From Rule-driven to Collective Intelligence Emergence: A Review of Research on Multi-robot Air-ground Collaboration
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摘要: 多机器人空地协同系统作为一种在搜索救援、自主探索等领域具有广泛应用前景的异构机器人协作系统, 近年来受到研究者的高度关注. 针对限制空地协同系统自治性能的低智能性、弱自主性挑战, 如何增强个体智能、提高群体协同自主性是加快空地系统应用落地亟需解决的关键问题. 近年来, 随着以深度学习、群体智能为代表的人工智能(Artificial intelligence, AI)算法在感知、决策等领域的不断发展, 将其应用于空地协同系统成为了当前的研究热点. 基于空地协同的自主化程度, 总结从规则驱动到群智涌现不同协作水平下的空地协同工作, 强调通过增强个体智能涌现群体智慧. 同时, 构建并拓宽空地协同群智系统的概念及要素, 阐述其自组织、自适应、自学习与持续演化的群智特性. 最后, 通过列举空地协同代表性应用场景, 总结空地协同所面临的挑战, 并展望未来方向.Abstract: The multi-robot air-ground collaboration system, which is crucial for search and rescue, exploration, and other fields, has garnered significant attention from researchers in recent years. Overcoming challenges related to limited intelligence and weak autonomy in such systems is essential to enhance individual intelligence and strengthen collective collaboration autonomy, thereby accelerating their practical applications. In recent years, with the continuous advancement of artificial intelligence (AI) algorithms in perception and decision-making, such as deep learning and collective intelligence, their applications to air-ground collaborative systems have become a research hotspot. Based on the level of autonomy in air-ground collaboration, this paper summarizes air-ground collaboration efforts at different collaboration levels, ranging from rule-driven approaches to collective intelligence emergence, emphasizing the enhancement of individual intelligence to achieve collective intelligence. Furthermore, this paper constructs the concepts and expands the features of the air-ground collaboration collective intelligence system, and outlines its self-organizing, self-adaptation, self-learning, and continuously evolving qualities. Finally, by listing representative application scenarios, this paper encapsulates the challenges and explores future directions in air-ground collaboration.
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近年来, 能源与环保问题越来越受到全球专家学者的关注, 汽车保有量的不断增加导致能源消耗与环境污染日益加剧, 同时也使得城市拥堵现象越来越严重[1]. 混合动力电动汽车(Hybrid electric vehicles, HEVs)具备传统汽车和纯电动汽车两者的优点, 既能够缓解纯电动汽车电池续航里程的问题, 又能够有效降低燃油汽车的能耗与污染问题, 是目前解决能源危机与环境污染的有效途径之一. 混合动力电动汽车的能量管理策略直接影响着车辆性能和燃油经济性, 而车辆驾驶工况是车辆动力性和燃油经济性的重要影响因素, 对能量管理起着至关重要的作用. 在实际驾驶环境中, 车辆的工况循环和速度变化往往是未知的, 给混合动力电动汽车的控制与能量管理带来了挑战.
目前, 混合动力电动汽车的能量管理控制策略的研究主要分为基于规则和基于优化的控制算法两大分支[2]. 基于规则的控制策略主要是根据车辆的不同转矩、车速、电池电量SOC或发动机效率map图进行工作模式划分, 制定规则进行切换控制[3-4]. 该控制策略算法简单且规则容易实现, 但无法适应不同工况和实时动态变化的需求, 因而往往通过结合其他智能控制算法(如模糊控制、神经网络)以获得更好的鲁棒性和适应性. 但在实际驾驶条件下, 仍无法保证最佳的控制性能[5-7]. 因此, 更多的研究开始关注并探索基于优化的能量管理控制策略. 基于既定的工况循环或已知的速度规划, 动态规划(Dynamic programming, DP)算法以其公认的全局最优性被广泛应用于混合动力能量管理控制, 但由于实际的驾驶循环往往都是未知的且其计算负担较高而受到制约, 因而难以进行实时控制而多用于评价或固定路线的能量管理[8-10]. 为了改善DP算法在实际应用中的局限性, 专家学者进行了各种改进与探索[11-12]. 另一方面, 为了更好地实现实时优化控制, 模型预测控制被普遍采用[13-14]. 比如, 文献[13-14]根据驾驶员意图采用模型预测算法对转矩分配或功率需求进行瞬时预测控制, 虽然能够实现实时优化, 但其预测控制效果基于初始状态的选择, 且无法实现全局最优.
上述能量管理研究都是针对单辆HEV车辆进行能量管理控制, 但实际道路上车辆并不是独立行驶, 往往是在车流中跟随前方车辆行驶. 因此, 车辆的行驶还会受到前车行驶模式和速度变化的影响, 所以混合动力电动汽车的能量管理需要与跟车控制相结合. 车辆跟车控制方面的研究已有数十年历史, 主要集中于自适应巡航控制 (Adaptive cruise control, ACC)[15-17]和车辆队列控制[18-21]. 车辆队列控制关注的是多个车辆的协同控制, 其重点是队列稳定性. ACC属于单车控制技术, 解决的是与前车保持安全距离的巡航控制问题, 已在很多中高档汽车中使用. 已有的自适应巡航控制大多针对内燃机车辆, 很少有混合动力电动汽车跟车控制方面的研究. 本文主要考虑车辆跟随前方车辆的安全控制和跟车过程中的能量管理问题, 队列稳定性并不属于本文研究范围.
