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GUIZILINI V , RAMOS F . Variational Hilbert regression for terrain modeling and trajectory optimization [J ] . The International Journal of Robotics Research , 2019 , 38 ( 12/13 ): 1375 - 1387 . DOI: 10.1177/0278364919844586 http://doi.org/10.1177/0278364919844586 http://journals.sagepub.com/doi/10.1177/0278364919844586 http://journals.sagepub.com/doi/10.1177/0278364919844586 The ability to generate accurate terrain models is of key importance in a wide variety of robotics tasks, ranging from path planning and trajectory optimization to environment exploration and mining applications. This paper introduces a novel regression methodology for terrain modeling that can approximate arbitrarily complex functions based on a series of simple kernel calculations, using variational Bayesian inference. A sparse feature vector is used to efficiently project input points into a high-dimensional reproducing kernel Hilbert space, according to a set of inducing points automatically generated from clustering available data. Each inducing point maintains its own regression model in addition to individual kernel parameters, and the entire set is iteratively optimized as more data are collected in order to maximize a global variational lower bound. We also show how kernel and regression model parameters can be jointly learned, to achieve a better approximation of the underlying function. Experimental results show that the proposed methodology consistently outperforms current state-of-the-art techniques, while producing a continuous model with a fully probabilistic treatment of uncertainties, well-defined gradients, and highly scalable to large-scale datasets. As a practical application of the proposed terrain modeling technique, we explore the problem of trajectory optimization, deriving gradients that allow the efficient generation of continuous paths using standard optimization algorithms, minimizing a series of useful properties (i.e. distance traveled, changes in elevation, and terrain variance).

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ZHOU B , YI J J , ZHANG X K , et al . An autonomous navigation approach for unmanned vehicle in outdoor unstructured terrain with dynamic and negative obstacles [J ] . Robotica , 2022 , 40 ( 8 ): 2831 - 2854 . DOI: 10.1017/S0263574721001983 http://doi.org/10.1017/S0263574721001983 https://www.cambridge.org/core/product/identifier/S0263574721001983/type/journal_article https://www.cambridge.org/core/product/identifier/S0263574721001983/type/journal_article At present, the study on autonomous unmanned ground vehicle navigation in an unstructured environment is still facing great challenges and is of great significance in scenarios where search and rescue robots, planetary exploration robots, and agricultural robots are needed. In this paper, we proposed an autonomous navigation method for unstructured environments based on terrain constraints. Efficient path search and trajectory optimization on octree map are proposed to generate trajectories, which can effectively avoid various obstacles in off-road environments, such as dynamic obstacles and negative obstacles, to reach the specified destination. We have conducted empirical experiments in both simulated and real environments, and the results show that our approach achieved superior performance in dynamic obstacle avoidance tasks and mapless navigation tasks compared to the traditional 2-dimensional or 2.5-dimensional navigation methods.

PHILIPP KRÜSI , FURGALE P , BOSSE M , et al . Driving on point clouds:motion planning, trajectory optimization, and terrain assessment in generic nonplanar environments [J ] . Journal of Field Robotics , 2017 , 34 ( 5 ): 940 - 984 . DOI: 10.1002/rob.2017.34.issue-5 http://doi.org/10.1002/rob.2017.34.issue-5 https://onlinelibrary.wiley.com/toc/15564967/34/5 https://onlinelibrary.wiley.com/toc/15564967/34/5

ZHANG K , YANG Y , FU M Y , et al . Traversability assessment and trajectory planning of unmanned ground vehicles with suspension systems on rough terrain [J ] . Sensors , 2019 , 19 ( 20 ): 4372 . DOI: 10.3390/s19204372 http://doi.org/10.3390/s19204372 https://www.mdpi.com/1424-8220/19/20/4372 https://www.mdpi.com/1424-8220/19/20/4372 This paper presents a traversability assessment method and a trajectory planning method. They are key features for the navigation of an unmanned ground vehicle (UGV) in a non-planar environment. In this work, a 3D light detection and ranging (LiDAR) sensor is used to obtain the geometric information about a rough terrain surface. For a given SE(2) pose of the vehicle and a specific vehicle model, the SE(3) pose of the vehicle is estimated based on LiDAR points, and then a traversability is computed. The traversability tells the vehicle the effects of its interaction with the rough terrain. Note that the traversability is computed on demand during trajectory planning, so there is not any explicit terrain discretization. The proposed trajectory planner finds an initial path through the non-holonomic A*, which is a modified form of the conventional A* planner. A path is a sequence of poses without timestamps. Then, the initial path is optimized in terms of the traversability, using the method of Lagrange multipliers. The optimization accounts for the model of the vehicle’s suspension system. Therefore, the optimized trajectory is dynamically feasible, and the trajectory tracking error is small. The proposed methods were tested in both the simulation and the real-world experiments. The simulation experiments were conducted in a simulator called Gazebo, which uses a physics engine to compute the vehicle motion. The experiments were conducted in various non-planar experiments. The results indicate that the proposed methods could accurately estimate the SE(3) pose of the vehicle. Besides, the trajectory cost of the proposed planner was lower than the trajectory costs of other state-of-the-art trajectory planners.

