48 lines
2.0 KiB
Mathematica
48 lines
2.0 KiB
Mathematica
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%*** CHAPTER 8: DYNAMICS OF OPEN CHAINS ***
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function M = MassMatrix(thetalist, Mlist, Glist, Slist)
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% Takes thetalist: A list of joint variables,
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% Mlist: List of link frames i relative to i-1 at the home position,
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% Glist: Spatial inertia matrices Gi of the links,
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% Slist: Screw axes Si of the joints in a space frame, in the format
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% of a matrix with the screw axes as the columns.
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% Returns M: The numerical inertia matrix M(thetalist) of an n-joint serial
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% chain at the given configuration thetalist.
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% This function calls InverseDynamics n times, each time passing a
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% ddthetalist vector with a single element equal to one and all other
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% inputs set to zero. Each call of InverseDynamics generates a single
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% column, and these columns are assembled to create the inertia matrix.
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% Example Input (3 Link Robot):
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%{
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clear; clc;
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thetalist = [0.1; 0.1; 0.1];
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M01 = [[1, 0, 0, 0]; [0, 1, 0, 0]; [0, 0, 1, 0.089159]; [0, 0, 0, 1]];
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M12 = [[0, 0, 1, 0.28]; [0, 1, 0, 0.13585]; [-1, 0 ,0, 0]; [0, 0, 0, 1]];
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M23 = [[1, 0, 0, 0]; [0, 1, 0, -0.1197]; [0, 0, 1, 0.395]; [0, 0, 0, 1]];
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M34 = [[1, 0, 0, 0]; [0, 1, 0, 0]; [0, 0, 1, 0.14225]; [0, 0, 0, 1]];
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G1 = diag([0.010267, 0.010267, 0.00666, 3.7, 3.7, 3.7]);
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G2 = diag([0.22689, 0.22689, 0.0151074, 8.393, 8.393, 8.393]);
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G3 = diag([0.0494433, 0.0494433, 0.004095, 2.275, 2.275, 2.275]);
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Glist = cat(3, G1, G2, G3);
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Mlist = cat(3, M01, M12, M23, M34);
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Slist = [[1; 0; 1; 0; 1; 0], ...
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[0; 1; 0; -0.089; 0; 0], ...
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[0; 1; 0; -0.089; 0; 0.425]];
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M = MassMatrix(thetalist, Mlist, Glist, Slist)
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%}
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% Output:
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% M =
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% 22.5433 -0.3071 -0.0072
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% -0.3071 1.9685 0.4322
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% -0.0072 0.4322 0.1916
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n = size(thetalist, 1);
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M = zeros(n);
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for i = 1: n
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ddthetalist = zeros(n, 1);
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ddthetalist(i) = 1;
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M(:, i) = InverseDynamics(thetalist, zeros(n, 1), ddthetalist, ...
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[0; 0; 0], [0; 0; 0; 0; 0; 0],Mlist, ...
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Glist, Slist);
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end
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end
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