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matlab: update optical flow derivation

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Support use of sensors with arbitrary orientation in body frame
This commit is contained in:
Paul Riseborough 2017-11-06 17:42:23 +11:00
parent cc651ac472
commit 16154423c8
3 changed files with 357 additions and 39 deletions
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74
matlab/scripts/Inertial Nav EKF/GenerateNavFilterEquations.m
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@ -228,25 +228,43 @@ reset(symengine);
%% derive equations for sequential fusion of optical flow measurements
load('StatePrediction.mat');
% range is defined as distance from camera focal point to centre of sensor fov
% Range is defined as distance from camera focal point to object measured
% along sensor Z axis
syms range real;
% calculate relative velocity in body frame
relVelBody = transpose(Tbn)*[vn;ve;vd];
% Define rotation matrix from body to sensor frame
syms Tbs_a_x Tbs_a_y Tbs_a_z real;
syms Tbs_b_x Tbs_b_y Tbs_b_z real;
syms Tbs_c_x Tbs_c_y Tbs_c_z real;
Tbs = [ ...
Tbs_a_x Tbs_a_y Tbs_a_z ; ...
Tbs_b_x Tbs_b_y Tbs_b_z ; ...
Tbs_c_x Tbs_c_y Tbs_c_z ...
];
% divide by range to get predicted angular LOS rates relative to X and Y
% axes. Note these are body angular rate motion compensated optical flow rates
losRateX = +relVelBody(2)/range;
losRateY = -relVelBody(1)/range;
% Calculate earth relative velocity in a non-rotating sensor frame
relVelSensor = Tbs * transpose(Tbn) * [vn;ve;vd];
save('temp1.mat','losRateX','losRateY');
% Divide by range to get predicted angular LOS rates relative to X and Y
% axes. Note these are rates in a non-rotating sensor frame
losRateSensorX = +relVelSensor(2)/range;
losRateSensorY = -relVelSensor(1)/range;
% calculate the observation Jacobian for the X axis
H_LOSX = jacobian(losRateX,stateVector); % measurement Jacobian
save('temp1.mat','losRateSensorX','losRateSensorY');
clear all;
reset(symengine);
load('StatePrediction.mat');
load('temp1.mat');
% calculate the observation Jacobian and Kalman gain for the X axis
H_LOSX = jacobian(losRateSensorX,stateVector); % measurement Jacobian
H_LOSX = simplify(H_LOSX);
save('temp2.mat','H_LOSX');
ccode(H_LOSX,'file','H_LOSX.c');
fix_c_code('H_LOSX.c');
K_LOSX = (P*transpose(H_LOSX))/(H_LOSX*P*transpose(H_LOSX) + R_LOS); % Kalman gain vector
K_LOSX = simplify(K_LOSX);
save('temp2.mat','H_LOSX','K_LOSX');
ccode([H_LOSX;transpose(K_LOSX)],'file','LOSX.c');