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周梦如 , 陈慧岩 , 熊光明 , 等 . 越野环境下无人履带平台的道路可通行性分析 [J ] . 兵工学报 , 2022 , 43 ( 10 ): 2485 - 2496 . DOI: 10.12382/bgxb.2021.0824 http://doi.org/10.12382/bgxb.2021.0824 针对越野环境下道路特征模糊、地形复杂的问题，基于相机与激光雷达融合感知的方案，提出一种针对无人履带平台道路可通行性分析方法。基于图像语义分割获取语义点云，进行可通行区域的粗提取；利用三维点云描述地面几何特征，同时考虑履带平台的通过性约束，对道路的可通行性进行分析；生成包含道路表面属性和地面几何信息的三维可通行性栅格地图。所提方法对于平台可通行性的定义反映了平台-环境的强耦合关系。试验结果表明，算法能够在线稳定地建立可通行性地图，对平台规划控制具有良好的引导作用，有利于无人履带平台在复杂越野环境下的稳定通行。

ZHOU M Y , CHEN H Y , XIONG G M , et al . Road traversability analysis of unmanned tracked platform in off-road environment [J ] . Acta Armamentarii , 2022 , 43 ( 10 ): 2485 - 2496 . (in Chinese) DOI: 10.12382/bgxb.2021.0824 http://doi.org/10.12382/bgxb.2021.0824 To deal with the problems of fuzzy road features and complex terrain in off-road environment, a road traversability analysis method for unmanned tracked platforms is proposed based on the fusion scheme of camera and lidar for sensing. Firstly, the semantic point cloud is obtained based on image semantic segmentation, and the passable area is roughly extracted. Then the three-dimensional point cloud is used to describe the ground geometric features, and road traversability is analyzed considering the trafficability constraints of the tracked platform. Finally, a three-dimensional traversable grid map containing road surface attributes and ground geometry information is generated. The definition of platform traversability in the proposed method reflects the strong coupling relationship between the platform and the environment. The experimental results show that the algorithm can stably establish the traversable map, provide good guidance for platform planning and control, and is conducive to the stable trafficability of the unmanned tracked platform in the complex off-road environment.

LIU X , LI D C , HE Y Q , et al . Efficient and multifidelity terrain modeling for 3D large-scale and unstructured environments [J ] . Journal of Field Robotics , 2022 , 39 ( 8 ): 1286 - 1322 . DOI: 10.1002/rob.v39.8 http://doi.org/10.1002/rob.v39.8 https://onlinelibrary.wiley.com/toc/15564967/39/8 https://onlinelibrary.wiley.com/toc/15564967/39/8

STÖLZLE M , MIKI T , GERDES L , et al . Reconstructing occluded elevation information in terrain maps with self-supervised learning [J ] . IEEE Robotics and Automation Letters , 2022 , 7 ( 2 ): 1697 - 1704 . DOI: 10.1109/LRA.2022.3141662 http://doi.org/10.1109/LRA.2022.3141662 https://ieeexplore.ieee.org/document/9676411/ https://ieeexplore.ieee.org/document/9676411/

DROESCHEL D , SCHWARZ M , BEHNKE S . Continuous mapping and localization for autonomous navigation in rough terrain using a 3D laser scanner [J ] . Robotics and Autonomous Systems , 2017 , 88 : 104 - 115 . DOI: 10.1016/j.robot.2016.10.017 http://doi.org/10.1016/j.robot.2016.10.017 https://linkinghub.elsevier.com/retrieve/pii/S0921889015303110 https://linkinghub.elsevier.com/retrieve/pii/S0921889015303110

HORNUNG A , WURM K M , BENNEWITZ M , et al . OctoMap: an efficient probabilistic 3D mapping framework based on octrees [J ] . Autonomous Robots , 2013 , 34 : 189 - 206 . DOI: 10.1007/s10514-012-9321-0 http://doi.org/10.1007/s10514-012-9321-0 http://link.springer.com/10.1007/s10514-012-9321-0 http://link.springer.com/10.1007/s10514-012-9321-0

YU J , FANG H Q , PU G L , et al . GeoSOT-OctoMap: an octree grid map model for autonomous driving [C ] // Proceedings of 2021 IEEE International Conference on Unmanned Systems . Beijing, China : IEEE , 202 : 5 - 10 .

RUETZ F , HERNÁNDEZ E , PFEIFFER M , et al . Ovpc mesh: 3d free-space representation for local ground vehicle navigation [C ] // Proceedings of 2019 International Conference on Robotics and Automation.Washington,D.C.,US:IEEE , 2019 : 8648 - 8654 .

BUCHANAN R , WELLHAUSEN L , BJELONIC M , et al . Perceptive whole-body planning for multilegged robots in confined spaces [J ] . Journal of Field Robotics , 2021 , 38 ( 1 ): 68 - 84 . DOI: 10.1002/rob.v38.1 http://doi.org/10.1002/rob.v38.1 https://onlinelibrary.wiley.com/toc/15564967/38/1 https://onlinelibrary.wiley.com/toc/15564967/38/1

徐鹏 , 丁亮 , 高海波 , 等 . 考虑足地作用的足式机器人环境表征与路径规划 [J ] . 机械工程学报 , 2020 , 56 ( 23 ): 21 - 33 . DOI: 10.3901/JME.2020.23.021 http://doi.org/10.3901/JME.2020.23.021 足式机器人在行走过程中，足端与地面之间的相互作用影响机器人的地面通过情况。足地作用与地表的几何形状和地面的物理特性息息相关，因此仅基于几何特性地图进行路径规划难以满足野外环境下规避松软沙土等非几何危险的需求。针对该问题，考虑足地作用力学提出包含几何与物理特性的环境模型进行足式机器人路径规划。通过简化和统一软硬地面下的足地作用模型，提出表征地面法向松软特性和切向摩擦特性的参数化指标，结合几何特性构建更全面的环境模型。综合考虑影响机器人通过性的地面几何与物理特征，重构路径规划的优化目标，通过图搜索算法实现最优路径规划。以六足机器人Elspider为对象进行仿真和试验，验证了所提出的方法能够有效规避非几何危险，实现了更安全、通过性更强的路径规划。

