Introduces a new "strain" equality mode (flex_edgeequality = 3) for flexcomps with trilinear interpolation. This mode enforces constraints on the three invariants of the Green-Lagrange strain tensor at 8 Gauss quadrature points within each flex element, resulting in 24 equality constraints per flexcomp.
Also fixes a bug when attaching a flex with constraints. PiperOrigin-RevId: 881349765 Change-Id: I8e6df8239488bfdc87d7e5b473568975e38c737e
This commit is contained in:
Alessio Quaglino
committed by
Copybara-Service
Copybara-Service
parent
fe6c81ed93
commit
713b5524bc
@@ -47,6 +47,26 @@
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//-------------------------- utility functions -----------------------------------------------------
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// basis functions for flex strain constraints
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static void basis(int order, int i, mjtNum p, mjtNum* phi, mjtNum* dphi) {
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if (order == 1) {
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*phi = (i == 0 ? 1 - p : p);
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*dphi = (i == 0 ? -1 : 1);
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} else {
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if (i == 0) {
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*phi = 2 * p * p - 3 * p + 1;
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*dphi = 4 * p - 3;
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} else if (i == 1) {
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*phi = 4 * (p - p * p);
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*dphi = 4 * (1 - 2 * p);
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} else {
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*phi = 2 * p * p - p;
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*dphi = 4 * p - 1;
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}
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}
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}
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// allocate efc arrays on arena, return 1 on success, 0 on failure
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static int arenaAllocEfc(const mjModel* m, mjData* d) {
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#undef MJ_M
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@@ -612,36 +632,336 @@ void mj_instantiateEquality(const mjModel* m, mjData* d) {
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size = 1;
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break;
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case mjEQ_FLEX:
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flex_edgeadr = m->flex_edgeadr[id[0]];
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flex_edgenum = m->flex_edgenum[id[0]];
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// add one constraint per non-rigid edge
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for (int e=flex_edgeadr; e < flex_edgeadr+flex_edgenum; e++) {
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// skip rigid
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if (m->flexedge_rigid[e]) {
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continue;
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}
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case mjEQ_FLEXSTRAIN: {
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// strain constraint mode: add 24 constraints (3 invariants at 8 Gauss points)
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int f = id[0];
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int nodenum = m->flex_nodenum[f];
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int* bodyid = m->flex_nodebodyid + m->flex_nodeadr[f];
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int order = m->flex_interp[f];
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// position error
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cpos[0] = d->flexedge_length[e] - m->flexedge_length0[e];
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// skip if not interpolated (order == 0 or no nodes)
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if (!order || !nodenum) {
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break;
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}
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// add constraint: sparse or dense
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if (issparse) {
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mj_addConstraint(m, d, d->flexedge_J+m->flexedge_J_rowadr[e], cpos, 0, 0,
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1, mjCNSTR_EQUALITY, i,
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m->flexedge_J_rownnz[e],
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m->flexedge_J_colind+m->flexedge_J_rowadr[e]);
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// allocate stack for node positions and Jacobians
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mj_markStack(d);
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mjtNum* xpos = mjSTACKALLOC(d, 3*nodenum, mjtNum);
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mjtNum* node_jac = mjSTACKALLOC(d, 3*nodenum*nv, mjtNum);
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int* chain_col = mjSTACKALLOC(d, nv, int);
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mjtNum* strain_jac = mjSTACKALLOC(d, nv, mjtNum);
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// compute global node positions from body states
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// Green-Lagrange strain E = ½(F'F - I) is rotationally invariant,
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// so we don't need corotational decomposition - use global positions directly
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int nstart = m->flex_nodeadr[f];
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for (int n = 0; n < nodenum; n++) {
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if (m->flex_centered[f]) {
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mju_copy3(xpos + 3*n, d->xpos + 3*bodyid[n]);
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} else {
