void
test_constraint(void)
{
int i,j,n,m;
static Matrix Jbig;
static Matrix dJbigdt;
static Vector dsbigdt;
static Matrix JbigMinvJbigt;
static Matrix JbigMinvJbigtinv;
static Matrix Minv;
static Matrix MinvJbigt;
static Matrix Jbigt;
static Vector dJbigdtdsbigdt;
static Matrix Jbart;
static Matrix Jbar;
static Vector lv;
static Vector lambda;
static Vector f;
static Matrix R;
static Vector v;
static int firsttime = TRUE;
int debug_print = TRUE;
if (firsttime) {
firsttime = FALSE;
Jbig = my_matrix(1,N_ENDEFFS*6,1,N_DOFS+6);
Jbigt = my_matrix(1,N_DOFS+6,1,N_ENDEFFS*6);
dJbigdt = my_matrix(1,N_ENDEFFS*6,1,N_DOFS+6);
JbigMinvJbigt = my_matrix(1,N_ENDEFFS*6,1,N_ENDEFFS*6);
JbigMinvJbigtinv = my_matrix(1,N_ENDEFFS*6,1,N_ENDEFFS*6);
Minv = my_matrix(1,N_DOFS+6,1,N_DOFS+6);
MinvJbigt = my_matrix(1,N_DOFS+6,1,N_ENDEFFS*6);
dsbigdt = my_vector(1,N_DOFS+6);
dJbigdtdsbigdt = my_vector(1,N_ENDEFFS*6);
Jbar = my_matrix(1,N_DOFS+6,1,N_ENDEFFS*6);
Jbart = my_matrix(1,N_ENDEFFS*6,1,N_DOFS+6);
lv = my_vector(1,N_ENDEFFS*6);
lambda = my_vector(1,N_ENDEFFS*6);
f = my_vector(1,N_DOFS+6);
R = my_matrix(1,N_CART,1,N_CART);
v = my_vector(1,N_CART);
// the base part of Jbig is just the identity matrix for both constraints
for (i=1; i<=6; ++i)
Jbig[i][N_DOFS+i] = 1.0;
for (i=1; i<=6; ++i)
Jbig[i+6][N_DOFS+i] = 1.0;
}
// build the Jacobian including the base -- just copy J into Jbig
mat_equal_size(J,N_ENDEFFS*6,N_DOFS,Jbig);
mat_trans(Jbig,Jbigt);
// build the Jacobian derivative
mat_equal_size(dJdt,N_ENDEFFS*6,N_DOFS,dJbigdt);
// build the augmented state derivate vector
for (i=1; i<=N_DOFS; ++i)
dsbigdt[i] = joint_state[i].thd;
for (i=1; i<=N_CART; ++i)
dsbigdt[N_DOFS+i] = base_state.xd[i];
for (i=1; i<=N_CART; ++i)
dsbigdt[N_DOFS+N_CART+i] = base_orient.ad[i];
// compute J-bar transpose
my_inv_ludcmp(rbdInertiaMatrix,N_DOFS+6, Minv);
mat_mult(Minv,Jbigt,MinvJbigt);
mat_mult(Jbig,MinvJbigt,JbigMinvJbigt);
my_inv_ludcmp(JbigMinvJbigt,N_ENDEFFS*6,JbigMinvJbigtinv);
mat_mult(MinvJbigt,JbigMinvJbigtinv,Jbar);
mat_trans(Jbar,Jbart);
// compute C+G-u
for (i=1; i<=N_DOFS; ++i)
f[i] = -joint_state[i].u;
for (i=1; i<=6; ++i)
f[N_DOFS+i] = 0.0;
vec_add(f,rbdCplusGVector,f);
// compute first part of lambda
mat_vec_mult(Jbart,f,lambda);
// compute second part of lambda
mat_vec_mult(dJbigdt,dsbigdt,dJbigdtdsbigdt);
mat_vec_mult(JbigMinvJbigtinv,dJbigdtdsbigdt,lv);
// compute final lambda
vec_sub(lambda,lv,lambda);
// ----------------------------------------------------------------------
// express lambda in the same coordinate at the foot sensors
/* rotation matrix from world to L_AAA coordinates:
we can borrow this matrix from the toes, which have the same
rotation, but just a different offset vector, which is not
needed here */
mat_trans_size(Alink[L_IN_HEEL],N_CART,N_CART,R);
// transform forces
for (i=1; i<=N_CART; ++i)
v[i] = lambda[N_CART*2+i];
mat_vec_mult(R,v,v);
if (debug_print) {
printf("LEFT Force: lx=% 7.5f sx=% 7.5f\n",v[1],misc_sim_sensor[L_CFx]);
printf("LEFT Force: ly=% 7.5f sy=% 7.5f\n",v[2],misc_sim_sensor[L_CFy]);
printf("LEFT Force: lz=% 7.5f sz=% 7.5f\n",v[3],misc_sim_sensor[L_CFz]);
}
misc_sensor[L_CFx] = v[1];
misc_sensor[L_CFy] = v[2];
misc_sensor[L_CFz] = v[3];
// transform torques
for (i=1; i<=N_CART; ++i)
v[i] = lambda[N_CART*2+N_CART+i];
mat_vec_mult(R,v,v);
if (debug_print) {
printf("LEFT Torque: lx=% 7.5f sx=% 7.5f\n",v[1],misc_sim_sensor[L_CTa]);
printf("LEFT Torque: ly=% 7.5f sy=% 7.5f\n",v[2],misc_sim_sensor[L_CTb]);
printf("LEFT Torque: lz=% 7.5f sz=% 7.5f\n",v[3],misc_sim_sensor[L_CTg]);
}
misc_sensor[L_CTa] = v[1];
misc_sensor[L_CTb] = v[2];
misc_sensor[L_CTg] = v[3];
/* rotation matrix from world to R_AAA coordinates :
we can borrow this matrix from the toes, which have the same
rotation, but just a different offset vector, which is not
needed here */
mat_trans_size(Alink[R_IN_HEEL],N_CART,N_CART,R);
// transform forces
for (i=1; i<=N_CART; ++i)
v[i] = lambda[i];
mat_vec_mult(R,v,v);
if (debug_print) {
printf("RIGHT Force: lx=% 7.5f sx=% 7.5f\n",v[1],misc_sim_sensor[R_CFx]);
printf("RIGHT Force: ly=% 7.5f sy=% 7.5f\n",v[2],misc_sim_sensor[R_CFy]);
printf("RIGHT Force: lz=% 7.5f sz=% 7.5f\n",v[3],misc_sim_sensor[R_CFz]);
}
misc_sensor[R_CFx] = v[1];
misc_sensor[R_CFy] = v[2];
misc_sensor[R_CFz] = v[3];
// transform torques
for (i=1; i<=N_CART; ++i)
v[i] = lambda[N_CART+i];
mat_vec_mult(R,v,v);
if (debug_print) {
printf("RIGHT Torque: lx=% 7.5f sx=% 7.5f\n",v[1],misc_sim_sensor[R_CTa]);
printf("RIGHT Torque: ly=% 7.5f sy=% 7.5f\n",v[2],misc_sim_sensor[R_CTb]);
printf("RIGHT Torque: lz=% 7.5f sz=% 7.5f\n",v[3],misc_sim_sensor[R_CTg]);
}
misc_sensor[R_CTa] = v[1];
misc_sensor[R_CTb] = v[2];
misc_sensor[R_CTg] = v[3];
if (debug_print)
getchar();
}
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];
}
}
}
