盖江涛 , 黄守道 , 周广明 , 等 . 双侧电机驱动的功率耦合机构传动方案设计方法 [J ] . 中国机械工程 , 2014 , 25 ( 13 ): 1739 - 1743 . 根据履带车辆传动特点提出了一种新的双侧电机耦合驱动传动方案。应用行星传动构件综合分析法，提出了方案优选的构件组合原则，建立了双侧电机耦合传动输入输出间的转速、转矩数学变换模型，并提出将特征参数转向再生功率机械利用率作为定量的评价指标。最终，形成了一种适用于双输入双输出功率耦合机构的传动方案设计方法，据此设计了双侧电机耦合驱动传动系统。计算表明，功率耦合机构能够实现履带车辆转向再生功率的机械回流，可降低电机的功率需求，所提出方案的电机功率需求仅为双侧电机独立驱动方案电机功率需求的0.65倍。分析结果验证了该设计方法的可行性和正确性。

GAI J T , HUANG S D , ZHOU G M , et al . Design method of power coupling mechanism scheme for double side motors coupling drive transmission [J ] . China Machanical Engineering , 2014 , 25 ( 13 ): 1739 - 1743 . (in Chinese)

盖江涛 , 李慎龙 , 周广明 , 等 . 一种履带车辆机电复合传动装置:中国, CN101985279A [P ] . 2011 -11-02.

GAI J T , LI S L , ZHOU G M , et al . A type of electro-mechanical transmission for tracked vehicle:CN101985279A [P ] . 2011 -11-02. (in Chinese)

闫清东 , 张连第 , 赵毓芹 , 等 . 坦克构造与设计 [M ] . 北京 : 北京理工大学出版社 , 2007 .

YAN Q D , ZHANG L D , ZHAO Y Q , et al . Tank construction and design [M ] . Beijing : Beijing Institute of Technology Press , 2007 . (in Chinese)

袁艺 , 盖江涛 , 韩政达 , 等 . 履带打滑条件下的电驱动车辆转向运动学研究 [J ] . 车辆与动力技术 , 2017 ( 1 ): 6 - 10 .

YUAN Y , GAI J T , HAN Z D , et al . Study on electric vehicle steering kinematics considered tracks’ skid and slip [J ] . Vehicle & Power Technology , 2017 ( 1 ): 6 - 10 . (in Chinese)

王红岩 , 王钦龙 , 芮强 , 等 . 高速履带车辆转向过程分析与试验验证 [J ] . 机械工程学报 , 2014 , 50 ( 16 ): 162 - 172 . 为了准确分析高速履带车辆在转向过程中运动学和动力学参数的变化规律，在考虑高速履带车辆转向离心力和履带滑动的条件下，建立计算两侧履带与地面之间的作用力、转向阻力矩、转向半径、转向角速度等参数的运动学、动力学模型。分析研究结果表明，转向时履带与地面之间的滑动使两侧履带的作用力随转向半径的增大而逐渐减小，离心力对车辆转向性能也有一定程度的影响；与传统转向理论的计算结果相比，考虑履带与地面之间滑动时的转向半径是传统理论计算值的1.5倍左右，转向角速度是传统理论计算值的67%左右。实车试验结果表明，文中所建立的转向模型具有较好的准确性，更符合高速履带车辆转向的实际情况。研究结果可为新型高速履带车辆转向机构的设计和转向过程控制提供理论支持。

WANG H Y , WANG Q L , RUI Q , et al . Analyzing and testing verification the performance about high-speed tracked vehicles in steering process [J ] . Journal of Mechanical Engineering , 2014 , 50 ( 16 ): 162 - 172 . (in Chinese) In order to analyse the kinematical and dynamic character parameters of steering process of high-speed tracked vehicle, the calculation model of kinematical and dynamic character parameters of acting force, turning resistance moment, turning radius, turning angular speed between tracks and ground is built, considering the influence of steering centrifugal force, the slipping of track-contact-ground. The analysis results show that steering centrifugal force has the some influence to the steering performance, the acting forces for out and inner tracks decrease along with the turning radius gradually in slipping steer situation. Compared to the calculation results based on traditional steering theory, which the turning radius is about 1.5 times, and the turning angular speed is 67% in slipping steer situation. Tracked vehicle testing results show that steering model established in this paper considering slip steering is accurate, which agrees with the actual turning process well, those research works provide the theoretical supported on the design of the new steering mechanism and the steering process control.

