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matrices.c
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matrices.c
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#include "matrices.h"
#include <math.h>
#include <stdio.h>
//-----------------------------------------------------
// The following Functions manage Vector operations:
// sum, subtraction, scalar-vector product
//-----------------------------------------------------
void vector_sum(float *a, float *b, float *res, int dim){
int i;
for(i = 0; i < dim; i++)
res[i] = a[i] + b[i];
}
void vector_sub(float *a, float *b, float *res, int dim){
int i;
for(i = 0; i < dim; i++)
res[i] = a[i] - b[i];
}
void vector_scal(float *a, float b, float *res, int dim){
int i;
for(i = 0; i < dim; i++)
res[i] = a[i]*b;
}
//-----------------------------------------------------
// The following Functions copies src vector in dest
// vector, both having dimension dim
//-----------------------------------------------------
void vector_copy(float* src, float* dest, int dim){
int i;
for(i = 0; i < dim; ++i)
dest[i] = src[i];
return;
}
//-----------------------------------------------------
// The following Function computes matrix-vector product
// y = A*x
//-----------------------------------------------------
void matvec_mul(float *x, float *y, int d1, int d2, float A[d1][d2]){
int i, j;
for(i = 0; i < d1; i++){
y[i] = 0;
for(j = 0; j < d2; j++)
y[i] += A[i][j]*x[j];
}
}
//-----------------------------------------------------
// The following Functions print matrices and vectors
//-----------------------------------------------------
void matrix_print(int row, int column, float m[row][column]){
int i, j;
for (i = 0; i < row; i++){
for (j = 0; j < column; j++)
printf("%g ", m[i][j]);
printf("\n");
}
}
void vector_print(int column, float v[column]){
int i;
for (i = 0; i < column; i++){
printf("%g ", v[i]);
printf("\n");
}
}
//-----------------------------------------------------
// The following Function computes the inverse of a
// 2x2 Matrix
//-----------------------------------------------------
void matrix_inverse(float A[2][2], float res[2][2]){
float det, a, b, c, d;
a = A[0][0];
b = A[0][1];
c = A[1][0];
d = A[1][1];
det = a*d - b*c;
if(det == 0){
printf("Matrice non invertibile: il determinante è nullo.\n");
return;
}
res[0][0] = d/det;
res[0][1] = -b/det;
res[1][0] = -c/det;
res[1][1] = a/det;
}
//-----------------------------------------------------
// The following Functions initialize to zero every
// element of a vector or matrix
//-----------------------------------------------------
void vector_set_zero(float *v, int dim){
int i;
for(i = 0; i < dim; ++i)
v[i] = 0;
return;
}
void matrix_set_zero(int row, int column, float m[row][column]){
int i, j;
for(i=0; i<row; i++)
for(j=0; j<column; j++)
m[i][j] = 0;
}
//-----------------------------------------------------
// The following Function updates Robot Kynematics
//-----------------------------------------------------
void update_kyn(float Tsee[4][4], state robot, int true_alpha){
float value;
float q1, q2, q3, q4, q5;
q1 = 0;
q2 = 0;
if(true_alpha)
q3 = robot.q3;
else
q3 = 0;
q4 = robot.q4;
q5 = robot.q5;
// First Row
value = cos(q4 + q5)*sin(q3) + cos(q3)*sin(q4 + q5);
Tsee[0][0] = value;
value = cos(q3)*cos(q4 + q5) - sin(q3)*sin(q4 + q5);
Tsee[0][1] = value;
value = 0.0;
Tsee[0][2] = value;
value = -(15.0/2.0) + q1 + (15*cos(q3))/2.0 - 3.0*sin(q3) -
sin(q3)*(3.0/2.0 - 6.0*cos(q4 + q5) + 6.0*sin(q4)) +
cos(q3)*(15.0/2.0 + 6.0*cos(q4) + 6.0*sin(q4 + q5));
Tsee[0][3] = value;
// Second Row
value = -cos(q3)*cos(q4 + q5) + sin(q3)*sin(q4 + q5);
Tsee[1][0] = value;
value = cos(q4 + q5)*sin(q3) + cos(q3)*sin(q4 + q5);
Tsee[1][1] = value;
value = 0.0;
Tsee[1][2] = value;
value = 1.5 + q2 + 3.0*cos(q3) + (15*sin(q3))/2 +
cos(q3)*(3.0/2.0 - 6*cos(q4 + q5) + 6*sin(q4)) +
sin(q3)*(15.0/2.0 + 6*cos(q4) + 6*sin(q4 + q5));
Tsee[1][3] = value;
// Third Row
Tsee[2][0] = 0.0;
Tsee[2][1] = 0.0;
Tsee[2][2] = 1.0;
Tsee[2][3] = 0.0;
// Fourth ROw
Tsee[3][0] = 0.0;
Tsee[3][1] = 0.0;
Tsee[3][2] = 0.0;
Tsee[3][3] = 1.0;
}
//-----------------------------------------------------
// The following Functions update dynamic Matrices for
// dynamic integration. There are two set of contraints
// which depend on the position of the end-effector:
// 1) Tne end-effector is not touching the ground
// 2) The end-effector is touching the ground