混合动力电动汽车跟车控制系统更为复杂, 既要考虑车辆的跟踪性能, 又要考虑车辆的能量管理问题. 近几年, 有少量关于混合动力电动汽车跟车控制和能量管理的研究. 比如, 文献[22]提出基于规则的混合动力电动汽车能量管理与自适应巡航控制方法, 该算法简单易实现, 但无法保证性能最优; 文献[23-24]分别给出一种基于驾驶员行为预测和车辆加速度预测的能量管理方法; 文献[25]给出混合动力电动汽车能量管理与自适应巡航控制的动态规划和在线查表方法; 文献[26]提出考虑道路坡度的HEV车辆队列控制与能量管理方法. 需要指出的是, 上述研究存在如下几方面的不足: 1)将能量管理与车辆巡航控制综合到同一成本函数, 参数较多, 计算负担较重, 且性能互相影响; 2)车辆环境工况中未充分利用前车信息, 需要进行加速度预测或假定参考值; 3)无法实现道路坡度和载荷实时变化的影响.
本文旨在针对混合动力电动汽车跟车控制与能量管理综合问题, 考虑前车与道路工况, 提出了基于安全距离的HEV车辆动态面控制(Dynamic surface control, DSC), 然后针对安全距离内的驾驶工况, 采用滚动动态规划算法进行混合动力电动汽车实时能量管理. 本文主要创新点和贡献如下:
1)考虑前车对行驶工况的影响以及混合动力电动汽车能量的综合控制, 通过车辆跟踪控制为动态规划算法提供工况循环, 既保证了控制的最优性又解决了算法对工况预测和速度规划的要求;
2)通过基于观测器的DSC跟车控制, 考虑了道路坡度和载荷实时变动对车辆跟踪控制性能与车辆能量消耗的影响;
3)基于安全距离的滚动动态规划算法, 解决了存储空间有限和在线计算负担大的问题, 可实现实时能量优化管理.
本文组织结构如下: 第1节给出HEV跟车系统、能量管理模型及控制目标, 第2节是基于安全车距的跟车控制器设计、稳定性分析以及能量管理动态规划方法, 第3节为仿真验证, 第4节是本文总结.
1. 系统模型与问题描述
考虑如图1所示的HEVs车辆跟踪系统, 其中,
${s_i}$ 、${s_q}$ 、${v_i}$ 、${v_q}$ 分别为当前车辆$i$ 、前车$q$ 的位置和速度,${P_i} $ 为车辆i的功率需求. 假设车辆已经配备了V2V等无线通信及传感装置, 能够获得前方车辆的状态信息(车辆的位置、速度).1.1 HEV车辆动力学模型
HEV车辆的纵向动力模型如下[27]
$$\left\{\begin{aligned} &{\dot s_i} = {v_i} \\ &{\dot v_i} = \frac{1}{{{m_i}}}({F_i} - {F_a} - {F_r} - {F_g}) \end{aligned}\right.$$ (1) 式中,
${m_i}$ 、${s_i}$ 、${v_i}$ 分别为当前车辆的质量、位置和速度,${F_i}$ 为车辆的牵引力或制动力,${F_a}$ 为车辆行驶过程中的空气阻力,${F_r}$ 为滚动阻力,${F_g}$ 为坡道阻力. 其中, 空气阻力由车辆行驶的速度、空气阻力系数${C_D}$ 、空气密度$\rho $ 和车辆的迎风面积$A$ 决定.$${F_a} = \frac{1}{2}{C_D}\rho Av_i^2$$ (2) 滚动阻力为
$${F_r} = \mu {m_i}g\cos \theta $$ (3) 式中,
$\mu $ 为滚动阻力系数,$g$ 为重力加速度,$\theta $ 表示道路坡度.车辆的坡道阻力为
$${F_g} = {m_i}g\sin \theta $$ (4) 综合式(1) ~ 式(4), 车辆的动力学模型表示为
$$ \left\{\begin{aligned} &{\dot s_i} = {v_i}\\ &{\ddot s_i} = {\dot v_i} = {b_1}{F_i} - {b_2}v_i^2 - {b_3}w \end{aligned}\right. $$ (5) 式中,
${b_1} ={1}/{{{m_i}}},$ ${b_2} ={C_D}\rho A /2m_i,$ ${b_3} = g ,$ $w = $ $ \mu \cos \theta \;+ \sin \theta,$ $w$ 表示道路坡度和路面情况, 未知且不确定. 为方便研究, 往往假定道路情况不变, 忽略了道路坡度和路面变化的影响, 本文则将其视为系统的扰动项, 并通过控制器设计对其观测补偿以更加符合实际情况, 同时也更能体现道路坡度对于HEV能量消耗的影响.理想的车间距定义为
$${d_a} = {s_q} - {s_i} - {l_i} - k\theta $$ (6) 式中,
${d_a}$ 为理想的车间距, 即在当前车速下制动且能保证不与前车相撞的最小安全距离;${s_q}$ 表示前车的位置;${l_i}$ 表示车辆的长度;$k > 0$ 为坡度系数.注 1. 文献中理想的车间距
${d_a}$ 多采用固定值[20, 27], 并不能很好地适应车速变化; 文献[24, 28]基于车速变化设定${d_a},$ 但往往由于车速实时变化使安全距离不断变化, 从而影响控制性能. 本文理想车间距${d_a}$ 基于道路限速决定, 通过智能交通系统获得当前道路限速并依据限速确定安全车距, 使${d}_{a} $ 既不会频繁变动, 也更符合交通法规和实际情况. 同时, 考虑坡度对安全距离的影响, 当$\theta > 0,$ 即车辆爬坡时, 安全车距相应缩短; 当$\theta < 0,$ 即车辆下坡时, 安全车距相应增加.1.2 HEV功率能量模型
