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Mujoco_WASM/plugin/elasticity/solid.cc
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Yuval Tassa 30b4309af9 Rename mjpPlugin.capabilities -> mjpPlugin.capabilityflags 
PiperOrigin-RevId: 495080532
Change-Id: I81743472b816a331890a7cb05bfb7a89ebf07ff9
2022-12-13 11:33:27 -08:00

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// Copyright 2022 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 <algorithm>
#include <cstddef>
#include <cstdio>
#include <sstream>
#include <optional>
#include <unordered_map>
#include <mujoco/mjplugin.h>
#include <mujoco/mjtnum.h>
#include <mujoco/mujoco.h>
#include "solid.h"
namespace mujoco::plugin::elasticity {
namespace {
// local tetrahedron numbering
constexpr int kNumEdges = Stencil3D::kNumEdges;
constexpr int kNumVerts = Stencil3D::kNumVerts;
constexpr int edge[kNumEdges][2] = {{0, 1}, {1, 2}, {2, 0},
{2, 3}, {0, 3}, {1, 3}};
constexpr int face[kNumVerts][3] = {{2, 1, 0}, {0, 1, 3}, {1, 2, 3}, {2, 0, 3}};
constexpr int e2f[kNumEdges][2] = {{2, 3}, {1, 3}, {2, 1},
{1, 0}, {0, 2}, {0, 3}};
constexpr int cube2tets[kNumEdges][kNumVerts] = {{0, 3, 1, 7}, {0, 1, 4, 7},
{1, 3, 2, 7}, {1, 2, 6, 7},
{1, 5, 4, 7}, {1, 6, 5, 7}};
// Cartesian distance between 3D vectors
mjtNum SquaredDist3(const mjtNum pos1[3], const mjtNum pos2[3]) {
mjtNum dif[3] = {pos1[0]-pos2[0], pos1[1]-pos2[1], pos1[2]-pos2[2]};
return dif[0]*dif[0] + dif[1]*dif[1] + dif[2]*dif[2];
}
// volume of a tetrahedron
mjtNum ComputeVolume(const mjtNum* x, const int v[kNumVerts]) {
mjtNum normal[3];
mjtNum edge1[3];
mjtNum edge2[3];
mjtNum edge3[3];
mju_sub3(edge1, x+3*v[1], x+3*v[0]);
mju_sub3(edge2, x+3*v[2], x+3*v[0]);
mju_sub3(edge3, x+3*v[3], x+3*v[0]);
mju_cross(normal, edge2, edge1);
return mju_dot3(normal, edge3) / 6;
}
// compute local basis
void ComputeBasis(mjtNum basis[9], const mjtNum* x, const int v[kNumVerts],
const int faceL[3], const int faceR[3], mjtNum volume) {
mjtNum normalL[3], normalR[3];
mjtNum edgesL[6], edgesR[6];
mju_sub3(edgesL+0, x+3*v[faceL[1]], x+3*v[faceL[0]]);
mju_sub3(edgesL+3, x+3*v[faceL[2]], x+3*v[faceL[0]]);
mju_sub3(edgesR+0, x+3*v[faceR[1]], x+3*v[faceR[0]]);
mju_sub3(edgesR+3, x+3*v[faceR[2]], x+3*v[faceR[0]]);
mju_cross(normalL, edgesL, edgesL+3);
mju_cross(normalR, edgesR, edgesR+3);
// we use as basis the symmetrized tensor products of the area normals of the
// two faces not adjacent to the edge; this is the 3D equivalent to the basis
// proposed in Weischedel "A discrete geometric view on shear-deformable shell
// models" in the remark at the end of section 4.1. This is also equivalent to
// linear finite elements but in a coordinate-free formulation.