//-----------------------------------------------------
void update_S2(float S2[4][2], state robot){
float value;
float q3, q4, q5;
q3 = robot.q3;
q4 = robot.q4;
q5 = robot.q5;
// First Row
value = -6*cos(q3)*(cos(q4 + q5) - sin(q4)) +
6*sin(q3)*(cos(q4) + sin(q4 + q5)) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5));
S2[0][0] = value;
value = -6*cos(q3 + q4 + q5) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*sin(q3 + q4 + q5))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5));
S2[0][1] = value;
// Second Row
value = (7.5*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5));
S2[1][0] = value;
value = (7.5*(-1.0 + 1.0*cos(q3) - 0.4*sin(q3))*sin(q3 + q4 + q5))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5));
S2[1][1] = value;
// Third Row
value = (-1.0*cos(q3 + q4) -1.0*sin(q3 + q4 + q5))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5));
S2[2][0] = value;
value = -((1.0*sin(q3 + q4 + q5))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)));
S2[2][1] = value;
// FOurth Row
value =(3.0*cos(q3 + q4) - 4.0*cos(q3 - q5) + 4.0*cos(q3 + q5) +
10.0*cos(q3 + q4 + q5) - 8.0*sin(q3) - 10.0*sin(q3 + q4) +
3.0*sin(q3 + q4 + q5))/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5));
S2[3][0] = value;
value =(4.0*cos(q3 + q5) + 10.0*cos(q3 + q4 + q5) - 4.0*sin(q3) +
3.0*sin(q3 + q4 + q5))/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5));
S2[3][1] = value;
}
void update_M1(float M1[2][2], state robot){
float value;
float q5;
q5 = robot.q5;
// First Row
value =180.0*(4.57118 + sin(q5));
M1[0][0] = value;
value =231.406 + 90*sin(q5);
M1[0][1] = value;
// Second Row
value = 231.406 + 90*sin(q5);
M1[1][0] = value;
value = 231.406;
M1[1][1] = value;
}
void update_C1(float C1[2][2], state robot, dot_state dot_robot){
float value;
float q3, q4, q5, dotq1, dotq2, dotq3, dotq4, dotq5;
q3 = robot.q3;
q4 = robot.q4;
q5 = robot.q5;
dotq1 = dot_robot.dq1;
dotq2 = dot_robot.dq2;
dotq3 = dot_robot.dq3;
dotq4 = dot_robot.dq4;
dotq5 = dot_robot.dq5;
// First Row
value = -112.5*dotq3*cos(q4) + (37.5*dotq1 - 56.25*dotq3)*cos(q3 + q4) +
180.0*dotq5*cos(q5) - 56.25*dotq3*cos(q4 + q5) -
7.5*dotq2*cos(q3 + q4 + q5) - 56.25*dotq3*cos(q3 + q4 + q5) +
281.25*dotq3*sin(q4) + 37.5*dotq2*sin(q3 + q4) +
281.25*dotq3*sin(q3 + q4) - 22.5*dotq3*sin(q4 + q5) +
7.5*dotq1*sin(q3 + q4 + q5) - 11.25*dotq3*sin(q3 + q4 + q5);
C1[0][0] = value;
value = 90.0*dotq5*cos(q5) - 56.25*dotq3*cos(q4 + q5) -
7.5*dotq2*cos(q3 + q4 + q5) - 56.25*dotq3*cos(q3 + q4 + q5) -
22.5*dotq3*sin(q4 + q5) + 7.5*dotq1*sin(q3 + q4 + q5) -
11.25*dotq3*sin(q3 + q4 + q5);
C1[0][1] = value;
// Second Row
value = -90.0*dotq4*cos(q5) +
45*dotq5*cos(q5) - 7.5*dotq2*cos(q3 + q4 + q5) -
45.0*dotq3*(1.0*cos(q3 - q5) + 1.0*cos(q3 + q5) + 1.25*cos(q4 + q5) +
1.25*cos(q3 + q4 + q5) + 0.5*sin(q4 + q5) +
0.25*sin(q3 + q4 + q5)) +
7.5*dotq1*sin(q3 + q4 + q5);
C1[1][0] = value;
value =-45.0*dotq4*cos(q5) -
45.0*dotq3*cos(q3 + q5) - 56.25*dotq3*cos(q4 + q5) -
7.5*dotq2*cos(q3 + q4 + q5) - 56.25*dotq3*cos(q3 + q4 + q5) -
22.5*dotq3*sin(q4 + q5) + 7.5*dotq1*sin(q3 + q4 + q5) -
11.25*dotq3*sin(q3 + q4 + q5);
C1[1][1] = value;
}
void update_G1(float G1[2], state robot){
float value;
float q3, q4, q5;
q3 = robot.q3;
q4 = robot.q4;
q5 = robot.q5;
// First Row
value = 0.0 + 735.0*cos(q3 + q4) + 147.0*sin(q3 + q4 + q5);
G1[0] = value;
// Second Row
value = 0.0 + 147.0*sin(q3 + q4 + q5);
G1[1] = value;
}
void update_M2(float M2[2][2], state robot){
float value;
float q3, q4, q5;
q3 = robot.q3;
q4 = robot.q4;
q5 = robot.q5;
//M2(0,0)
value = 1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(178771.0 -
745.625*cos(q3) - 49842.0*cos(2*q3) + 126469.0*cos(q4) +
186.406*cos(2*q4) - 1864.06*cos(q3 + q4) -
41005.5*cos(2*(q3 + q4)) - 124605.0*cos(2*q3 + q4) -
372.813*cos(q3 + 2*q4) + 8262.0*cos(2*(q3 - q5)) +
7056.0*cos(q4 - q5) - 7056.0*cos(2*q3 + q4 - q5) -
16524.0*cos(2*q5) + 8262.0*cos(2*(q3 + q5)) -
21168.0*cos(q4 + q5) - 186.406*cos(2*(q4 + q5)) +
41005.5*cos(2*(q3 + q4 + q5)) + 21168.0*cos(2*q3 + q4 + q5) +
35280.0*cos(2*q3 + 2*q4 + q5) - 41310.0*cos(q4 + 2*q5) +
41310.0*cos(2*q3 + q4 + 2*q5) + 372.813*cos(q3 + 2*(q4 + q5)) +
21168.0*sin(q4) - 17640.0*sin(2*(q3 + q4)) -
21168.0*sin(2*q3 + q4) + 372.813*sin(q3 - q5) +
33183.0*sin(2*q3 - q5) - 41310.0*sin(q4 - q5) +
41310.0*sin(2*q3 + q4 - q5) + 191278.0*sin(q5) -
372.813*sin(q3 + q5) - 33183.0*sin(2*q3 + q5) +
126469.0*sin(q4 + q5) - 1864.06*sin(q3 + q4 + q5) +