芮强 , 王红岩 , 王钦龙 , 等 . 基于剪应力模型的履带车辆转向力矩分析与试验 [J ] . 兵工学报 , 2015 , 36 ( 6 ): 968 - 977 . DOI: 10.3969/j.issn.1000-1093.2015.06.002 http://doi.org/10.3969/j.issn.1000-1093.2015.06.002 为了研究在打滑条件下的履带车辆转向性能，提高履带车辆转向模型的模拟精度，建立了考虑履带滑转、滑移及转向离心力影响的高速履带车辆稳态转向模型。根据剪切应力-剪切位移关系模型推导了两侧履带牵引力、制动力及转向阻力矩的计算公式。在此基础上，根据力平衡关系构建了履带车辆转向运动学方程，并采用迭代计算方法进行求解。以某型装备综合传动装置的高速履带车辆为对象，通过试验测试结果与计算结果的对比分析，对履带车辆转向模型的准确性进行了验证。基于履带车辆稳态转向模型，研究了履带车辆转向运动学及动力学特性随转向半径及车速的变化规律，结果表明：当履带车辆转向速度越高，转向半径越小时，离心力对转向性能的影响越显著。

RUI Q , WANG H Y , WANG Q L , et al . Analysis and experiment of tracked vehicle steering torque based on shear stress model [J ] . Acta Armamentarii , 2015 , 36 ( 6 ): 968 - 977 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2015.06.002 http://doi.org/10.3969/j.issn.1000-1093.2015.06.002 For the study of steering performance of tracked vehicles under skidding, a steady-state steering model of tracked vehicle, which takes the skid and slippage of tracks and centrifugal force into consideration, is established to improve the simulating accuracy of the tracked vehicle steering model. Expressions of driving force and braking force of outside track and inside track, and steering resistance torque of tracked vehicles are derived using shear stress-shear displacement relationship model, respectively. According to force and torque equilibrium theory, the steering dynamic equations of tracked vehicle are established and solved by iterative algorithm. Taking a certain type of tracked vehicle with the integrated transmission device as the object,the accuracy of steering model of tracked vehicles is verified by comparing the experimental and calculated results. The rules of changing the kinematics and dynamic steering performance of tracked vehicles with turning radius and running velocity are deeply studied based on the steady-state steering model of tracked vehicle. The results show that the influence of the steering centrifugal force on steering performance increases significantly with the increase in running velocity and the decrease in turning radius.

SAID A M , LAKMAL D S , KASPAR A . Track-terrain modelling and traversability prediction for tracked vehicles on soft terrain [J ] . Journal of Terramechanics , 2010 , 47 ( 3 ): 151 - 160 . DOI: 10.1016/j.jterra.2010.02.001 http://doi.org/10.1016/j.jterra.2010.02.001 https://linkinghub.elsevier.com/retrieve/pii/S0022489810000042 https://linkinghub.elsevier.com/retrieve/pii/S0022489810000042