XU P , DING L , GAO H B , et al . Environmental characterization and path planning for legged robots considering foot-terrain interaction [J ] . Journal of Mechanical Engineering , 2020 , 56 ( 23 ): 21 - 33 . (in Chinese) DOI: 10.3901/JME.2020.23.021 http://doi.org/10.3901/JME.2020.23.021 During the walking of a legged robot, the interactions between its end of feet and the terrain strongly affect the traversability of the robot. Foot-terrain interaction is closely related to the geometry of the terrain surface and the physical characteristics of it. Therefore, path planning based on geometric map alone is difficult to meet the demand of avoiding non-geometric hazards such as soft sand in the wild. To solve this problem, an environment model including geometric and physical characteristics is proposed in consideration of foot-terrain interaction for path planning of legged robots. By simplifying and unifying the foot-terrain interaction model under soft and rigid terrain, parameterized indexes characterizing the normal softness and tangential friction characteristics of the terrain are proposed, and a more comprehensive environment model is constructed by combining geometric characteristics and the proposed physical characteristics. Comprehensively considering the ground geometric and physical characteristics affecting the robot's traversability, the optimization target of path planning is reconstructed and the optimal path is planned for legged robots with graph search algorithm. Simulation and experiments with the hexapod robot Elspider verified that the proposed method can effectively avoid non-geometric hazards and plan a safer and more reliable path to traverse.

BOUMAN A , GINTING M F , ALATUR N , et al . Autonomous spot: long-range autonomous exploration of extreme environments with legged locomotion [C ] // Proceedings of 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems.Washington,D.C.,US:IEEE , 2020 : 2518 - 2525 .

POLEVOY A , KNUTH C , POPEK K M , et al . Complex terrain navigation via model error prediction [C ] // Proceedings of 2022 International Conference on Robotics and Automation. Washington,D.C.,US:EEE , 2022 : 9411 - 9417 .

HU J J , BAO C Y , OZAY M , et al . Deep depth completion from extremely sparse data: a survey:arXiv:2205.05335 [R ] . Ithaca,NY,US:Cornell University , 2022 :2205.05335.

GAO B , PAN Y C , LI C K , et al . Are we hungry for 3D LiDAR data for semantic segmentation? a survey of datasets and methods [J ] . IEEE Transactions on Intelligent Transportation Systems , 2021 , 23 ( 7 ): 6063 - 6081 . DOI: 10.1109/TITS.2021.3076844 http://doi.org/10.1109/TITS.2021.3076844 https://ieeexplore.ieee.org/document/9430028/ https://ieeexplore.ieee.org/document/9430028/

HU J M , HU Y H , LU C , et al . Integrated path planning for unmanned differential steering vehicles in off-road environment with 3D terrains and obstacles [J ] . IEEE Transactions on Intelligent Transportation Systems , 2021 , 23 ( 6 ): 5562 - 5572 . DOI: 10.1109/TITS.2021.3054921 http://doi.org/10.1109/TITS.2021.3054921 https://ieeexplore.ieee.org/document/9345385/ https://ieeexplore.ieee.org/document/9345385/

THORESEN M , NIELSEN N H , MATHIASSEN K , et al . Path planning for UGVs based on traversability hybrid A * [J ] . IEEE Robotics and Automation Letters , 2021 , 99 : 1 - 1 .

陈慧岩 , 关海杰 , 刘海鸥 , 等 . 履带平台无人驾驶系统基于语义信息的模块串联方法 [J ] . 兵工学报 , 2022 , 43 ( 11 ): 2705 - 2716 . DOI: 10.12382/bgxb.2021.0832 http://doi.org/10.12382/bgxb.2021.0832 为提高无人履带平台在复杂越野环境下的通行能力，提出一种通过语义信息串联无人驾驶系统中环境感知、运动规划、运动控制模块的方法。环境感知模块通过相机与激光雷达的融合感知方法，利用图像语义信息与激光雷达点云特征，结合平台通过性几何参数，对环境中可通行区域进行粗提取，之后在可通行区域利用高斯聚类模型对环境进行精细的可通行度分析，最终生成具有不同通行度语义信息的三维栅格地图；运动规划模块在考虑平台运动学模型、动力学约束以及平滑过渡约束的基础上,结合地形与道路表面属性生成行为运动基元，通过对基元的分层式在线选择生成具有行为语义的轨迹；运动控制模块基于模型预测控制算法充分考虑平台驱动电机的执行能力、跟踪偏差以及控制稳定性，借助运动规划给出的行为运动基元语义属性，对控制目标函数权重系数进行实时更新，减小轨迹跟踪的横向误差，航向误差以及速度误差。最终利用中型混合动力无人履带平台进行了实车验证，结果表明：所提运动规划方法结果相较于基于平面二值栅格地图规划的轨迹在平均俯仰角、平均侧倾角、平均曲率分别降低46.1%、46.5%、14.2%；所提出基于行为语义轨迹变参数运动控制方法相较于定参数的运动控制方法分别在横向偏差、航向偏差、速度偏差降低17.1%、2.7%、6.1%。

