Path planning of coal mine foot robot by integrating improved A* algorithm and dynamic window approach
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摘要: 为提高煤矿足式机器人路径规划算法的运行效率、搜索精度及避障灵活性,提出了一种融合改进A*算法与动态窗口法(DWA)的煤矿足式机器人路径规划方法。首先对A*算法进行改进,通过去冗余节点策略减短规划路径的长度,通过改进邻域搜索方式和代价函数提高路径规划速度,采用分段二阶贝塞尔曲线进行路径平滑。将改进A*算法规划出的路径节点依次作为局部路径规划DWA的局部目标点进行算法融合,筛选邻近的障碍物节点,从而再次缩短路径长度,并通过调整DWA代价函数中的权值比例提升避障性能。针对机器人遇到无法避开的障碍物而陷入“假死”状态的问题,以当前初始点为起点,重新调用融合算法,即重新进行全局路径规划,将得到的新节点代替原有的局部目标点,按照新路径进行后续工作。仿真结果表明:在保证机器人行走安全稳定的基础上,改进A*算法较传统A*算法的计算时间缩短了65%,路径长度缩短了24.1%,路径节点数量减少了27.65%,最终得出的路径更为平滑;融合算法进一步提升了全局路径规划能力,在多障碍物环境下能够绕开新增的动态和静态障碍物;机器人遇到“L”型障碍物进入“假死”状态时,在“假死”位置重新进行全局路径规划,更新行走路径,成功到达了最终目标点。基于融合算法的JetHexa六足机器人路径规划实验结果验证了融合算法的有效性和优越性。Abstract: In order to improve the operational efficiency, search precision, and obstacle avoidance flexibility of the path planning algorithm for coal mine foot robot, a path planning method for coal mine foot robots is proposed, which integrates the improved A* algorithm and the dynamic window approach (DWA). Firstly, the A* algorithm is improved by reducing the length of the planned path through a redundant node removal strategy. The method improves the neighborhood search method and cost function to increase the speed of path planning, and uses segmented second-order Bessel curves for path smoothing. The path nodes planned by the improved A* algorithm are sequentially used as local target points for local path planning DWA for algorithmic fusion. The method filters neighboring obstacle nodes to shorten the path length again, and improves obstacle avoidance performance by adjusting the weight ratio in the DWA cost function. In response to the problem of robots falling into a "feigned death" state when encountering unavoidable obstacles, the method starts from the current initial point, the fusion algorithm is called up again. The global path planning is carried out again, and the new nodes obtained replace the original local target points, and the subsequent work is carried out according to the new route. The simulation results show that, while ensuring the safety and stability of robot walking, the improved A* algorithm reduces the calculation time by 65%, the path length by 24.1%, and the number of path nodes by 27.65% compared to the traditional A* algorithm, resulting in a smoother path. The fusion algorithm further enhances the global path planning capability, enabling it to bypass newly added dynamic and static obstacles in multi obstacle environments. When the robot encounters an L-shaped obstacle and enters a "feigned death" state, it reconducts global path planning at the "feigned death" position, updates its walking path, and successfully reaches the final target point. The experimental results of path planning for JetHexa hexapod robot based on fusion algorithm have verified the effectiveness and superiority of the fusion algorithm.