fix_c_code('LOSX.c');
clear all;
reset(symengine);
@ -254,35 +272,13 @@ load('StatePrediction.mat');
load('temp1.mat');
% calculate the observation Jacobian for the Y axis
H_LOSY = jacobian(losRateY,stateVector); % measurement Jacobian
H_LOSY = jacobian(losRateSensorY,stateVector); % measurement Jacobian
H_LOSY = simplify(H_LOSY);
save('temp3.mat','H_LOSY');
ccode(H_LOSY,'file','H_LOSY.c');
fix_c_code('H_LOSY.c');
clear all;
reset(symengine);
load('StatePrediction.mat');
load('temp1.mat');
load('temp2.mat');
% calculate Kalman gain vector for the X axis
K_LOSX = (P*transpose(H_LOSX))/(H_LOSX*P*transpose(H_LOSX) + R_LOS); % Kalman gain vector
K_LOSX = simplify(K_LOSX);
ccode(K_LOSX,'file','K_LOSX.c');
fix_c_code('K_LOSX.c');
clear all;
reset(symengine);
load('StatePrediction.mat');
load('temp1.mat');
load('temp3.mat');
% calculate Kalman gain vector for the Y axis
K_LOSY = (P*transpose(H_LOSY))/(H_LOSY*P*transpose(H_LOSY) + R_LOS); % Kalman gain vector
K_LOSY = simplify(K_LOSY);
ccode(K_LOSY,'file','K_LOSY.c');
fix_c_code('K_LOSY.c');
save('temp3.mat','H_LOSY','K_LOSY');
ccode([H_LOSY;transpose(K_LOSY)],'file','LOSY.c');
fix_c_code('LOSY.c');
% reset workspace
clear all;

160
matlab/scripts/Inertial Nav EKF/LOSX.c Normal file
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@ -0,0 +1,160 @@
float t2 = 1.0f/range;
float t3 = Tbs.b.y*q0*2.0f;
float t4 = Tbs.b.x*q3*2.0f;
float t18 = Tbs.b.z*q1*2.0f;
float t5 = t3+t4-t18;
float t6 = Tbs.b.y*q1*2.0f;
float t7 = Tbs.b.z*q0*2.0f;
float t16 = Tbs.b.x*q2*2.0f;
float t8 = t6+t7-t16;
float t9 = Tbs.b.x*q0*2.0f;
float t10 = Tbs.b.z*q2*2.0f;
float t17 = Tbs.b.y*q3*2.0f;
float t11 = t9+t10-t17;
float t12 = Tbs.b.x*q1*2.0f;
float t13 = Tbs.b.y*q2*2.0f;
float t14 = Tbs.b.z*q3*2.0f;
float t15 = t12+t13+t14;
float t19 = q0*q0;
float t20 = q1*q1;
float t21 = q2*q2;
float t22 = q3*q3;
float t23 = q0*q3*2.0f;
float t24 = q0*q2*2.0f;
float t25 = q1*q3*2.0f;
float t26 = q0*q1*2.0f;
float t27 = t19+t20-t21-t22;
float t28 = Tbs.b.x*t27;
float t29 = q1*q2*2.0f;
float t30 = t24+t25;
float t31 = Tbs.b.z*t30;
float t32 = t19-t20+t21-t22;
float t33 = Tbs.b.y*t32;
float t34 = t23+t29;
float t35 = Tbs.b.x*t34;
float t36 = q2*q3*2.0f;
float t37 = t19-t20-t21+t22;
float t38 = Tbs.b.z*t37;
float t39 = t24-t25;
float t40 = t26+t36;
float t41 = Tbs.b.y*t40;
float t60 = Tbs.b.x*t39;
float t42 = t38+t41-t60;
float t43 = t8*vd;
float t44 = t5*ve;
float t45 = t11*vn;
float t46 = t43+t44+t45;
float t47 = t5*vd;
float t48 = t15*vn;
