【水下】鱼类激励水下航行器的同步游泳与编队控制附matlab代码

本文介绍了用于稳定机器鱼模型中平行和圆周运动的非线性控制方法,基于Chaplygin雪橇模型,通过鱼机器人之间的通信进行协作。控制策略不依赖于反馈线性化,数值模拟展示了其有效性。

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🔥 内容介绍

本文提出了一种非线性控制设计,用于稳定机器鱼模型学校中的平行和圆周运动。鱼机器人的闭环游泳动力学由典型的 Chaplygin 雪橇代表,这是一种由内转子驱动的非完整机械系统。鱼机器人根据连接的无向通信图交换相对状态信息,并形成耦合的非线性二阶振荡器系统。先前关于恒速自驱动粒子集体运动的工作是我们方法的基础。然而,与自驱动粒子不同的是,鱼机器人遵循极限循环动力学,以维持周期性拍动,以不同的速度向前运动。平行运动和圆周运动是在平均意义上实现的。所提出的控制律不包括代理动力学的反馈线性化。数值模拟说明了该方法。

📣 部分代码

clear; close all;  clc;addpath('./brewer');addpath('./cmocean_v2.0/cmocean');addpath('./export_fig/');lastk = 200; % this many points are used to plot final limit cycle% parametersm = 1.4;l = 0.31;d = 0.5;b = 0.1395;a = (m*l^2)/(b*d);N = 8;T = 20*120; % total simulation time% parallel gainsk1 = 0.5;k2 = 2;% circular gainsk1c = k1;k2c = k2;k3c = -.3;vref = 0*b*k1/(m*l);omegaref = 0.2;% create communication topology%% graph used by Laplacian controllers % %all-to-all% D = eye(N,N)*(N-1);% A = ones(N,N);% for i =1:1:N%     A(i,i) = 0;% end% L = D-A;% rng(3);% circulantL = zeros(N,N);for i = 1:1:N   L(i,i) = 2;   % aft neighbor   if ( i == 1)       L(i,end) = -1;   else       L(i,i-1) = -1;   end   % fore neighbor   if ( i == N)       L(i,1) = -1;   else      L(i,i+1) = -1;    end       end%% ploting% plot colorsshift = 2;%cmap = parula(N); %cmap = cmocean('ice',N);cmap = cmocean('deep',N+shift);% shiftcmap = cmap(shift:end,:);%% initial conditions% %Random heading and random angular rate% theta0 = rand([N 1])*2*pi;% omega0 = rand([N 1])*1;% %Random heading and zero angular rate% r0 = rand(N,1)*10 + rand(N,1)*10*1i;% v0 = 0*rand(N,1);% % % theta0 = [0 45 90]'*pi/180;% % omega0 = 0.1*[-1 0.5 1]';% theta0 = rand([N 1])*pi;% omega0 = rand(N,1)*0;% Equal heading and equal angular rate% theta0 = [ones(N,1)*0];% omega0 = [ones(N,1)*1]% Equal heading and random angular rate% theta0 = [ones(N,1)*0];% omega0 = rand([N 1])*1;% % Np fish anti-parallel and random angular rate% Np  = 1;% theta0 = [ones([Np 1])*0; ones([N-Np 1])*pi ];% omega0 = rand([N 1])*1;% % circular initial formation% th_circ = [0:2*pi/(N):2*pi];% th_circ = th_circ(1:end-1)';% R = 5;% r0 = R*cos(th_circ) + R*sin(th_circ)*1i;% v0 = 0*rand(N,1);% theta0 = rand([N 1])*2*pi;% omega0 = 0*rand(N,1);% line initial formationLinit = 5;dely = 0;r0 = linspace(-Linit/2,Linit/2,N)' - 1i*dely;v0 = 0*rand(N,1);theta0 = rand([N 1])*2*pi;omega0 = 0*rand(N,1);% % from paul's code% zfix =[         0         0    1.3110         0    8.7639    9.5789;%     0         0    1.7552         0    8.9461    5.3317;%     0         0    0.4410         0    0.8504    6.9188;%     0         0    0.6224         0    0.3905    3.1552;%     0         0    2.5156         0    1.6983    6.8650;%     0         0    3.0419         0    8.7814    8.3463;%     0         0    0.9847         0    0.9835    0.1829;%     0         0    2.1750         0    4.2111    7.5014];% x0 = zfix(:,5);% y0 = zfix(:,6);% r0 = x0 + 1i * y0;% theta0 = zfix(:,3);% v0 = zeros(N,1);% omega0 = zeros(N,1);z0 = [r0; theta0; v0; omega0];%% simulation tspan = [0:0.1:T];%options = odeset('reltol',1e-12,'abstol',1e-12);options = odeset('reltol',1e-3,'abstol',1e-3);[t,zhist] = ode45(@parallelSys,tspan,z0,[],m,l,b,d,k1,k2,N,L,a,vref,omegaref,k1c,k2c,k3c);%% plotsx_hist = real(zhist(:,1:N));y_hist = imag(zhist(:,1:N));th_hist = zhist(:,N+1:2*N);v_hist = zhist(:,2*N+1:3*N);omega_hist = zhist(:,3*N+1:4*N);grayRGB = [1 1 1]*0.5;figure;hold on;Lfish = 2;for i = 1:1:N    plot(x_hist(:,i),y_hist(:,i),'Color',cmap(i,:),'linewidth',1);         endfor i = 1:1:N   [xFish,yFish] = fishCoords(x_hist(end,i), y_hist(end,i), Lfish, th_hist(end,i));   