舰船科学技术  2020, Vol. 42 Issue (6): 89-94    DOI: 10.3404/j.issn.1672-7649.2020.06.018 PDF

Analysis of AUV docking collision based on ADAMS and multiple nonlinear regression
WANG Xiang, ZHANG Yong-lin
School of Electronics and Information, Jiangsu University of Science and Techology, Zhenjiang 212003, China
Abstract: According to the collision problem in the docking process of AUV. Established AUV dynamics model and collision force model. A simulation model was built in the dynamic analysis software ADAMS(automatic dynamic analysis of mechanical systems) to imitate the docking process. Analyzed four factors that impacted on the whole docking process, including the shape of cone entrance, the gap between the center line of the AUV and the center line of the docking device, deflection angle of the AUV center and the center axis of the docking device and the initial velocity of the AUV. The simulation results showed that the small opening angle of the cone, the small gap and the small initial velocity of the AUV were beneficial to the docking process. The multivariate nonlinear regression method was used to analyze the relationship between the maximum collision force and the influencing factors, and the regression equation of the maximum collision force and its influencing factors was obtained.
Key words: AUV underwater docking     collision analysis     ADAMS simulation     multiple nonlinear regression
0 引　言

1 对接过程动力学模型的构建 1.1 AUV水动力建模

1.1.1 惯性类水动力

 ${f_i} = - \sum\limits_{j = 1}^6 {{m_{ij}}{{\dot v}_j}} \text{。}$ (1)

 $\begin{gathered} \tiny \left[ {\begin{array}{*{20}{c}} X \\ Y \\ Z \\ K \\ M \\ N \end{array}} \right] = \hfill \\ - \tiny \left[ \!\!\!\!{\begin{array}{*{20}{c}} {\frac{1}{2}\rho {L^3}{{X'}_{\dot u}}}&0&0&0&0&0 \\ 0&{\frac{1}{2}\rho {L^3}{{Y'}_{\dot v}}}&0&0&0&{\frac{1}{2}\rho {L^4}{{N'}_{\dot v}}} \\ 0&0&{\frac{1}{2}\rho {L^3}{{Z'}_{\dot w}}}&0&{\frac{1}{2}\rho {L^4}{{M'}_{\dot w}}}&0 \\ 0&0&0&{\frac{1}{2}\rho {L^5}{{K'}_{\dot p}}}&0&0 \\ 0&0&{\frac{1}{2}\rho {L^4}{{Z'}_{\dot q}}}&0&{\frac{1}{2}\rho {L^5}{{M'}_{\dot q}}}&0 \\ 0&{\frac{1}{2}\rho {L^4}{{Y'}_{\dot r}}}&0&0&0&{\frac{1}{2}\rho {L^4}{{N'}_{\dot r}}} \end{array}} \!\!\!\!\right]\left[ \!\!\!\!{\begin{array}{*{20}{c}} {\dot u} \\ {\dot v} \\ {\dot w} \\ {\dot p} \\ {\dot q} \\ {\dot r} \end{array}} \!\!\!\!\right] \text{。} \end{gathered}$ (2)
1.1.2 粘性类水动力