考虑Power-split HEV[26], 其结构如图2所示,
${P}_{L} $ 指其他电器载荷, 从功率平衡的角度, 车辆i的功率${P_i}$ 由电池功率和发动机功率共同提供, 即$$ \left\{\begin{aligned} &{P_i}(k) = {P_{\rm{eng}}}(k) + {P_{\rm{batt}}}(k)\\ &{P_{\rm{eng}}} = {T_{\rm{eng}}}{\omega _{\rm{eng}}}\\ &{P_{\rm{batt}}} = {T_{m1}}{\omega _{m1}}{\eta _{m1}} + {T_{m2}}{\omega _{m2}}{\eta _{m2}} \end{aligned}\right. $$ (7) 其中,
${P_{\rm{eng}}}$ 和${P_{\rm{batt}}}$ 分别表示发动机功率和电池功率, 电池功率为正表示电池正在放电, 为负则代表电池正处于充电状态.${\omega _{m1}},$ ${\omega _{m2}},$ ${\omega _{\rm{eng}}}$ 与${T_{m1}},$ ${T_{m2}},$ ${T_{\rm{eng}}}$ 分别表示电动机1、电动机2与发动机的转速与转矩;${\eta _{m1}},$ ${\eta _{m2}}$ 为电机效率.由行星轮机构的运动关系, 其转速满足
$$ \left\{\begin{aligned} &{\omega _s} = - \alpha {\omega _r} + (1 + \alpha ){\omega _c}\\ &{\omega _{m1}} = - \alpha \varepsilon {\omega _{\rm{req}}} + (1 + \alpha ){\omega _{\rm{eng}}}\\ &{\omega _{m2}} = \varepsilon {\omega _{\rm{req}}} \end{aligned}\right. $$ (8) 式中,
${\omega _r},$ ${\omega _c},$ ${\omega _s}$ 分别表示齿圈、行星架和太阳轮的转速, 分别和发动机、电机1和电机2相连;$\alpha $ 为齿圈相对于太阳轮的传动比;${\omega _{\rm{req}}}$ 为车轮转速;$\varepsilon $ 为主减速器的传动比, 转矩关系为$$ \left\{\begin{aligned} &{T_{m1}} = - \frac{1}{{1 + \alpha }}{T_{\rm{eng}}}\\ &{T_{m2}} =\frac{{{T_{\rm{req}}}}}{\varepsilon } - \frac{\alpha }{{1 + \alpha }}{T_{\rm{eng}}} \end{aligned}\right. $$ (9) 式中,
${T_{\rm{req}}}$ 为车轮转矩.根据电池内阻模型, 电池的功率
${P_{\rm{batt}}}$ 为$$ \left\{\begin{aligned} &{P_{\rm{batt}}} = V \times {I_{\rm{batt}}}\\ &{P_{\rm{batt}}} = {V_{oc}}{I_{\rm{batt}}} - I_{\rm{batt}}^2{R_{\rm{batt}}} \end{aligned}\right. $$ (10) 求解式(10)
$${I_{\rm{batt}}} = - \frac{{{V_{oc}} \pm \sqrt {{V_{oc}}^2 - 4{P_{\rm{batt}}}(t){R_{\rm{batt}}}} }}{{2{R_{\rm{batt}}}}}$$ (11) 由于相同功率下, 电池电压越大其电流越小. 因此忽略较大取值, 电池的SOC动态表示为
$$ \begin{split} S\dot OC =\;& - \frac{{{I_{\rm{batt}}}}}{{{Q_{\rm{batt}}}}}=\\ & - \frac{{{V_{oc}} - \sqrt {{V_{oc}}^2 - 4{P_{\rm{batt}}}(k){R_{\rm{batt}}}} }}{{2{Q_{\rm{batt}}}{R_{\rm{batt}}}}} \end{split} $$ (12) 式中,
${I_{\rm{batt}}}$ 为电池电流,${V_{oc}}$ 表示电池输出电压,${R_{\rm{batt}}}$ 为电池的内阻,${Q_{\rm{batt}}}$ 表示电池电量.发动机的功率
${P_{\rm{eng}}}$ 由发动机转矩和转速计算得到$${P_{\rm{eng}}} = {T_{\rm{eng}}}{\omega _{\rm{eng}}}$$ (13) 式中,
${\omega _{\rm{eng}}}$ 与${T_{\rm{eng}}}$ 分别表示发动机的转速和转矩.发动机的燃油消耗率为发动机的转速
${\omega _{\rm{eng}}}$ 和转矩${T_{\rm{eng}}}$ 的函数, 通常由发动机台架试验获得. 图3为Advisor中发动机油耗map图.$${\dot m_f} = \psi ({\omega _{\rm{eng}}},\;{T_{\rm{eng}}})$$ (14) 式中,
${\dot m_f}$ 为燃油消耗率.因此, 对于一定工况循化下的功率需求, 根据HEV功率平衡与行星轮机构运动关系, 可以通过发动机的转矩和转速控制进行HEV车辆的能量优化管理.