CHEN H Y , GUAN H J , LIU H O , et al . A semantic information-based module series method for unmanned tracked driving systems [J ] . Acta Armamentarii , 2022 , 43 ( 11 ): 2705 - 2716 . (in Chinese) DOI: 10.12382/bgxb.2021.0832 http://doi.org/10.12382/bgxb.2021.0832 To improve the performance of unmanned tracked platforms in complex off-road environment, this study proposes a semantic information-based method to integrate the environment perception, motion planning and motion control modules of the unmanned system. Through the fusion perception method of camera and lidar, image semantic information and lidar point cloud features are obtained by the environment perception module, and then the traversable area is roughly determined by combining geometric parameters of the platform. Finally, a three-dimensional grid map with different traversability information is generated, after the Gaussian clustering model is used to conduct a fine traversability analysis of the environment in the traversable area. Platform kinematics and dynamic constraints are considered in the motion planning module. On the basis of smooth transition constraints, terrain and road surface attributes are taken into account to generate behavior motion primitives, and the trajectories with behavior semantics are generated using hierarchical online selection of primitives. The motion control module is based on model predictive control which considers the execution ability, tracking deviation, and control stability of the platform drive motor. Based on the semantic attributes of the behavior motion primitives provided by motion planning, the weight coefficient of the control objective function is updated in real time to reduce lateral deviation, heading deviation, and speed deviation of trajectory tracking. Finally, the medium-sized hybrid unmanned tracked platform is used for verification. The results show that the motion planning method proposed in this paper are 46.1%, 46.5% and 14.2% lower in average pitch angle, average roll angle and average curvature than the trajectory planning result using the plane binary grid map. Compared with the motion control method with fixed parameters, the proposed variable-parameter motion control method based on behavior semantic trajectory reduces the lateral deviation, heading deviation, and speed deviation by 17.1%, 2.7% and 6.1%, respectively.

JI Y , TANAKA Y , TAMURA Y , et al . Adaptive motion planning based on vehicle characteristics and regulations for off-road UGVs [J ] . IEEE Transactions on Industrial Informatics , 2018 , 99 : 1 - 1 .

MENG X R , CAO Z Q , LIANG S , et al . A terrain description method for traversability analysis based on elevation grid map [J ] . International Journal of Advanced Robotic Systems , 2018 , 15 ( 1 ): 1729881417751530.

AHTIAINEN J , STOYANOV T , SAARINEN J . Normal distributions transform traversability maps: LIDAR-only approach for traversability mapping in outdoor environments [J ] . Journal of Field Robotics , 2017 , 34 ( 3 ): 600 - 621 . DOI: 10.1002/rob.2017.34.issue-3 http://doi.org/10.1002/rob.2017.34.issue-3 https://onlinelibrary.wiley.com/toc/15564967/34/3 https://onlinelibrary.wiley.com/toc/15564967/34/3

TAKEMURA R , ISHIGAMI G . Traversability-based trajectory planning with quasi-dynamic vehicle model in loose soil [C ] // Proceedings of 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems.Washington,D.C.,US:IEEE , 2021 : 8411 - 8417 .

GUAN T R , HE Z P , SONG R T , et al . TNS:terrain traversability mapping and navigation system for autonomous excavators:arXiv:2109.06250 [R ] . Ithaca,NY,US:Cornell University , 2021 :2109.06250.

HADDELER G , CHAN J L , YOU Y W , et al . Explore bravely:wheeled-legged robots traverse in unknown rough environment [C ] // Proceedings of 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems.Las Vegas, NV, US:IEEE , 2020 : 7521 - 7526 .

WAIBEL G G , LÖW T , NASS M , et al . How rough is the path? terrain traversability estimation for local and global path planning [J ] . IEEE Transactions on Intelligent Transportation Systems , 2022 , 23 ( 9 ): 16462 - 16473 . DOI: 10.1109/TITS.2022.3150328 http://doi.org/10.1109/TITS.2022.3150328 https://ieeexplore.ieee.org/document/9721819/ https://ieeexplore.ieee.org/document/9721819/

WEERAKOON K , SATHYAMOORTHY A J , PATEL U , et al . Terp: reliable planning in uneven outdoor environments using deep reinforcement learning [C ] // Proceedings of 2022 International Conference on Robotics and Automation.Washington,D.C.,US:IEEE , 2022 : 9447 - 9453 .

MARTINEZ J L , MORAN M , MORALES J , et al . Supervised learning of natural-terrain traversability with synthetic 3D laser scans [J ] . Applied Sciences , 2020 , 10 ( 3 ): 1140 . DOI: 10.3390/app10031140 http://doi.org/10.3390/app10031140 https://www.mdpi.com/2076-3417/10/3/1140 https://www.mdpi.com/2076-3417/10/3/1140 Autonomous navigation of ground vehicles on natural environments requires looking for traversable terrain continuously. This paper develops traversability classifiers for the three-dimensional (3D) point clouds acquired by the mobile robot Andabata on non-slippery solid ground. To this end, different supervised learning techniques from the Python library Scikit-learn are employed. Training and validation are performed with synthetic 3D laser scans that were labelled point by point automatically with the robotic simulator Gazebo. Good prediction results are obtained for most of the developed classifiers, which have also been tested successfully on real 3D laser scans acquired by Andabata in motion.