曾庆含 , 马晓军 , 廖自力 , 等 . 双侧电驱动履带车辆等效条件积分滑模稳定转向控制 [J ] . 兵工学报 , 2016 , 37 ( 8 ): 1351 - 1358 . DOI: 10.3969/j.issn.1000-1093.2016.08.002 http://doi.org/10.3969/j.issn.1000-1093.2016.08.002 履带车辆转向阻力随行驶状态呈现非线性、大范围变化的现象，且由于车辆惯性大、电机驱动能力有限，易进入深度饱和状态，而双侧电机动力相互独立，要实现车辆全速度范围的稳定转向必须对两侧力矩进行有效控制。针对以上问题，设计了一种横摆角速度控制律。开展转向动力学分析，提出速度、横摆角速度转向控制结构；设计了一种带等效控制项的条件积分滑模控制算法，通过引入等效控制项，提高系统响应速度，减小滑模抖振；通过引入条件积分控制项，使滑模控制项边界层外与经典滑模性能一致，鲁棒性强，边界层内平滑切换为Anti-Windup结构的PI控制，便于消除误差，抑制积分饱和。Matlab与RecurDyn联合仿真表明，提出的算法具备跟踪能力强、抗扰动和饱和、输出控制量平滑的优点，能够实现车辆稳定转向控制。

ZENG Q H , MA X J , LIAO Z L , et al . Stable steer control of electric drive tracked vehicle based on equivalent sliding mode technique with conditional integrator [J ] . Acta Armamentarii , 2016 , 37 ( 8 ): 1351 - 1358 . (in Chinese)

刘翼 , 盖江涛 , 陈泳丹 , 等 . 电传动履带车辆转向自适应控制策略仿真分析 [J ] . 车辆与动力技术 , 2015 ( 1 ): 5 - 10 .

LIU Y , GAI J T , CHEN Y D , et al . Self-adaptive steering control of electric drive for tracked vehicle [J ] . Vehicle & Power Technology , 2015 ( 1 ): 5 - 10 . (in Chinese)

张杰 , 袁东 , 张朋 , 等 . 双侧电传动履带车辆模糊前馈反馈转向控制 [J ] . 兵工学报 , 2020 , 41 ( 8 ): 1688 - 1696 . DOI: 10.3969/j.issn.1000-1093.2020.08.023 http://doi.org/10.3969/j.issn.1000-1093.2020.08.023 针对双侧电传动履带车辆转向控制存在目标跟踪慢和抗干扰性能差等问题，通过车辆动力学分析和驾驶员操控信号解析，在直接转矩控制的基础上设计了一种模糊前馈-反馈转向控制算法。该算法将方向盘转角及变化率作为模糊控制输入，对两侧电机目标转矩进行前馈补偿；采用转向半径的偏差及变化率作为模糊控制输入，对目标转矩差进行反馈修正。通过实时仿真系统dSPACE平台构建车辆的硬件在环实时仿真平台，对控制策略的实时性和可行性进行了验证。结果表明，模糊前馈-反馈控制在车辆不同速度和不同转向半径工况下均能有效缩短转向动态响应时间，同时转向轨迹的抗扰性能得到了提高，实现了车辆快速稳定转向。

ZHANG J , YUAN D , ZHANG P , et al . Steeringcontrol based on fuzzy feedforward and feedback for dual-motor electric drive tracked vehicle [J ] . Acta Armamentarii , 2020 , 41 ( 8 ): 1688 - 1696 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.08.023 http://doi.org/10.3969/j.issn.1000-1093.2020.08.023 The steering control of dual-motor electric drive tracked vehicle has slow target tracking and poor anti-interference performance. For the above problems, a fuzzy feedforward and feedback steering control algorithm based on direct torque control was proposed by analyzing the vehicular dynamic performance and the driver controlling signal. The steering angle and the changing rate are set as the inputs of fuzzy feedforward control, based on which the target torques of the dual motors are compensated in feedforward. Furthermore, the deviation and changing rate of steering radius are set as the inputs of the fuzzy feedback control, from where the target torque difference is revised in feedback. Then the effectiveness and feasibility of the control strategy are validated by building and using a hardware in-loop real-time simulation platform with dSPACE. The results show that the fuzzy feedforward and feedback control can effectively shorten the dynamic response time of steering when the tracked vehicle turns at different radii and different speeds, and the anti-interference of steering trajectory is improved, which can realize faster and more stable steering.