fill(xFish,yFish,cmap(i,:), 'linewidth',1); hold on;      plot(xFish,yFish, 'k', 'linewidth',1); hold on;    plot(x_hist(end-lastk:end,i),y_hist(end-lastk:end,i),'m','Linewidth',2);endplot(x_hist(1,:),y_hist(1,:),'ko','MarkerFaceColor','k','MarkerSize',3)xlabel('X (m)');ylabel('Y (m)');box on;axis square;axis equal;axis tight;set(gcf,'Color','w')set(gca,'FontSize',16,'FontName','Arial')%export_fig('parallel_fish_tracks.pdf')% figure;% for i = 1:1:N% plot(t,mod(th_hist(:,i),2*pi)*180/pi,'linewidth',2,'Color',cmap(i,:),'linewidth',2);% hold on;% end% ylabel('Heading (deg.)');% xlabel('Time (sec.)');% set(gca,'FontSize',16,'FontName','Arial')% ylim([0 270]);% xlim([0 90]);% yticks([0:90:360]);% set(gcf,'Color','w')% %export_fig('parallel_t_vs_theta.pdf')figure;for i = 1:1:Nplot(v_hist(:,i), omega_hist(:,i)*180/pi,'Color',cmap(i,:));hold on;plot(v_hist(end-lastk:end,i),omega_hist(end-lastk:end,i)*180/pi,'m','Linewidth',2); plot(v_hist(1,i),omega_hist(1,i)*180/pi,'ko','MarkerFaceColor','k','MarkerSize',3)hold on;endset(gca,'FontSize',16,'FontName','Arial')set(gcf,'Color','w');xlabel('Speed (m/s)');axis square;ylabel('Angular Rate (deg/s)');%export_fig('parallel_v_vs_omega.pdf')% figure;% for i = 1:1:N% plot(mod(th_hist(:,i),2*pi)*180/pi, omega_hist(:,i)*180/pi,'Color',cmap(i,:));% hold on;% plot(mod(th_hist(end-lastk:end,1),2*pi)*180/pi,omega_hist(end-lastk:end,1)*180/pi,'k','Linewidth',2); % plot(mod(th_hist(1,i),2*pi)*180/pi,omega_hist(1,i)*180/pi,'ko','MarkerFaceColor','k','MarkerSize',3)% end% set(gca,'FontSize',16,'FontName','Arial')% set(gcf,'Color','w');% xlabel('Heading (deg)');% xlim([0 360]);% axis square;% ylabel('Angular Rate (deg/s)');% xlim([0 360]);% %export_fig('parallel_th_vs_omega.pdf')function xdot = parallelSys(t,x,m,l,b,d,k1,k2,N,L,a,vref,omegaref,k1c,k2c,k3c)% unpack stater = x(1:N);theta = x(N+1:2*N);v = x(2*N+1:3*N);omega = x(3*N+1:4*N);%% Parallel: Laplacian controlu = zeros(N,1);couplingTerm1 = zeros(N,1);for k = 1:1:N    Lk = L(k,:);    val1 = 1i * exp(1i * theta(k) );    val2 = Lk * exp(1i * theta );        couplingTerm1(k) = complexIP(val1,val2);    endu_p_lap = -b*k1*omega + b*k2/N*couplingTerm1;%% Parallel: All-to-all controlcouplingTerm2 = zeros(N,1);for k = 1:1:N    for j = 1:1:N        couplingTerm2(k) = couplingTerm2(k) - sin( theta(j) - theta(k) );    endendu_p_all = -b*k1*omega + b*k2/N*couplingTerm2;%% Circular: LaplaciancouplingTerm_c_lap = zeros(N,1);coefficient = ( (l/d)*omega  - vref/omegaref);c = r + vref/omegaref*1i*exp(1i*theta);for k = 1:1:N    Lk = L(k,:);        val1 = exp(1i * theta(k) );    val2 = Lk * c; %exp(1i * c);        couplingTerm_c_lap(k) = complexIP(val1,val2);    end u_c_lap = -b*k1c*omega - b*k2c*sin(theta - omegaref*t) ...     - b*k3c*coefficient.*couplingTerm_c_lap; % figure(10);% plot(real(r),imag(r),'bo'); hold on;% plot(real(c),imag(c),'r+');% hold on;%% switch control from parallel/circular etc. hereu = u_c_lap; % circular, laplacian%u = u_p_lap; % parallel laplacian%u = u_p_all; % prallel all-to-all%% dynamics%omegadot = -a*omega.^3 + -u/b; % simplified modelomegadot = -m*l/b*v.*omega + -u/b; % actual model% state ratexdot(1:N,1) = v.*exp(1i*theta);% r-dot trailing edge%xdot(1:N,1) = v.*exp(1i*theta) + l*omega.*1i.*exp(1i*theta);% r-dot for CMxdot(N+1:2*N,1) = omega;%th-dotxdot(2*N+1:3*N,1) = l*omega.^2 - d*v;%v-dotxdot(3*N+1:4*N,1) = omegadot;end

⛳️ 运行结果

🔗 参考文献

P. Ghanem, A. Wolek and D. A. Paleyv, "Planar Formation Control of a School of Robotic Fish," 2020 American Control Conference (ACC), Denver, CO, USA, 2020, pp. 1653-1658, doi: 10.23919/ACC45564.2020.9147969.

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