WELLHAUSEN L , DOSOVITSKIY A , RANFTL R , et al . Where should I walk? predicting terrain properties from images via self-supervised learning [J ] . IEEE Robotics and Automation Letters , 2019 , 4 ( 2 ): 1509 - 1516 . DOI: 10.1109/LSP.2016. http://doi.org/10.1109/LSP.2016. https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7083369 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7083369

孙志群 , 李强 , 袁卫 , 等 . 路面激励对火箭炮行进间发射控制的影响研究 [J ] . 兵器装备工程学报 , 2021 , 42 ( 4 ): 37 - 41 .

SUN Z Q , LI Q , YUAN W , et al . Study on effect of road excitation on rocket launch control between travels [J ] . Journal of Ordnance Equipment Engineering , 2021 , 42 ( 4 ): 37 - 41 . (in Chinese)

马宪永 , 全蔚闻 , 董泽蛟 , 等 . 随机不平度激励下车辆-沥青路面动力学响应分析 [J ] . 机械工程学报 , 2021 , 57 ( 12 ): 40 - 50 . DOI: 10.3901/JME.2021.12.040 http://doi.org/10.3901/JME.2021.12.040 高效准确地获取随机不平度激励下车辆-沥青路面交互作用特性，对路面友好型车辆设计、路面服役性能评估极为必要。采取解析法和顺序解耦的求解思路，首先推导随机不平度激励下1/4车辆模型的随机动荷载；而后借助相对坐标变换和Fourier积分变换，基于波传递方法，推导移动车辆随机动荷载作用下黏弹性多层体系沥青路面动力响应解析解，并编制相应的数值计算程序。通过车辆-路面动力学响应算例分析，得出沿车辆移动方向各纵向位置处的沥青路面动力响应幅值与随机动荷载相关。通过车辆-路面系统参数影响分析，可以发现，降低悬架和轮胎刚度系数、增大悬架阻尼系数可以降低沥青层底纵向应变，有利于提高路面疲劳寿命；轮胎阻尼系数对路面动力响应几乎无影响；路面不平度的劣化会显著加剧路面疲劳损伤；增大车辆移动速度会降低沥青层底纵向应变均值，但会增大其变异系数，故为了准确评估路面疲劳寿命，需充分考虑车辆移动速度对动力响应均值和变异系数的综合影响。

MA X Y , QUAN W W , DONG Z J , et al . Research on dynamic response of vehicle and asphalt pavement interaction under random unevenness excitation [J ] . Journal of Mechanical Engineering , 2021 , 57 ( 12 ): 40 - 50 . (in Chinese) DOI: 10.3901/JME.2021.12.040 http://doi.org/10.3901/JME.2021.12.040 Obtaining the vehicle and asphalt pavement interaction characteristics under the excitation of random unevenness efficiently and accurately are necessary for road-friendly vehicle design and pavement performance evaluation. The analytical method and the solution idea of sequential decoupling are adopted. Firstly, the random dynamic load of the quarter vehicle model under random unevenness excitation is derived. Then, with the help of relative coordinate transform and Fourier integral transform, the analytical solution for the dynamic response of the viscoelastic multilayered asphalt pavement subjected to the random dynamic moving load is derived based on the wave propagation method, and the numerical program is compiled. Through analyzing the example of vehicle-pavement dynamic response, it can be found that the dynamic response amplitude of the asphalt pavement at each longitudinal position along the vehicle moving direction is related to the random dynamic load. Through the parameter analysis of vehicle-pavement system, it can be found that reducing the suspension and tire stiffness coefficients, or increasing the suspension damping coefficient can reduce the longitudinal strain at the bottom of the asphalt layer, which is beneficial to improve the pavement fatigue life; Tire damping coefficient has almost no effect on pavement dynamic response; The deterioration of pavement unevenness can significantly exacerbate pavement fatigue damage; Increasing the vehicle moving speed can reduce the average value of longitudinal strain at the bottom of the asphalt layer, but increase its variation coefficient, thus the effect of the vehicle moving speed on the average value and variation coefficient of the dynamic response should be comprehensively considered to evaluate the pavement fatigue life accurately.

单春来 , 赵凯 , 孟超 , 等 . 不同行驶系统对战车稳定性的影响研究 [J ] . 火炮发射与控制学报 , 2021 , 42 ( 3 ): 16 - 22 .

SHAN C L , ZHAO K , MENG C , et al . Study of the effect of different driving systems on the stability of combat vehicles [J ] . Journal of Gun Launch & Control , 2021 , 42 ( 3 ): 16 - 22 . (in Chinese)

张宝振 , 王汉平 , 张哲 , 等 . 二维路面不平度的分形构造方法 [J ] . 兵工学报 , 2020 , 41 ( 12 ): 2389 - 2396 . DOI: 10.3969/j.issn.1000-1093.2020.12.003 http://doi.org/10.3969/j.issn.1000-1093.2020.12.003 精确的路面不平度模型是车辆动态性能仿真研究的关键。根据Weierstrass-Mandelbrot(W-M)分形函数，按照功率谱及相干函数的定义，推导出左右轮分形模型组分中相位角的解析相干关系；结合W-M分形函数以及不同轮辙路面谱阵的Cholesky分解，分别构造考虑相位角相干性以及基于轮辙路面谱阵Cholesky分解的二维路面分形模拟模型。理论研究发现，当分形尺度参数γ→1时，根据W-M分形函数推导出的路面分形模拟法等价于谐波叠加法，且基于轮辙路面谱阵Cholesky分解的分形模型更具普遍意义，考虑相位角相干性的分形模型只是其一种特例。仿真结果表明，当γ→1时，所构造两个模型的轮辙自功率谱及左右轮相干函数均与对应参考标准吻合较好，验证了两个模型的精度和可信性。

