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Quaternion difference fix #9

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Quaternion difference fix #9

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c6f7626
Quaternion difference fix
akkshay0107 Sep 24, 2024
0da70e0
Fixed quaternion convention in Controller to match with Plant
akkshay0107 Sep 27, 2024
08ac305
Fixed calculation of jacobians in LQR controller
akkshay0107 Oct 22, 2024
97d9800
Fixed version of simulink model & signs in the derivatives
akkshay0107 Oct 31, 2024
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Binary file modified Model_Mk2.slx
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46 changes: 43 additions & 3 deletions lib/get_segment_traj.m
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Original file line number Diff line number Diff line change
Expand Up @@ -13,16 +13,56 @@
J9 = Jmat(3, 3);

%Calculate A matrix in state space representation
A = subs(Jx, [x; u; consts], [zeros(length(xcrit2), 1); ucrit2; constants]);
A = subs(Jx, [x; u; consts], [xcrit2; ucrit2; constants]);
A = double(subs(A, [J1 J2 J3; J4 J5 J6; J7 J8 J9], MOI));

%Calculate B matrix in state space representation
B = subs(Ju, [x; u; consts], [zeros(length(xcrit2), 1); ucrit2; constants]);
B = subs(Ju, [x; u; consts], [xcrit2; ucrit2; constants]);
B = double(subs(B, [J1 J2 J3; J4 J5 J6; J7 J8 J9], MOI));

%Defining quaternion components and angular velocity
q1 = x(7);
q2 = x(8);
q3 = x(9);
qChange = [q1; q2; q3];
q0 = sqrt(1 - q1^2 - q2^2 - q3^2);
q1r = xcrit2(7);
q2r = xcrit2(8);
q3r = xcrit2(9);
qChange_r = [q1r; q2r; q3r];
q0r = sqrt(1 - q1r^2 - q2r^2 - q3r^2);
omega = x(10:12);

%Defining required matrices for calculation of correct jacobians
% delta x = H * xref + G * x
% H = blkdiag(-eye(3),-eye(3),-q0*eye(3),-eye(3)); (not required)
skewMat = [q0r,q3r,-q2r;
-q3r, q0r, q1r;
q2r,-q1r,q0r];
G = blkdiag(eye(3),eye(3),skewMat,eye(3));

Jq0_qv = 1/q0 * (qChange_r * qChange.');
Jq0dot_qv = 0.5 * (qChange_r * omega.');
Jq0dot_omega = 0.5 * (qChange_r * qChange.');

DH = blkdiag(zeros(3),zeros(3),Jq0_qv,zeros(3));
DHdot = [zeros(3),zeros(3),zeros(3),zeros(3);
zeros(3),zeros(3),zeros(3),zeros(3);
zeros(3),zeros(3),Jq0dot_qv,Jq0dot_omega;
zeros(3),zeros(3),zeros(3),zeros(3)];

%Calculate matrices DH DHdot and G
G = double(subs(G, qChange, xcrit2(7:9)));
DH = double(subs(DH, qChange, xcrit2(7:9)));
DHdot = double(subs(DHdot, [qChange,omega], xcrit(7:12)));

%New A and B matrices for delta x dot = f_d(delta x, u)
Ad = (DHdot + G*A)/(DH + G);
Bd = G*B;

%Optimal control gain matrix K, solution S, and poles P
try
[Ksegment, ~, ~] = lqr(A, B, Q, R);
[Ksegment, ~, ~] = lqr(Ad, Bd, Q, R);
catch e
disp(e.message);
error("LQR gain generation threw the error above!");
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