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mujoco / data /src /engine /engine_core_constraint.c
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introvoyz041
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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_core_constraint.h"
#include <stdio.h>
#include <stddef.h>
#include <mujoco/mjdata.h>
#include <mujoco/mjmacro.h>
#include <mujoco/mjmodel.h>
#include <mujoco/mjsan.h> // IWYU pragma: keep
#include <mujoco/mjxmacro.h>
#include "engine/engine_core_smooth.h"
#include "engine/engine_io.h"
#include "engine/engine_support.h"
#include "engine/engine_util_blas.h"
#include "engine/engine_util_errmem.h"
#include "engine/engine_util_misc.h"
#include "engine/engine_util_sparse.h"
#include "engine/engine_util_spatial.h"
#ifdef MEMORY_SANITIZER
#include <sanitizer/msan_interface.h>
#endif
#ifdef mjUSEPLATFORMSIMD
#if defined(__AVX__) && !defined(mjUSESINGLE)
#define mjUSEAVX
#endif // defined(__AVX__) && !defined(mjUSESINGLE)
#endif // mjUSEPLATFORMSIMD
//-------------------------- utility functions -----------------------------------------------------
// allocate efc arrays on arena, return 1 on success, 0 on failure
static int arenaAllocEfc(const mjModel* m, mjData* d) {
#undef MJ_M
#define MJ_M(n) m->n
#undef MJ_D
#define MJ_D(n) d->n
// move arena pointer to end of contact array
d->parena = d->ncon * sizeof(mjContact);
// poison remaining memory
#ifdef ADDRESS_SANITIZER
ASAN_POISON_MEMORY_REGION(
(char*)d->arena + d->parena, d->narena - d->pstack - d->parena);
#endif
#define X(type, name, nr, nc) \
d->name = mj_arenaAllocByte(d, sizeof(type) * (nr) * (nc), _Alignof(type)); \
if (!d->name) { \
mj_warning(d, mjWARN_CNSTRFULL, d->narena); \
mj_clearEfc(d); \
d->parena = d->ncon * sizeof(mjContact); \
return 0; \
}
MJDATA_ARENA_POINTERS_SOLVER
#undef X
#undef MJ_M
#define MJ_M(n) n
#undef MJ_D
#define MJ_D(n) n
return 1;
}
// determine type of friction cone
int mj_isPyramidal(const mjModel* m) {
if (m->opt.cone == mjCONE_PYRAMIDAL) {
return 1;
} else {
return 0;
}
}
// determine type of constraint Jacobian
int mj_isSparse(const mjModel* m) {
if (m->opt.jacobian == mjJAC_SPARSE ||
(m->opt.jacobian == mjJAC_AUTO && m->nv >= 60)) {
return 1;
} else {
return 0;
}
}
// determine type of solver
int mj_isDual(const mjModel* m) {
if (m->opt.solver == mjSOL_PGS || m->opt.noslip_iterations > 0) {
return 1;
} else {
return 0;
}
}
// assign/clamp contact friction parameters
void mj_assignFriction(const mjModel* m, mjtNum* target, const mjtNum* source) {
if (mjENABLED(mjENBL_OVERRIDE)) {
for (int i=0; i < 5; i++) {
target[i] = mju_max(mjMINMU, m->opt.o_friction[i]);
}
} else {
for (int i=0; i < 5; i++) {
target[i] = mju_max(mjMINMU, source[i]);
}
}
}
// assign/override contact reference parameters
void mj_assignRef(const mjModel* m, mjtNum* target, const mjtNum* source) {
if (mjENABLED(mjENBL_OVERRIDE)) {
mju_copy(target, m->opt.o_solref, mjNREF);
} else {
mju_copy(target, source, mjNREF);
}
}
// assign/override contact impedance parameters
void mj_assignImp(const mjModel* m, mjtNum* target, const mjtNum* source) {