float t62 = t8*ve;
float t49 = t47+t48-t62;
float t50 = t15*ve;
float t51 = t8*vn;
float t63 = t11*vd;
float t52 = t50+t51-t63;
float t53 = t15*vd;
float t54 = t11*ve;
float t64 = t5*vn;
float t55 = t53+t54-t64;
float t56 = t23-t29;
float t65 = Tbs.b.y*t56;
float t57 = t28+t31-t65;
float t58 = t26-t36;
float t66 = Tbs.b.z*t58;
float t59 = t33+t35-t66;
float t61 = P[0][0]*t2*t46;
float t67 = P[1][1]*t2*t49;
float t68 = P[4][0]*t2*t57;
float t69 = P[5][0]*t2*t59;
float t70 = P[6][0]*t2*t42;
float t71 = P[1][0]*t2*t49;
float t72 = P[2][0]*t2*t52;
float t73 = P[3][0]*t2*t55;
float t74 = t61+t68+t69+t70+t71+t72+t73;
float t75 = t2*t46*t74;
float t76 = P[4][1]*t2*t57;
float t77 = P[5][1]*t2*t59;
float t78 = P[6][1]*t2*t42;
float t79 = P[0][1]*t2*t46;
float t80 = P[2][1]*t2*t52;
float t81 = P[3][1]*t2*t55;
float t82 = t67+t76+t77+t78+t79+t80+t81;
float t83 = t2*t49*t82;
float t84 = P[4][2]*t2*t57;
float t85 = P[5][2]*t2*t59;
float t86 = P[6][2]*t2*t42;
float t87 = P[0][2]*t2*t46;
float t88 = P[1][2]*t2*t49;
float t89 = P[2][2]*t2*t52;
float t90 = P[3][2]*t2*t55;
float t91 = t84+t85+t86+t87+t88+t89+t90;
float t92 = t2*t52*t91;
float t93 = P[4][3]*t2*t57;
float t94 = P[5][3]*t2*t59;
float t95 = P[6][3]*t2*t42;
float t96 = P[0][3]*t2*t46;
float t97 = P[1][3]*t2*t49;
float t98 = P[2][3]*t2*t52;
float t99 = P[3][3]*t2*t55;
float t100 = t93+t94+t95+t96+t97+t98+t99;
float t101 = t2*t55*t100;
float t102 = P[4][4]*t2*t57;
float t103 = P[5][4]*t2*t59;
float t104 = P[6][4]*t2*t42;
float t105 = P[0][4]*t2*t46;
float t106 = P[1][4]*t2*t49;
float t107 = P[2][4]*t2*t52;
float t108 = P[3][4]*t2*t55;
float t109 = t102+t103+t104+t105+t106+t107+t108;
float t110 = t2*t57*t109;
float t111 = P[4][5]*t2*t57;
float t112 = P[5][5]*t2*t59;
float t113 = P[6][5]*t2*t42;
float t114 = P[0][5]*t2*t46;
float t115 = P[1][5]*t2*t49;
float t116 = P[2][5]*t2*t52;
float t117 = P[3][5]*t2*t55;
float t118 = t111+t112+t113+t114+t115+t116+t117;
float t119 = t2*t59*t118;
float t120 = P[4][6]*t2*t57;
float t121 = P[5][6]*t2*t59;
float t122 = P[6][6]*t2*t42;
float t123 = P[0][6]*t2*t46;
float t124 = P[1][6]*t2*t49;
float t125 = P[2][6]*t2*t52;
float t126 = P[3][6]*t2*t55;
float t127 = t120+t121+t122+t123+t124+t125+t126;
float t128 = t2*t42*t127;
float t129 = R_LOS+t75+t83+t92+t101+t110+t119+t128;
float t130 = 1.0f/t129;
H_LOS[0] = t2*t46;
H_LOS[1] = t2*t49;
H_LOS[2] = t2*t52;
H_LOS[3] = t2*t55;
H_LOS[4] = t2*(t28+t31-Tbs.b.y*(t23-q1*q2*2.0));
H_LOS[5] = t2*(t33+t35-Tbs.b.z*(t26-q2*q3*2.0));
