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Mujoco_WASM/src/engine/engine_collision_sdf.c
T
Alessio Quaglino 4ea778f2d3 Add octree support to MJX API. 
Also, enable the touch sensor to use the octree SDF.

PiperOrigin-RevId: 783313462
Change-Id: I0032c2a7164f4770aa10a3612db3fd70bea954db
2025-07-15 06:44:43 -07:00

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// Copyright 2021 DeepMind Technologies Limited
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "engine/engine_collision_sdf.h"
#include <stdio.h>
#include <mujoco/mjdata.h>
#include <mujoco/mjmodel.h>
#include <mujoco/mjsan.h> // IWYU pragma: keep
#include <mujoco/mjtnum.h>
#include "engine/engine_collision_primitive.h"
#include "engine/engine_io.h"
#include "engine/engine_plugin.h"
#include "engine/engine_sort.h"
#include "engine/engine_util_blas.h"
#include "engine/engine_util_errmem.h"
#include "engine/engine_util_misc.h"
#include "engine/engine_util_spatial.h"
#define MAXSDFFACE 1300
#define MAXMESHPNT 500
//---------------------------- interpolated sdf -------------------------------------------
mjtNum boxProjection(mjtNum point[3], const mjtNum box[6]) {
mjtNum r[3] = {point[0] - box[0], point[1] - box[1], point[2] - box[2]};
mjtNum q[3] = {mju_abs(r[0]) - box[3], mju_abs(r[1]) - box[4],
mju_abs(r[2]) - box[5]};
mjtNum dist_sqr = 0;
mjtNum eps = 1e-6;
// skip the projection if inside
if (q[0] <= 0 && q[1] <= 0 && q[2] <= 0) {
return mju_max(q[0], mju_max(q[1], q[2]));
}
// in-place projection inside the box if outside
if ( q[0] >= 0 ) {
dist_sqr += q[0] * q[0];
point[0] -= r[0] > 0 ? (q[0]+eps) : -(q[0]+eps);
}
if ( q[1] >= 0 ) {
dist_sqr += q[1] * q[1];
point[1] -= r[1] > 0 ? (q[1]+eps) : -(q[1]+eps);
}
if ( q[2] >= 0 ) {
dist_sqr += q[2] * q[2];
point[2] -= r[2] > 0 ? (q[2]+eps) : -(q[2]+eps);
}
return mju_sqrt(dist_sqr);
}
// find the octree leaf containing the point p, return the index of the leaf and
// populate the weights of the interpolated function (if w is not null) and of
// its gradient (if dw is not null) using the vertices as degrees of freedom for
// trilinear interpolation.
static int findOct(mjtNum w[8], mjtNum dw[8][3], const mjtNum* oct_aabb,
const int* oct_child, const mjtNum p[3]) {
int stack = 0;
mjtNum eps = 1e-8;
int niter = 100;
while (niter-- > 0) {
int node = stack;
mjtNum vmin[3], vmax[3];
if (node == -1) { // SHOULD NOT OCCUR
mju_error("Invalid node number");
return -1;
}
for (int j = 0; j < 3; j++) {
vmin[j] = oct_aabb[6*node+j] - oct_aabb[6*node+3+j];
vmax[j] = oct_aabb[6*node+j] + oct_aabb[6*node+3+j];
}
// check if the point is inside the aabb of the octree node
if (p[0] + eps < vmin[0] || p[0] - eps > vmax[0] ||
p[1] + eps < vmin[1] || p[1] - eps > vmax[1] ||
p[2] + eps < vmin[2] || p[2] - eps > vmax[2]) {
continue;
}
mjtNum coord[3] = {(p[0] - vmin[0]) / (vmax[0] - vmin[0]),
(p[1] - vmin[1]) / (vmax[1] - vmin[1]),
(p[2] - vmin[2]) / (vmax[2] - vmin[2])};
// check if the node is a leaf
if (oct_child[8*node+0] == -1 && oct_child[8*node+1] == -1 &&
oct_child[8*node+2] == -1 && oct_child[8*node+3] == -1 &&
oct_child[8*node+4] == -1 && oct_child[8*node+5] == -1 &&
oct_child[8*node+6] == -1 && oct_child[8*node+7] == -1) {
for (int j = 0; j < 8; j++) {
if (w) {
w[j] = (j & 1 ? coord[0] : 1 - coord[0]) *
(j & 2 ? coord[1] : 1 - coord[1]) *
(j & 4 ? coord[2] : 1 - coord[2]);
}
if (dw) {