1.3 本文目标
本文的控制目标是将车辆跟踪控制与混合动力电动汽车能量管理相结合, 设计控制器实现安全距离内HEV车辆的跟踪控制以保证车辆的安全性, 同时通过跟踪控制提供准确的实时工况信息以保证优化的能量管理. 即满足以下两点要求:
1)跟踪稳定性: 考虑实际的交通状况, 即有前车的情况下进行基于安全车距
${d_a}$ 下的车辆跟踪控制, 设计控制器跟踪前车速度${v_q},$ 即${v_i} \to {v_q},$ 并保证车辆的位置跟踪误差${\delta _i} = {s_i} - ({s_q} - {d_a} - l)$ 收敛到零的一个邻域内;2)燃油经济性: 以前方车辆速度
${v_q}$ 轨迹作为当前HEV车辆的驾驶工况, 在安全车距${d_a}$ 内, 对HEV车辆$i$ 进行实时能量优化管理. 即在满足系统约束条件下, 使HEV车辆的燃油消耗成本最低:$$\min J = \int_{{t_0}}^{{t_f}} {{{\dot m}_f}} (t){\rm{d}}t = \int_{{t_0}}^{{t_f}} \psi ({\omega _{\rm{eng}}},\;{T_{\rm{eng}}}){\rm{d}}t$$ 注 2. 在实际的交通状况下, 若没有前方车辆, 则采用虚拟车辆代替前车, 以当前道路限速作为虚拟车辆的车速, 以当前限速下的理想车距为安全距离. 以当前限速下的理想车距为安全距离确定前车位置, 既保证车辆的行驶安全性, 也更符合实际的道路交通状况; 车辆以当前限速为参考车速, 可使车辆更接近于能耗高效区间, 既有利于节省能耗, 又能够提高道路的交通效率.
2. 基于安全车距的车辆跟踪与能量管理
考虑存在前方行驶车辆的实际道路交通状况, 将HEV车辆的车辆跟踪与能量管理控制相结合. 首先采用DSC设计基于安全车距的跟踪控制器进行车辆位置与速度的跟踪控制, 在保证车辆安全驾驶的同时为HEV车辆能量管理提供实时驾驶工况; 然后在安全距离内应用滚动动态规划算法对发动机与蓄电池功率进行优化分配, 使能量消耗最小.
2.1 基于安全车距的车辆DSC跟踪控制
为实现更好的跟踪效果并为能量管理提供准确的工况信息, 在设计DSC控制器前, 首先对路面情况进行观测.
1)观测器的设计
由式(5)可得
$${b_3}w = {b_1}{F_i} - {b_2}v_i^2 - {\dot v_i}$$ (15) 设计观测器如下
$$\dot {\hat w} = {k_0}[{b_1}{F_i} - {b_2}v_i^2 - {\dot v_i} - {b_3}\hat w]$$ (16) 式中,
${k_0}$ 为观测器增益, 且${k_0} > 0.$ 定义辅助变量
$z = \hat w + {k_0}{v_i},$ 则$$\dot z = \dot {\hat w} + {k_0}{\dot v_i}$$ (17) 将式(16)代入式(17)得
$$ \begin{split} \dot z =\;& \dot {\hat w} + {k_0}{\dot v_i} = {k_0}[{b_1}{F_i} - {b_2}v_i^2 - {\dot v_i} - {b_3}\hat w] + {k_0}{\dot v_i}=\\ &{k_0}[{b_1}{F_i} - {b_2}v_i^2 - {b_3}\hat w]=\\ & {k_0}[{b_1}{F_i} - {b_2}v_i^2 - {b_3}(z - {k_0}{v_i})] \\[-10pt] \end{split} $$ (18) 2)补偿控制器设计
驱动力由两部分构成
$${F_i} = {F_{\rm{dsc}}} - {F_w}$$ (19) 式中,
${F_{\rm{dsc}}}$ 表示DSC控制器输出,${F_w}$ 为克服道路坡度与路面阻力的补偿控制.将式(19)代入式(5)得
$${\dot v_i} = {b_1}{F_{\rm{dsc}}} - {b_1}{F_w} - {b_2}v_i^2 - {b_3}w$$ (20) 针对观测到的路面状况, 设计补偿控制器
$${F_w} = - \frac{{{b_3}}}{{{b_1}}}\hat w$$ (21) 定义观测器误差
$$\tilde w = w - \hat w$$ (22) 对式(22)求导
$$\dot {\tilde w} = \dot w - \dot {\hat w}$$ (23) 在城市工况下道路坡度通常比较平缓, 因此
$\dot w = 0,$ 结合式(15)、式(16)得$$ \begin{split} \dot {\tilde w} =\;& - \dot {\hat w} = - {k_0}[{b_1}{F_i} - {b_2}v_i^2 - {\dot v_i} - {b_3}\hat w]=\\ &- {k_0}[({b_2}v_i^2 +{\dot v_i} + {b_3}w) - {b_2}v_i^2 - {\dot v_i} - {b_3}\hat w]=\\ & - {k_0}{b_3}\tilde w\\[-10pt] \end{split} $$ (24) 将式(21)、式(22)代入式(20), 则
$${\dot v_i} = {b_1}{F_{\rm{dsc}}} - {b_2}v_i^2 - {b_3}\tilde w$$ (25) 因此, 系统(5)转化为
