73 lines
2.8 KiB
Matlab
73 lines
2.8 KiB
Matlab
%*** CHAPTER 8: DYNAMICS OF OPEN CHAINS ***
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function taulist = InverseDynamics(thetalist,dthetalist,ddthetalist,g, ...
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Ftip,Mlist,Glist,Slist)
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% Takes thetalist: n-vector of joint variables,
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% dthetalist: n-vector of joint rates,
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% ddthetalist: n-vector of joint accelerations,
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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
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% 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.
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% Returns taulist: The n-vector of required joint forces/torques.
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% This function uses forward-backward Newton-Euler iterations to solve the
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% equation:
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% taulist = Mlist(thetalist)ddthetalist + 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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ddthetalist = [2; 1.5; 1];
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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(4,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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taulist = InverseDynamics(thetalist,dthetalist,ddthetalist,g,Ftip, ...
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Mlist,Glist,Slist)
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%}
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% Output:
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% taulist =
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% 74.6962
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% -33.0677
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% -3.2306
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n = size(thetalist,1);
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Mi = eye(4);
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Ai = zeros(6,n);
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AdTi = zeros(6,6,n + 1);
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Vi = zeros(6,n + 1);
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Vdi = zeros(6,n + 1);
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Vdi(4:6,1) = -g;
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AdTi(:,:,n + 1) = Adjoint(TransInv(Mlist(:,:,n + 1)));
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Fi = Ftip;
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taulist = zeros(n,1);
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for i=1:n
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Mi = Mi * Mlist(:,:,i);
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Ai(:,i) = Adjoint(TransInv(Mi)) * Slist(:,i);
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AdTi(:,:,i) = Adjoint(MatrixExp6(VecTose3(Ai(:,i) * -thetalist(i))) ...
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* TransInv(Mlist(:,:,i)));
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Vi(:,i + 1) = AdTi(:,:,i) * Vi(:,i) + Ai(:,i) * dthetalist(i);
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Vdi(:,i + 1) = AdTi(:,:,i) * Vdi(:,i) + Ai(:,i) * ddthetalist(i) ...
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+ ad(Vi(:,i + 1)) * Ai(:,i) * dthetalist(i) ;
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end
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for i = n:-1:1
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Fi = AdTi(:,:,i + 1)'* Fi + Glist(:,:,i) * Vdi(:,i + 1) ...
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- ad(Vi(:,i + 1))' * (Glist(:,:,i) * Vi(:,i + 1));
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taulist(i) = Fi' * Ai(:,i);
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end
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end |