H_LOS[6] = t2*t42;
Kfusion[0] = t130*(t61+P[0][6]*t2*t42+P[0][1]*t2*t49+P[0][2]*t2*t52+P[0][3]*t2*t55+P[0][4]*t2*t57+P[0][5]*t2*t59);
Kfusion[1] = t130*(t67+P[1][0]*t2*t46+P[1][6]*t2*t42+P[1][2]*t2*t52+P[1][3]*t2*t55+P[1][4]*t2*t57+P[1][5]*t2*t59);
Kfusion[2] = t130*(t89+P[2][0]*t2*t46+P[2][6]*t2*t42+P[2][1]*t2*t49+P[2][3]*t2*t55+P[2][4]*t2*t57+P[2][5]*t2*t59);
Kfusion[3] = t130*(t99+P[3][0]*t2*t46+P[3][6]*t2*t42+P[3][1]*t2*t49+P[3][2]*t2*t52+P[3][4]*t2*t57+P[3][5]*t2*t59);
Kfusion[4] = t130*(t102+P[4][0]*t2*t46+P[4][6]*t2*t42+P[4][1]*t2*t49+P[4][2]*t2*t52+P[4][3]*t2*t55+P[4][5]*t2*t59);
Kfusion[5] = t130*(t112+P[5][0]*t2*t46+P[5][6]*t2*t42+P[5][1]*t2*t49+P[5][2]*t2*t52+P[5][3]*t2*t55+P[5][4]*t2*t57);
Kfusion[6] = t130*(t122+P[6][0]*t2*t46+P[6][1]*t2*t49+P[6][2]*t2*t52+P[6][3]*t2*t55+P[6][4]*t2*t57+P[6][5]*t2*t59);
Kfusion[7] = t130*(P[7][0]*t2*t46+P[7][6]*t2*t42+P[7][1]*t2*t49+P[7][2]*t2*t52+P[7][3]*t2*t55+P[7][4]*t2*t57+P[7][5]*t2*t59);
Kfusion[8] = t130*(P[8][0]*t2*t46+P[8][6]*t2*t42+P[8][1]*t2*t49+P[8][2]*t2*t52+P[8][3]*t2*t55+P[8][4]*t2*t57+P[8][5]*t2*t59);
Kfusion[9] = t130*(P[9][0]*t2*t46+P[9][6]*t2*t42+P[9][1]*t2*t49+P[9][2]*t2*t52+P[9][3]*t2*t55+P[9][4]*t2*t57+P[9][5]*t2*t59);
Kfusion[10] = t130*(P[10][0]*t2*t46+P[10][6]*t2*t42+P[10][1]*t2*t49+P[10][2]*t2*t52+P[10][3]*t2*t55+P[10][4]*t2*t57+P[10][5]*t2*t59);
Kfusion[11] = t130*(P[11][0]*t2*t46+P[11][6]*t2*t42+P[11][1]*t2*t49+P[11][2]*t2*t52+P[11][3]*t2*t55+P[11][4]*t2*t57+P[11][5]*t2*t59);
Kfusion[12] = t130*(P[12][0]*t2*t46+P[12][6]*t2*t42+P[12][1]*t2*t49+P[12][2]*t2*t52+P[12][3]*t2*t55+P[12][4]*t2*t57+P[12][5]*t2*t59);
Kfusion[13] = t130*(P[13][0]*t2*t46+P[13][6]*t2*t42+P[13][1]*t2*t49+P[13][2]*t2*t52+P[13][3]*t2*t55+P[13][4]*t2*t57+P[13][5]*t2*t59);
Kfusion[14] = t130*(P[14][0]*t2*t46+P[14][6]*t2*t42+P[14][1]*t2*t49+P[14][2]*t2*t52+P[14][3]*t2*t55+P[14][4]*t2*t57+P[14][5]*t2*t59);
Kfusion[15] = t130*(P[15][0]*t2*t46+P[15][6]*t2*t42+P[15][1]*t2*t49+P[15][2]*t2*t52+P[15][3]*t2*t55+P[15][4]*t2*t57+P[15][5]*t2*t59);
Kfusion[16] = t130*(P[16][0]*t2*t46+P[16][6]*t2*t42+P[16][1]*t2*t49+P[16][2]*t2*t52+P[16][3]*t2*t55+P[16][4]*t2*t57+P[16][5]*t2*t59);
Kfusion[17] = t130*(P[17][0]*t2*t46+P[17][6]*t2*t42+P[17][1]*t2*t49+P[17][2]*t2*t52+P[17][3]*t2*t55+P[17][4]*t2*t57+P[17][5]*t2*t59);
Kfusion[18] = t130*(P[18][0]*t2*t46+P[18][6]*t2*t42+P[18][1]*t2*t49+P[18][2]*t2*t52+P[18][3]*t2*t55+P[18][4]*t2*t57+P[18][5]*t2*t59);
Kfusion[19] = t130*(P[19][0]*t2*t46+P[19][6]*t2*t42+P[19][1]*t2*t49+P[19][2]*t2*t52+P[19][3]*t2*t55+P[19][4]*t2*t57+P[19][5]*t2*t59);