17640.0*sin(2*(q3 + q4 + q5)) - 124605.0*sin(2*q3 + q4 + q5) +
372.813*sin(2*q4 + q5) - 745.625*sin(q3 + 2*q4 + q5) -
82010.9*sin(2*q3 + 2*q4 + q5) - 7056.0*sin(q4 + 2*q5) +
7056.0*sin(2*q3 + q4 + 2*q5));
M2[0][0] = value;
//M2(0,1)
value = 1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(90600.7 -
372.813*cos(q3) - 25011.0*cos(2*q3) + 64078.3*cos(q4) +
171.953*cos(2*q4) - 466.016*cos(q3 + q4) -
78.75*cos(2*(q3 + q4)) - 41703.8*cos(2*q3 + q4) -
93.2031*cos(q3 + 2*q4) + 3528.0*cos(q4 - q5) - 8262.0*cos(2*q5) +
8262.0*cos(2*(q3 + q5)) - 10584.0*cos(q4 + q5) -
104.453*cos(2*(q4 + q5)) + 41016.7*cos(2*(q3 + q4 + q5)) +
14112.0*cos(2*q3 + q4 + q5) + 17640.0*cos(2*q3 + 2*q4 + q5) -
20655.0*cos(q4 + 2*q5) + 41310.0*cos(2*q3 + q4 + 2*q5) +
279.609*cos(q3 + 2*(q4 + q5)) + 10584.0*sin(q4) -
7056.0*sin(2*q3 + q4) + 93.2031*sin(q3 - q5) +
8340.75*sin(2*q3 - q5) - 20655.0*sin(q4 - q5) + 95728.9*sin(q5) -
279.609*sin(q3 + q5) - 24932.3*sin(2*q3 + q5) +
63740.8*sin(q4 + q5) - 1398.05*sin(q3 + q4 + q5) +
17640.0*sin(2*(q3 + q4 + q5)) - 83351.3*sin(2*q3 + q4 + q5) +276.406*sin(2*q4 + q5) - 372.813*sin(q3 + 2*q4 + q5) -
41095.5*sin(2*q3 + 2*q4 + q5) - 3528.0*sin(q4 + 2*q5) +
7056.0*sin(2*q3 + q4 + 2*q5));
M2[0][1] = value;
//M2(1,0)
value = 1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*(90600.7 - 372.812*cos(q3) -
25011.0*cos(2*q3) + 64078.3*cos(q4) + 171.953*cos(2*q4) -
466.016*cos(q3 + q4) - 78.75*cos(2*(q3 + q4)) -
41703.8*cos(2*q3 + q4) - 93.2031*cos(q3 + 2*q4) +
3528.0*cos(q4 - q5) - 8262.0*cos(2*q5) + 8262.0*cos(2*(q3 + q5)) -
10584.0*cos(q4 + q5) - 104.453*cos(2*(q4 + q5)) +
41016.7*cos(2*(q3 + q4 + q5)) + 14112.0*cos(2*q3 + q4 + q5) +
17640.0*cos(2*q3 + 2*q4 + q5) - 20655.0*cos(q4 + 2*q5) +
41310.0*cos(2*q3 + q4 + 2*q5) + 279.609*cos(q3 + 2*(q4 + q5)) +
10584.0*sin(q4) - 7056.0*sin(2*q3 + q4) + 93.2031*sin(q3 - q5) +
8340.75*sin(2*q3 - q5) - 20655.0*sin(q4 - q5) + 95728.9*sin(q5) -
279.609*sin(q3 + q5) - 24932.3*sin(2*q3 + q5) +
63740.8*sin(q4 + q5) - 1398.05*sin(q3 + q4 + q5) +
17640.0*sin(2*(q3 + q4 + q5)) - 83351.3*sin(2*q3 + q4 + q5) +
276.406*sin(2*q4 + q5) - 372.812*sin(q3 + 2*q4 + q5) -
41095.5*sin(2*q3 + 2*q4 + q5) - 3528.0*sin(q4 + 2*q5) +
7056.0*sin(2*q3 + q4 + 2*q5));
M2[1][0] = value;
//M2(1,1)
value = 1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(82406.2 -
186.406*cos(q3) - 8419.5*cos(2*q3) + 43817.0*cos(q4) +
250.703*cos(2*q4) + 8262.0*cos(2*(q3 + q5)) -
7056.0*cos(q4 + q5) - 93.2031*cos(2*(q4 + q5)) +
41028.0*cos(2*(q3 + q4 + q5)) + 7056.0*cos(2*q3 + q4 + q5) +
41310.0*cos(2*q3 + q4 + 2*q5) + 186.406*cos(q3 + 2*(q4 + q5)) +
7056.0*sin(q4) + 16867.9*sin(q5) - 186.406*sin(q3 + q5) -
16681.5*sin(2*q3 + q5) + 43029.5*sin(q4 + q5) -
932.031*sin(q3 + q4 + q5) + 17640.0*sin(2*(q3 + q4 + q5)) -
42097.5*sin(2*q3 + q4 + q5) + 343.906*sin(2*q4 + q5) -
186.406*sin(q3 + 2*q4 + q5) - 157.5*sin(2*q3 + 2*q4 + q5) +
7056.0*sin(2*q3 + q4 + 2*q5));
M2[1][1] = value;
}
void update_C2(float C2[2][2], state robot, dot_state dot_robot){
float value;
float q3, q4, q5;
float dotq1, dotq2, dotq3, dotq4, dotq5;
q3 = robot.q3;
q4 = robot.q4;
q5 = robot.q5;
dotq1 = dot_robot.dq1;
dotq2 = dot_robot.dq2;
dotq3 = dot_robot.dq3;
dotq4 = dot_robot.dq4;
dotq5 = dot_robot.dq5;
//C2(0,0)
value = 37.5*dotq1*cos(q3 + q4) + 180.0*dotq5*cos(q5) -
7.5*dotq2*cos(q3 + q4 + q5) + 37.5*dotq2*sin(q3 + q4) -
1/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))*56.25*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(1.0*dotq3*cos(
q4 + q5) + (-2.0*dotq3 - 1.0*dotq4 - 1.0*dotq5)*cos(
q3 + q4 + q5) - 5.0*dotq3*sin(q4) + 10.0*dotq3*sin(q3 + q4) +
5.0*dotq4*sin(q3 + q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))) +
1/2*dotq3*(-225.0*cos(q4) - 112.5*cos(q3 + q4) -
112.5*cos(q4 + q5) - 112.5*cos(q3 + q4 + q5) + 562.5*sin(q4) +
562.5*sin(q3 + q4) - 45.0*sin(q4 + q5) -
22.5*sin(q3 + q4 + q5)) +
7.5*dotq1*sin(
q3 + q4 + q5) + (-6*cos(q3)*(cos(q4 + q5) - sin(q4)) +
6*sin(q3)*(cos(q4) + sin(q4 + q5)) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5)))*(37.5*dotq3*cos(
q4) + (-75.0*dotq3 - 37.5*dotq4)*cos(q3 + q4) +
7.5*dotq3*sin(q4 + q5) - 15.0*dotq3*sin(q3 + q4 + q5) -
7.5*dotq4*sin(q3 + q4 + q5) - 7.5*dotq5*sin(q3 + q4 + q5)) -
1/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))
*37.5*(1.0*cos(q3 + q4) +
1.0*sin(q3 + q4 + q5))*(-6.0*dotq3*cos(
q3 - q4) + (1.0*dotq1 - 3.0*dotq3 + 3.0*dotq4)*cos(q4) +