 ${{F}} = [X,Y,Z,K,M,N]'\text{。}$

 $\begin{split} X = & {X_{uu}}{u^2} + {X_{vv}}{v^2} + {X_{ww}}{w^2} + {X_{rr}}{r^2} + {X_{qq}}{q^2} + \\ & {X_{vr}}vr + {X_{wq}}wq + {X_{pr}}pr + {X_{wp}}wp\text{，} \\ \end{split}$ (3)
 $\begin{split} Y = & {Y_0} + {Y_v}v + {Y_r}r + {Y_{r\left| r \right|}}r\left| r \right| + {Y_p}p + {Y_{p\left| p \right|}}p\left| p \right| + \\ & {Y_{vw}}vw + {Y_{v\left| v \right|}}v\left| {\sqrt {{v^2} + {w^2}} } \right|{\rm{ + }}{Y_{v\left| r \right|}}\frac{v}{{\left| v \right|}}\left| {\sqrt {{v^2} + {w^2}} } \right|\left| r \right|+ \\ &{Y_{vq}}vq + {Y_{wp}}wp + {Y_{pq}}pq + {Y_{wr}}wr + {Y_{qr}}qr\text{，} \end{split}$ (4)
 $\begin{split} Z = & {Z_0} + {Z_w}w + {Z_q}q + {Z_{q\left| q \right|}}q\left| q \right| + {Z_{ww}}{w^2} + {Z_{vv}}{v^2} + {Z_{rr}}{r^2}+ \\ & {Z_{pp}}{p^2} + {Z_{w\left| w \right|}}w\left| {\sqrt {{v^2} + {w^2}} } \right|{\rm{ + }}{Z_{ww}}\left| {w\sqrt {{v^2} + {w^2}} } \right|+ \\ & {Z_{w\left| q \right|}}\frac{w}{{\left| w \right|}}\left| {\sqrt {{v^2} + {w^2}} } \right|\left| q \right| + {Z_{wq}}wq + {Z_{vp}}vp + \\ & {Z_{pr}}pr + {Z_{vr}}vr + {Z_{\left| w \right|}}\left| w \right| \text{，} \\[-13pt] \end{split}$ (5)
 $\begin{split} K = & {K_0} + {K_v}v + {K_r}r + {K_{r\left| r \right|}}r\left| r \right| + {K_p}p + {K_{p\left| p \right|}}p\left| p \right| + \\ & {K_{vw}}vw + {K_{v\left| v \right|}}v\left| {\sqrt {{v^2} + {w^2}} } \right|{\rm{ + }}{K_{vq}}vq + {K_{wp}}wp + \\ & {K_{wr}}wr + {K_{pq}}pq + {K_{qr}}qr \text{，} \end{split}$ (6)
 $\begin{split} M = & {M_0} + {M_w}w + {M_q}q + {M_{q\left| q \right|}}q\left| q \right| + {M_{ww}}{w^2} + {M_{vv}}{v^2}+ \\ & {M_{vr}}vr + {M_{rr}}{r^2} + {M_{pp}}{p^2} + {M_{w\left| w \right|}}w\left| {\sqrt {{v^2} + {w^2}} } \right|+ \\ & {\rm{ }}{M_{ww}}\left| {w\sqrt {{v^2} + {w^2}} } \right| + {M_{w\left| q \right|}}\frac{w}{{\left| w \right|}}\left| {\sqrt {{v^2} + {w^2}} } \right|\left| q \right|{M_{wq}}wq + \\ & {M_{vp}}vp + {M_{pr}}pr + {M_{\left| w \right|}}w \text{，}\\[-13pt] \end{split}$ (7)
 $\begin{split} N = & {N_0} + {N_v}v + {N_r}r + {N_{r\left| r \right|}}r\left| r \right| + {N_p}p + {N_{p\left| p \right|}}p\left| p \right|+ \\ & {N_{vw}}vw + {N_{v\left| v \right|}}v\left| {\sqrt {{v^2} + {w^2}} } \right|{\rm{ + }}{N_{v\left| r \right|}}\frac{v}{{\left| v \right|}}\left| {\sqrt {{v^2} + {w^2}} } \right|\left| r \right|+ \\ & {N_{vq}}vq + {N_{wp}}wp + {N_{pq}}pq + {N_{qr}}qr + {N_{wr}}wr \text{。} \end{split}$ (8)
1.2 碰撞接触力建模

 $F = {F_n} + {F_s}\text{。}$ (9)

 ${F_n} = K{\delta ^n} + \lambda {\delta ^n}\dot \delta \text{，}$ (10)

 $e = - \frac{{v_1^{} - {v_{10}}}}{{{v_0} - {v_{00}}}}\text{。}$ (11)

 $e = - \frac{{{v_1}}}{{{v_0}}}\text{。}$ (12)

AUV对接碰撞过程中能量损失可近似为AUV动能的变化：

 $\Delta E = \frac{1}{2}m({v_0}^2 - {v_1}^2) = \frac{1}{2}(1 - {e^2})m{v_0}^2\text{。}$ (13)

 $\Delta E = \oint {\lambda {\delta ^n}\dot \delta } {\rm d}\delta \approx 2\int_0^{{\delta _m}} {\lambda {\delta ^n}\dot \delta } {\rm d}\delta = \frac{{2\lambda m{v_0}^3}}{{3k}}\text{。}$ (14)
 图 1 接触中的滞后回线 Fig. 1 Hysteresis loop in contact

 $\lambda = \frac{{3k(1 - {e^2})}}{4}\frac{1}{{{v_0}}}\text{，}$ (15)

 ${F_n} = K{\delta ^n}\left[ {1 + \frac{{3(1 - {e^2})}}{4}\frac{{\dot \delta }}{{{v_0}}}} \right]\text{。}$ (16)

2 对接过程仿真分析 2.1 IMPACT冲击函数法求解碰撞力

ADAMS中接触力算法有2种，分别是惩罚函数法和IMPACT冲击函数法。惩罚函数法需要确定惩罚系数和补偿系数2个参数，这2个参数目前没有文献讲述其确切的确定方法，故本文采用IMPACT冲击函数法求解碰撞力。在ADAMS函数库中，IMPACT冲击函数的格式为[12] $IMPACT(q,\dot q,{q_1},k,e,{c_{\max }},d)$ ，具体表达式为：