$$ \left\{\begin{aligned} {\dot s_i} =\;& {v_i}\\ {\ddot s_i} =\;& {\dot v_i} = {b_1}{F_{\rm{dsc}}} - {b_2}v_i^2 - {b_3}\tilde w \end{aligned}\right. $$ (26) 3)动态面控制器设计
首先, 定义第一动态面为位置误差
$$ {Z_1} = {\delta _i} = {s_i} - ({s_q} - {d_a} - l) $$ (27) 则
$${\dot Z_1} = {\dot s_i} - {\dot s_q} = {v_i} - {\dot s_q}$$ (28) 取虚拟控制量
$$\alpha = - {k_1}{Z_1} + {\dot s_q}$$ (29) 其中,
$ {k_1} > 0. $ $$\dot \alpha = - {k_1}{\dot Z_1} + {\dot v_q}$$ $\alpha $ 通过一阶滤波得到$$ T{\dot \alpha _f} + {\alpha _f} = \alpha ,\;{\alpha _f}(0) = \alpha (0) $$ (30) 其中,
$T$ 为时间常数,$T > 0.$ 定义滤波误差
$$e = {\alpha _f} - \alpha $$ (31) 对其求导得
$$\dot e = {\dot \alpha _f} - \dot \alpha $$ (32) 然后, 定义第二动态面
$${Z_2} = {v_i} - {\alpha _f}$$ (33) 将式(29)、式(31)、式(33)代入式(28)得
$$ \begin{split} {\dot Z_1} =\;& {\dot s_i} - {\dot s_q} = {v_i} - {\dot s_q}={Z_2} + {\alpha _f} - {\dot s_q} =\\ &{Z_2} +e +\alpha - {\dot s_q}=\\ &{Z_2} + e + ( - {k_1}{Z_1} +{\dot s_q}) -{\dot s_q}=\\ &{Z_2} + e - {k_1}{Z_1} \end{split} $$ (34) 将式(29) ~ 式(31)、式(34)代入式(32)得
$$ \begin{split} \dot e =\;& {\dot \alpha _f} - \dot \alpha = \frac{{\alpha - {\alpha _f}}}{T} - \dot \alpha =\\ & \frac{{ - e}}{T} - ( - {k_1}{\dot Z_1} + {\ddot s_q}) = \frac{{ - e}}{T} + {k_1}{\dot Z_1} - {\ddot s_q}=\\ & \frac{{ - e}}{T} + {k_1}({Z_2} + e - {k_1}{Z_1}) - {\ddot s_q}=\\ & \left({k_1} - \frac{1}{T}\right)e + {k_1}{Z_2} - k_1^2{Z_1} - {\ddot s_q} \end{split} $$ (35) 设计DSC控制器
$$ \begin{split} {F_{\rm{dsc}}} =\;& - \frac{1}{{{b_1}}}( - {b_2}v_i^2 + {k_2}{Z_2} - {\dot \alpha _f})= \\ & - \frac{1}{{{b_1}}}\left( - {b_2}v_i^2 + {k_2}{Z_2} - \frac{{\alpha - {\alpha _f}}}{T}\right) \end{split} $$ (36) 其中,
$ {k_2} > 0. $ 对式(33)求导, 并将式(25)、式(36)代入得
$$ \begin{split} {\dot Z_2} =\;& {\dot v_i} - {\dot \alpha _f}=\\ & {b_1}{F_{\rm{dsc}}} - {b_2}v_i^2 - {b_3}\tilde w - {\dot \alpha _f}=\\ & {b_1}\left[ - \frac{1}{{{b_1}}}( - {b_2}v_i^2 + {k_2}{Z_2} - {\dot \alpha _f})\right] - {b_2}v_i^2 -\\ & {b_3}\tilde w - {\dot \alpha _f}=- {k_2}{Z_2} - {b_3}\tilde w \end{split} $$ (37) 定义Lyapunov函数
$$V = \frac{1}{2}Z_1^2 + \frac{1}{2}Z_2^2 + \frac{1}{2}{e^2} + \frac{1}{2}{\tilde w^2}$$ (38) 对式(38)求导, 并将式(24)、式(34)、式(35)、式(37)代入得
$$ \begin{split} \dot V = \;&{Z_1}{\dot Z_1} + {Z_2}{\dot Z_2} + e\dot e + \tilde w\dot {\tilde w}=\\ &{Z_1}({Z_2} + e -{k_1}{Z_1}) + {Z_2}( - {k_2}{Z_2} - {b_3}\tilde w)\; +\\ &e\left(\left({k_1} - \frac{1}{T}\right)e+ {k_1}{Z_2} - k_1^2{Z_1} - {\ddot s_q}\right) +\\ & \tilde w( - {k_0}{b_3}\tilde w)={Z_1}{Z_2} + (1 - k_1^2){Z_1}e \;- \\ &{k_1}Z_1^2 - {k_2}Z_2^2 - {b_3}{Z_2}\tilde w+{\boldsymbol{}}\left({k_1} - \frac{1}{T}\right){e^2}\; +\\ & {k_1}{Z_2}e - {\ddot s_q}e - {k_0}{b_3}{\tilde w^2} \end{split} $$ (39) 根据杨氏不等式