3.0*dotq3*cos(q3 + q4) + 1.5*dotq4*cos(q3 + q4) -
2.4*dotq3*cos(q3 - q5) + 2.4*dotq5*cos(q3 - q5) -
3.0*dotq3*cos(q3 - q4 - q5) + 2.4*dotq3*cos(q3 + q5) +
2.4*dotq5*cos(q3 + q5) - 0.2*dotq2*cos(q4 + q5) -
3.0*dotq3*cos(q4 + q5) + 1.5*dotq4*cos(q4 + q5) +
3.0*dotq5*cos(q4 + q5) + 3.0*dotq3*cos(q3 + q4 + q5) +
1.5*dotq4*cos(q3 + q4 + q5) + 1.5*dotq5*cos(q3 + q4 + q5) -
1.5*dotq5*cos(q3)*cos(q3 + q4 + q5) - 12.0*dotq3*sin(q3) +
0.6*dotq5*cos(q3 + q4 + q5)*sin(q3) - 15.0*dotq3*sin(q3 - q4) +
1.0*dotq2*sin(q4) + 15.0*dotq3*sin(q4) - 7.5*dotq4*sin(q4) -
15.0*dotq3*sin(q3 + q4) - 7.5*dotq4*sin(q3 + q4) +
1.2*dotq3*sin(q3 - q4 - q5) + 0.2*dotq1*sin(q4 + q5) -
0.6*dotq3*sin(q4 + q5) + 0.6*dotq4*sin(q4 + q5) +
1.2*dotq5*sin(q4 + q5) + 0.6*dotq3*sin(q3 + q4 + q5) +
0.3*dotq4*sin(q3 + q4 + q5) + 0.3*dotq5*sin(q3 + q4 + q5) -
0.6*dotq5*cos(q3)*sin(q3 + q4 + q5) -
1.5*dotq5*sin(q3)*sin(q3 + q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(372.813 + 450.0*cos(q3) +
562.5*cos(q4) + 562.5*cos(q3 + q4) - 45.0*cos(q4 + q5) -
22.5*cos(q3 + q4 + q5) + 225.0*sin(q4) + 112.5*sin(q3 + q4) -
90.0*sin(q3 - q5) + 90.0*sin(q3 + q5) + 112.5*sin(q4 + q5) +
112.5*sin(
q3 + q4 + q5))*(dotq5*(0.5*cos(q3 - q5) - 0.5*cos(q3 + q5) -
2.5*cos(q3 + q4 + q5) + 1.0*sin(q3)) +
dotq4*(sin(
q3)*(2.0 + 2.5*cos(q5)*sin(q4) + 2.0*sin(q5) +
cos(q4)*(2.5 + 2.5*sin(q5))) +
cos(q3)*(-2.5*cos(q4)*cos(q5) +
sin(q4)*(2.5 + 2.5*sin(q5)))) +
1.0*(1.0*cos(q3 + q4 + q5) -
1.0*sin(q3 + q4))*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(q3 + q4 + q5))) +
1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 3)*(3.0*cos(q3 + q4) -
4.0*cos(q3 - q5) + 4.0*cos(q3 + q5) + 10.0*cos(q3 + q4 + q5) -
8.0*sin(q3) - 10.0*sin(q3 + q4) +
3.0*sin(q3 + q4 +
q5))*(149.625*(dotq5*(0.5*cos(q3 - q5) - 0.5*cos(q3 + q5) -
2.5*cos(q3 + q4 + q5) + 1.0*sin(q3)) +
dotq4*(sin(
q3)*(2.0 + 2.5*cos(q5)*sin(q4) + 2.0*sin(q5) +
cos(q4)*(2.5 + 2.5*sin(q5))) +
cos(q3)*(-2.5*cos(q4)*cos(q5) +
sin(q4)*(2.5 + 2.5*sin(q5)))) +
1.0*(1.0*cos(q3 + q4 + q5) -
1.0*sin(q3 + q4))*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(q3 + q4 + q5))) +
149.625*(dotq5*(cos(
q3)*(-10.0 - 25.0*cos(q5)*sin(q4) +
cos(q4)*(7.5*cos(q5) - 25.0*sin(q5)) - 10.0*sin(q5) -
7.5*sin(q4)*sin(q5)) +
sin(q3)*(-3.0 +
cos(q5)*(-20.0 - 25.0*cos(q4) - 7.5*sin(q4)) -
3.0*sin(q5) - 7.5*cos(q4)*sin(q5) +
sin(q4)*(-8.0 + 17.0*sin(q5)))) +
8.0*(1.0*cos(q3) + 1.25*cos(q3 + q4) -
0.375*cos(q3 + q4 + q5) + 0.375*sin(q3 + q4) -
0.5*sin(q3 - q5) + 0.5*sin(q3 + q5) +
1.25*sin(q3 + q4 + q5))*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(q3 + q4 + q5)) +
dotq4*((2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5))*(-10.0*cos(q3 + q4) +
3.0*cos(q3 + q4 + q5) - 3.0*sin(q3 + q4) -
10.0*sin(q3 + q4 + q5)) -
3.0*(1.0*cos(q4 + q5) - 1.0*sin(q4))*(1.0*cos(q3 + q4) -
1.33333*cos(q3 - q5) + 1.33333*cos(q3 + q5) +
3.33333*cos(q3 + q4 + q5) - 2.66667*sin(q3) -
3.33333*sin(q3 + q4) + 1.0*sin(q3 + q4 + q5))))) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*(75.0*cos(q3 + q4) +
15.0*sin(q3 + q4 + q5))*(-7.5*dotq5*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(0.5*cos(q3 - q5) - 0.5*cos(q3 + q5) -
2.5*cos(q3 + q4 + q5) + 1.0*sin(q3)) +
18.75*dotq4*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(cos(
q3)*(1.0*cos(q4)*cos(q5) + sin(q4)*(-1.0 - 1.0*sin(q5))) +
sin(q3)*(-0.8 - 1.0*cos(q5)*sin(q4) +
cos(q4)*(-1.0 - 1.0*sin(q5)) - 0.8*sin(q5))) +
3.0*(1.0*dotq4*cos(q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(
q3 + q4 + q5))*(1.0*cos(2*q3 + q4) +
2.5*cos(q3 + q4 + q5) - 2.5*cos(2*q3 + q4 + q5) -
2.5*sin(q3 + q4) + 2.5*sin(2*q3 + q4) +
1.0*sin(2*q3 + q4 + q5))) + (15.0*cos(q3 + q4 + q5) -
75.0*sin(q3 + q4))*(dotq5*(6*cos(q4 + q5)*sin(q3) +
6*cos(q3)*sin(q4 + q5) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(cos(q3)*cos(q4 + q5) -
1.0*sin(q3)*sin(q4 + q5)))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) + (
3.0*cos(q4 + q5)*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*- (
6.0*sin(q4 + q5)*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))) +
dotq4*(6*sin(q3)*(cos(q4 + q5) - sin(q4)) +
6*cos(q3)*(cos(q4) + sin(q4 + q5)) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(1.0*cos(q3 + q4 + q5) - 1.0*sin(q3 + q4)))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*3.0*(1.0*cos(q4 + q5) -
1.0*sin(q4))*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))) - (
3.0*(2.0*cos(q4) +