dw[j][0] = (j & 1 ? 1 : -1) *
(j & 2 ? coord[1] : 1 - coord[1]) *
(j & 4 ? coord[2] : 1 - coord[2]);
dw[j][1] = (j & 1 ? coord[0] : 1 - coord[0]) *
(j & 2 ? 1 : -1) *
(j & 4 ? coord[2] : 1 - coord[2]);
dw[j][2] = (j & 1 ? coord[0] : 1 - coord[0]) *
(j & 2 ? coord[1] : 1 - coord[1]) *
(j & 4 ? 1 : -1);
}
}
return node;
}
// compute which of 8 children to visit next
int x = coord[0] < .5 ? 1 : 0;
int y = coord[1] < .5 ? 1 : 0;
int z = coord[2] < .5 ? 1 : 0;
stack = oct_child[8 * node + 4*z + 2*y + x];
}
mju_error("Node not found"); // SHOULD NOT OCCUR
return -1;
}
// sdf
mjtNum oct_distance(const mjModel* m, const mjtNum p[3], int meshid) {
int octadr = m->mesh_octadr[meshid];
int* oct_child = m->oct_child + 8*octadr;
mjtNum* oct_aabb = m->oct_aabb + 6*octadr;
mjtNum* oct_coeff = m->oct_coeff + 8*octadr;
if (octadr == -1) {
mjERROR("Octree not found in mesh %d", meshid);
return 0;
}
mjtNum w[8];
mjtNum sdf = 0;
mjtNum point[3] = {p[0], p[1], p[2]};
mjtNum boxDist = boxProjection(point, oct_aabb);
if (boxDist > 0) {
return boxDist;
}
int node = findOct(w, NULL, oct_aabb, oct_child, point);
for (int i = 0; i < 8; ++i) {
sdf += w[i] * oct_coeff[8*node + i];
}
return sdf;
}
// gradient of sdf
void oct_gradient(const mjModel* m, mjtNum grad[3], const mjtNum point[3], int meshid) {
mju_zero3(grad);
mjtNum p[3] = {point[0], point[1], point[2]};
int octadr = m->mesh_octadr[meshid];
int* oct_child = m->oct_child + 8*octadr;
mjtNum* oct_aabb = m->oct_aabb + 6*octadr;
mjtNum* oct_coeff = m->oct_coeff + 8*octadr;
if (octadr == -1) {
mjERROR("Octree not found in mesh %d", meshid);
}
// analytic in the interior
if (boxProjection(p, oct_aabb) <= 0) {
mjtNum dw[8][3];
int node = findOct(NULL, dw, oct_aabb, oct_child, p);
for (int i = 0; i < 8; ++i) {
grad[0] += dw[i][0] * oct_coeff[8*node + i];
grad[1] += dw[i][1] * oct_coeff[8*node + i];
grad[2] += dw[i][2] * oct_coeff[8*node + i];
}
return;
}
// finite difference in the exterior
mjtNum eps = 1e-8;
mjtNum dist0 = oct_distance(m, point, meshid);
mjtNum pointX[3] = {point[0]+eps, point[1], point[2]};
mjtNum distX = oct_distance(m, pointX, meshid);
mjtNum pointY[3] = {point[0], point[1]+eps, point[2]};
mjtNum distY = oct_distance(m, pointY, meshid);
mjtNum pointZ[3] = {point[0], point[1], point[2]+eps};
mjtNum distZ = oct_distance(m, pointZ, meshid);
grad[0] = (distX - dist0) / eps;
grad[1] = (distY - dist0) / eps;
grad[2] = (distZ - dist0) / eps;
}
//---------------------------- primitives sdf ---------------------------------------------
static void radialField3d(mjtNum field[3], const mjtNum a[3], const mjtNum x[3],
const mjtNum size[3]) {
field[0] = -size[0] / a[0];
field[1] = -size[1] / a[1];
field[2] = -size[2] / a[2];
mju_normalize3(field);
// flip sign if necessary
if (x[0] < 0) field[0] = -field[0];
if (x[1] < 0) field[1] = -field[1];
if (x[2] < 0) field[2] = -field[2];
}
static mjtNum geomDistance(const mjModel* m, const mjData* d, const mjpPlugin* p,
int i, const mjtNum x[3], mjtGeom type) {
mjtNum a[3], b[3];
const mjtNum* size = m->geom_size+3*i;
// see https://iquilezles.org/articles/distfunctions/
switch (type) {
case mjGEOM_PLANE:
return x[2];
case mjGEOM_SPHERE:
return mju_norm3(x) - size[0];
case mjGEOM_BOX:
// compute shortest distance to box surface if outside, otherwise
// intersect with a unit gradient that linearly rotates from radial to the face normals