 $IMPACT = \left\{ {\begin{array}{*{20}{l}} 0, &{{\text{当}}q > {q_1}};\\ {k{{({q_1} - q)}^e} - {c_{\max }}},&{}\\ {\dot q \cdot {\rm step}(q,{q_1}, - d,1,{q_1},0)},&{{\text{当}}q \le {q_1}}\text{。} \end{array}} \right.$

1）刚度系数 $k$

 $k = \frac{4}{{3{\text π} ({\sigma _1} + {\sigma _2})}}{(\frac{{{r_1}{r_2}}}{{{r_1} + {r_2}}})^{1/2}}\text{，}$ (17)
 ${\sigma _i} = \frac{{1 - v_i^2}}{{{\text π} {E_i}}}(i = 1,2)\text{。}$ (18)

2）力指数e

3）最大阻尼系数 ${c_{\max }}$

4）渗透量d

2.2 对接过程分析

 图 2 AUV水下对接系统模型 Fig. 2 AUV underwater docking system model

 图 3 AUV与导流罩碰撞情况 Fig. 3 AUV with flow deflector

 图 4 碰撞合力变化图像 Fig. 4 Collision force change image
2.3 AUV对接碰撞影响因素分析

1）不同开口角度对仿真结果的影响

2）不同偏心距对仿真结果的影响

3）不同初速度对仿真结果的影响

4）不同偏角 $\beta$ 对仿真结果的影响

3 多元非线性回归

AUV在对接碰撞的过程中，AUV头部与对接装置的导向罩的接触力大小是评价对接过程稳定性的主要指标之一。AUV与导向罩的接触力越大，越不利于AUV与回收装置的对接，AUV与导向罩的接触力越小，则对接的成功率越高。本文以偏心距 $d$ ，偏角 $\beta$ ，导向罩开口角度 $\alpha$ 以及对接时的初速度 ${v_0}$ 为变量，利用多元非线性回归模型得到最大碰撞力与偏心距 $d$ ，偏角 $\beta$ ，导向罩开口角度 $\theta$ 以及对接时的初速度 ${v_0}$ 之间的表达式。使用Matlab中自带的regress函数对于多元线性回归方法系数的求解

${Y_i} = {\beta _0} + {\beta _1}{X_{1i}} + {\beta _2}{X_{2i}} + \cdot \cdot \cdot + {\beta _k}{X_{ki}} + {u_i} i = 1,2,...,n$

 \begin{aligned} F = & - 2005 + 16889d + 184\theta + 1210\beta + 258{v_0} - \\ & 18902{d^2} + 4915{v_0}^2 - 16{\beta ^2} \text{。} \\ \end{aligned}

 图 6 残差图 Fig. 6 Residual map

4 结　语

 [1] MILLER A. B., B. M. Miller. Determination of the AUV velocity with the aid of seabed acoustic sensing[J]. Journal of Communications Technology and Electronics, 2018, 63(6). [2] ROBERT S, McEwen, MEMBER, etal. Docking control system for a 54-cm-diameter(21-in)AUV. IEEE Journal of Oceanic Engineering. 2008, 33(4): 550-562P. [3] KONGSBERG S I H O. Underwater mobile docking of autonomous underwater vehicles. Oceans 12 MTS/IEEE Conference, Hampton Roads, VA. 2012: 1-15. [4] TANG J. YU Y, NIE Y. An autonomous underwater vehicle docking system based on optical guidance[J]. Ocean Engineering, 2015, 104(6): 639-648. [5] 李开飞. AUV水下对接关键技术及对接碰撞问题研究[D]. 哈尔滨: 哈尔滨工程大学, 2017. [6] 张医博, 唐元贵, 要振江. 便携式AUV水下对接过程中的碰撞分析与罩式对接平台优化设计[J]. 海洋技术学报, 2017, 36(05): 27-31. [7] 袁培银, 刘俊良, 雷林, 等. 船舶与海洋平台碰撞的动力响应研究[J]. 舰船科学技术, 2018, 40(03): 27-32+45. [8] 王林, 王强强. 半潜式海洋平台与供应船碰撞的理论方法研究[J]. 中国水运(下半月), 2016, 16(11): 20-23. [9] 刘平, 王林. LS-DYNA软件对某半潜式海洋平台发生碰撞的分析[J]. 解放军理工大学学报(自然科学版), 2015, 16(05): 465-470. [10] 赵国良, 许可, 赵春城, 等. 导向喇叭口剖面半径对AUV回收的影响[J]. 水下无人系统学报, 2018, 26(02): 166-173. [11] WANG S, SUN X J, WANG Y H, et al. Dynamic modeling and motion simulation for a winged hybird-driven underwater glider[J]. China Ocean Engineering, 2011, 25(1): 97-112. DOI:10.1007/s13344-011-0008-7 [12] 史剑光, 李德骏, 杨灿军, 等. 水下自主机器人接驳碰撞过程分析[J]. 浙江大学学报(工学版), 2015, 49(03): 497-504.