2.0*sin(q4 + q5))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*7.5*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(
q3 + q4 + q5))*(-1.6*cos(q3) - 2.0*cos(q3 + q4) +
1.0*cos(2*q3 + q4) + 0.2*cos(q3 + q4 + q5) +
0.4*cos(2*q3 + q4 + q5) - 0.2*sin(q3 + q4) -
0.4*sin(2*q3 + q4) + 0.8*sin(q3 - q5) - 0.8*sin(q3 + q5) -
2.0*sin(q3 + q4 + q5) + 1.0*sin(2*q3 + q4 + q5))) +
1/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))
*7.5*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5)))*(15.0*dotq5*cos(q3 + q4 + q5) +
dotq3*(15.0*cos(q3 + q4 + q5) - 75.0*sin(q3 + q4)) +
dotq4*(15.0*cos(q3 + q4 + q5) - 75.0*sin(q3 + q4)) + (
1215.0*(1.0*dotq3*cos(
q3) + (-0.0123457*dotq4 - 0.0123457*dotq5)*cos(q4 + q5) +
2.5*dotq3*sin(q3) +
0.0617284*dotq4*sin(q4))*(1.0*cos(q3 + q4) +
1.0*sin(q3 + q4 + q5)))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(-847.5 +
3037.5*cos(q3) + 75.0*cos(q4) - 1215.0*sin(q3) +
15.0*sin(q4 + q5))*(dotq5*(0.5*cos(q3 - q5) -
0.5*cos(q3 + q5) - 2.5*cos(q3 + q4 + q5) + 1.0*sin(q3)) +
dotq4*(sin(
q3)*(2.0 + 2.5*cos(q5)*sin(q4) + 2.0*sin(q5) +
cos(q4)*(2.5 + 2.5*sin(q5))) +
cos(q3)*(-2.5*cos(q4)*cos(q5) +
sin(q4)*(2.5 + 2.5*sin(q5)))) +
1.0*(1.0*cos(q3 + q4 + q5) -
1.0*sin(q3 + q4))*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(q3 + q4 + q5))) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 +
q5), 2)*405.0*(-7.5*dotq5*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(0.5*cos(q3 - q5) - 0.5*cos(q3 + q5) -
2.5*cos(q3 + q4 + q5) + 1.0*sin(q3)) +
18.75*dotq4*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(cos(
q3)*(1.0*cos(q4)*cos(q5) + sin(q4)*(-1.0 - 1.0*sin(q5))) +
sin(q3)*(-0.8 - 1.0*cos(q5)*sin(q4) +
cos(q4)*(-1.0 - 1.0*sin(q5)) - 0.8*sin(q5))) +
3.0*(1.0*dotq4*cos(q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(
q3 + q4 + q5))*(1.0*cos(2*q3 + q4) +
2.5*cos(q3 + q4 + q5) - 2.5*cos(2*q3 + q4 + q5) -
2.5*sin(q3 + q4) + 2.5*sin(2*q3 + q4) +
1.0*sin(2*q3 + q4 + q5)))) + (-6*cos(
q3)*(cos(q4 + q5) - sin(q4)) +
6*sin(q3)*(cos(q4) + sin(q4 + q5)) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5)))*(dotq3*(-75.0*cos(q3 + q4) -
15.0*sin(q3 + q4 + q5)) +
dotq4*(-75.0*cos(q3 + q4) - 15.0*sin(q3 + q4 + q5)) -
15.0*dotq5*sin(q3 + q4 + q5) + (
75.0*(40.5*dotq3*cos(q3) + 1.0*dotq4*cos(q4) -
16.2*dotq3*sin(q3) + 0.2*dotq4*sin(q4 + q5) +
0.2*dotq5*sin(q4 + q5))*(1.0*cos(q3 + q4) +
1.0*sin(q3 + q4 + q5)))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(369.0 -
1215.0*cos(q3) + 15.0*cos(q4 + q5) - 3037.5*sin(q3) -
75.0*sin(q4))*(dotq5*(0.5*cos(q3 - q5) - 0.5*cos(q3 + q5) -
2.5*cos(q3 + q4 + q5) + 1.0*sin(q3)) +
dotq4*(sin(
q3)*(2.0 + 2.5*cos(q5)*sin(q4) + 2.0*sin(q5) +
cos(q4)*(2.5 + 2.5*sin(q5))) +
cos(q3)*(-2.5*cos(q4)*cos(q5) +
sin(q4)*(2.5 + 2.5*sin(q5)))) +
1.0*(1.0*cos(q3 + q4 + q5) -
1.0*sin(q3 + q4))*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(q3 + q4 + q5))) +
405.0*(dotq5*(6*cos(q4 + q5)*sin(q3) + 6*cos(q3)*sin(q4 + q5) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(cos(q3)*cos(q4 + q5) -
1.0*sin(q3)*sin(q4 + q5)))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) + (
3.0*cos(q4 + q5)*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*- (
6.0*sin(q4 + q5)*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))) +
dotq4*(6*sin(q3)*(cos(q4 + q5) - sin(q4)) +
6*cos(q3)*(cos(q4) + sin(q4 + q5)) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(1.0*cos(q3 + q4 + q5) - 1.0*sin(q3 + q4)))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*3.0*(1.0*cos(q4 + q5) -
1.0*sin(q4))*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))) - (
3.0*(2.0*cos(q4) +
2.0*sin(q4 + q5))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*7.5*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(
q3 + q4 + q5))*(-1.6*cos(q3) - 2.0*cos(q3 + q4) +
1.0*cos(2*q3 + q4) + 0.2*cos(q3 + q4 + q5) +
0.4*cos(2*q3 + q4 + q5) - 0.2*sin(q3 + q4) -
0.4*sin(2*q3 + q4) + 0.8*sin(q3 - q5) -
0.8*sin(q3 + q5) - 2.0*sin(q3 + q4 + q5) +
1.0*sin(2*q3 + q4 + q5)))) +
1/(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5))*(-1.0*cos(q3 + q4) -
1.0*sin(q3 + q4 + q5))*(37.5*dotq1*cos(q3 + q4) -
7.5*dotq2*cos(q3 + q4 + q5) + 37.5*dotq2*sin(q3 + q4) -
1/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))
*4556.25*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(1.0*dotq3*cos(
q3) + (-0.0246914*dotq4 - 0.0246914*dotq5)*cos(q4 + q5) +
0.0123457*dotq4*cos(q3 + q4 + q5) +
0.0123457*dotq5*cos(q3 + q4 + q5) + 2.5*dotq3*sin(q3) +
0.123457*dotq4*sin(q4) -