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mju_zero(jac[0], nv); // reuse first row of jac[0]
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int rowadr = m->flexedge_J_rowadr[e];
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int rownnz = m->flexedge_J_rownnz[e];
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for (int k=0; k<rownnz; k++) {
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jac[0][m->flexedge_J_colind[rowadr+k]] = d->flexedge_J[rowadr+k];
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}
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mj_addConstraint(m, d, jac[0], cpos, 0, 0, 1, mjCNSTR_EQUALITY, i, 0, NULL);
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mju_mulMatVec3(xpos + 3*n, d->xmat + 9*bodyid[n], m->flex_node + 3*(n + nstart));
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mju_addTo3(xpos + 3*n, d->xpos + 3*bodyid[n]);
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}
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}
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// compute node Jacobians in global frame (3*nodenum rows x nv cols)
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mjtNum* blk_jac = mjSTACKALLOC(d, 3*nv, mjtNum);
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mju_zero(node_jac, 3*nodenum*nv);
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for (int n = 0; n < nodenum; n++) {
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int chain_nnz = mj_bodyChain(m, bodyid[n], chain_col);
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mju_zero(blk_jac, 3*nv);
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mj_jacSparse(m, d, blk_jac, NULL, xpos + 3*n, bodyid[n], chain_nnz, chain_col);
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// expand sparse Jacobian to dense row format
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for (int r = 0; r < 3; r++) {
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for (int k = 0; k < chain_nnz; k++) {
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node_jac[(3*n + r)*nv + chain_col[k]] = blk_jac[r*chain_nnz + k];
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}
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}
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}
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// compute combined chain for all nodes (for sparse mode)
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int* combined_chain = mjSTACKALLOC(d, nv, int);
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int combined_nnz = 0;
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if (issparse) {
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// mark which DOFs are used by any node body
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int* dof_used = mjSTACKALLOC(d, nv, int);
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mju_zeroInt(dof_used, nv);
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for (int n = 0; n < nodenum; n++) {
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int temp_chain[200]; // max DOFs per body
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int temp_nnz = mj_bodyChain(m, bodyid[n], temp_chain);
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for (int k = 0; k < temp_nnz; k++) {
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dof_used[temp_chain[k]] = 1;
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}
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}
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// build combined chain from marked DOFs
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for (int q = 0; q < nv; q++) {
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if (dof_used[q]) {
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combined_chain[combined_nnz++] = q;
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}
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}
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}
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// Gauss-Legendre quadrature points in [0,1]^3
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// order=1: 2x2x2=8 points, order=2: 3x3x3=27 points
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int nquad = order + 1; // quadrature order per axis
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int ngauss = nquad * nquad * nquad; // total Gauss points
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// 1D Gauss-Legendre points and weights on [0,1]
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mjtNum gp1d[3]; // max 3 points for order=2
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if (nquad == 2) {
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gp1d[0] = 0.5 - 0.5/mju_sqrt(3.0); // ~ 0.211
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gp1d[1] = 0.5 + 0.5/mju_sqrt(3.0); // ~ 0.789
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} else { // nquad == 3
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gp1d[0] = 0.5 - 0.5*mju_sqrt(0.6); // ~ 0.113
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gp1d[1] = 0.5; // 0.5
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gp1d[2] = 0.5 + 0.5*mju_sqrt(0.6); // ~ 0.887
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}
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// build 3D Gauss points array (max 27 points)
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mjtNum gauss[27][3];
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for (int gi = 0; gi < nquad; gi++) {
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for (int gj = 0; gj < nquad; gj++) {
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for (int gk = 0; gk < nquad; gk++) {
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int idx = gi*nquad*nquad + gj*nquad + gk;
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gauss[idx][0] = gp1d[gi];
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gauss[idx][1] = gp1d[gj];
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gauss[idx][2] = gp1d[gk];
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}
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}
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}
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// loop over Gauss points