$$\left\{ {\begin{aligned} &{{Z_1}{Z_2} \leq \frac{1}{4}Z_1^2 + Z_2^2} \\ &{(1 - k_1^2){Z_1}e \leq (1 + k_1^2)\left(\frac{1}{4}Z_1^2 + {e^2}\right)} \\ &{ - {b_3}{Z_2}\tilde w \leq \left| { - {b_3}{Z_2}\tilde w} \right| \leq {b_3}\left(Z_2^2 + \frac{1}{4}{{\tilde w}^2}\right)} \\ & {{k_1}{Z_2}e \leq k_1^2Z_2^2 + \frac{1}{4}{e^2}} \\ &{ - {{\ddot s}_q}e \leq \left| { - {{\ddot s}_q}e} \right| \leq {e^2} + \frac{1}{4}\ddot s_q^2} \end{aligned}} \right.$$ (40) 因此
$$ \begin{split} \dot V \leq\;& - \left({k_1} - \frac{1}{2} - \frac{1}{4}k_1^2\right)Z_1^2 - ( - k_1^2 + {k_2} - 1 -\\ & {b_3})Z_2^2- \left(\frac{1}{T} - \frac{9}{4} - {k_1} - k_1^2\right){e^2} - \\ &{b_3}\left({k_0} - \frac{1}{4}\right){\tilde w^2} + \frac{1}{4}\ddot s_q^2 \end{split} $$ (41) 为保证系统的跟踪稳定性, 引入下列引理.
引理 1[29]. 对于非线性系统, 存在正定函数
$V$ 满足下列微分不等式$$\dot V \leq - \varsigma V + C$$ (42) 其中,
$V > 0,$ $C \geq 0.$ 对于${t_0},$ $V(t)$ 满足不等式$$ \begin{split} &0 \leq V(t) \leq\dfrac{ [C - (C - \varsigma V({t_0}))\exp ( - \varsigma (t - {t_0}))]}{\varsigma} ,\;\\ &\qquad\forall t \geq {t_0}\\[-10pt] \end{split} $$ (43) 即
$V(t)$ 以指数收敛率$\varsigma $ 最终一致收敛于$C/\varsigma, $ 则系统最终一致有界.根据引理1, 对于非线性系统(26), 存在正定函数式(38). 根据式(40), 只要
$$ \left\{ {\begin{aligned} &{{k_1} - \frac{1}{2} - \frac{1}{4}k_1^2 \geq 0} \\ &{ - k_1^2 + {k_2} - 1 - {b_3} \geq 0} \\ &{\frac{1}{T} - \frac{9}{4} - {k_1} - k_1^2 \geq 0} \\ &{{k_0} - \frac{1}{4} \geq 0} \end{aligned}} \right. $$ (44) 则
$\dot V \le - \varsigma V + C,$ 其中$$\begin{split} \varsigma =\;& \min \left(\left({k_1} - \frac{1}{2} - \frac{1}{4}k_1^2\right),\;\left( - k_1^2 + {k_2} - 1 - {b_3}\right),\right.\\ &\left.\left(\frac{1}{T} - \frac{9}{4} - {k_1} - k_1^2\right),\;\left({k_0} - \frac{1}{4}\right)\right) \end{split}$$ 则系统最终一致有界. 因此, Lyapunov函数
$V$ 一致有界, 适当地选择观测器增益、滤波器时间常数和控制器参数能够使得$\varsigma $ 足够大,$C/\varsigma $ 足够小, 使观测器误差和系统跟踪误差收敛到零的一个邻域内.注 3. 基于车辆非线性动态模型, 对道路情况
$w$ 进行观测补偿, 使DSC跟踪系统能够更好地适应道路变化, 具有更好的跟踪性能; 同时, 既无需进行速度预测也考虑了道路坡度对HEV车辆能量管理的影响, 为HEV的能量管理提供了保障.2.2 基于滚动DP的HEV能量管理
将车辆跟踪控制与HEV能量管理相结合, 既保证了车辆的跟踪安全性, 又为当前HEV车辆提供了工况循环信息. 因此, 本节采用动态规划策略在安全车距内对HEV车辆进行能量优化管理, 使HEV在满足各种约束条件下, 通过优化发动机与蓄电池功率分配使系统的性能指标即燃油消耗降至最低.