a[0] = mju_abs(x[0]) - size[0];
a[1] = mju_abs(x[1]) - size[1];
a[2] = mju_abs(x[2]) - size[2];
if (a[0] >= 0 || a[1] >= 0 || a[2] >= 0) {
b[0] = mju_max(a[0], 0);
b[1] = mju_max(a[1], 0);
b[2] = mju_max(a[2], 0);
return mju_norm3(b) + mju_min(mju_max(a[0], mju_max(a[1], a[2])), 0);
}
radialField3d(b, a, x, size);
mjtNum t[3];
t[0] = -a[0] / mju_abs(b[0]);
t[1] = -a[1] / mju_abs(b[1]);
t[2] = -a[2] / mju_abs(b[2]);
return -mju_min(t[0], mju_min(t[1], t[2])) * mju_norm3(b);
case mjGEOM_CAPSULE:
a[0] = x[0];
a[1] = x[1];
a[2] = x[2] - mju_clip(x[2], -size[1], size[1]);
return mju_norm3(a) - size[0];
case mjGEOM_ELLIPSOID:
a[0] = x[0] / size[0];
a[1] = x[1] / size[1];
a[2] = x[2] / size[2];
b[0] = a[0] / size[0];
b[1] = a[1] / size[1];
b[2] = a[2] / size[2];
mjtNum k0 = mju_norm3(a);
mjtNum k1 = mju_norm3(b);
return k0 * (k0 - 1.0) / k1;
case mjGEOM_CYLINDER:
a[0] = mju_sqrt(x[0]*x[0]+x[1]*x[1]) - size[0];
a[1] = mju_abs(x[2]) - size[1];
b[0] = mju_max(a[0], 0);
b[1] = mju_max(a[1], 0);
return mju_min(mju_max(a[0], a[1]), 0) + mju_norm(b, 2);
case mjGEOM_SDF:
if (p) {
return p->sdf_distance(x, d, i);
} else {
return oct_distance(m, x, i);
}
case mjGEOM_MESH:
return oct_distance(m, x, i);
default:
mjERROR("sdf collisions not available for geom type %d", type);
return 0;
}
}
static void geomGradient(mjtNum gradient[3], const mjModel* m, const mjData* d,
const mjpPlugin* p, int i, const mjtNum x[3],
mjtGeom type) {
mjtNum a[3], b[3], c, e;
const mjtNum* size = m->geom_size+3*i;
// see https://iquilezles.org/articles/distfunctions/
switch (type) {
case mjGEOM_PLANE:
mju_zero3(gradient);
gradient[2] = 1;
break;
case mjGEOM_SPHERE:
mju_copy3(gradient, x);
c = mju_norm3(x);
gradient[0] *= 1. / c;
gradient[1] *= 1. / c;
gradient[2] *= 1. / c;
break;
case mjGEOM_BOX:
mju_zero3(gradient);
a[0] = mju_abs(x[0]) - size[0];
a[1] = mju_abs(x[1]) - size[1];
a[2] = mju_abs(x[2]) - size[2];
int k = a[0] > a[1] ? 0 : 1;
int l = a[2] > a[k] ? 2 : k;
if (a[l] < 0) {
radialField3d(gradient, a, x, size);
} else {
b[0] = mju_max(a[0], 0);
b[1] = mju_max(a[1], 0);
b[2] = mju_max(a[2], 0);
c = mju_norm3(b);
gradient[0] = a[0] > 0 ? b[0] / c * x[0] / mju_abs(x[0]) : 0;
gradient[1] = a[1] > 0 ? b[1] / c * x[1] / mju_abs(x[1]) : 0;
gradient[2] = a[2] > 0 ? b[2] / c * x[2] / mju_abs(x[2]) : 0;
}
break;
case mjGEOM_CAPSULE:
a[0] = x[0];
a[1] = x[1];
a[2] = x[2] - mju_clip(x[2], -size[1], size[1]);
c = mju_norm3(a);
gradient[0] = a[0] / c;
gradient[1] = a[1] / c;
gradient[2] = a[2] / c;
break;
case mjGEOM_ELLIPSOID:
a[0] = x[0] / size[0];
a[1] = x[1] / size[1];
a[2] = x[2] / size[2];
b[0] = a[0] / size[0];
b[1] = a[1] / size[1];
b[2] = a[2] / size[2];
mjtNum k0 = mju_norm3(a);
mjtNum k1 = mju_norm3(b);
mjtNum invK0 = 1. / k0;
mjtNum invK1 = 1. / k1;
mjtNum gk0[3] = {b[0]*invK0, b[1]*invK0, b[2]*invK0};
mjtNum gk1[3] = {b[0]*invK1/(size[0]*size[0]),
b[1]*invK1/(size[1]*size[1]),
b[2]*invK1/(size[2]*size[2])};
mjtNum df_dk0 = (2.*k0 - 1.) * invK1;
mjtNum df_dk1 = k0*(k0 - 1.) * invK1 * invK1;
gradient[0] = gk0[0]*df_dk0 - gk1[0]*df_dk1;
gradient[1] = gk0[1]*df_dk0 - gk1[1]*df_dk1;
gradient[2] = gk0[2]*df_dk0 - gk1[2]*df_dk1;
mju_normalize3(gradient);
break;
case mjGEOM_CYLINDER:
c = mju_sqrt(x[0]*x[0]+x[1]*x[1]);
e = mju_abs(x[2]);
a[0] = c - size[0];
a[1] = e - size[1];
mjtNum grada[3] = {x[0] / mju_max(c, 1. / mjMAXVAL),
x[1] / mju_max(c, 1. / mjMAXVAL),