程军伟 , 高连华 , 王红岩 , 等 . 履带车辆转向分析 [J ] . 兵工学报 , 2007 , 28 ( 9 ): 1110 - 1115 . 分析了履带接地段滑动时履带车辆的转向规律。推导了履带接地压力为均匀分布与集中载荷2种典型条件下转向所需牵引力、制动力、转向阻力矩、转向半径及转向角速度的表达式。采用迭代法求解转向平面运动方程，并与实车试验作了比较。试验结果表明：建立的考虑履带接地段滑动时的转向模型是合理的；接地压力均匀分布条件下考虑履带接地段滑动时，转向半径较传统转向理论计算值增大，转向角速度低于传统转向理论计算值；集中载荷条件下车辆转向更为困难。

CHENG J W , GAO L H , WANG H Y , et al . Analysis on the steering of tracked vehicles [J ] . Acta Armamentarii , 2007 , 28 ( 9 ): 1110 - 1115 . (in Chinese)

JAVIER M S , RAUL G L . Modeling track-terrain interaction for transient robotic vehicle maneuvers [J ] . Journal of Terramechanics , 2008 , 45 ( 9 ): 65 - 78 . DOI: 10.1016/j.jterra.2008.07.003 http://doi.org/10.1016/j.jterra.2008.07.003 https://linkinghub.elsevier.com/retrieve/pii/S0022489808000359 https://linkinghub.elsevier.com/retrieve/pii/S0022489808000359

盖江涛 , 刘春生 , 马长军 , 等 . 考虑履带滑转滑移的电驱动履带车辆转向控制 [J ] . 兵工学报 , 2021 , 42 ( 10 ): 2092 - 2101 . DOI: 10.3969/j.issn.1000-1093.2021.10.005 http://doi.org/10.3969/j.issn.1000-1093.2021.10.005 为消除车辆转向过程中履带滑转滑移对电驱动车辆运动学控制的影响，准确实现车辆的转向轨迹控制，对考虑履带滑转滑移的电驱动车辆转向控制策略进行研究。分析表征履带车辆转向过程滑转滑移特性的转向半径修正系数及转向角速度修正系数，在此基础上提出考虑履带滑转滑移的转向控制策略，利用转向半径修正系数及转向角速度修正系数对电机转速控制指令进行修正。通过仿真和试验，对比了不考虑履带滑转滑移的转向控制策略和考虑履带滑转滑移的转向控制策略。结果表明，考虑履带滑转滑移的转向控制策略可以准确地实现转向控制目标，验证了该转向控制策略的可行性。

GAI J T , LIU C S , MA C J , et al . Steering control of electric tracked vehicle considering tracks’ skid and slip [J ] . Acta Armamentarii , 2021 , 42 ( 10 ): 2092 - 2101 . (in Chinese)

盖江涛 , 黄守道 , 周广明 , 等 . 双电机耦合驱动履带车辆自适应滑膜转向控制 [J ] . 兵工学报 , 2015 , 36 ( 3 ): 405 - 411 . DOI: 10.3969/j.issn.1000-1093.2015.03.004 http://doi.org/10.3969/j.issn.1000-1093.2015.03.004 针对双电机耦合驱动履带车辆转向动力学模型具有多输入多输出（MIMO）、非线性且参数不确定的特点，对系统进行解耦，分解为车速控制系统和转向角速度控制系统。在车速控制系统中为实现车速跟踪误差的收敛，根据期望车速与当前速度信息，提出了鲁棒滑模变结构控制算法；在转向角速度控制系统中，提出了针对转向角速度的模糊滑模自适应控制算法。通过“驾驶员—控制器”在环的双电机耦合驱动履带车辆实时仿真系统，对控制算法进行了仿真实验验证，证明了该控制算法的有效性。

GAI J T , HUANG S D , ZHOU G M , et al . Adaptive sliding mode steering control of double motor coupling drive transmission for tracked vehicle [J ] . Acta Armamentarii , 2015 , 36 ( 3 ): 405 - 411 . (in Chinese)

王志翔 . 高速机电复合传动履带车辆转向稳定控制研究 [D ] . 北京 : 北京理工大学 , 2017 .