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// get reference positions from m->flex_node0 (Cartesian positions at qpos0)
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mjtNum* refpos = mjSTACKALLOC(d, 3*nodenum, mjtNum);
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for (int n = 0; n < nodenum; n++) {
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mju_copy3(refpos + 3*n, m->flex_node0 + 3*(n + nstart));
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}
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for (int g = 0; g < ngauss; g++) {
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mjtNum* p = gauss[g];
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// compute current position gradient dxcur/dxi
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mjtNum Fcur[9];
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mju_defGradient(Fcur, p, xpos, order);
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// compute reference position gradient dxref/dxi
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mjtNum Fref[9];
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mju_defGradient(Fref, p, refpos, order);
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// compute true deformation gradient F = Fcur * inv(Fref)
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// F maps from reference to current configuration
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mjtNum Fref_inv[9];
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mju_transpose(Fref_inv, Fref, 3, 3); // start with transpose for cofactor
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mjtNum det = Fref[0]*(Fref[4]*Fref[8] - Fref[5]*Fref[7]) -
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Fref[1]*(Fref[3]*Fref[8] - Fref[5]*Fref[6]) +
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Fref[2]*(Fref[3]*Fref[7] - Fref[4]*Fref[6]);
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// compute adjugate (cofactor transposed)
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Fref_inv[0] = (Fref[4]*Fref[8] - Fref[5]*Fref[7]) / det;
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Fref_inv[1] = -(Fref[1]*Fref[8] - Fref[2]*Fref[7]) / det;
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Fref_inv[2] = (Fref[1]*Fref[5] - Fref[2]*Fref[4]) / det;
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Fref_inv[3] = -(Fref[3]*Fref[8] - Fref[5]*Fref[6]) / det;
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Fref_inv[4] = (Fref[0]*Fref[8] - Fref[2]*Fref[6]) / det;
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Fref_inv[5] = -(Fref[0]*Fref[5] - Fref[2]*Fref[3]) / det;
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Fref_inv[6] = (Fref[3]*Fref[7] - Fref[4]*Fref[6]) / det;
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Fref_inv[7] = -(Fref[0]*Fref[7] - Fref[1]*Fref[6]) / det;
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Fref_inv[8] = (Fref[0]*Fref[4] - Fref[1]*Fref[3]) / det;
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// F = Fcur * Fref_inv
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mjtNum F[9];
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mju_mulMatMat(F, Fcur, Fref_inv, 3, 3, 3);
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// compute C = F'*F (right Cauchy-Green tensor)
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mjtNum C[9];
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mju_mulMatTMat3(C, F, F);
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// compute Green-Lagrange strain E = 0.5*(C - I)
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mjtNum E[9];
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for (int j = 0; j < 9; j++) {
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E[j] = 0.5 * C[j];
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}
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E[0] -= 0.5;
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E[4] -= 0.5;
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E[8] -= 0.5;
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// compute 3 invariants of E
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// I1 = tr(E) = E[0] + E[4] + E[8]
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mjtNum I1 = E[0] + E[4] + E[8];
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// I2 = 0.5*(tr(E)^2 - tr(E^2))
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mjtNum trE2 = E[0]*E[0] + E[1]*E[3] + E[2]*E[6] +
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E[3]*E[1] + E[4]*E[4] + E[5]*E[7] +
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E[6]*E[2] + E[7]*E[5] + E[8]*E[8];
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mjtNum I2 = 0.5 * (I1*I1 - trE2);
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// I3 = det(E)
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mjtNum I3 = E[0]*(E[4]*E[8] - E[5]*E[7]) -
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E[1]*(E[3]*E[8] - E[5]*E[6]) +
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E[2]*(E[3]*E[7] - E[4]*E[6]);
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// compute shape function gradients at this Gauss point
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// grad[n][k] = d(basis_n)/d(p_k), for n in [0, nodenum), k in [0,3)
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// indexing matches mju_defGradient: idx = i*(order+1)^2 + j*(order+1) + k
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mjtNum grad[27][3]; // max 27 nodes for order=2
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int npoint = (order + 1) * (order + 1) * (order + 1);
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for (int n = 0; n < npoint; n++) {
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int stride = order + 1;
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int ix = n / (stride * stride);
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int iy = (n / stride) % stride;
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int iz = n % stride;
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mjtNum phi_x, phi_y, phi_z, dphi_x, dphi_y, dphi_z;
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basis(order, ix, p[0], &phi_x, &dphi_x);