x[2] / mju_max(e, 1. / mjMAXVAL)};
int j = a[0] > a[1] ? 0 : 1;
if (a[j] < 0) {
gradient[0] = j == 0 ? grada[0] : 0;
gradient[1] = j == 0 ? grada[1] : 0;
gradient[2] = j == 1 ? grada[2] : 0;
} else {
b[0] = mju_max(a[0], 0);
b[1] = mju_max(a[1], 0);
mjtNum bnorm = mju_max(mju_norm(b, 2), 1./mjMAXVAL);
gradient[0] = grada[0] * b[0] / bnorm;
gradient[1] = grada[1] * b[0] / bnorm;
gradient[2] = grada[2] * b[1] / bnorm;
}
break;
case mjGEOM_SDF:
if (p) {
p->sdf_gradient(gradient, x, d, i);
} else {
oct_gradient(m, gradient, x, i);
}
break;
case mjGEOM_MESH:
oct_gradient(m, gradient, x, i);
break;
default:
mjERROR("sdf collisions not available for geom type %d", type);
}
}
//---------------------------- helper functions -------------------------------------------
// signed distance function
mjtNum mjc_distance(const mjModel* m, const mjData* d, const mjSDF* s, const mjtNum x[3]) {
mjtNum y[3];
switch (s->type) {
case mjSDFTYPE_SINGLE:
return geomDistance(m, d, s->plugin[0], s->id[0], x, s->geomtype[0]);
case mjSDFTYPE_INTERSECTION:
mju_mulMatVec3(y, s->relmat, x);
mju_addTo3(y, s->relpos);
return mju_max(geomDistance(m, d, s->plugin[0], s->id[0], x, s->geomtype[0]),
geomDistance(m, d, s->plugin[1], s->id[1], y, s->geomtype[1]));
case mjSDFTYPE_MIDSURFACE:
mju_mulMatVec3(y, s->relmat, x);
mju_addTo3(y, s->relpos);
return geomDistance(m, d, s->plugin[0], s->id[0], x, s->geomtype[0]) -
geomDistance(m, d, s->plugin[1], s->id[1], y, s->geomtype[1]);
case mjSDFTYPE_COLLISION:
mju_mulMatVec3(y, s->relmat, x);
mju_addTo3(y, s->relpos);
mjtNum A = geomDistance(m, d, s->plugin[0], s->id[0], x, s->geomtype[0]);
mjtNum B = geomDistance(m, d, s->plugin[1], s->id[1], y, s->geomtype[1]);
return A + B + mju_abs(mju_max(A, B));
default:
mjERROR("SDF type not available");
return 0;
}
}
// gradient of sdf
void mjc_gradient(const mjModel* m, const mjData* d, const mjSDF* s,
mjtNum gradient[3], const mjtNum x[3]) {
mjtNum y[3];
const mjtNum* point[2] = {x, y};
mjtNum grad1[3], grad2[3];
switch (s->type) {
case mjSDFTYPE_INTERSECTION:
mju_mulMatVec3(y, s->relmat, x);
mju_addTo3(y, s->relpos);
int i = geomDistance(m, d, s->plugin[0], s->id[0], x, s->geomtype[0]) >
geomDistance(m, d, s->plugin[1], s->id[1], y, s->geomtype[1]) ? 0 : 1;
geomGradient(gradient, m, d, s->plugin[i], s->id[i], point[i], s->geomtype[i]);
if (i == 1) {
mju_mulMatTVec3(gradient, s->relmat, gradient);
}
break;
case mjSDFTYPE_MIDSURFACE:
mju_mulMatVec3(y, s->relmat, x);
mju_addTo3(y, s->relpos);
geomGradient(grad1, m, d, s->plugin[0], s->id[0], x, s->geomtype[0]);
mju_normalize3(grad1);
geomGradient(grad2, m, d, s->plugin[1], s->id[1], y, s->geomtype[1]);
mju_mulMatTVec3(grad2, s->relmat, grad2);
mju_normalize3(grad2);
mju_sub3(gradient, grad1, grad2);
mju_normalize3(gradient);
break;
case mjSDFTYPE_COLLISION:
mju_mulMatVec3(y, s->relmat, x);
mju_addTo3(y, s->relpos);
mjtNum A = geomDistance(m, d, s->plugin[0], s->id[0], x, s->geomtype[0]);
mjtNum B = geomDistance(m, d, s->plugin[1], s->id[1], y, s->geomtype[1]);
geomGradient(grad1, m, d, s->plugin[0], s->id[0], x, s->geomtype[0]);
geomGradient(grad2, m, d, s->plugin[1], s->id[1], y, s->geomtype[1]);
mju_mulMatTVec3(grad2, s->relmat, grad2);
gradient[0] = grad1[0] + grad2[0];
gradient[1] = grad1[1] + grad2[1];
gradient[2] = grad1[2] + grad2[2];
mju_addToScl3(gradient, A > B ? grad1 : grad2, mju_max(A, B) > 0 ? 1 : -1);
