/*!*****************************************************************************
*******************************************************************************
\note compute_kinematics
\date June 99
\remarks
computes kinematic variables
*******************************************************************************
Function Parameters: [in]=input,[out]=output
none
******************************************************************************/
static void
compute_kinematics(void)
{
int i,j,r,o;
static int firsttime = TRUE;
static SL_DJstate *temp;
static Matrix last_J;
static Matrix last_Jbase;
if (firsttime) {
temp=(SL_DJstate *)my_calloc((unsigned long)(n_dofs+1),sizeof(SL_DJstate),MY_STOP);
last_J = my_matrix(1,6*n_endeffs,1,n_dofs);
last_Jbase = my_matrix(1,6*n_endeffs,1,2*N_CART);
}
/* compute the desired link positions */
linkInformationDes(joint_des_state,&base_state,&base_orient,endeff,
joint_cog_mpos_des,joint_axis_pos_des,joint_origin_pos_des,
link_pos_des,Alink_des,Adof_des);
/* the desired endeffector information */
for (i=1; i<=N_CART; ++i) {
for (j=1; j<=n_endeffs; ++j) {
cart_des_state[j].x[i] = link_pos_des[link2endeffmap[j]][i];
}
}
/* the desired quaternian of the endeffector */
for (j=1; j<=n_endeffs; ++j) {
linkQuat(Alink_des[link2endeffmap[j]],&(cart_des_orient[j]));
}
/* addititional link information */
linkInformation(joint_state,&base_state,&base_orient,endeff,
joint_cog_mpos,joint_axis_pos,joint_origin_pos,
link_pos,Alink,Adof);
/* create the endeffector information */
for (i=1; i<=N_CART; ++i) {
for (j=1; j<=n_endeffs; ++j) {
cart_state[j].x[i] = link_pos[link2endeffmap[j]][i];
}
}
/* the quaternian of the endeffector */
for (j=1; j<=n_endeffs; ++j) {
linkQuat(Alink[link2endeffmap[j]],&(cart_orient[j]));
}
/* the COG position */
compute_cog();
/* the jacobian */
jacobian(link_pos,joint_origin_pos,joint_axis_pos,J);
baseJacobian(link_pos,joint_origin_pos,joint_axis_pos,Jbase);
jacobian(link_pos_des,joint_origin_pos_des,joint_axis_pos_des,Jdes);
baseJacobian(link_pos_des,joint_origin_pos_des,joint_axis_pos_des,Jbasedes);
/* numerical time derivative of Jacobian */
if (!firsttime) {
mat_sub(J,last_J,dJdt);
mat_mult_scalar(dJdt,(double)ros_servo_rate,dJdt);
mat_sub(Jbase,last_Jbase,dJbasedt);
mat_mult_scalar(dJbasedt,(double)ros_servo_rate,dJbasedt);
}
mat_equal(J,last_J);
mat_equal(Jbase,last_Jbase);
/* compute the cartesian velocities and accelerations */
for (j=1; j<=n_endeffs; ++j) {
for (i=1; i<=N_CART; ++i) {
cart_state[j].xd[i] = 0.0;
cart_state[j].xdd[i] = 0.0;
cart_orient[j].ad[i] = 0.0;
cart_orient[j].add[i] = 0.0;
cart_des_state[j].xd[i] = 0.0;
cart_des_orient[j].ad[i] = 0.0;
/* contributations from the joints */
for (r=1; r<=n_dofs; ++r) {
cart_state[j].xd[i] += J[(j-1)*6+i][r] * joint_state[r].thd;
cart_orient[j].ad[i] += J[(j-1)*6+i+3][r] * joint_state[r].thd;
cart_des_state[j].xd[i] += Jdes[(j-1)*6+i][r] *joint_des_state[r].thd;
cart_des_orient[j].ad[i]+= Jdes[(j-1)*6+i+3][r] * joint_des_state[r].thd;
cart_state[j].xdd[i] += J[(j-1)*6+i][r] * joint_state[r].thdd +
dJdt[(j-1)*6+i][r] * joint_state[r].thd;
cart_orient[j].add[i] += J[(j-1)*6+i+3][r] * joint_state[r].thdd +
dJdt[(j-1)*6+i+3][r] * joint_state[r].thd;