根据发动机功率与转矩之间的关系式(13), HEV车辆油耗模型式(14)转化为
$${\dot m_f} = \varphi ({\omega _{\rm{eng}}},\;{P_{\rm{eng}}})$$ (45) 式中,
$\varphi (\cdot)$ 表示油耗率与发动机转速、功率之间的函数关系. 图4为基于Advisor车辆参数转化后的不同转速下车辆油耗模型.离散化控制目标为
$$\mathop {\min }\limits_{{P_{\rm{eng}}}} J = \sum\limits_{k = 0}^{N - 1} {\varphi ({\omega _{\rm{eng}}},\;{P_{\rm{eng}}}} ,\;k)$$ (46) 约束条件满足
$$ \begin{split} &SOC(k + 1) = f(SOC(k),\;{P_{\rm{eng}}}(k),\;k)\\ &k = 0,\;1,\cdots,\; N - 1 \end{split} $$ (47) $$\left\{ \begin{aligned} &{SO{C^{\min }} \leq SOC \leq SO{C^{\max }}} \\ &{{P_{\rm{batt}}}^{\min } \leq {P_{\rm{batt}}} \leq {P_{\rm{batt}}}^{\max }} \\ &{{P_{\rm{eng}}}^{\min } \leq {P_{\rm{eng}}} \leq {P_{\rm{eng}}}^{\max }} \\ &{{\omega _{\rm{eng}}}^{\min } \leq {\omega _{\rm{eng}}} \leq {\omega _{\rm{eng}}}^{\max }} \end{aligned}\right.$$ (48) 式中,
${( \cdot )^{\min }}$ 与${( \cdot )^{\max }}$ 分别表示最小值、最大值.考虑采样时间内
$\Delta SOC(k)$ 的约束, 进一步减少状态空间和计算量, 以实现实时控制.$$ \begin{split} &\Delta SOC(k) = SOC(k + 1) - SOC(k)=\\ &\qquad- \frac{{{V_{oc}} - \sqrt {{V_{oc}}^2 - 4{P_{\rm{batt}}}(k){R_{\rm{batt}}}} }}{{2{Q_{\rm{batt}}}{R_{\rm{batt}}}}}=\\ &\qquad - \frac{{{V_{oc}} - \sqrt {{V_{oc}}^2 - 4[{P_i}(k) - {P_{\rm{eng}}}(k)]{R_{\rm{batt}}}} }}{{2{Q_{\rm{batt}}}{R_{\rm{batt}}}}} \end{split} $$ (49) $$ \begin{split} &\Delta SOC{(k)_{\max (\min )}} =\\ &\qquad- \frac{{{V_{oc}} - \sqrt {{V_{oc}}^2 - 4{P_{{\rm{batt}}\_\max (\min )}}(k){R_{\rm{batt}}}} }}{{2{Q_{\rm{batt}}}{R_{\rm{batt}}}}}\\ &\qquad SO{C_{k\min }} \le SOC(k) \leq SO{C_{k\max }} \end{split} $$ (50) 滚动DP算法的计算过程如下:
1)在安全距离内进行初始化并定义时间及状态存储空间;
2)根据跟踪控制安全距离内的当前车辆i的车速轨迹, 得到车辆速度和功率
${v_i}(k),$ ${P_i}(k),$ $k=N, $ $N - 1,\cdots,\;1;$ 3)对于阶段k 对应的
${v_i}(k),$ ${P_i}(k),$ 考虑阶段状态约束$SO{C_j}(k) \in [SO{C_{k\min }},\;SO{C_{k\max }}],$ 计算所有状态转移所对应的变化量${J_{ij}}(k),$ 并求得所有状态j对应的成本函数最优值${J_k} = \min [{J_{ij}}(k)\; + {J_j}(k + 1)];$ 4)进入到下一阶段
$k = k - 1,$ 重复步骤3)直到$k = 1,$ 找到成本函数最低的最优控制和状态;5)以优化结果作为安全车距内的控制输入, 滚动执行整个优化过程.
注 4. 第2.1节基于观测器补偿的DSC控制器为安全距离内的动态规划算法提供了准确的驾驶工况循环, 保证了能量管理的有效性; 在安全车距内考虑单位步长内电池SOC变化的约束, 使得HEV能量管理的状态空间和控制空间大大缩减, 减少了计算负担, 更有利于HEV能量管理的实时性.
3. 仿真研究
对HEV车辆跟踪与能量管理进行仿真研究, 并与Advisor中的能量管理控制结果进行比较, 验证所采用控制策略的有效性.
3.1 DSC车辆跟踪控制仿真验证
考虑跟车行驶的工况, HEV车辆参数如表1所示. 假设前车按照ECE城市工况循环行驶, 总距离约为1 km, 其最高限速为50 km/h, 道路坡度如图5所示, 车辆初始安全距离设为30 m. DSC跟踪控制器参数根据式(44)分别选为:
${k_0} = 0.5{\text{、}}$ ${k_1} = 2{\text{、}}$ ${k_2} = 30{\text{、}}$ $T = 1,$ 仿真结果如图6、图7所示.表 1 HEV车辆主要参数Table 1 Parameters of HEV参数 数值 单位 参数 数值 单位 整车质量 1332 kg 车轮半径 0.287 m 重力加速度 9.81 N/kg 迎风面积 1.746 m2 车身长度 3 m 空气密度 1.29 kg/m3 风阻系数 0.3 — 滚动阻力系数 0.3 m/s 图6为车辆跟踪的位置与车距变化曲线, 具有较好的位置跟踪性能, 且考虑了坡度的变化对车间距进行了适当的调整. 图7中, 两种控制器均能实现较好的速度跟踪, 但通过局部放大可以看出具有补偿控制器的DSC控制能够更快地适应实时的速度变化, 具有更好的适应性和跟踪控制效果.