break;
case mjSDFTYPE_SINGLE:
geomGradient(gradient, m, d, s->plugin[0], s->id[0], point[0], s->geomtype[0]);
break;
default:
mjERROR("SDF type not available");
}
}
// get sdf from geom id
const mjpPlugin* mjc_getSDF(const mjModel* m, int id) {
int instance = m->geom_plugin[id];
const int nslot = mjp_pluginCount();
const int slot = m->plugin[instance];
const mjpPlugin* sdf = mjp_getPluginAtSlotUnsafe(slot, nslot);
if (!sdf) mjERROR("invalid plugin slot: %d", slot);
if (!(sdf->capabilityflags & mjPLUGIN_SDF)) {
mjERROR("Plugin is not a signed distance field at slot %d", slot);
}
return sdf;
}
// map (pos12, mat12) as (xpos2, xmat2)^-1 \circ (xpos1, xmat1)
static void mapPose(const mjtNum xpos1[3], const mjtNum xquat1[4],
const mjtNum xpos2[3], const mjtNum xquat2[4],
mjtNum pos12[3], mjtNum mat12[9]) {
mjtNum negpos[3], negquat[4], quat12[4];
mju_negPose(negpos, negquat, xpos2, xquat2);
mju_mulPose(pos12, quat12, negpos, negquat, xpos1, xquat1);
mju_quat2Mat(mat12, quat12);
}
//---------------------------- narrow phase -----------------------------------------------
// comparison function for contact sorting
static inline int distcmp(int* i, int* j, void* context) {
mjtNum d1 = ((mjtNum*)context)[*i];
mjtNum d2 = ((mjtNum*)context)[*j];
if (d1 < d2) {
return -1;
} else if (d1 == d2) {
return 0;
} else {
return 1;
}
}
// define distSort function for contact sorting
mjSORT(distSort, int, distcmp)
// check if the collision point already exists
static int isknown(const mjtNum* points, const mjtNum x[3], int cnt) {
for (int i = 0; i < cnt; i++) {
if (mju_dist3(x, points + 3*i) < mjMINVAL) {
return 1;
}
}
return 0;
}
// adds candidate point to result
static int addContact(mjtNum* points, mjContact* con, const mjtNum x[3],
const mjtNum pos2[3], const mjtNum quat2[4], mjtNum dist,
int cnt, const mjModel* m, const mjSDF* s, mjData* d) {
// check if there is a collision
if (dist > 0 || isknown(points, x, cnt)) {
return cnt;
} else {
mju_copy3(points+3*cnt, x);
}
// compute normal in local coordinates
mjtNum norm[3], vec[3];
mjc_gradient(m, d, s, norm, x);
mju_scl3(norm, norm, -1);
// construct contact
con[cnt].dist = dist;
mju_rotVecQuat(con[cnt].frame, norm, quat2);
mju_zero3(con[cnt].frame+3);
mju_makeFrame(con[cnt].frame);
mju_scl3(vec, con[cnt].frame, -con[cnt].dist/2);
mju_rotVecQuat(con[cnt].pos, x, quat2);
mju_addTo3(con[cnt].pos, pos2);
mju_addTo3(con[cnt].pos, vec);
return cnt+1;
}
// finds minimum of Frank-Wolfe objective
static mjtNum stepFrankWolfe(mjtNum x[3], const mjtNum* corners, int ncorners,
const mjModel* m, const mjSDF* sdf, mjData* d) {
for (int step=0; step < m->opt.sdf_iterations; step++) {
mjtNum best = 1e10, fun, s[3], grad[3];
// evaluate gradient
mjc_gradient(m, d, sdf, grad, x);
// evaluate all corners
for (int i=0; i < ncorners; i++) {
// compute sdf
fun = mju_dot3(corners + 3*i, grad);
// save argmin
if (fun < best) {
best = fun;
mju_copy3(s, corners + 3*i);
}
}
// update collision point
mju_subFrom3(s, x);
mju_addToScl3(x, s, 2. / (step+2.));
}
// compute distance
return mjc_distance(m, d, sdf, x);
}
// finds minimum using gradient descent
static mjtNum stepGradient(mjtNum x[3], const mjModel* m, const mjSDF* s,
mjData* d, int niter) {
const mjtNum c = .1; // reduction factor for the target decrease in the objective function