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0. 引言
我国煤矿井下电压等级多,大多数煤矿采用127 V或660 V作为矿用电源的交流输入电压。随着煤矿井下自动化程度提高,各种监测、通信设备用于供电电压为1 140 V的综采工作面,部分煤矿要求矿用电源能够直接接入1 140 V供电系统中。
MT/T 408—1995《煤矿用直流稳压电源》要求矿用电源交流输入电压波动范围为标称值的75%~110%,在127 V供电系统中,交流输入电压下限值约为95 V,在1 140 V供电系统中,交流输入电压上限值为1 254 V。煤矿井下环境复杂,矿用电源输入端与井下供电端之间采用数千米长的电缆进行连接,在相同负载下,交流输入电压越低,电流越大,供电电缆线损越严重。当127 V电压波动至标称值的75%时,供电电缆压降约为20 V,矿用电源输入电压约为70 V。当1 140 V电压波动至标称值的110%时,保留10%的电压裕量,矿用电源输入电压约为1 400 V。在满足煤矿电压等级的前提下,最大程度地提高矿用电源的输入电压范围,使矿用电源能够自适应70~1 400 V交流电压,是矿用电源发展趋势。
目前矿用电源主要采用反激变换器拓扑结构,如文献[1]采用多个反激变换器串联,降低了功率管电压应力,具有结构简单、成本低的特点,但功率管占空比受到限制,反激变换器电压增益小,无法自适应70~1 400 V交流电压。文献[2]提出了基于三电平变换器的宽范围开关电源,但功率管电压应力大,输入交流电压为95~825 V,无法应用于煤矿1 140 V供电系统中。文献[3-6]提出了LLC变换器,采用谐振工作方式,降低了功率管损耗,提高了效率,但受限于变换器谐振工作频率,电压增益无法增大。文献[7-9]设计的变换器为非隔离型,不满足输入输出电气隔离要求,且功率管电压应力大。文献[10-11]为降低功率管电压应力,采用多电平拓扑结构,但引入过多二极管和电容,导致控制复杂,不利于电源的稳定性且成本高。本文提出了一种矿用宽输入电压范围级联变换器设计方案,通过电容串联分压降低功率管电压应力,采用Buck变换器与LLC变换器串联方式提高变换器电压增益。
1. 级联变换器设计
矿用宽输入电压范围级联变换器由3路相同的Buck变换器和LLC变换器组成,如图1所示。交流电经不控整流电路整流后,通过电容串联分压分成3路幅值相近的电压,作为Buck变换器输入电压;Buck变换器将电压调节至一定范围,作为LLC变换器输入电压;LLC变换器利用压频变换,输出稳定的直流电压。
1.1 Buck变换器
交流输入电压经整流后得到的直流电压Udc被电容C11,C21,C31分压,每个电容电压约为Udc/3,使Buck变换器中功率管Q11,Q21,Q31承受的电压应力为直流电压的1/3;储能滤波电感L11,L21,L31和滤波电容C12,C22,C32对Buck变换器输出电压进行滤波储能;当Q11,Q21,Q31断开时,二极管D11,D21,D31进行续流。
由于输入电压范围宽,Buck变换器采用输出电压闭环和输入电压前馈补偿环相结合控制方式,调节Q11,Q21,Q31占空比,并对占空比进行限幅,维持输出电压稳定,如图2所示。图2中,Uref1为Buck变换器给定电压,Ubus_set为前馈补偿环基准电压,Uin为输入电压,Gvd(s)为占空比扰动与输出电压扰动的传递函数,UBuck为输出电压,Kvf1为Buck变换器电压反馈系数。
占空比扰动与输出电压扰动的传递函数为
$$ {G_{{\rm{vd}}}(s)} = \dfrac{U_{\rm{in}}}{{s^2}{L_{11}}{C_{12}} +{\dfrac{sL_{11}}{R}}+1}$$ (1) 式中:s为拉普拉斯算子;R为Buck变换器等效负载。
1.2 LLC变换器
LLC变换器中功率管Q12,Q13,Q22,Q23,Q32,Q33组成半桥;谐振电容Cr1,Cr2,Cr3和谐振变压器 T1,T2,T3组成谐振网络,其中Lr1,Lr2,Lr3分别为谐振变压器T1,T2,T3漏磁电感,Lm1,Lm2,Lm3分别为谐振变压器T1,T2,T3励磁电感;二极管D12,D13,D22,D23,D32,D33将谐振电压整流成直流电压,并在功率管关闭时进行续流;C13,C23,C33为输出滤波电容。
为实现LLC变换器稳压输出,采用脉冲频率调制技术对输出电压进行闭环控制,通过压控振荡器对功率管Q12,Q13,Q22,Q23,Q32,Q33进行变频驱动,改变谐振网络工作频率,稳定输出电压,如图3所示。图3中,Uref2为LLC变换器给定电压,Kvf2为LLC变换器电压反馈系数,Uout为LLC变换器输出电压。
在最低输入电压或最高条件下需调节LLC变换器电压增益进行稳压,变换器电压增益为[12]
$$\begin{aligned} & M = \left| {\frac{{{\omega ^2}{C_{{\rm{r}}1}}{R_{{\rm{ac}}}}{L_{{\rm{m}}1}}}}{{{\rm{j}}\omega {L_{{\rm{m}}1}}(1 - {\omega ^2}{L_{{\rm{r}}1}}{C_{{\rm{r}}1}}) + {R_{{\rm{ac}}}}\left[ {1 - {\omega ^2}{C_{{\rm{r}}1}}({L_{{\rm{m}}1}} + {L_{{\rm{r}}1}})} \right]}}} \right| \hfill \\&{} \end{aligned}$$ (2) 式中:ω为谐振角频率;Rac为谐振变压器初级等效负载。
当LLC变换器输入电压为最高电压时,变换器需提供最小电压增益:
$${ {M_{\min}}= \frac{{L_{{\rm{m}}1} + {L_{{\rm{r}}1}}}}{{L_{{\rm{m}}1}}} = \frac{{k + 1}}{k} }$$ (3) 式中k为励磁电感和初级漏磁电感比值。