3.2 能量管理优化仿真
基于跟踪控制的车速工况与功率需求, 应用滚动动态规划算法进行数值仿真研究.
图8为车速工况与功率需求曲线, 由图可以看出车辆在加速过程中的功率大于零且逐渐增加; 车辆速度减小时, 车辆功率为负, 处于再生制动状态. 在图9中, HEV车辆电池SOC随着行驶工况与电池能量的消耗与回收而发生变化. 图10为基于跟踪工况下的HEV功率分配曲线. 当车速较低时, HEV所需的功率主要由电池通过电动机提供; 随着车辆速度与功率需求的增加, 发动机和电动机共同工作提供能量; 当车速下降时, HEV通过再生制动进行能量回收. 表2为采用该策略与Advisor中能量管理策略的燃油消耗对比, 百公里油耗提高了约12 %, 由此可以看出本文所采用的方法具有良好的燃油经济性.
表 2 燃油消耗对比Table 2 Comparison of fuel consumption优化方法 (ECE 工况) 燃油消耗 (l/100 km) 提高 (%) Advisor 6.3 — 本文算法 4.68 12 4. 结论
本文研究了混合动力电动汽车的车辆跟踪与能量管理控制. 考虑在有前车的道路工况下, 基于安全车距设计了具有观测补偿的动态面跟踪控制算法, 为HEV车辆能量管理提供了驾驶工况, 并在安全距离内对HEV采用滚动动态规划算法进行能量管理. 考虑单位步长内电池SOC变化的约束进一步缩小对SOC状态搜索空间, 更有利于车辆的安全控制和实时的能量优化管理. 需要指出的是, 本文未考虑车辆在交叉路口、红灯或转弯时的安全车距与速度跟踪问题, 我们将在后续研究中更全面地考虑各种复杂交通情况下的混合动力电动汽车跟车控制与能量管理问题, 并将进一步研究多个HEV车辆的队列控制与能量管理问题.
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图 5 空地机器人无线通信((a) 集中式; (b) 分布式; (c) 移动自组织网络)
Fig. 5 Wireless communications of air-ground robots ((a) Centralized; (b) Distributed; (c) Mobile ad-hoc network)
图 7 生物群智迁移映射空地协同群智系统
Fig. 7 Biological collective intelligence transfer and mapping air-ground collaboration collective intelligence system
表 1 通信方式分析
Table 1 Analysis of communication methods
通信方式 设备 常见任务 常见环境 通信范围 特点 研究代表 有线通信 光缆 搜索救援 范围有限的室外区域 取决于光缆长度 准确性高, 不易出错,
但会影响空地主体机动性[9, 48] 集中式 ZigBee WiFi节点 数据收集 室内, 范围有限的
室外区域0 ~ 100 m 依赖于中心节点, 准确性高,
但通信效率低[49−51] 分布式 WiFi节点 大规模建图 室外 与空地机器人数目成正比 不依赖中心节点, 鲁棒性强,
但通信范围有限[15, 53] 移动自组织网络 IEEE 802.11中继器
LoRA节点搜索救援 隧道等通信设施
缺乏的场景可随节点个数增加
不断扩大不依赖中心节点, 抗干扰能力强,
通信范围广, 灵活部署[9, 30, 42, 54] 
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表 2 空地协同中的语义分割算法应用总结
Table 2 Application summary of semantic segmentation algorithm in air-ground collaboration
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表 5 空地协同等级分类方法总结
Table 5 Summary of classification methods for air-ground collaboration level
等级分类 代表研究 任务 方法 决策拓扑 实验环境 非自主等级协同 [9] 探索地下隧道 基于图的路径规划器, 地图融合算法 分布式 Sim2Real [80] 协作攀爬 未知环境可穿越性地形判断 集中式 Real 弱自主等级协同 [59] 探索地下隧道 BPMN表示法, 有限状态机 集中式 Real [112] 区域搜索 神经进化算法 分布式 Sim [108] 海上平台作业 多角色目标分配 集中式 Sim [110] 野外建图 规约语言, 确定性有限状态机 集中式 Sim [111] 目标跟踪 多智能体强化学习 分布式 Sim 强自主等级协同 [113] 提供通信计算服务 目标层次分解 分布式 Sim [114] 协同作战 PDDL模型, 基于图的任务分解 集中式 Sim [115] 提供通信计算服务 Lyapunov优化法 集中式 Sim
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表 6 空地模拟器总结
Table 6 Summary of air-ground simulator
仿真环境 物理引擎 是否开源 特点 不足 Gazebo 支持ODE、Bullet、Simbody和DART 是 ROS集成使用, 支持多种插件 视觉渲染效果差 MORSE BGE 是 分布计算, 自由度可控 同步性差, 无法精确动力学建模 Pybullet Bullet 是 跨平台, 操作简单 运行效率慢 CoppeliaSim 支持ODE、Bullet和Vortex 是 分布式, 支持ROS接口,
支持多语言编程视觉渲染效果差, 运行效率慢 AirSim UE4 是 跨平台, 视觉逼真 动力学仿真效果差, 物理接口不足 Collaborative robots Sim ODE 否 基于Gazebo强物理交互 视觉渲染效果差, 运行速率慢 Gibson Env 神经网络 是 融入真实数据, 逼真的渲染效果 需要采集大量真实数据
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