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basis(order, iy, p[1], &phi_y, &dphi_y);
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basis(order, iz, p[2], &phi_z, &dphi_z);
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grad[n][0] = dphi_x * phi_y * phi_z;
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grad[n][1] = phi_x * dphi_y * phi_z;
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grad[n][2] = phi_x * phi_y * dphi_z;
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}
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// compute Jacobian for each invariant
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mjtNum invariants[3] = {I1, I2, I3};
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for (int inv = 0; inv < 3; inv++) {
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cpos[0] = invariants[inv];
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// compute dI/dE (3x3 symmetric, stored as 9)
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mjtNum dIdE[9];
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if (inv == 0) {
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// dI1/dE = I (identity)
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mju_zero(dIdE, 9);
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dIdE[0] = dIdE[4] = dIdE[8] = 1.0;
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} else if (inv == 1) {
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// dI2/dE = tr(E)*I - E
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mju_zero(dIdE, 9);
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dIdE[0] = I1 - E[0];
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dIdE[4] = I1 - E[4];
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dIdE[8] = I1 - E[8];
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dIdE[1] = -E[1]; dIdE[3] = -E[3];
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dIdE[2] = -E[2]; dIdE[6] = -E[6];
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dIdE[5] = -E[5]; dIdE[7] = -E[7];
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} else {
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// dI3/dE = cofactor(E) = det(E) * E^{-T} for invertible E
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// For small strain, use adjugate directly
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dIdE[0] = E[4]*E[8] - E[5]*E[7];
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dIdE[1] = -(E[1]*E[8] - E[2]*E[7]);
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dIdE[2] = E[1]*E[5] - E[2]*E[4];
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dIdE[3] = -(E[3]*E[8] - E[5]*E[6]);
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dIdE[4] = E[0]*E[8] - E[2]*E[6];
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dIdE[5] = -(E[0]*E[5] - E[2]*E[3]);
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dIdE[6] = E[3]*E[7] - E[4]*E[6];
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dIdE[7] = -(E[0]*E[7] - E[1]*E[6]);
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dIdE[8] = E[0]*E[4] - E[1]*E[3];
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}
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// dI/dx_n = sum over i,j: dI/dE_ij * dE_ij/dx_n
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// where dE_ij/dx_n = 0.5 * d(F'F)_ij/dx_n
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// d(F'F)_ij/dx_n = sum_k (dF_ki/dx_n * F_kj + F_ki * dF_kj/dx_n)
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//
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// With F = Fcur * Fref_inv:
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// dF_ab/d(x_n)_c = sum_k (dFcur_ak/d(x_n)_c) * Fref_inv[kb]
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// = sum_k delta_{ac} * grad[n][k] * Fref_inv[kb]
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// So only row a=c contributes
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// compute dI/dx for all nodes (3*nodenum values)
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mjtNum* dIdx = mjSTACKALLOC(d, 3*nodenum, mjtNum);
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mju_zero(dIdx, 3*nodenum);
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for (int n = 0; n < nodenum; n++) {
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for (int c = 0; c < 3; c++) { // component of x_n
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mjtNum dI = 0;
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for (int ij = 0; ij < 9; ij++) {
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int ii = ij / 3; // row of E/C
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int jj = ij % 3; // col of E/C
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// dF_ab/d(x_n)_c = sum_k grad[n][k] * Fref_inv[kb] (only for a=c)
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// dC_ij/d(x_n)_c = dF_ci * F_cj + F_ci * dF_cj
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// = (sum_k grad[n][k]*Fref_inv[ki]) * F_cj
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// + F_ci * (sum_k grad[n][k]*Fref_inv[kj])
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// compute dF_ci = sum_k grad[n][k] * Fref_inv[ki]
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mjtNum dF_ci = 0;
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for (int k = 0; k < 3; k++) {
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dF_ci += grad[n][k] * Fref_inv[k*3 + ii];
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}
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// compute dF_cj = sum_k grad[n][k] * Fref_inv[kj]
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mjtNum dF_cj = 0;
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for (int k = 0; k < 3; k++) {
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dF_cj += grad[n][k] * Fref_inv[k*3 + jj];
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}
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mjtNum dC_ij = dF_ci * F[c*3 + jj] + F[c*3 + ii] * dF_cj;
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// dE_ij = 0.5 * dC_ij
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dI += dIdE[ij] * 0.5 * dC_ij;
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}
