我的 MATLAB 版本没有包含 quatrotate 函数,所以我使用 MathWorks 提供的公式编写了自己的函数here。问题是,我没有得到他们在我的函数中的例子中得到的答案,或者当我手工计算它时。
在他们的示例下,如果我输入以下内容,则应该得到一个n向量[-1 1 1]:
q = [1 0 1 0]; r = [1 1 1]; n = quarotate(q, r)
n =
-1.0000 1.0000 1.0000
在我的函数中,我得到了:
[-3 1 1]
我在这里想念什么?我搜索得越多,我就越困惑。据我所知,答案应该是 [-3 1 1]。
这是我写的函数:
function [n] = quatrotate(q,r)
%Rotate a given acceleration vector by a given quaternion
%
%Inputs:
% q: A matrix containing a set of quaternion vectors of the
% form q = [w,x,y,z]
% r: A matrix containing a set of linear acceleration vectors
% of the form r= [i,j,k] (also known as [x,y,z])
%
% Outputs:
% n: The solved matrix containing the rotated vector of each linear
% acceleration component
%
%This assumes that the quaternion is normalised (sqw + sqx + sqy + sqz =1),
%if not it should be normalised before doing the conversion.
%To normalise divide qx, qy, qz and qw by n where n=sqrt(qx2 + qy2 + qz2 + qw2)
for k = 1:size(q,1)
rot=[(1-2.*q(k,3).^2-2.*q(k,4).^2) 2.*(q(k,2).*q(k,3)+q(k,1).*q(k,4))...
2.*(q(k,2).*q(k,4)-q(k,1).*q(k,3));2.*(q(k,2).*q(k,3)-q(k,1).*q(k,4))...
(1-2.*q(k,2).^2-2.*q(k,4).^2) 2.*(q(k,3).*q(k,4)+q(k,1).*q(k,2));...
2.*(q(k,2).*q(k,4)+q(k,1).*q(k,3)) 2.*(q(k,3).*q(k,4)-q(k,1).*q(k,2))...
(1-2.*q(k,2).^2-2.*q(k,3).^2)];
n(k,:) = rot*r(k,:)';
end
提前致谢!
首先,您需要计算给定四元数的模数q
:
for index = size(q,1):-1:1
mod(index,:) = norm(q(index,:),2);
end
然后将其标准化:
qn = q./(mod* ones(1,4));
现在使用以下公式计算直接余弦矩阵:
dcm = zeros(3,3,size(qn,1));
dcm(1,1,:) = qn(:,1).^2 + qn(:,2).^2 - qn(:,3).^2 - qn(:,4).^2;
dcm(1,2,:) = 2.*(qn(:,2).*qn(:,3) + qn(:,1).*qn(:,4));
dcm(1,3,:) = 2.*(qn(:,2).*qn(:,4) - qn(:,1).*qn(:,3));
dcm(2,1,:) = 2.*(qn(:,2).*qn(:,3) - qn(:,1).*qn(:,4));
dcm(2,2,:) = qn(:,1).^2 - qn(:,2).^2 + qn(:,3).^2 - qn(:,4).^2;
dcm(2,3,:) = 2.*(qn(:,3).*qn(:,4) + qn(:,1).*qn(:,2));
dcm(3,1,:) = 2.*(qn(:,2).*qn(:,4) + qn(:,1).*qn(:,3));
dcm(3,2,:) = 2.*(qn(:,3).*qn(:,4) - qn(:,1).*qn(:,2));
dcm(3,3,:) = qn(:,1).^2 - qn(:,2).^2 - qn(:,3).^2 + qn(:,4).^2;
根据MATLAB文档,可以r
通过计算得出向量的旋转dcm
如下:
if ( size(q,1) == 1 )
% Q is 1-by-4
qout = (dcm*r')';
elseif (size(r,1) == 1)
% R is 1-by-3
for i = size(q,1):-1:1
qout(i,:) = (dcm(:,:,i)*r')';
end
else
% Q is M-by-4 and R is M-by-3
for i = size(q,1):-1:1
qout(i,:) = (dcm(:,:,i)*r(i,:)')';
end
end
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