0.0617284*dotq4*sin(q3 + q4))*(sin(
q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))) +
56.25*dotq3*(1.0*cos(q3 + q4) - 0.8*cos(q3 - q5) +
0.8*cos(q3 + q5) + 1.0*cos(q3 + q4 + q5) - 4.0*sin(q3) -
5.0*sin(q3 + q4) + 0.2*sin(q3 + q4 + q5)) +
7.5*dotq1*sin(q3 + q4 + q5) +
dotq5*(90.0*cos(q3 - q5) + 90.0*cos(q3 + q5) +
112.5*cos(q4 + q5) + 112.5*cos(q3 + q4 + q5) +
45.0*sin(q4 + q5) + 22.5*sin(q3 + q4 + q5)) +
dotq4*(225.0*cos(q4) + 112.5*cos(q3 + q4) + 112.5*cos(q4 + q5) +
112.5*cos(q3 + q4 + q5) - 562.5*sin(q4) -
562.5*sin(q3 + q4) + 45.0*sin(q4 + q5) +
22.5*sin(q3 + q4 + q5)) +
1/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))
*56.25*(1.0*cos(q3 + q4) +
1.0*sin(q3 + q4 + q5))*((-27.0*dotq1 - 10.8*dotq2 +
4.0*dotq3)*cos(q3) + (4.0*dotq3 - 8.0*dotq4)*cos(q3 - q4) -
4.0*dotq4*cos(q4) + 1.0*dotq4*cos(q3 + q4) -
0.8*dotq4*cos(q3 - q5) + 2.0*dotq3*cos(q3 - q4 - q5) -
4.0*dotq4*cos(q3 - q4 - q5) - 4.0*dotq5*cos(q3 - q4 - q5) -
3.2*dotq5*cos(q5) + 0.8*dotq4*cos(q3 + q5) +
0.8*dotq5*cos(q3 + q5) - 4.0*dotq4*cos(q4 + q5) -
4.0*dotq5*cos(q4 + q5) + 1.0*dotq4*cos(q3 + q4 + q5) +
1.0*dotq5*cos(q3 + q4 + q5) + 10.8*dotq1*sin(q3) -
27.0*dotq2*sin(q3) - 132.68*dotq3*sin(q3) -
4.0*dotq4*sin(q3) - 0.4*dotq5*sin(q3) +
10.0*dotq3*sin(q3 - q4) - 20.0*dotq4*sin(q3 - q4) +
20.0*dotq4*sin(q4) - 5.0*dotq4*sin(q3 + q4) -
0.8*dotq3*sin(q3 - q4 - q5) + 1.6*dotq4*sin(q3 - q4 - q5) +
1.6*dotq5*sin(q3 - q4 - q5) - 0.8*dotq4*sin(q4 + q5) -
0.8*dotq5*sin(q4 + q5) + 0.2*dotq4*sin(q3 + q4 + q5) +
0.2*dotq5*sin(q3 + q4 + q5)) + (-6*cos(
q3)*(cos(q4 + q5) - sin(q4)) +
6*sin(q3)*(cos(q4) + sin(q4 + q5)) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5)))*(-1518.75*dotq3*cos(q3) -
75.0*dotq4*cos(q4) + 37.5*dotq4*cos(q3 + q4) +
607.5*dotq3*sin(q3) - 15.0*dotq4*sin(q4 + q5) -
15.0*dotq5*sin(q4 + q5) + 7.5*dotq4*sin(q3 + q4 + q5) +
7.5*dotq5*sin(q3 + q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(38416.9 -
14926.5*cos(q3) + 1125.0*cos(q3 - q4) + 1125.0*cos(q4) -
90.0*cos(q3 - q4 - q5) - 45.0*cos(q4 + q5) - 450.0*sin(q3) -
450.0*sin(q3 - q4) + 225.0*sin(q4) - 225.0*sin(q3 - q4 - q5) +
180.0*sin(q5) +
225.0*sin(
q4 + q5))*(dotq5*(0.5*cos(q3 - q5) - 0.5*cos(q3 + q5) -
2.5*cos(q3 + q4 + q5) + 1.0*sin(q3)) +
dotq4*(sin(
q3)*(2.0 + 2.5*cos(q5)*sin(q4) + 2.0*sin(q5) +
cos(q4)*(2.5 + 2.5*sin(q5))) +
cos(q3)*(-2.5*cos(q4)*cos(q5) +
sin(q4)*(2.5 + 2.5*sin(q5)))) +
1.0*(1.0*cos(q3 + q4 + q5) -
1.0*sin(q3 + q4))*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(q3 + q4 + q5))) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 +
q5), 2)*149.625*(dotq5*(cos(
q3)*(-10.0 - 25.0*cos(q5)*sin(q4) +
cos(q4)*(7.5*cos(q5) - 25.0*sin(q5)) - 10.0*sin(q5) -
7.5*sin(q4)*sin(q5)) +
sin(q3)*(-3.0 +
cos(q5)*(-20.0 - 25.0*cos(q4) - 7.5*sin(q4)) -
3.0*sin(q5) - 7.5*cos(q4)*sin(q5) +
sin(q4)*(-8.0 + 17.0*sin(q5)))) +
8.0*(1.0*cos(q3) + 1.25*cos(q3 + q4) -
0.375*cos(q3 + q4 + q5) + 0.375*sin(q3 + q4) -
0.5*sin(q3 - q5) + 0.5*sin(q3 + q5) +
1.25*sin(q3 + q4 + q5))*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(q3 + q4 + q5)) +
dotq4*((2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5))*(-10.0*cos(q3 + q4) +
3.0*cos(q3 + q4 + q5) - 3.0*sin(q3 + q4) -
10.0*sin(q3 + q4 + q5)) -
3.0*(1.0*cos(q4 + q5) - 1.0*sin(q4))*(1.0*cos(q3 + q4) -
1.33333*cos(q3 - q5) + 1.33333*cos(q3 + q5) +
3.33333*cos(q3 + q4 + q5) - 2.66667*sin(q3) -
3.33333*sin(q3 + q4) + 1.0*sin(q3 + q4 + q5)))) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*(-847.5 + 3037.5*cos(q3) + 75.0*cos(q4) -
1215.0*sin(q3) +
15.0*sin(q4 + q5))*(-7.5*dotq5*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(0.5*cos(q3 - q5) - 0.5*cos(q3 + q5) -
2.5*cos(q3 + q4 + q5) + 1.0*sin(q3)) +
18.75*dotq4*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(cos(
q3)*(1.0*cos(q4)*cos(q5) + sin(q4)*(-1.0 - 1.0*sin(q5))) +
sin(q3)*(-0.8 - 1.0*cos(q5)*sin(q4) +
cos(q4)*(-1.0 - 1.0*sin(q5)) - 0.8*sin(q5))) +
3.0*(1.0*dotq4*cos(q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(
q3 + q4 + q5))*(1.0*cos(2*q3 + q4) +
2.5*cos(q3 + q4 + q5) - 2.5*cos(2*q3 + q4 + q5) -
2.5*sin(q3 + q4) + 2.5*sin(2*q3 + q4) +
1.0*sin(2*q3 + q4 + q5))) + (369.0 - 1215.0*cos(q3) +
15.0*cos(q4 + q5) - 3037.5*sin(q3) -
75.0*sin(
q4))*(dotq5*(6*cos(q4 + q5)*sin(q3) +
6*cos(q3)*sin(q4 + q5) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(cos(q3)*cos(q4 + q5) -
1.0*sin(q3)*sin(q4 + q5)))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) + (
