54 lines
2.4 KiB
Mathematica
54 lines
2.4 KiB
Mathematica
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%*** CHAPTER 8: DYNAMICS OF OPEN CHAINS ***
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function ddthetalist = ForwardDynamics(thetalist, dthetalist, taulist, ...
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g, Ftip, Mlist, Glist, Slist)
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% Takes thetalist: A list of joint variables,
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% dthetalist: A list of joint rates,
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% taulist: An n-vector of joint forces/torques,
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% g: Gravity vector g,
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% Ftip: Spatial force applied by the end-effector expressed in frame
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% {n+1},
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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 ddthetalist: The resulting joint accelerations.
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% This function computes ddthetalist by solving:
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% Mlist(thetalist) * ddthetalist = taulist - c(thetalist,dthetalist) ...
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% - g(thetalist) - Jtr(thetalist) * Ftip
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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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dthetalist = [0.1; 0.2; 0.3];
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taulist = [0.5; 0.6; 0.7];
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g = [0; 0; -9.8];
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Ftip = [1; 1; 1; 1; 1; 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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ddthetalist = ForwardDynamics(thetalist, dthetalist, taulist, g, ...
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Ftip, Mlist, Glist, Slist)
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%}
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% Output:
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% ddthetalist =
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% -0.9739
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% 25.5847
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% -32.9150
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ddthetalist = MassMatrix(thetalist, Mlist, Glist, Slist) ...
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\ (taulist - VelQuadraticForces(thetalist, dthetalist, ...
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Mlist, Glist, Slist) ...
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- GravityForces(thetalist, g, Mlist, Glist, Slist) ...
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- EndEffectorForces(thetalist, Ftip, Mlist, Glist, ...
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Slist));
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end
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