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
basis[3*i+j] = ( normalL[i]*normalR[j] +
normalR[i]*normalL[j] ) / (36*2*volume*volume);
}
}
}
// update edge lengths
void UpdateSquaredLengths(std::vector<mjtNum>& len,
const std::vector<std::pair<int, int> >& edges,
const mjtNum* x) {
for (int e = 0; e < len.size(); e++) {
const mjtNum* p0 = x + 3*edges[e].first;
const mjtNum* p1 = x + 3*edges[e].second;
len[e] = SquaredDist3(p0, p1);
}
}
// gradients of edge lengths with respect to vertex positions
void GradSquaredLengths(mjtNum gradient[kNumEdges][2][3],
const mjtNum* x,
const int v[kNumVerts],
const int edge[kNumEdges][2]) {
for (int e = 0; e < kNumEdges; e++) {
for (int d = 0; d < 3; d++) {
gradient[e][0][d] = x[3*v[edge[e][0]]+d] - x[3*v[edge[e][1]]+d];
gradient[e][1][d] = x[3*v[edge[e][1]]+d] - x[3*v[edge[e][0]]+d];
}
}
}
// reads numeric attributes
bool CheckAttr(const char* name, const mjModel* m, int instance) {
char* end;
std::string value = mj_getPluginConfig(m, instance, name);
value.erase(std::remove_if(value.begin(), value.end(), isspace), value.end());
strtod(value.c_str(), &end);
return end == value.data() + value.size();
}
struct PairHash
{
template <class T1, class T2>
std::size_t operator() (const std::pair<T1, T2>& pair) const {
return std::hash<T1>()(pair.first) ^ std::hash<T2>()(pair.second);
}
};
} // namespace
// factory function
std::optional<Solid> Solid::Create(const mjModel* m, mjData* d, int instance) {
if (CheckAttr("nx", m, instance) &&
CheckAttr("ny", m, instance) &&
CheckAttr("nz", m, instance) &&
CheckAttr("poisson", m, instance) &&
CheckAttr("young", m, instance)) {
int nx = strtod(mj_getPluginConfig(m, instance, "nx"), nullptr);
int ny = strtod(mj_getPluginConfig(m, instance, "ny"), nullptr);
int nz = strtod(mj_getPluginConfig(m, instance, "nz"), nullptr);
mjtNum nu = strtod(mj_getPluginConfig(m, instance, "poisson"), nullptr);
mjtNum E = strtod(mj_getPluginConfig(m, instance, "young"), nullptr);
mjtNum damp =
strtod(mj_getPluginConfig(m, instance, "damping"), nullptr);
return Solid(m, d, instance, nx, ny, nz, nu, E, damp);
} else {
mju_warning("Invalid parameter specification in solid plugin");
return std::nullopt;
}
}
// create map from tetrahedra to vertices and edges and from edges to vertices
void Solid::CreateStencils(int nx, int ny, int nz) {
elements.resize(nt);
// create a tetrahedral mesh by splitting a grid of hexahedral cells
for (int ix = 0; ix < nx-1; ix++) {
for (int iy = 0; iy < ny-1; iy++) {
for (int iz = 0; iz < nz-1; iz++) {
int t = 6*(nz-1)*(ny-1)*ix + 6*(nz-1)*iy + 6*iz;
int vert[8] = {
nz*ny*(ix+0) + nz*(iy+0) + iz+0,
nz*ny*(ix+1) + nz*(iy+0) + iz+0,
nz*ny*(ix+1) + nz*(iy+1) + iz+0,
nz*ny*(ix+0) + nz*(iy+1) + iz+0,
nz*ny*(ix+0) + nz*(iy+0) + iz+1,
nz*ny*(ix+1) + nz*(iy+0) + iz+1,
nz*ny*(ix+1) + nz*(iy+1) + iz+1,
nz*ny*(ix+0) + nz*(iy+1) + iz+1,
};
for (int s = 0; s < 6; s++) {
for (int v = 0; v < kNumVerts; v++) {
elements[t+s].vertices[v] = vert[cube2tets[s][v]];
}
}
}
}
}
// map from edge vertices to their index in `edges` vector
std::unordered_map<std::pair<int, int>, int, PairHash> edge_indices;
// loop over all tetrahedra
for (int t = 0; t < nt; t++) {
int* v = elements[t].vertices;
// compute edges to vertices map for fast computations
for (int e = 0; e < kNumEdges; e++) {
auto pair = std::pair(
std::min(v[edge[e][0]], v[edge[e][1]]),
std::max(v[edge[e][0]], v[edge[e][1]])
);
// if edge is already present in the vector only store its index
auto [it, inserted] = edge_indices.insert({pair, ne});
if (inserted) {
edges.push_back(pair);
elements[t].edges[e] = ne++;
} else {
elements[t].edges[e] = it->second;
}
}
}
}
// plugin constructor
Solid::Solid(const mjModel* m, mjData* d, int instance, int nx, int ny, int nz,
mjtNum nu, mjtNum E, mjtNum damp): damping(damp) {
// count plugin bodies
nv = ne = 0;
for (int i = 1; i < m->nbody; i++) {
if (m->body_plugin[i] == instance) {
if (!nv++) {
i0 = i;
}
}
}
// allocate arrays
nc = (nx-1)*(ny-1)*(nz-1); // number of cubes
nt = 6*nc; // number of tets
metric.assign(kNumEdges*kNumEdges*nt, 0); // metric induced by the geometry
// generate tetrahedra from the vertices
CreateStencils(nx, ny, nz);
// loop over all tetrahedra
for (int t = 0; t < nt; t++) {