const mjtNum rho = .5; // reduction factor for the gradient scaling (alpha)
const mjtNum amin = 1e-4; // minimum value for alpha
mjtNum dist = mjMAXVAL;
for (int step=0; step < niter; step++) {
mjtNum grad[3];
mjtNum alpha = 2.; // initial line search factor scaling the gradient
// the units of the gradient depend on s->type
// evaluate gradient
mjc_gradient(m, d, s, grad, x);
// sanity check
if (isnan(grad[0]) || grad[0] > mjMAXVAL || grad[0] < -mjMAXVAL ||
isnan(grad[1]) || grad[1] > mjMAXVAL || grad[1] < -mjMAXVAL ||
isnan(grad[2]) || grad[2] > mjMAXVAL || grad[2] < -mjMAXVAL) {
return mjMAXVAL;
}
// save current solution
mjtNum x0[] = {x[0], x[1], x[2]};
// evaluate distance
mjtNum dist0 = mjc_distance(m, d, s, x0);
mjtNum wolfe = - c * alpha * mju_dot3(grad, grad);
// backtracking line search
do {
alpha *= rho;
wolfe *= rho;
mju_addScl3(x, x0, grad, -alpha);
dist = mjc_distance(m, d, s, x);
} while (alpha > amin && dist - dist0 > wolfe);
// if no improvement, early stop
if (dist0 < dist) {
return dist;
}
}
// the distance will be used for the contact creation
return dist;
}
//---------------------------- bounding box vs sdf -------------------------------------------------
// stricter triangle collision
static int triangleIntersect(const mjtNum triangle[9], const mjModel* m,
const mjSDF* sdf, mjData* d) {
mjtNum edges[6];
mjtNum normal[3], center[3];
mjtNum v[9], cross[9], p[3];
mjtNum kDistanceScl = 10.;
// triangle normal
mju_sub3(edges+0, triangle+3, triangle);
mju_sub3(edges+3, triangle+6, triangle);
mju_cross(normal, edges, edges+3);
mju_normalize3(normal);
// fourth point
mju_scl3(p, triangle, 1./3.);
mju_addToScl3(p, triangle+3, 1./3.);
mju_addToScl3(p, triangle+6, 1./3.);
mjtNum h = -mjc_distance(m, d, sdf, p)/kDistanceScl;
mju_addToScl3(p, normal, -h);
// circumsphere center
mju_sub3(v+0, triangle+0, p);
mju_sub3(v+3, triangle+3, p);
mju_sub3(v+6, triangle+6, p);
mju_cross(cross+0, v+3, v+6);
mju_cross(cross+3, v+6, v+0);
mju_cross(cross+6, v+0, v+3);
mju_scl3(center, cross, mju_dot3(v, v));
mju_addToScl3(center, cross+3, mju_dot3(v+3, v+3));
mju_addToScl3(center, cross+6, mju_dot3(v+6, v+6));
mju_scl3(center, center, 1./(2.*mju_dot3(v, cross)));
// circumsphere radius
mjtNum r = mju_sqrt(mju_dot3(center, center));
// coordinate change
mju_addTo3(center, p);
return mjc_distance(m, d, sdf, center) < r;
}
// intersect with circumsphere of bounding box
static int boxIntersect(const mjtNum bvh[6], const mjtNum offset[3],
const mjtNum rotation[9], const mjModel* m,
const mjSDF* s, mjData* d) {
mjtNum candidate[3];
mjtNum r = mju_norm3(bvh+3);
mju_mulMatVec3(candidate, rotation, bvh);
mju_addTo3(candidate, offset);
// check if inside the bounding box
return mjc_distance(m, d, s, candidate) < r;
}
//---------------------------- mesh vs sdf broad phase --------------------------------------------
// tree vs sdf binary search
static void collideBVH(const mjModel* m, mjData* d, int g,
const mjtNum offset[3], const mjtNum rotation[9],
int* faces, int* npoints, int* n0,
const mjSDF* sdf) {
const int bvhadr = m->mesh_bvhadr[m->geom_dataid[g]];
const int* faceid = m->bvh_nodeid + bvhadr;
const mjtNum* bvh = m->bvh_aabb + 6*bvhadr;
const int* child = m->bvh_child + 2*bvhadr;
mjtByte* bvh_active = m->vis.global.bvactive ? d->bvh_active + bvhadr : NULL;
mj_markStack(d);
// TODO(quaglino): Store bvh max depths to make this bound tighter.