WANG Z X . Research on steering stability control of high-speed electromechanical composite transmission tracked vehicle [D ] . Beijing : Beijing Institute of Technology , 2017 . (in Chinese)

王博 . 机电复合传动履带车辆转向过程性能预测研究 [D ] . 北京 : 北京理工大学 , 2016 .

WANG B . Research on the performance prediction of the steering process of tracked vehicles with electromechanical compound transmission [D ] . Beijing : Beijing Institute of Technology , 2016 . (in Chinese)

张林晖 . 基于转矩的履带车辆转向过程协调控制研究 [D ] . 北京 : 北京理工大学 , 2015 .

ZHANG L H . Research on torque-based coordinated control of tracked vehicle steering process [D ] . Beijing : Beijing Institute of Technology , 2015 . (in Chinese)

李荣利 , 李善乐 , 芮强 , 等 . 考虑履带滑动的履带车辆转向载荷比分析与验证 [J ] . 机械工程师 , 2018 ( 1 ): 92 - 95 .

LI R L , LI S L , RUI Q , et al . Verification and analysis on steering power ratio of tracked vehicle within track slid taking into consideration [J ] . Chinese Journal of Mechanical Engineering , 2018 ( 1 ): 92 - 95 . (in Chinese)

熊光明 , 鲁浩 , 郭孔辉 , 等 . 基于滑动参数实时估计的履带车辆运行轨迹预测方法研究 [J ] . 兵工学报 , 2017 , 38 ( 3 ): 600 - 607 . DOI: 10.3969/j.issn.1000-1093.2017.03.025 http://doi.org/10.3969/j.issn.1000-1093.2017.03.025 要实现履带车辆的无人驾驶，在轨迹规划阶段需要准确预测其未来一段时间内的运动轨迹，然而履带与地面之间的滑动使车辆运动轨迹的准确预测变得非常困难。通过研究转向过程中履带接地段的运动，建立基于瞬时转向中心的履带车辆运动学模型。针对车辆的相对位姿是滑动参数的泛函，雅可比矩阵难以求解的问题，通过对泛函微分方程线性化，推导了雅可比矩阵的解析解。根据车辆相对位置计算值和测量值的差值，运用Levenberg-Marquardt算法迭代求解滑动参数，并结合给定控制序列预测未来一段时间内车辆的运动轨迹。该方法不需要提前知道土壤参数，并且能够实时估计滑动参数，以适应路面变化。实车试验结果表明，与传统轨迹预测方法相比，利用该方法预测车辆轨迹时，车辆位置偏差减少30%以上。

XIONG G M , LU H , GUO K H , et al . Research on trajectory prediction of tracked vehicles based on real time slip estimation [J ] . Acta Armamentarii , 2017 , 38 ( 3 ): 600 - 607 . (in Chinese)

邹渊 , 孙逢春 , 张承宁 . 电传动履带车辆“驾驶员-综合控制器”在环的双侧驱动控制实时仿真 [J ] . 机械工程学报 , 2007 , 43 ( 3 ): 193 - 198 . 为了在系统设计阶段及早验证控制方案可行性，把“驾驶员—综合控制器”纳入电传动履带车辆双侧驱动控制仿真闭环，建立双侧驱动电传动履带车辆及驱动系统模型。采用真实的驾驶员操纵设备和产品型综合控制器，不同控制策略使用不同CAN通讯协议匹配，被控对象及其外界环境通过数学模型在dSPACE中实时运算来模拟实现，构建包括CAN通讯在内的电传动履带车辆“驾驶员—综合控制器”在环双侧驱动控制实时仿真平台。基于该平台展开以驾驶员操作为输入的硬件在环仿真。仿真结果表明：该平台能进一步验证产品型综合控制器动力学控制算法代码，分析评估不同控制策略下车辆的机动性能。

ZOU Y , SUN F C , ZHANG C N . Electric tracked vehicle real-time simulation of dual-motor driving control with driver-global controller in-loop [J ] . Chinese Journal of Mechanical Engineering , 2007 , 43 ( 3 ): 193 - 198 . (in Chinese)