Kfusion[20] = t130*(P[20][0]*t2*t46+P[20][6]*t2*t42+P[20][1]*t2*t49+P[20][2]*t2*t52+P[20][3]*t2*t55+P[20][4]*t2*t57+P[20][5]*t2*t59);
Kfusion[21] = t130*(P[21][0]*t2*t46+P[21][6]*t2*t42+P[21][1]*t2*t49+P[21][2]*t2*t52+P[21][3]*t2*t55+P[21][4]*t2*t57+P[21][5]*t2*t59);
Kfusion[22] = t130*(P[22][0]*t2*t46+P[22][6]*t2*t42+P[22][1]*t2*t49+P[22][2]*t2*t52+P[22][3]*t2*t55+P[22][4]*t2*t57+P[22][5]*t2*t59);
Kfusion[23] = t130*(P[23][0]*t2*t46+P[23][6]*t2*t42+P[23][1]*t2*t49+P[23][2]*t2*t52+P[23][3]*t2*t55+P[23][4]*t2*t57+P[23][5]*t2*t59);

162
matlab/scripts/Inertial Nav EKF/LOSY.c Normal file
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@ -0,0 +1,162 @@
float t2 = 1.0f/range;
float t3 = Tbs.a.y*q0*2.0f;
float t4 = Tbs.a.x*q3*2.0f;
float t18 = Tbs.a.z*q1*2.0f;
float t5 = t3+t4-t18;
float t6 = Tbs.a.y*q1*2.0f;
float t7 = Tbs.a.z*q0*2.0f;
float t16 = Tbs.a.x*q2*2.0f;
float t8 = t6+t7-t16;
float t9 = Tbs.a.x*q0*2.0f;
float t10 = Tbs.a.z*q2*2.0f;
float t17 = Tbs.a.y*q3*2.0f;
float t11 = t9+t10-t17;
float t12 = Tbs.a.x*q1*2.0f;
float t13 = Tbs.a.y*q2*2.0f;
float t14 = Tbs.a.z*q3*2.0f;
float t15 = t12+t13+t14;
float t19 = q0*q0;
float t20 = q1*q1;
float t21 = q2*q2;
float t22 = q3*q3;
float t23 = q0*q3*2.0f;
float t24 = q0*q2*2.0f;
float t25 = q1*q3*2.0f;
float t26 = q0*q1*2.0f;
float t27 = t19+t20-t21-t22;
float t28 = Tbs.a.x*t27;
float t29 = q1*q2*2.0f;
float t30 = t24+t25;
float t31 = Tbs.a.z*t30;
float t32 = t19-t20+t21-t22;
float t33 = Tbs.a.y*t32;
float t34 = t23+t29;
float t35 = Tbs.a.x*t34;
float t36 = q2*q3*2.0f;
float t37 = t19-t20-t21+t22;
float t38 = Tbs.a.z*t37;
float t39 = t24-t25;
float t40 = t26+t36;
float t41 = Tbs.a.y*t40;
float t60 = Tbs.a.x*t39;
float t42 = t38+t41-t60;
float t43 = t8*vd;
float t44 = t5*ve;
float t45 = t11*vn;
float t46 = t43+t44+t45;
float t47 = t5*vd;
float t48 = t15*vn;
float t62 = t8*ve;
float t49 = t47+t48-t62;
float t50 = t15*ve;
float t51 = t8*vn;
float t63 = t11*vd;
float t52 = t50+t51-t63;
float t53 = t15*vd;
float t54 = t11*ve;
float t64 = t5*vn;
float t55 = t53+t54-t64;
float t56 = t23-t29;
float t65 = Tbs.a.y*t56;
float t57 = t28+t31-t65;
float t58 = t26-t36;
float t66 = Tbs.a.z*t58;
float t59 = t33+t35-t66;
float t61 = P[0][0]*t2*t46;
float t67 = P[1][1]*t2*t49;
float t68 = P[4][0]*t2*t57;
float t69 = P[5][0]*t2*t59;
float t70 = P[6][0]*t2*t42;
float t71 = P[1][0]*t2*t49;
float t72 = P[2][0]*t2*t52;
float t73 = P[3][0]*t2*t55;
float t74 = t61+t68+t69+t70+t71+t72+t73;