ZHANG B Z , WANG H P , ZHANG Z , et al . Fractal construction method of 2D road roughness [J ] . Acta Armamentarii , 2020 , 41 ( 12 ): 2389 - 2396 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.12.003 http://doi.org/10.3969/j.issn.1000-1093.2020.12.003 Accurate road roughness model is the key to the simulation research on vehicle dynamic performance. Based on the Weierstrass-Mandelbrot(W-M) function and the definitions of power spectral density(PSD) and coherence function，the analytic coherence relation of the phase angles in the components of fractal model for the left and right wheels is derived. The 2D road roughness fractal models which considers on the phase angle coherence and the Cholesky decomposition of PSD matrix of road roughness are established, respectively，by combining with W-M fractal function and the Cholesky decomposition of PSD matrix of road roughness with different wheelmarks.Theoretical research shows that the road simulation method based on W-M fractal function is equivalent to the harmonic superposition method for γ→1.The fractal model based on the Cholesky decomposition of PSD matrix of road roughness is a universal model，and the fractal model based on the coherence of phase angle is a special case of the above model. Simulated results show that the auto-PSDs of the two models are in good agreement with the corresponding reference PSD，and the accuracy and credibility of the two models are verified consequently for γ→1.

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王红岩 , 郝丙飞 , 于魁龙 , 等 . 坦克底盘-火炮系统动力学建模及火炮振动特性分析 [J ] . 兵器装备工程学报 , 2017 , 38 ( 12 ): 6 - 12 .

WANG H Y , HAO B F , YU K L , et al . Dynamics modeling for tank chassis-gun system and analysis for gun vibration [J ] . Journal of Ordnance Equipment Engineering , 2017 , 38 ( 12 ): 6 - 12 . (in Chinese)

陈宇 , 杨国来 , 付羽翀 , 等 . 高速机动条件下坦克行进间火炮非线性振动动力学研究 [J ] . 兵工学报 , 2019 , 40 ( 7 ): 1339 - 1348 . DOI: 10.3969/j.issn.1000-1093.2019.07.002 http://doi.org/10.3969/j.issn.1000-1093.2019.07.002 为研究高速机动条件下坦克行进间非线性振动情况，基于动态协同仿真方法，建立了坦克行进间机械、电气与液压联合仿真模型。分别在机电一体化仿真软件Amesim中建立液压子系统模型，在仿真软件MATLAB/Simulink中建立控制子系统模型，在多体系统动力学软件RecurDyn中建立考虑身管柔性等多个非线性因素的坦克机械系统模型。运用谐波叠加法分别编写了考虑左右履带不平度相干性的D级、F级三维路面不平度计算程序。动力学计算结果表明：身管柔性会造成炮口振动的振幅大于摇架处；当路面不平度较小且行驶速度较低时，炮口相对于摇架整体向下弯曲；随着路面不平度的增大和行驶速度的提高，车体及摇架稳定性急剧恶化，稳定器无法保证稳定精度，此时，身管柔性造成的炮口与摇架处高低角位移差异显著减小；身管柔性因素对于射击精度的影响难以通过简单的静态修正得以解决，还需综合考虑坦克的行驶工况。

CHEN Y , YANG G L , FU Y C , et al . Dynamic simulation on nonlinear vibration of marching tank gun under high mobility conditions [J ] . Acta Armamentarii , 2019 , 40 ( 7 ): 1339 - 1348 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.07.002 http://doi.org/10.3969/j.issn.1000-1093.2019.07.002 A novel dynamic co-simulation methodology is presented to establish a mechanical-electrical-hydraulic integrated dynamic model of marching tank for studying the nonlinear vibration of marching tank under high mobility conditions. A property hydraulic subsystem model is established in Amesim, a tank mechanical system model, in which several nonlinear factors, such as barrel flexibility, are considered, is builded using RecurDyn, and a control system model is also builded using MATLAB/Simulink. A calculation program of the three-dimensional road roughness considering the coherence of left and right tracks was created using the sinusoid superposition method. The calculated results show that the muzzle vibration amplitude is larger than that of cradle because of barrel’s flexibility. When the road roughness is small and the running speed is low, the muzzle bends downward relative to the cradle. With the increase in road roughness and running speed, the stability of hull and cradle is getting worse, and the stabilizer cannot guarantee the stabilization accuracy. The difference of elevation angular displacement between muzzle and cradle caused by barrel’s flexibility is significantly reduced. Therefore, the influence of barrel’s flexibility on the firing accuracy cannot be solved by static correction simply, and the driving condition should be considered. Key

CHEN Y , YANG G L . Dynamic simulation of tank stabilizer based on adaptive control [J ] . Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science , 2019 , 233 ( 9 ): 3038 - 3049 . DOI: 10.1177/0954406218802315 http://doi.org/10.1177/0954406218802315 Tank stabilizer is a control system keeping the bore axis in the desired sighting angle. For the control problem of the stabilizer in the case of uncertain parameters, the adaptive control method is introduced to design the vertical tank stabilizer with the nonlinear dynamic model of vertical stabilizer given in the paper. In the design, the multiple parameter uncertainties of the hydraulic servo system are fully considered and the linear feedback control is used to improve the asymptotic stability of the system. The vertical stabilizer of tank is simulated in MATLAB/Simulink environment. In addition, a dynamic model of tank on the move is established based on multi-body system theory, vehicle terramechanics and gun launch dynamics. Then the established dynamic model is combined with the designed controller based on the RecurDyn/Control module. The numerical calculation results show that the adaptive control method can effectively control the muzzle vibration of tank on the move and it can satisfy the requirement of actual vertical stabilization accuracy. But some nonlinear factors of the gun such as the flexibility of the barrel will seriously influence the desired stabilization accuracy of the vertical tank stabilizer. A comparison experiment between adaptive control and proportional-integral-derivative control is also presented to show the effectiveness of the adaptive control method. The research provides a feasible way to improve the firing accuracy of tank firing on the move.

