].自动化学报,2015,41(3):486-496.CHEN Cheng,HE Yu-qing,BU Chun-guang,et al.Feasible Trajectory Generation for Autonomous Vehicles Based on Quartic Bezier Curve [J].Acta Automatica Sinica,2015,41 (3):486-496.
[18] WANG H,KEARNEY J,ATKINSON K.Arc-length Parameterized Spline Curves for Real-time Simulation [C] // HAGEN H.Proceedings of the Fifth International Conference:Curve and Surface Design.Brentwood:Nashboro Press,2003:387-396.
[19] GUENTER B,PARENT R.Computing the Arc Length of Parametric Curves [J].IEEE Computer Graphics & Applications,1990,10 (3):72-78.
[20] 许小勇,钟太勇.三次样条插值函数的构造与MATLAB实现[J].兵工自动化,2006,25(11):76-78.XU Xiao-yong,ZHONG Tai-yong.Construction and Realization of Cubic Spline Interpolation Function [J].Ordnance Industry Automation,2006,25 (11):76-78.
[21] KALMAN RE.A New Approach to Linear Filtering and Prediction Problems [J].Journal of Basic Engineering Transactions,1960,82:35-44.