# In an assignment A(I) = B, the number of elements in B and I must be the same.

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Qiaoli Ji on 20 Dec 2017
Commented: Image Analyst on 20 Dec 2017
In an assignment A(I) = B, the number of elements in B and I must be the same.
Error in step (line 18) dy(3) = 0.1e1 / l ^ 2 / (-cos(y(2)) ^ ......
%% the main first function function xc = totalmotion (q1_0, q2_0, dq1_0, dq2_0) global_constants; global M; % hip mass global m; % foot mass global l; % leg length global r; % the slop angle
global g; % gravity acceleration global delta_t; % compute interval step global rad; rad = 180/pi; global Kp; % the proportional coefficient global Kd; % the differential coefficient global q2d; % the desired value of q2 tspan = [0:delta_t:2]; options = odeset('abstol',1e-13,'reltol',1e-13,'events',@collision); y0 = [q1_0 q2_0 dq1_0 dq2_0]; %%% initial state p(1) = M; p(2) = m; p(3) = r; p(4) = l; [t,y]=ode45(@step,tspan,y0,options,p);
n=length(t);
for i =1:n
q1 = y(i,1); q2 = y(i,2);
x_0 = 0;
y_0 = 0;
x1 = x_0;%%%%calculate the spacial positions of the links.
y1 = y_0;
xh = x1 + l * sin(-q1 + r);
yh = y1 + l * cos(-q1 + r);
x2 = double(-l * sin(-q2 - q1 + r) + x1 + l * sin(-q1 + r));
y2 = double(-l * cos(-q2 - q1 + r) + y1 + l * cos(-q1 + r));
xc = (M * (x1 + l * sin(-q1 + r)) + m * (-l * sin(-q2 - q1 + r) + x1 + l * sin(-q1 + r))) / (M + 0.2e1 * m);
end
end
%%% the second function function dy = step(t,y,p) M = p(1); m = p(2); r = p(3); l = p(4);
dy = zeros(4,1);
dy(1) = y(3);
dy(2) = y(4);
dy(3) = 0.1e1 / l ^ 2 / (-cos(y(2)) ^ 2 * m + M + m) * (-0.2e1 * sin(y(2)) * y(3) * y(4) * l ^ 2 * m - y(4) ^ 2 * sin(y(2)) * l ^ 2 * m - M * sin(-y(1) + r) * g * l - sin(-y(1) + r) * g * l * m + sin(-y(2) - y(1) + r) * m * g * l) + 0.1e1 / l ^ 2 * (cos(y(2)) - 0.1e1) / (-cos(y(2)) ^ 2 * m + M + m) * (Kp * (q2d - y(2)) - Kd * y(4) + sin(y(2)) * y(3) ^ 2 * l ^ 2 * m + sin(-y(2) - y(1) + r) * m * g * l);
dy(4) = 0.1e1 / l ^ 2 * (cos(y(2)) - 0.1e1) / (-cos(y(2)) ^ 2 * m + M + m) * (-0.2e1 * sin(y(2)) * y(3) * y(4) * l ^ 2 * m - y(4) ^ 2 * sin(y(2)) * l ^ 2 * m - M * sin(-y(1) + r) * g * l - sin(-y(1) + r) * g * l * m + sin(-y(2) - y(1) + r) * m * g * l) + 0.1e1 / l ^ 2 * (-0.2e1 * cos(y(2)) * m + M + 0.2e1 * m) / m / (-cos(y(2)) ^ 2 * m + M + m) * (Kp * (q2d - y(2)) - Kd * y(4) + sin(y(2)) * y(3) ^ 2 * l ^ 2 * m + sin(-y(2) - y(1) + r) * m * g * l);

Star Strider on 20 Dec 2017
I cannot follow what you are doing, and I cannot run your code.
However, the most likely problem is that you need to vectorize your code, since otherwise MATLAB will interpret multiply, divide, and exponentiation operations as matrix rather than element-wise array operations. That means using the ‘dot operator’, substituting ‘.*’ for ‘*’, ‘./’ for ‘/’, and ‘./’ for ‘^’.
Use the vectorize (link) fiunction, and see the documentation on Array vs. Matrix Operations (link) for details.
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Star Strider on 20 Dec 2017
My pleasure.
You have to vectorize your equations, as I demonstrated. I cannot do this for you.

Image Analyst on 20 Dec 2017
You probably need to use the "dot" versions of * / ^ etc.
Put a dot/period before each mathematical operator, to do element-by-element operation instead of a matrix operation, and see how that goes.
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Image Analyst on 20 Dec 2017
dy(3) = 0.1e1 / l ^ 2 / (-cos(y(2)) ^ 2 * m + M + m) * (-0.2e1 * sin(y(2)) * y(3) * y(4) * l ^ 2 * m - y(4) ^ 2 * sin(y(2)) * l ^ 2 * m - M * sin(-y(1) + r) * g * l - sin(-y(1) + r) * g * l * m + sin(-y(2) - y(1) + r) * m * g * l) + 0.1e1 / l ^ 2 * (cos(y(2)) - 0.1e1) / (-cos(y(2)) ^ 2 * m + M + m) * (Kp * (q2d - y(2)) - Kd * y(4) + sin(y(2)) * y(3) ^ 2 * l ^ 2 * m + sin(-y(2) - y(1) + r) * m * g * l);
try
dy(3) = 0.1e1 ./ l .^ 2 ./ (-cos(y(2)) .^ 2 .* m + M + m) .* (-0.2e1 .* sin(y(2)) .* y(3) .* y(4) .* l .^ 2 .* m - y(4) .^ 2 * sin(y(2)) .* l .^ 2 .........
etc.