float t75 = t2*t46*t74;
float t76 = P[4][1]*t2*t57;
float t77 = P[5][1]*t2*t59;
float t78 = P[6][1]*t2*t42;
float t79 = P[0][1]*t2*t46;
float t80 = P[2][1]*t2*t52;
float t81 = P[3][1]*t2*t55;
float t82 = t67+t76+t77+t78+t79+t80+t81;
float t83 = t2*t49*t82;
float t84 = P[4][2]*t2*t57;
float t85 = P[5][2]*t2*t59;
float t86 = P[6][2]*t2*t42;
float t87 = P[0][2]*t2*t46;
float t88 = P[1][2]*t2*t49;
float t89 = P[2][2]*t2*t52;
float t90 = P[3][2]*t2*t55;
float t91 = t84+t85+t86+t87+t88+t89+t90;
float t92 = t2*t52*t91;
float t93 = P[4][3]*t2*t57;
float t94 = P[5][3]*t2*t59;
float t95 = P[6][3]*t2*t42;
float t96 = P[0][3]*t2*t46;
float t97 = P[1][3]*t2*t49;
float t98 = P[2][3]*t2*t52;
float t99 = P[3][3]*t2*t55;
float t100 = t93+t94+t95+t96+t97+t98+t99;
float t101 = t2*t55*t100;
float t102 = P[4][4]*t2*t57;
float t103 = P[5][4]*t2*t59;
float t104 = P[6][4]*t2*t42;
float t105 = P[0][4]*t2*t46;
float t106 = P[1][4]*t2*t49;
float t107 = P[2][4]*t2*t52;
float t108 = P[3][4]*t2*t55;
float t109 = t102+t103+t104+t105+t106+t107+t108;
float t110 = t2*t57*t109;
float t111 = P[4][5]*t2*t57;
float t112 = P[5][5]*t2*t59;
float t113 = P[6][5]*t2*t42;
float t114 = P[0][5]*t2*t46;
float t115 = P[1][5]*t2*t49;
float t116 = P[2][5]*t2*t52;
float t117 = P[3][5]*t2*t55;
float t118 = t111+t112+t113+t114+t115+t116+t117;
float t119 = t2*t59*t118;
float t120 = P[4][6]*t2*t57;
float t121 = P[5][6]*t2*t59;
float t122 = P[6][6]*t2*t42;
float t123 = P[0][6]*t2*t46;
float t124 = P[1][6]*t2*t49;
float t125 = P[2][6]*t2*t52;
float t126 = P[3][6]*t2*t55;
float t127 = t120+t121+t122+t123+t124+t125+t126;
float t128 = t2*t42*t127;
float t129 = R_LOS+t75+t83+t92+t101+t110+t119+t128;
float t130 = 1.0f/t129;
H_LOS[0] = -t2*t46;
H_LOS[1] = -t2*t49;
H_LOS[2] = -t2*t52;
H_LOS[3] = -t2*t55;
H_LOS[4] = -t2*(t28+t31-Tbs.a.y*(t23-q1*q2*2.0f));
H_LOS[5] = -t2*(t33+t35-Tbs.a.z*(t26-q2*q3*2.0f));
H_LOS[6] = -t2*t42;
Kfusion[0] = -t130*(t61+P[0][6]*t2*t42+P[0][1]*t2*t49+P[0][2]*t2*t52+P[0][3]*t2*t55+P[0][4]*t2*t57+P[0][5]*t2*t59);
Kfusion[1] = -t130*(t67+P[1][0]*t2*t46+P[1][6]*t2*t42+P[1][2]*t2*t52+P[1][3]*t2*t55+P[1][4]*t2*t57+P[1][5]*t2*t59);
Kfusion[2] = -t130*(t89+P[2][0]*t2*t46+P[2][6]*t2*t42+P[2][1]*t2*t49+P[2][3]*t2*t55+P[2][4]*t2*t57+P[2][5]*t2*t59);
Kfusion[3] = -t130*(t99+P[3][0]*t2*t46+P[3][6]*t2*t42+P[3][1]*t2*t49+P[3][2]*t2*t52+P[3][4]*t2*t57+P[3][5]*t2*t59);
Kfusion[4] = -t130*(t102+P[4][0]*t2*t46+P[4][6]*t2*t42+P[4][1]*t2*t49+P[4][2]*t2*t52+P[4][3]*t2*t55+P[4][5]*t2*t59);