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dIdx[3*n + c] = dI;
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}
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}
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// strain_jac[q] = sum_n sum_c dIdx[3*n+c] * node_jac[(3*n+c)*nv + q]
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mju_zero(strain_jac, nv);
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for (int n = 0; n < nodenum; n++) {
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for (int c = 0; c < 3; c++) {
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int row = 3*n + c;
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for (int q = 0; q < nv; q++) {
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strain_jac[q] += dIdx[row] * node_jac[row*nv + q];
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}
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}
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}
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// add constraint: sparse or dense
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if (issparse) {
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// convert dense strain_jac to sparse format
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mjtNum* sparse_jac = mjSTACKALLOC(d, combined_nnz, mjtNum);
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for (int k = 0; k < combined_nnz; k++) {
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sparse_jac[k] = strain_jac[combined_chain[k]];
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}
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mj_addConstraint(m, d, sparse_jac, cpos, 0, 0, 1, mjCNSTR_EQUALITY, i,
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combined_nnz, combined_chain);
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} else {
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mj_addConstraint(m, d, strain_jac, cpos, 0, 0, 1, mjCNSTR_EQUALITY, i, 0, NULL);
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}
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}
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}
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mj_freeStack(d);
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break;
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}
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case mjEQ_FLEX:
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// edge constraint mode: add one constraint per non-rigid edge
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flex_edgeadr = m->flex_edgeadr[id[0]];
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flex_edgenum = m->flex_edgenum[id[0]];
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for (int e=flex_edgeadr; e < flex_edgeadr+flex_edgenum; e++) {
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// skip rigid
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||||
if (m->flexedge_rigid[e]) {
|
||||
continue;
|
||||
}
|
||||
|
||||
// position error
|
||||
cpos[0] = d->flexedge_length[e] - m->flexedge_length0[e];
|
||||
|
||||
// add constraint: sparse or dense
|
||||
if (issparse) {
|
||||
mj_addConstraint(m, d, d->flexedge_J+m->flexedge_J_rowadr[e], cpos, 0, 0,
|
||||
1, mjCNSTR_EQUALITY, i,
|
||||
m->flexedge_J_rownnz[e],
|
||||
m->flexedge_J_colind+m->flexedge_J_rowadr[e]);
|
||||
} else {
|
||||
mju_zero(jac[0], nv); // reuse first row of jac[0]
|
||||
int rowadr = m->flexedge_J_rowadr[e];
|
||||
int rownnz = m->flexedge_J_rownnz[e];
|
||||
for (int k=0; k<rownnz; k++) {
|
||||
jac[0][m->flexedge_J_colind[rowadr+k]] = d->flexedge_J[rowadr+k];
|
||||
}
|
||||
mj_addConstraint(m, d, jac[0], cpos, 0, 0, 1, mjCNSTR_EQUALITY, i, 0, NULL);
|
||||
}
|
||||
}
|
||||
break;
|
||||
|
||||
case mjEQ_FLEXVERT:
|
||||
// add two constraints per vertex
|
||||
@@ -1186,6 +1506,26 @@ void mj_diagApprox(const mjModel* m, mjData* d) {
|
||||
i--;
|
||||
break;
|
||||
|
||||
case mjEQ_FLEXSTRAIN: {
|
||||
// strain constraints: 24 constraints, use average node inv weight
|
||||
int flex_id = m->eq_obj1id[id];
|
||||
int nodenum = m->flex_nodenum[flex_id];
|
||||
int nstart = m->flex_nodeadr[flex_id];
|
||||
mjtNum avg_invweight = 0;
|
||||
for (int n = 0; n < nodenum; n++) {
|
||||
int bodyid = m->flex_nodebodyid[nstart + n];
|
||||
avg_invweight += m->body_invweight0[2*bodyid];
|
||||
}
|
||||
avg_invweight /= nodenum;
|
||||
for (int c = 0; c < 24; c++) {
|
||||
dA[i++] = avg_invweight;
|
||||
}
|
||||
|
||||
// adjust constraint counter
|
||||
i--;
|
||||
break;
|
||||
}
|
||||
|
||||
default:
|
||||
mjERROR("unknown constraint type %d", d->efc_type[i]); // SHOULD NOT OCCUR
|
||||
}
|
||||
@@ -1788,6 +2128,31 @@ static int mj_ne(const mjModel* m, mjData* d, int* nnz) {
|
||||
}
|
||||
break;
|
||||
|
||||
case mjEQ_FLEXSTRAIN: {
|
||||
// strain constraints: 3 invariants × ngauss Gauss points
|
||||
// skip if not interpolated (order == 0 or no nodes)
|
||||
int order = m->flex_interp[id[0]];
|
||||
int nodenum = m->flex_nodenum[id[0]];
|
||||
if (!order || !nodenum) {
|
||||
break;
|
||||
}
|
||||
int nquad = order + 1; // 2 for order=1, 3 for order=2
|
||||
int ngauss = nquad * nquad * nquad; // 8 or 27
|
||||
size = 3 * ngauss; // 24 or 81
|
||||
|
||||
if (nnz) {
|
||||
// NV is sum of all node Jacobians
|
||||
int nstart = m->flex_nodeadr[id[0]];
|
||||
for (int n = 0; n < nodenum; n++) {
|
||||
int bodyid = m->flex_nodebodyid[nstart + n];
|
||||
NV += mj_bodyChain(m, bodyid, chain);
|
||||
}
|
||||
// each constraint row shares this NV
|
||||
NV = size * NV;
|
||||
}
|
||||
break;
|
||||
}
|
||||
|
||||
default:
|
||||
// might occur in case of the now-removed distance equality constraint
|
||||
mjERROR("unknown constraint type %d", m->eq_type[i]); // SHOULD NOT OCCUR
|
||||
@@ -1795,7 +2160,8 @@ static int mj_ne(const mjModel* m, mjData* d, int* nnz) {
|
||||
|
||||
// accumulate counts; flex NV already accumulated
|
||||
ne += mj_addConstraintCount(m, size, NV);
|
||||
if (m->eq_type[i] == mjEQ_FLEX || m->eq_type[i] == mjEQ_FLEXVERT) {
|
||||
if (m->eq_type[i] == mjEQ_FLEX || m->eq_type[i] == mjEQ_FLEXVERT ||
|
||||
m->eq_type[i] == mjEQ_FLEXSTRAIN) {
|
||||
nnze += NV;
|
||||
} else {
|
||||
nnze += size*NV;
|
||||
|
||||
Reference in New Issue
Block a user