Question

我基本上有一个28参数的非线性方程。当f(x) = 0时，我可以测量14个参数，并且我有数据生成133个方程，其中包含14个测量参数。我现在需要找到导致最小残差的14个未知参数（无约束）的值。

我相信MATLAB优化工具箱（fsolve）应该完成这项工作。我的目标函数是3个转换矩阵的乘积，因此很长，没有明确写出。

function fRMS= MyObjectiveFunction(xi)
syms sx sy aa bb cc ro tau omega x y z alpha beta gamma 
xi = [ sx, sy, aa, bb, cc, ro, tau, omega, x,y,z, alpha, beta, gamma];
load CalibData.mat  n1 n2 n3 n4 n5 n6 n7 n8 n9 t1 t2 t3 u v
rTp=[cos(omega)*cos(tau) cos(omega)*sin(tau)*sin(ro)-sin(omega)*cos(ro) cos(omega)*sin(tau)*cos(ro)+sin(omega)*sin(ro) aa;...
  sin(omega)*cos(tau) sin(omega)*sin(tau)*sin(ro)+cos(omega)*cos(ro) sin(omega)*sin(tau)*cos(ro)-cos(omega)*sin(ro) bb;...
  -sin(tau) cos(tau)*sin(ro) cos(tau)*cos(ro) cc;...
  0 0 0 1];

cTt=[cos(alpha)*cos(beta) cos(alpha)*sin(beta)*sin(gamma)-sin(alpha)*cos(gamma) cos(alpha)*sin  (beta)*cos(gamma)+sin(alpha)*sin(gamma) x;...
 sin(alpha)*cos(beta) sin(alpha)*sin(beta)*sin(gamma)+cos(alpha)*cos(gamma) sin(alpha)*sin(beta)*cos(gamma)-cos(alpha)*sin(gamma) y;...
 -sin(beta) cos(beta)*sin(gamma) cos(beta)*cos(gamma) z; 0 0 0 1]; % (labspace to bucket space)


for frame=1:133 % 133 frames
     tTr(:,:,frame)=[n1(frame) n2(frame) n3(frame) t1(frame); n4(frame) n5(frame) n6(frame) t2  (frame); n7(frame) n8(frame) n9(frame) t3(frame); 0 0 0 1];
    Px(:,frame)=[sx*u(frame); sy*v(frame); 0; 1];
   Cx(:,frame)= cTt*tTr(:,:,frame)*rTp*Px(:,frame);
    f(frame)= Cx(3,frame); % Z=0
end

fRMS=rms(f); % Objective function

使用优化工具箱时，出现以下错误。这可能是我将值传递给符号变量的结果。我非常感谢您帮助解决错误或提供替代方法来解决这个问题。

  Error using mupadmex
  Error in MuPAD command: DOUBLE cannot convert the input expression into a double array.
  If the input expression contains a symbolic variable, use the VPA function instead.

非常感谢!!

优化非线性方程求解器matlab

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