int max_stack = m->mesh_bvhnum[m->geom_dataid[g]];
struct CollideTreeArgs_ {
int node;
};
typedef struct CollideTreeArgs_ CollideTreeArgs;
CollideTreeArgs* stack = mjSTACKALLOC(d, max_stack, CollideTreeArgs);
int nstack = 0;
stack[nstack].node = 0;
nstack++;
while (nstack) {
(*n0)++;
// pop from stack
nstack--;
int node = stack[nstack].node;
// node1 is a leaf
if (faceid[node] != -1) {
if (boxIntersect(bvh+6*node, offset, rotation, m, sdf, d)) {
faces[*npoints] = faceid[node];
if (++(*npoints) == MAXSDFFACE) {
mju_warning("mjc_MeshSDF: too many bounding volumes, some contacts may be missed");
mj_freeStack(d);
return;
}
if (bvh_active) bvh_active[node] = 1;
}
continue;
}
// if no intersection at intermediate levels, stop
if (!boxIntersect(bvh+6*node, offset, rotation, m, sdf, d)) {
continue;
}
if (bvh_active) bvh_active[node] = 1;
// recursive call
for (int i=0; i < 2; i++) {
if (child[2*node+i] != -1) {
if (nstack >= max_stack) mjERROR("BVH stack depth exceeded.");
stack[nstack].node = child[2*node+i];
nstack++;
}
}
}
mj_freeStack(d);
}
//------------------------------ collision functions -----------------------------------------------
// collision between a height field and a signed distance field
int mjc_HFieldSDF(const mjModel* m, const mjData* d, mjContact* con, int g1, int g2, mjtNum margin) {
mju_warning("HField vs SDF collision not yet supported!");
return 0;
}
// collision between a mesh and a signed distance field
int mjc_MeshSDF(const mjModel* m, const mjData* d, mjContact* con, int g1, int g2, mjtNum margin) {
mjGETINFO;
mjtNum offset[3], rotation[9], corners[9], x[3], depth;
mjtNum points[3*MAXSDFFACE], dist[MAXMESHPNT], candidate[3*MAXMESHPNT];
int vertadr = m->mesh_vertadr[m->geom_dataid[g1]];
int faceadr = m->mesh_faceadr[m->geom_dataid[g1]];
int cnt=0, npoints=0, ncandidate=0, n0=0, faces[MAXSDFFACE]={-1}, index[MAXMESHPNT];
// get sdf plugin
int instance = m->geom_plugin[g2];
const mjpPlugin* sdf_ptr = instance == -1 ? NULL : mjc_getSDF(m, g2);
instance = instance == -1 ? m->geom_dataid[g2] : instance;
mjtGeom geomtype = mjGEOM_SDF;
// copy into data
mjSDF sdf;
sdf.id = &instance;
sdf.type = mjSDFTYPE_SINGLE;
sdf.plugin = &sdf_ptr;
sdf.geomtype = &geomtype;
// compute transformation from g1 to g2
mjtNum sdf_quat[4], quat1[4];
mju_mat2Quat(quat1, mat1);
mju_mat2Quat(sdf_quat, mat2);
mapPose(pos1, quat1, pos2, sdf_quat, offset, rotation);
// binary tree search
collideBVH(m, (mjData*)d, g1, offset, rotation, faces, &npoints, &n0, &sdf);
// Frank-Wolfe algorithm
for (int i=0; i < npoints; i++) {
int face = faceadr + faces[i];
for (int v=0; v < 3; v++) {
mjtNum vec[3] = {
m->mesh_vert[3*(vertadr+m->mesh_face[3*face+v])+0],
m->mesh_vert[3*(vertadr+m->mesh_face[3*face+v])+1],
m->mesh_vert[3*(vertadr+m->mesh_face[3*face+v])+2],
};
// transform local 1 (mesh) to local 2 (sdf)
mju_mulMatVec3(corners+3*v, rotation, vec);
mju_addTo3(corners+3*v, offset);
}
// stricter culling
if (!triangleIntersect(corners, m, &sdf, (mjData*)d)) {
continue;
}
// starting point
x[0] = (corners[0]+corners[3]+corners[6])/3;
x[1] = (corners[1]+corners[4]+corners[7])/3;
x[2] = (corners[2]+corners[5]+corners[8])/3;
// SHOULD NOT OCCUR
if (ncandidate == MAXMESHPNT)mjERROR("too many contact points");
// Frank-Wolfe
depth = stepFrankWolfe(x, corners, 3, m, &sdf, (mjData*)d);
// store candidate if there is penetration
if (depth < 0) {
mju_copy3(candidate + 3*ncandidate, x);
index[ncandidate] = ncandidate;
dist[ncandidate++] = depth;
}
}
// sort contacts using depth
if (ncandidate > 1) {
int buf[MAXMESHPNT];
distSort(index, buf, ncandidate, dist);
}
// add only the first mjMAXCONPAIR pairs
for (int i=0; i < mju_min(ncandidate, mjMAXCONPAIR); i++) {
cnt = addContact(points, con, candidate + 3*index[i], pos2, sdf_quat,
dist[index[i]], cnt, m, &sdf, (mjData*)d);
}
return cnt;
}
// collision between two SDFs
int mjc_SDF(const mjModel* m, const mjData* d, mjContact* con, int g1, int g2, mjtNum margin) {