3.0*cos(q4 + q5)*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*- (
6.0*sin(q4 + q5)*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))) +
dotq4*(6*sin(q3)*(cos(q4 + q5) - sin(q4)) +
6*cos(q3)*(cos(q4) + sin(q4 + q5)) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(1.0*cos(q3 + q4 + q5) - 1.0*sin(q3 + q4)))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*3.0*(1.0*cos(q4 + q5) -
1.0*sin(q4))*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))) - (
3.0*(2.0*cos(q4) +
2.0*sin(q4 + q5))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*7.5*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(
q3 + q4 + q5))*(-1.6*cos(q3) - 2.0*cos(q3 + q4) +
1.0*cos(2*q3 + q4) + 0.2*cos(q3 + q4 + q5) +
0.4*cos(2*q3 + q4 + q5) - 0.2*sin(q3 + q4) -
0.4*sin(2*q3 + q4) + 0.8*sin(q3 - q5) -
0.8*sin(q3 + q5) - 2.0*sin(q3 + q4 + q5) +
1.0*sin(2*q3 + q4 + q5))));
C2[0][0] = value;
//C2(0,1)
value = 90*dotq5*cos(q5) - 7.5*dotq2*cos(q3 + q4 + q5) +
dotq3*(-56.25*cos(q4 + q5) - 56.25*cos(q3 + q4 + q5) -
22.5*sin(q4 + q5) - 11.25*sin(q3 + q4 + q5)) +
7.5*dotq1*sin(q3 + q4 + q5) -
1/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))*56.25*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(1.0*dotq3*cos(
q4 + q5) + (-2.0*dotq3 - 1.0*dotq4 - 1.0*dotq5)*cos(
q3 + q4 + q5) - 5.0*dotq3*sin(q4) + 10.0*dotq3*sin(q3 + q4) +
5.0*dotq4*sin(q3 + q4))*sin(q3 + q4 + q5) -
1/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))
*22.5*sin(
q3 + q4 +
q5)*(-10.0*dotq3*cos(
q3 - q4) + (1.66667*dotq1 - 5.0*dotq3 + 5.0*dotq4)*cos(q4) +
5.0*dotq3*cos(q3 + q4) + 2.5*dotq4*cos(q3 + q4) -
4.0*dotq3*cos(q3 - q5) + 4.0*dotq5*cos(q3 - q5) -
5.0*dotq3*cos(q3 - q4 - q5) + 4.0*dotq3*cos(q3 + q5) +
4.0*dotq5*cos(q3 + q5) - 0.333333*dotq2*cos(q4 + q5) -
5.0*dotq3*cos(q4 + q5) + 2.5*dotq4*cos(q4 + q5) +
2.5*dotq5*cos(q4 + q5) + 5.0*dotq3*cos(q3 + q4 + q5) +
2.5*dotq4*cos(q3 + q4 + q5) + 2.5*dotq5*cos(q3 + q4 + q5) -
20.0*dotq3*sin(q3) - 25.0*dotq3*sin(q3 - q4) +
1.66667*dotq2*sin(q4) + 25.0*dotq3*sin(q4) -
12.5*dotq4*sin(q4) - 25.0*dotq3*sin(q3 + q4) -
12.5*dotq4*sin(q3 + q4) + 2.0*dotq3*sin(q3 - q4 - q5) +
0.333333*dotq1*sin(q4 + q5) - 1.0*dotq3*sin(q4 + q5) +
1.0*dotq4*sin(q4 + q5) + 1.0*dotq5*sin(q4 + q5) +
1.0*dotq3*sin(q3 + q4 + q5) + 0.5*dotq4*sin(q3 + q4 + q5) +
0.5*dotq5*sin(q3 + q4 + q5)) -
1/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))
*225.0*(1.0*dotq3*cos(q4) + (-2.0*dotq3 - 1.0*dotq4)*cos(q3 + q4) +
0.2*dotq3*sin(q4 + q5) - 0.4*dotq3*sin(q3 + q4 + q5) -
0.2*dotq4*sin(q3 + q4 + q5) -
0.2*dotq5*sin(q3 + q4 + q5))*(cos(
q3 + q4 + q5)*(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) + (0.25 +
0.5*cos(q3) - 1.0*cos(q4 + q5) + 1.25*sin(q3) +
1.0*sin(q4))*sin(q3 + q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(372.813 + 450.0*cos(q3) +
562.5*cos(q4) + 562.5*cos(q3 + q4) - 45.0*cos(q4 + q5) -
22.5*cos(q3 + q4 + q5) + 225.0*sin(q4) + 112.5*sin(q3 + q4) -
90.0*sin(q3 - q5) + 90.0*sin(q3 + q5) + 112.5*sin(q4 + q5) +
112.5*sin(q3 + q4 + q5))*((-1.0*dotq4 - 0.5*dotq5)*cos(
q3 + q5) + (-2.5*dotq4 - 2.5*dotq5 +
1.0*dotq4*cos(q3 + q4))*cos(q3 + q4 + q5) -
0.5*dotq5*cos(q3 + 2*q4 + q5) + 1.0*dotq4*sin(q3) +
1.0*dotq5*sin(q3) + 0.5*dotq4*sin(2*(q3 + q4 + q5)) +
0.5*dotq5*sin(2*(q3 + q4 + q5))) +
1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 3)*(3.0*cos(q3 + q4) -
4.0*cos(q3 - q5) + 4.0*cos(q3 + q5) + 10.0*cos(q3 + q4 + q5) -
8.0*sin(q3) - 10.0*sin(q3 + q4) +
3.0*sin(q3 + q4 +
q5))*(149.625*(dotq5*((2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5))*(3.0*cos(q3 + q4 + q5) -
4.0*sin(q3 + q5) - 10.0*sin(q3 + q4 + q5)) -
4.0*cos(q4 + q5)*(1.0*cos(q3 + q5) +
2.5*cos(q3 + q4 + q5) - 1.0*sin(q3) +
0.75*sin(q3 + q4 + q5))) +
dotq4*((2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5))*(3.0*cos(q3 + q4 + q5) -
10.0*sin(q3 + q4 + q5)) -
4.0*(1.0*cos(q4 + q5) - 1.0*sin(q4))*(1.0*cos(q3 + q5) +
2.5*cos(q3 + q4 + q5) - 1.0*sin(q3) +
0.75*sin(q3 + q4 + q5))) +
4.0*(1.0*cos(q3) - 0.75*cos(q3 + q4 + q5) + 1.0*sin(q3 + q5) +
2.5*sin(q3 + q4 + q5))*(1.0*dotq4*cos(
q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(q3 + q4 + q5))) +
149.625*((-1.0*dotq4 - 0.5*dotq5)*cos(
q3 + q5) + (-2.5*dotq4 - 2.5*dotq5 +
1.0*dotq4*cos(q3 + q4))*cos(q3 + q4 + q5) -
0.5*dotq5*cos(q3 + 2*q4 + q5) + 1.0*dotq4*sin(q3) +
1.0*dotq5*sin(q3) + 0.5*dotq4*sin(2*(q3 + q4 + q5)) +
0.5*dotq5*sin(2*(q3 + q4 + q5)))) + (-6*cos(
q3)*(cos(q4 + q5) - sin(q4)) +