Kfusion[5] = -t130*(t112+P[5][0]*t2*t46+P[5][6]*t2*t42+P[5][1]*t2*t49+P[5][2]*t2*t52+P[5][3]*t2*t55+P[5][4]*t2*t57);
Kfusion[6] = -t130*(t122+P[6][0]*t2*t46+P[6][1]*t2*t49+P[6][2]*t2*t52+P[6][3]*t2*t55+P[6][4]*t2*t57+P[6][5]*t2*t59);
Kfusion[7] = -t130*(P[7][0]*t2*t46+P[7][6]*t2*t42+P[7][1]*t2*t49+P[7][2]*t2*t52+P[7][3]*t2*t55+P[7][4]*t2*t57+P[7][5]*t2*t59);
Kfusion[8] = -t130*(P[8][0]*t2*t46+P[8][6]*t2*t42+P[8][1]*t2*t49+P[8][2]*t2*t52+P[8][3]*t2*t55+P[8][4]*t2*t57+P[8][5]*t2*t59);
Kfusion[9] = -t130*(P[9][0]*t2*t46+P[9][6]*t2*t42+P[9][1]*t2*t49+P[9][2]*t2*t52+P[9][3]*t2*t55+P[9][4]*t2*t57+P[9][5]*t2*t59);
Kfusion[10] = -t130*(P[10][0]*t2*t46+P[10][6]*t2*t42+P[10][1]*t2*t49+P[10][2]*t2*t52+P[10][3]*t2*t55+P[10][4]*t2*t57+P[10][5]*t2*t59);
Kfusion[11] = -t130*(P[11][0]*t2*t46+P[11][6]*t2*t42+P[11][1]*t2*t49+P[11][2]*t2*t52+P[11][3]*t2*t55+P[11][4]*t2*t57+P[11][5]*t2*t59);
Kfusion[12] = -t130*(P[12][0]*t2*t46+P[12][6]*t2*t42+P[12][1]*t2*t49+P[12][2]*t2*t52+P[12][3]*t2*t55+P[12][4]*t2*t57+P[12][5]*t2*t59);
Kfusion[13] = -t130*(P[13][0]*t2*t46+P[13][6]*t2*t42+P[13][1]*t2*t49+P[13][2]*t2*t52+P[13][3]*t2*t55+P[13][4]*t2*t57+P[13][5]*t2*t59);
Kfusion[14] = -t130*(P[14][0]*t2*t46+P[14][6]*t2*t42+P[14][1]*t2*t49+P[14][2]*t2*t52+P[14][3]*t2*t55+P[14][4]*t2*t57+P[14][5]*t2*t59);
Kfusion[15] = -t130*(P[15][0]*t2*t46+P[15][6]*t2*t42+P[15][1]*t2*t49+P[15][2]*t2*t52+P[15][3]*t2*t55+P[15][4]*t2*t57+P[15][5]*t2*t59);
Kfusion[16] = -t130*(P[16][0]*t2*t46+P[16][6]*t2*t42+P[16][1]*t2*t49+P[16][2]*t2*t52+P[16][3]*t2*t55+P[16][4]*t2*t57+P[16][5]*t2*t59);
Kfusion[17] = -t130*(P[17][0]*t2*t46+P[17][6]*t2*t42+P[17][1]*t2*t49+P[17][2]*t2*t52+P[17][3]*t2*t55+P[17][4]*t2*t57+P[17][5]*t2*t59);
Kfusion[18] = -t130*(P[18][0]*t2*t46+P[18][6]*t2*t42+P[18][1]*t2*t49+P[18][2]*t2*t52+P[18][3]*t2*t55+P[18][4]*t2*t57+P[18][5]*t2*t59);
Kfusion[19] = -t130*(P[19][0]*t2*t46+P[19][6]*t2*t42+P[19][1]*t2*t49+P[19][2]*t2*t52+P[19][3]*t2*t55+P[19][4]*t2*t57+P[19][5]*t2*t59);
Kfusion[20] = -t130*(P[20][0]*t2*t46+P[20][6]*t2*t42+P[20][1]*t2*t49+P[20][2]*t2*t52+P[20][3]*t2*t55+P[20][4]*t2*t57+P[20][5]*t2*t59);
Kfusion[21] = -t130*(P[21][0]*t2*t46+P[21][6]*t2*t42+P[21][1]*t2*t49+P[21][2]*t2*t52+P[21][3]*t2*t55+P[21][4]*t2*t57+P[21][5]*t2*t59);
Kfusion[22] = -t130*(P[22][0]*t2*t46+P[22][6]*t2*t42+P[22][1]*t2*t49+P[22][2]*t2*t52+P[22][3]*t2*t55+P[22][4]*t2*t57+P[22][5]*t2*t59);
Kfusion[23] = -t130*(P[23][0]*t2*t46+P[23][6]*t2*t42+P[23][1]*t2*t49+P[23][2]*t2*t52+P[23][3]*t2*t55+P[23][4]*t2*t57+P[23][5]*t2*t59);