mjGETINFO;
size1 = m->geom_aabb + 6*g1;
size2 = m->geom_aabb + 6*g2;
int cnt = 0;
mjtNum x[3], y[3], dist, vec1[3], vec2[3];
mjtNum aabb1[6] = {mjMAXVAL, mjMAXVAL, mjMAXVAL, -mjMAXVAL, -mjMAXVAL, -mjMAXVAL};
mjtNum aabb2[6] = {mjMAXVAL, mjMAXVAL, mjMAXVAL, -mjMAXVAL, -mjMAXVAL, -mjMAXVAL};
mjtNum aabb[6] = {mjMAXVAL, mjMAXVAL, mjMAXVAL, -mjMAXVAL, -mjMAXVAL, -mjMAXVAL};
// second geom must be an SDF
if (m->geom_type[g2] != mjGEOM_SDF) {
mjERROR("geom is not an SDF");
}
// compute transformations from/to g1 to/from g2
mjtNum quat1[4], quat2[4];
mjtNum offset21[3], rotation21[9], rotation12[9];
mjtNum offset12[3], offset2[3], rotation2[9];
mju_mat2Quat(quat1, mat1);
mju_mat2Quat(quat2, mat2);
mapPose(pos1, quat1, pos1, quat1, offset2, rotation2);
mapPose(pos2, quat2, pos1, quat1, offset21, rotation21);
mapPose(pos1, quat1, pos2, quat2, offset12, rotation12);
// axis-aligned bounding boxes in g1 frame
for (int i=0; i < 8; i++) {
vec1[0] = (i&1 ? size1[0]+size1[3] : size1[0]-size1[3]);
vec1[1] = (i&2 ? size1[1]+size1[4] : size1[1]-size1[4]);
vec1[2] = (i&4 ? size1[2]+size1[5] : size1[2]-size1[5]);
vec2[0] = (i&1 ? size2[0]+size2[3] : size2[0]-size2[3]);
vec2[1] = (i&2 ? size2[1]+size2[4] : size2[1]-size2[4]);
vec2[2] = (i&4 ? size2[2]+size2[5] : size2[2]-size2[5]);
mju_mulMatVec3(vec2, rotation21, vec2);
mju_addTo3(vec2, offset21);
for (int k=0; k < 3; k++) {
aabb1[0+k] = mju_min(aabb1[0+k], vec1[k]);
aabb1[3+k] = mju_max(aabb1[3+k], vec1[k]);
aabb2[0+k] = mju_min(aabb2[0+k], vec2[k]);
aabb2[3+k] = mju_max(aabb2[3+k], vec2[k]);
}
}
// intersection of aabbs
for (int k=0; k < 3; k++) {
aabb[0+k] = mju_max(aabb1[0+k], aabb2[0+k]);
aabb[3+k] = mju_min(aabb1[3+k], aabb2[3+k]);
}
// no intersection if max < min
if (aabb[3] < aabb[0] || aabb[4] < aabb[1] || aabb[5] < aabb[2]) {
return cnt;
}
// create sdf pointers
int instance[2];
const mjpPlugin* sdf_ptr[2];
mjtGeom geomtypes[2] = {m->geom_type[g2], m->geom_type[g1]};
instance[0] = m->geom_plugin[g2];
sdf_ptr[0] = instance[0] == -1 ? NULL : mjc_getSDF(m, g2);
// get sdf plugins
if (m->geom_type[g1] == mjGEOM_SDF) {
instance[1] = m->geom_plugin[g1];
sdf_ptr[1] = instance[1] == -1 ? NULL : mjc_getSDF(m, g1);
} else {
instance[1] = g1;
sdf_ptr[1] = NULL;
}
// reset visualization count
if (sdf_ptr[0]) {
sdf_ptr[0]->reset(m, NULL, (void*)(d->plugin_data[instance[0]]), instance[0]);
}
// copy into sdf
mjSDF sdf;
instance[0] = instance[0] == -1 ? m->geom_dataid[g2] : instance[0];
instance[1] = instance[1] == -1 ? m->geom_dataid[g1] : instance[1];
sdf.id = instance;
sdf.relpos = offset21;
sdf.relmat = rotation21;
sdf.plugin = sdf_ptr;
sdf.geomtype = geomtypes;
// minimize sdf intersection
mjtNum contacts[3*mjMAXCONPAIR];
int i = 0, j = 0;
while (i < m->opt.sdf_initpoints) {
x[0] = aabb[0] + (aabb[3]-aabb[0]) * mju_Halton(j, 2);
x[1] = aabb[1] + (aabb[4]-aabb[1]) * mju_Halton(j, 3);
x[2] = aabb[2] + (aabb[5]-aabb[2]) * mju_Halton(j, 5);
mju_mulMatVec3(y, rotation2, x);
mju_addTo3(y, offset2);
mju_mulMatVec3(x, rotation12, y);
mju_addTo3(x, offset12);
j++;
// here a criterion for rejecting points could be inserted
i++;
// start counters
if (sdf_ptr[0]) {
sdf_ptr[0]->compute(m, (mjData*)d, instance[0], mjPLUGIN_SDF);
}
// gradient descent - we use a special function of the two SDF as objective
sdf.type = mjSDFTYPE_COLLISION;
dist = stepGradient(x, m, &sdf, (mjData*)d, m->opt.sdf_iterations);
// inexact SDFs can yield spurious collisions, filter them by projecting on the midsurface
sdf.type = mjSDFTYPE_INTERSECTION;
dist = stepGradient(x, m, &sdf, (mjData*)d, 1);
// contact point and normal - we use the midsurface where SDF1=SDF2 as zero level set
sdf.type = mjSDFTYPE_MIDSURFACE;
cnt = addContact(contacts, con, x, pos2, quat2, dist, cnt, m, &sdf, (mjData*)d);
// SHOULD NOT OCCUR
if (cnt > mjMAXCONPAIR) {
mjERROR("too many contact points");
}
}
return cnt;
}
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