}
/* contributations from the base */
for (r=1; r<=N_CART; ++r) {
cart_state[j].xd[i] += Jbase[(j-1)*6+i][r] * base_state.xd[r];
cart_orient[j].ad[i] += Jbase[(j-1)*6+i+3][r] * base_state.xd[r];
cart_state[j].xd[i] += Jbase[(j-1)*6+i][3+r] * base_orient.ad[r];
cart_orient[j].ad[i] += Jbase[(j-1)*6+i+3][3+r] * base_orient.ad[r];
cart_des_state[j].xd[i] += Jbasedes[(j-1)*6+i][r] * base_state.xd[r];
cart_des_orient[j].ad[i] += Jbasedes[(j-1)*6+i+3][r] * base_state.xd[r];
cart_des_state[j].xd[i] += Jbasedes[(j-1)*6+i][3+r] * base_orient.ad[r];
cart_des_orient[j].ad[i] += Jbasedes[(j-1)*6+i+3][3+r] * base_orient.ad[r];
cart_state[j].xdd[i] += Jbase[(j-1)*6+i][r] * base_state.xdd[r] +
dJbasedt[(j-1)*6+i][r] * base_state.xd[r];
cart_orient[j].add[i] += Jbase[(j-1)*6+i+3][r] * base_state.xdd[r] +
dJbasedt[(j-1)*6+i+3][r] * base_state.xd[r];
cart_state[j].xdd[i] += Jbase[(j-1)*6+i][3+r] * base_orient.add[r] +
dJbasedt[(j-1)*6+i][3+r] * base_orient.ad[r];
cart_orient[j].add[i] += Jbase[(j-1)*6+i+3][3+r] * base_orient.add[r] +
dJbasedt[(j-1)*6+i+3][3+r] * base_orient.ad[r];
}
}
/* compute quaternion derivatives */
quatDerivatives(&(cart_orient[j]));
quatDerivatives(&(cart_des_orient[j]));
for (r=1; r<=N_QUAT; ++r)
cart_des_orient[j].qdd[r] = 0.0; // we don't have dJdes_dt so far
}
/* reset first time flag */
firsttime = FALSE;
}
void expm(Matrix A, Matrix B, double h) {
static int firsttime = TRUE;
static Matrix M;
static Matrix M2;
static Matrix M3;
static Matrix D;
static Matrix N;
if (firsttime) {
firsttime = FALSE;
M = my_matrix(1,3*N_DOFS,1,3*N_DOFS);
M2 = my_matrix(1,3*N_DOFS,1,3*N_DOFS);
M3 = my_matrix(1,3*N_DOFS,1,3*N_DOFS);
D = my_matrix(1,3*N_DOFS,1,3*N_DOFS);
N = my_matrix(1,3*N_DOFS,1,3*N_DOFS);
}
int norm = 0;
double c = 0.5;
int q = 6; // uneven p-q order for Pade approx.
int p = 1;
int i,j,k;
// Form the big matrix
mat_mult_scalar(A, h, A);
mat_equal_size(A, 2*N_DOFS, 2*N_DOFS, M);
for (i = 1; i <= 2*N_DOFS; ++i) {
for (j = 1; j <= N_DOFS; ++j) {
M[i][2*N_DOFS + j] = h * B[i][j];
}
}
//print_mat("M is:\n", M);
// scale M by power of 2 so that its norm < 1/2
norm = (int)(log2(inf_norm(M))) + 2;
//printf("Inf norm of M: %f \n", inf_norm(M));
if (norm < 0)
norm = 0;
mat_mult_scalar(M, 1/pow(2,(double)norm), M);
//printf("Norm of M logged, floored and 2 added is: %d\n", norm);
//print_mat("M after scaling is:\n", M);
for (i = 1; i <= 3*N_DOFS; i++) {
for (j = 1; j <= 3*N_DOFS; j++) {
N[i][j] = c * M[i][j];
D[i][j] = -c * M[i][j];
}
N[i][i] = N[i][i] + 1.0;
D[i][i] = D[i][i] + 1.0;
}
// set M2 equal to M
mat_equal(M, M2);
// start pade approximation
for (k = 2; k <= q; k++) {
c = c * (q - k + 1) / (double)(k * (2*q - k + 1));
mat_mult(M,M2,M2);
mat_mult_scalar(M2,c,M3);
mat_add(N,M3,N);
if (p == 1)
mat_add(D,M3,D);
else
mat_sub(D,M3,D);
p = -1 * p;
}
// multiply denominator with nominator i.e. D\E
my_inv_ludcmp(D, 3*N_DOFS, D);
mat_mult(D,N,N);
// undo scaling by repeated squaring
for (k = 1; k <= norm; k++)
mat_mult(N,N,N);
// get the matrices out
// read off the entries
for (i = 1; i <= 2*N_DOFS; i++) {
for (j = 1; j <= 2*N_DOFS; j++) {
A[i][j] = N[i][j];
}
for (j = 1; j <= N_DOFS; j++) {
B[i][j] = N[i][2*N_DOFS + j];
}
}
}