int* v = elements[t].vertices;
for (int i = 0; i < kNumVerts; i++) {
if (m->body_plugin[i0+v[i]] != instance) {
mju_error("This body does not have the requested plugin instance");
}
}
// tetrahedron volume
mjtNum volume = ComputeVolume(m->body_pos+3*i0, v);
// local geometric quantities
mjtNum basis[kNumEdges][9] = {{0}, {0}, {0}, {0}, {0}, {0}};
mjtNum trT[kNumEdges] = {0};
mjtNum trTT[kNumEdges*kNumEdges] = {0};
// compute edge basis
for (int e = 0; e < kNumEdges; e++) {
ComputeBasis(basis[e], m->body_pos+3*i0, v,
face[e2f[e][0]], face[e2f[e][1]], volume);
}
// compute first invariant i.e. trace(strain)
for (int e = 0; e < kNumEdges; e++) {
for (int i = 0; i < 3; i++) {
trT[e] += basis[e][4*i];
}
}
// compute second invariant i.e. trace(strain^2)
for (int ed1 = 0; ed1 < kNumEdges; ed1++) {
for (int ed2 = 0; ed2 < kNumEdges; ed2++) {
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
trTT[kNumEdges*ed1+ed2] += basis[ed1][3*i+j] * basis[ed2][3*j+i];
}
}
}
}
// material parameters
mjtNum mu = E / (2*(1+nu)) * volume;
mjtNum la = E*nu / ((1+nu)*(1-2*nu)) * volume;
// assembly of strain metric tensor
for (int ed1 = 0; ed1 < kNumEdges; ed1++) {
for (int ed2 = 0; ed2 < kNumEdges; ed2++) {
int index = kNumEdges*kNumEdges*t + kNumEdges*ed1 + ed2;
metric[index] = mu * trTT[kNumEdges*ed1+ed2] + la * trT[ed2]*trT[ed1];
}
}
}
// allocate array
reference.assign(ne, 0);
deformed.assign(ne, 0);
previous.assign(ne, 0);
// compute edge lengths at equilibrium
UpdateSquaredLengths(reference, edges, m->body_pos+3*i0);
previous = reference;
}
void Solid::Compute(const mjModel* m, mjData* d, int instance) {
UpdateSquaredLengths(deformed, edges, d->xpos+3*i0);
// loop over all elements
for (int t = 0; t < nt; t++) {
int* v = elements[t].vertices;
// compute length gradient with respect to dofs
mjtNum gradient[kNumEdges][2][3];
GradSquaredLengths(gradient, d->xpos+3*i0, v, edge);
// we add generalized Rayleigh damping as decribed in Section 5.2 of
// Kharevych et al., "Geometric, Variational Integrators for Computer
// Animation" http://multires.caltech.edu/pubs/DiscreteLagrangian.pdf
// compute elongation
mjtNum elongation[kNumEdges];
mjtNum kD = damping / m->opt.timestep;
for (int e = 0; e < kNumEdges; e++) {
int idx = elements[t].edges[e];
elongation[e] = deformed[idx] - reference[idx] +
( deformed[idx] - previous[idx] ) * kD;
}
// we now multiply the elongations by the precomputed metric tensor,
// notice that if metric=diag(1/reference) then this would yield a
// mass-spring model
// compute local force
mjtNum force[kNumVerts*3] = {0};
int offset = kNumEdges*kNumEdges;
for (int ed1 = 0; ed1 < kNumEdges; ed1++) {
for (int ed2 = 0; ed2 < kNumEdges; ed2++) {
for (int i = 0; i < 2; i++) {
for (int x = 0; x < 3; x++) {
force[3 * edge[ed2][i] + x] +=
elongation[ed1] * gradient[ed2][i][x] *
metric[offset * t + kNumEdges * ed1 + ed2];
}
}
}
}
// insert into global force
for (int i = 0; i < kNumVerts; i++) {
for (int x = 0; x < 3; x++) {
d->qfrc_passive[m->body_dofadr[i0]+3*v[i]+x] -= force[3*i+x];
}
}
}
// update stored lengths
previous = deformed;
}
void Solid::RegisterPlugin() {
mjpPlugin plugin;
mjp_defaultPlugin(&plugin);
plugin.name = "mujoco.elasticity.solid";
plugin.capabilityflags |= mjPLUGIN_PASSIVE;
const char* attributes[] = {"nx", "ny", "nz", "young", "poisson", "damping"};
plugin.nattribute = sizeof(attributes) / sizeof(attributes[0]);
plugin.attributes = attributes;
plugin.nstate = +[](const mjModel* m, int instance) { return 0; };
plugin.init = +[](const mjModel* m, mjData* d, int instance) {
auto elasticity_or_null = Solid::Create(m, d, instance);
if (!elasticity_or_null.has_value()) {
return -1;
}
d->plugin_data[instance] = reinterpret_cast<uintptr_t>(
new Solid(std::move(*elasticity_or_null)));
return 0;
};
plugin.destroy = +[](mjData* d, int instance) {
delete reinterpret_cast<Solid*>(d->plugin_data[instance]);
d->plugin_data[instance] = 0;
};
plugin.compute =
+[](const mjModel* m, mjData* d, int instance, int capability_bit) {
auto* elasticity = reinterpret_cast<Solid*>(d->plugin_data[instance]);
elasticity->Compute(m, d, instance);
};
mjp_registerPlugin(&plugin);
}
} // namespace mujoco::plugin::elasticity
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