当LLC变换器输入电压为最低电压时,变换器需提供最大电压增益:
$${{ M_{\max}} = \frac{{U_{{\rm{inmax}}} }}{{U_{{\rm{inmin}} }}}{M_{\min}} }$$ (4) 式中:Uinmax为LLC变换器最高输入电压;Uinmin为LLC变换器最低输入电压。
LLC变换器中谐振变压器匝比为
$$ n = \frac{{U_{{\rm{inmax}} }}}{{2(U_{\text{out}} + 2U_{\rm{f}})}}{M_{\min}} $$ (5) 式中Uf为谐振变压器次级整流二极管压降。
由式(5)及LLC变换器整体效率E和输出功率Pout计算谐振变压器初级等效负载:
$$ R_{\rm{ac}} = \frac{{8{n^2}U_{{\rm{out}}}^2}}{{{\text{π} ^2}P_{{\rm{out}}}}}E $$ (6) 谐振电容为
$$ {C_{{\rm{r}}1}} = \frac{1}{{2 \text{π} Qf_{\min}R_{{\rm{ac}}}}} $$ (7) 式中:Q为品质因数;fmin为最低谐振频率。
谐振变压器漏磁电感为
$$ {L}_{{\rm{r}}1}=\frac{1}{(2\text{π} f_{\min}{)}^{2}C_{{\rm{r}}1}} $$ (8) 谐振变压器励磁电感为
$$ {L_{{\text{m}}1}} = \frac{{{{(k + 1)}^2}}}{{2k + 1}}{L_{{\rm{r}}1}} $$ (9) 2. 仿真与实验
为验证矿用宽输入电压范围级联变换器的有效性,利用Matlab建立级联变换器仿真模型,并搭建样机进行实验。Buck变换器功率管采用耐压1 200 V的IGBT,LLC变换器功率管采用耐压100 V的MOSFET。级联变换器参数见表1。
表 1 矿用宽输入电压范围级联变换器参数Table 1. Parameters of mine cascaded converter with wide input voltage range参数 数值 参数 数值 输入电压/V 70~1 400 LLC变换器漏磁电感/μH 12 输出电压/V 35 LLC变换器励磁电感/μH 1.3 额定功率/W 200 LLC变换器谐振电容/μF 1 Buck变换器电感/mH 1 LLC变换器输出电容/μF 1 000 Buck变换器电容/μF 1 000 变压器匝比 2∶3∶3 IGBT开关频率/kHz 35 LLC变换器PI调节器
比例系数65 Buck变换器PI调节器比例系数 15 LLC变换器PI调节器
积分系数1 Buck变换器PI调节器积分系数 2 LLC变换器压控振荡器
转换精度比例因数8 仿真模拟负载突变情况下输出电压的稳定性,如图4所示。当输出电流由0.4 A突增至2.4 A,并经0.1 s后突减至0.4 A时,负载效应在3%以内,满足MT/T 408—1995中负载效应不大于5%的要求。
当输入电压为AC70 V时,Buck变换器、LLC变换器功率管驱动实验波形如图5所示。可看出Buck变换器功率管IGBT开关频率为35 kHz,占空比为0.95,未出现全开通现象;LLC变换器功率管MOSFET开关频率为40 kHz,占空比固定为0.5,MOSFET工作于脉冲频率调制。
输入电压为AC70 V且空载、满载条件下,输出电压和电流实验波形如图6所示。可看出输出电压平均值由空载时的34.91 V变化至满载时的34.90 V,输出电压偏离值在0.3%以内,满足MT/T 408—1995中输出电压偏离值不超过5%的要求。
当输入电压为AC1 400 V时,Buck变换器、LLC变换器功率管驱动实验波形如图7所示。可看出Buck变换器功率管IGBT开关频率为35 kHz,占空比为0.05,未出现全关闭现象;LLC变换器功率管MOSFET开关频率为60 kHz,占空比固定为0.5,MOSFET工作于脉冲频率调制。
输入电压为AC1 400 V且空载、满载条件下,输出电压和电流实验波形如图8所示。可看出输出电压平均值由空载时的35.01 V变化至满载时的34.98 V,输出电压偏离值在0.3%以内,满足MT/T 408—1995中输出电压偏离值不超过5%的要求。
3. 结语
矿用宽输入电压范围级联变换器能够在AC70~1 400 V输入电压波动范围内,输出电压稳定,电压偏离值在5%以内,且负载效应在5%以内,满足MT/T 408—1995要求,同时具有输入输出电气隔离性能,可应用于多电压等级的矿用电气设备。
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表 1 邻域删除策略
Table 1 Neighborhood deletion strategy
角度区间 删除邻域 −22.5°≤θ<22.5° 出发点左侧邻域 22.5°≤θ<67.5° 出发点左下侧邻域 67.5°≤θ<112.5° 出发点下侧邻域 112.5°≤θ<157.5° 出发点右下侧邻域 −180°≤θ<−157.5° 或 157.5°≤θ<180° 出发点右侧邻域 −157.5°≤θ<−112.5° 出发点右上侧邻域 −112.5°≤θ<−67.5° 出发点上侧邻域 −67.5°≤θ<−22.5° 出发点左上侧邻域 表 2 A*算法改进前后性能对比
Table 2 Comparison of performance before and after A* algorithm improvement
算法 规划时间/s 规划路径长度/cm 路径节点数/个 传统A*算法 1.20 55.6 47 应用去冗余节点 1.19 38.8 31 改进A*算法 0.42 42.2 34 表 3 算法改进前后性能对比
Table 3 Comparison of performance before and after algorithm improvement
算法 规划时间/s 路径长度/cm A*算法+DWA 1.97 424 改进A*算法+DWA 1.10 368 -
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