6*sin(q3)*(cos(q4) + sin(q4 + q5)) - (
3.0*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) + 2.5*sin(q3) +
2.0*sin(q4))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5))))/(
2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5)))*(-15.0*dotq3*sin(q3 + q4 + q5) -
15.0*dotq4*sin(q3 + q4 + q5) - 15.0*dotq5*sin(q3 + q4 + q5) + (
75.0*(40.5*dotq3*cos(q3) + 1.0*dotq4*cos(q4) -
16.2*dotq3*sin(q3) + 0.2*dotq4*sin(q4 + q5) +
0.2*dotq5*sin(q4 + q5))*sin(q3 + q4 + q5))/(
2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(369.0 -
1215.0*cos(q3) + 15.0*cos(q4 + q5) - 3037.5*sin(q3) -
75.0*sin(q4))*((-1.0*dotq4 - 0.5*dotq5)*cos(
q3 + q5) + (-2.5*dotq4 - 2.5*dotq5 +
1.0*dotq4*cos(q3 + q4))*cos(q3 + q4 + q5) -
0.5*dotq5*cos(q3 + 2*q4 + q5) + 1.0*dotq4*sin(q3) +
1.0*dotq5*sin(q3) + 0.5*dotq4*sin(2*(q3 + q4 + q5)) +
0.5*dotq5*sin(2*(q3 + q4 + q5))) -
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 +
q5), 2)*1215.0*(1.0*dotq5*(1.0*cos(
q3 + q4 + q5)*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) + 2.0*sin(q4))*(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5)) +
2.0*cos(q4 + q5)*(-0.25 - 0.5*cos(q3) + 1.0*cos(q4 + q5) -
1.25*sin(q3) - 1.0*sin(q4))*sin(q3 + q4 + q5) +
2.0*sin(q4 + q5)*(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))*sin(
q3 + q4 + q5) -
2.0*pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*sin(
q3 + q4 + q5)) +
1.0*dotq4*(1.0*cos(
q3 + q4 + q5)*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) + 2.0*sin(q4))*(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5)) +
2.0*(1.0*cos(q4 + q5) - 1.0*sin(q4))*(-0.25 - 0.5*cos(q3) +
1.0*cos(q4 + q5) - 1.25*sin(q3) - 1.0*sin(q4))*sin(
q3 + q4 + q5) +
2.0*(1.0*cos(q4) + 1.0*sin(q4 + q5))*(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5))*sin(q3 + q4 + q5) -
2.0*pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*sin(
q3 + q4 + q5)) +
2.5*(1.0*dotq4*cos(q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(
q3 + q4 + q5))*(0.8*cos(q3) - 0.2*cos(q3 + q4 + q5) -
0.4*cos(2*q3 + q4 + q5) + 0.8*sin(q3 + q5) +
2.0*sin(q3 + q4 + q5) - 1.0*sin(2*q3 + q4 + q5)))) -
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*3.0*(15.0*cos(q3 + q4 + q5) -
75.0*sin(q3 +
q4))*(1.0*dotq5*(1.0*cos(
q3 + q4 + q5)*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) + 2.0*sin(q4))*(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5)) +
2.0*cos(q4 + q5)*(-0.25 - 0.5*cos(q3) + 1.0*cos(q4 + q5) -
1.25*sin(q3) - 1.0*sin(q4))*sin(q3 + q4 + q5) +
2.0*sin(q4 + q5)*(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))*sin(
q3 + q4 + q5) -
2.0*pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*sin(
q3 + q4 + q5)) +
1.0*dotq4*(1.0*cos(
q3 + q4 + q5)*(0.5 + 1.0*cos(q3) - 2.0*cos(q4 + q5) +
2.5*sin(q3) + 2.0*sin(q4))*(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5)) +
2.0*(1.0*cos(q4 + q5) - 1.0*sin(q4))*(-0.25 - 0.5*cos(q3) +
1.0*cos(q4 + q5) - 1.25*sin(q3) - 1.0*sin(q4))*sin(
q3 + q4 + q5) +
2.0*(1.0*cos(q4) + 1.0*sin(q4 + q5))*(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5))*sin(q3 + q4 + q5) -
2.0*pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*sin(
q3 + q4 + q5)) +
2.5*(1.0*dotq4*cos(q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(
q3 + q4 + q5))*(0.8*cos(q3) - 0.2*cos(q3 + q4 + q5) -
0.4*cos(2*q3 + q4 + q5) + 0.8*sin(q3 + q5) +
2.0*sin(q3 + q4 + q5) - 1.0*sin(2*q3 + q4 + q5))) +
1/pow(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5), 2)*(75.0*cos(q3 + q4) +
15.0*sin(q3 + q4 + q5))*(-1.5*dotq5*(1.0*cos(q3 + q5) +
5.0*cos(q3 + q4 + q5) + 1.0*cos(q3 + 2*q4 + q5) -
2.0*sin(q3))*(2.5 - 2.5*cos(q3) + 1.0*sin(q3)) -
3.0*dotq4*(1.0*cos(q3 + q5) + 2.5*cos(q3 + q4 + q5) -
1.0*sin(q3))*(2.5 - 2.5*cos(q3) + 1.0*sin(q3)) +
3.0*(1.0*dotq4*cos(q3 + q4) + (1.0*dotq4 + 1.0*dotq5)*sin(
q3 + q4 + q5))*(2.5*cos(q3 + q4 + q5) -
2.5*cos(2*q3 + q4 + q5) + 1.0*sin(2*q3 + q4 + q5))) +
1/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5))
*7.5*(-1.0 + 1.0*cos(q3) -
0.4*sin(q3))*(sin(q3)*(cos(q4 + q5) - 1.0*sin(q4)) +
cos(q3)*(cos(q4) + sin(q4 + q5)))*(15.0*dotq3*cos(
q3 + q4 + q5) + 15.0*dotq4*cos(q3 + q4 + q5) +
15.0*dotq5*cos(q3 + q4 + q5) + (
1215.0*(1.0*dotq3*cos(
q3) + (-0.0123457*dotq4 - 0.0123457*dotq5)*cos(q4 + q5) +
2.5*dotq3*sin(q3) + 0.0617284*dotq4*sin(q4))*sin(
q3 + q4 + q5))/(2.5 + 1.0*cos(q4) + 1.0*sin(q4 + q5)) +
1/pow(2.5 + 1.0*cos(q4) +
1.0*sin(q4 + q5), 2)*(-847.5 + 3037.5*cos(q3) + 75.0*cos(q4) -
1215.0*sin(q3) +