CHEN Y , YANG G L , SUN Q Z . Dynamic simulation on vibration control of marching tank gun based on adaptive robust control [J ] . Journal of Low Frequency Noise, Vibration and Active Control , 2020 , 39 ( 2 ): 416 - 434 . DOI: 10.1177/1461348419846685 http://doi.org/10.1177/1461348419846685 http://journals.sagepub.com/doi/10.1177/1461348419846685 http://journals.sagepub.com/doi/10.1177/1461348419846685 In order to better understand the dynamic behavior and decrease the muzzle vibration of marching tank, a mechanical–electrical–hydraulic integrated dynamic model of marching tank was established based on a novel dynamic co-simulation method. The hydraulic system model was modeled in Amesim and the dynamic model of marching tank was established in RecurDyn based on multi-body system theory, vehicle terramechanics, and gun launch dynamics. The control system model was modeled in MATLAB/Simulink. Therein, the adaptive robust control algorithm was introduced to design the vertical stabilizer controller and the simulation program of the designed controller was developed by C language. The simulation results show that the muzzle vibration of marching tank can be controlled effectively by the ARC method. Furthermore, the muzzle error compensation signal was added in the designed controller to weaken the detrimental effect of the barrel flexibility on muzzle vibration. This work provides an approach to investigate the dynamic behavior of marching tank considering effects among the mechanical, hydraulic, and control subsystems.

李伟 , 韩崇伟 , 刘爱峰 , 等 . 干扰速率补偿式火炮线自稳定跟踪控制建模与仿 [J ] . 兵工学报 , 2022 , 43 ( 6 ): 1233 - 1245 . DOI: 10.12382/bgxb.2021.0295 http://doi.org/10.12382/bgxb.2021.0295 为适应动基座、高射角条件下火炮高精度的稳定跟踪控制的需求，提出一种基于大地坐标系下干扰速率补偿式火炮线自稳定控制方法，以有效抑制自行火炮车体姿态扰动对火炮线指向的影响。根据指向稳定的火炮线在动基座上的运动规律，设计新的干扰速率测量陀螺安装方式，推导在大地坐标系下的方位向和高低向干扰速率解耦补偿值，并在传统的高炮随动基础上应用干扰速率前馈补偿，实现火炮线自稳定和控制解耦。由于火炮稳定只涉及炮塔回转、火炮俯仰两个自由度且都存在偏心矩等因素，采用牛顿-欧拉法建立运动车体与火炮、炮塔之间的动力学模型，并考虑传动机构的刚度和齿隙的非线性，结合执行电机模型和经典闭环控制，以车体航向、俯仰、横滚各幅值为7°，周期为2 s的三轴复合摇摆条件，分别对该控制策略在忽略弹性、考虑动弹性的两种情况下对该控制策略进行仿真研究。仿真结果表明，所提稳定控制方法实现了稳定射角不低于60°，在传动弹性条件下的稳定误差不大于0.5 mrad，正弦稳定跟踪误差不大于2.8 mrad，同时实现了高低向和方位向的的控制解耦，为火炮线高响应、高精度稳定控制提供了新的研究思路和方法。

LI W , HAN C W , LIU A F , et al . Modeling and simulation of self-stable gun line control using interference rate compesation [J ] . Acta Armamentarii , 2022 , 43 ( 6 ): 1233 - 1245 . (in Chinese) DOI: 10.12382/bgxb.2021.0295 http://doi.org/10.12382/bgxb.2021.0295 A self-stabilizing control method for gun line based on interference rate compensation in geodetic coordinates is proposed to achieve the high precision stability and tracking control of gun under the conditions of moving base and high firing angle. The proposed method can used to effectively restrain the influence of self-propelled artillery attitude disturbance on the gun line pointing. According to the motion law of stable gun line on a moving base，a mounting mode of interference rate measuring gyro is designed，and the decoupling compensation values of the azimuth and pitching interference rate in geodetic coordinates are derived. On the basis of the traditional anti-aircraft gun servo principle，the interference rate feed-forward compensation is applied to realize the self-stabilization and control decoupling of gun line. Since the gun stability is only related to two degrees of freedom of turret rotation and gun pitching，both of which have eccentricity moment and other factors. The Newton-Euler approach is used to establish a dynamic model of moving carrier，gun and turret. The nonlinear stiffness and backlash of transmission mechanism are considered combined with the executive motor model and classical closed-loop control. The control strategy is simulated in the two cases of ignoring elasticity and considering elasticity，respectively，under the conditions of three-axis compound swaying with the heading，pitching，rolling amplitudes of 7° and period of 2 s of vehicle body. The simulated results show that the proposed stability control method with interference rate compensation is used to achieve the stable firing angle of more than 60°，the stability control error of less than 0.5 mrad and the sinusoidal stability tracking control error of less than 2.8 mrad，and the control decoupling of pitching an azimuth is realized.

张鑫 , 张辉 , 王宝宝 , 等 . 某自行高炮刚柔耦合动力学建模方法研究 [J ] . 火炮发射与控制学报 , 2022 , 43 ( 5 ): 15 - 23 .

ZHANG X , ZHANG H , WANG B B , et al . Research on a rigid-flexible coupling dynamics modeling method of a self-propelled anti-aircraft gun [J ] . Journal of Gun Launch & Control , 2022 , 43 ( 5 ): 15 - 23 . (in Chinese)

孙国轩 , 宫新宇 , 时岩 , 等 . 基于差分进化算法的自行高炮随动系统PID参数整定 [J ] . 兵工学报 , 2021 , 42 ( 5 ): 903 - 912 . DOI: 10.3969/j.issn.1000-1093.2021.05.002 http://doi.org/10.3969/j.issn.1000-1093.2021.05.002 针对传统PID参数整定效率低且无法考虑构件间力元等因素对参数整定的影响问题，建立随动系统机电联合仿真模型，利用智能优化算法整定PID参数。建立了考虑行进间车体姿态扰动的随动控制系统模型，并结合上装虚拟样机建立随动系统的机电联合仿真模型，采用实车试验方法验证联合仿真模型的正确性。在此基础上，以时间乘以误差绝对值积分为优化目标函数，利用差分进化算法对PID参数进行整定，与原模型控制参数和遗传算法整定的参数进行比较。联合仿真结果表明：与原模型控制参数相比，使用差分进化算法整定的PID参数进行仿真，火力线控制误差的均方根值和标准差分别减少24.06%和25.20%，且收敛速度比遗传算法快；该建模方法和参数整定方法有效可行，对火力线控制精度优化具有理论参考价值。

SUN G X , GONG X Y , SHI Y , et al . PID parameter tuning of self-propelled antiaircraft gun servo system based on differential evolution algorithm [J ] . Acta Armamentarii , 2021 , 42 ( 5 ): 903 - 912 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.05.002 http://doi.org/10.3969/j.issn.1000-1093.2021.05.002 The traditional PID parameter tuning efficiency is low and the influence of factors such as force elements among components on the parameter tuning can not be considered. An electromechanical co-simulation model of servo system is established, and the PID parameters are tuned using intelligent optimization algorithm. A servo control system model considering the attitude disturbance of moving body is established, and an electromechanical joint simulation model of servo system is established by combining with the upper mounting virtual prototype. The method of real vehicle test is used to verify the correctness of the joint simulation model. On this basis, the integral of time multiplied by the absolute value of error is used as the optimization objective function, and the PID parameters are tuned using the differential evolution algorithm (DE), and compared with the original model control parameters and the genetic algorithm (GA) tuning parameters. The joint simulation results show that,compared with the original model control parameters, the RMS value and standard deviation of the axis of firepower control error are reduced by 24.06% and 25.20%, respectively, by using the PID parameters tuned by the differential evolution algorithm for simulation, and the convergence speed is faster than that of genetic algorithm. The modeling method and parameter tuning method are effective and feasible, and have theoretical reference value for the optimization of the control accuracy axis of firepower.

魏连震 , 龚建伟 , 陈慧岩 , 等 . 基于强化学习补偿的地面无人战车行进间跟瞄自适应控制 [J ] . 兵工学报 , 2022 , 43 ( 8 ): 1947 - 1955 . DOI: 10.12382/bgxb.2021.0786 http://doi.org/10.12382/bgxb.2021.0786 针对底盘运动和路面起伏对地面无人战车行进间跟瞄带来的非线性干扰问题，提出一种 基于强化学习补偿的地面无人战车行进间跟瞄自适应控制方法。该跟瞄控制方法由主控制器与补偿控制器两部分构成，主控制器利用PID控制算法结合当前跟瞄误差得到主控制量，补偿控制器利用Dueling Q 网络强化学习算法对战车当前状态和局部规划路径附近的路面起伏信息进行处理得到补偿控制量。建立地面无人战车一体化运动学模型，对基于强化学习的补偿控制算法进行阐述；基于V-REP动力学软件在三维场景中进行仿真验证。实验结果表明：基于强化学习补偿的跟瞄控制方法对底盘运动和路面起伏具备较好的自适应能力，有效地提升了无人战车行进间跟瞄的准确性与稳定性。

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HAUSER K , LATOMBE J C . Multi-modal motion planning in non-expansive spaces [J ] . International Journal of Robotics Research , 2010 , 29 ( 7 ): 897 - 915 . DOI: 10.1177/0278364909352098 http://doi.org/10.1177/0278364909352098 http://journals.sagepub.com/doi/10.1177/0278364909352098 http://journals.sagepub.com/doi/10.1177/0278364909352098 Motion planning problems encountered in manipulation and legged locomotion have a distinctive multi-modal structure, where the space of feasible configurations consists of intersecting submanifolds, often of different dimensionalities. Such a feasible space does not possess expansiveness, a property that characterizes whether planning queries can be solved efficiently with traditional probabilistic roadmap (PRM) planners. In this paper we present a new PRM-based multi-modal planning algorithm for problems where the number of intersecting manifolds is finite. We also analyze the completeness properties of this algorithm. More specifically, we show that the algorithm converges quickly when each submanifold is individually expansive and establish a bound on the expected running time in that case. We also present an incremental variant of the algorithm that has the same convergence properties, but works better for problems with a large number of submanifolds by considering subsets of submanifolds likely to contain a solution path. These algorithms are demonstrated in geometric examples and in a legged locomotion planner.

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