if (mjENABLED(mjENBL_OVERRIDE)) {
mju_copy(target, m->opt.o_solimp, mjNIMP);
} else {
mju_copy(target, source, mjNIMP);
}
}
// assign/override contact margin
mjtNum mj_assignMargin(const mjModel* m, mjtNum source) {
if (mjENABLED(mjENBL_OVERRIDE)) {
return m->opt.o_margin;
} else {
return source;
}
}
// compute element bodies and weights for given contact point, return #bodies
// if v is one of the element vertices, reduce element to fragment
static int mj_elemBodyWeight(const mjModel* m, const mjData* d, int f, int e, int v,
const mjtNum point[3], int* body, mjtNum* weight) {
// get flex info
int dim = m->flex_dim[f];
const int* edata = m->flex_elem + m->flex_elemdataadr[f] + e*(dim+1);
const mjtNum* vert = d->flexvert_xpos + 3*m->flex_vertadr[f];
// compute inverse distances from contact point to element vertices
// save body ids, find vertex v in element
int vid = -1;
for (int i=0; i <= dim; i++) {
mjtNum dist = mju_dist3(point, vert+3*edata[i]);
weight[i] = 1.0/(mju_max(mjMINVAL, dist));
body[i] = m->flex_vertadr[f] + edata[i];
// check if element vertex matches v
if (edata[i] == v) {
vid = i;
}
}
// v found in e: skip and shift remaining
if (vid >= 0) {
while (vid < dim) {
weight[vid] = weight[vid+1];
body[vid] = body[vid+1];
vid++;
}
dim--;
}
// normalize weights
mju_normalize(weight, dim+1);
return dim+1;
}
// compute body weights for a given contact vertex, return #bodies
static int mj_vertBodyWeight(const mjModel* m, const mjData* d, int f, int v,
const mjtNum point[3], int* body, mjtNum* weight, mjtNum bw) {
mjtNum* coord = m->flex_vert0 + 3*v;
int nstart = m->flex_nodeadr[f];
int nend = m->flex_nodeadr[f] + m->flex_nodenum[f];
int nb = 0;
for (int i = nstart; i < nend; i++) {
mjtNum w = ((i-nstart)&1 ? coord[2] : 1-coord[2]) *
((i-nstart)&2 ? coord[1] : 1-coord[1]) *
((i-nstart)&4 ? coord[0] : 1-coord[0]);
if (w < 1e-5) {
continue;
}
if (weight) weight[nb] = w * bw;
body[nb++] = m->flex_nodebodyid[i];
}
return nb;
}
// add contact to d->contact list; return 0 if success; 1 if buffer full
int mj_addContact(const mjModel* m, mjData* d, const mjContact* con) {
// if nconmax is specified and ncon >= nconmax, warn and return error
if (m->nconmax != -1 && d->ncon >= m->nconmax) {
mj_warning(d, mjWARN_CONTACTFULL, d->ncon);
return 1;
}
// move arena pointer back to the end of the existing contact array and invalidate efc_ arrays
d->parena = d->ncon * sizeof(mjContact);
#ifdef ADDRESS_SANITIZER
ASAN_POISON_MEMORY_REGION(
(char*)d->arena + d->parena, d->narena - d->pstack - d->parena);
#endif
mj_clearEfc(d);
// copy contact
mjContact* dst = mj_arenaAllocByte(d, sizeof(mjContact), _Alignof(mjContact));
if (!dst) {
mj_warning(d, mjWARN_CONTACTFULL, d->ncon);
return 1;
}
*dst = *con;
// increase counter, return success
d->ncon++;
return 0;
}
// add #size rows to constraint Jacobian; set pos, margin, frictionloss, type, id
static void mj_addConstraint(const mjModel* m, mjData* d,
const mjtNum* jac, const mjtNum* pos,
const mjtNum* margin, mjtNum frictionloss,
int size, int type, int id, int NV, const int* chain) {
int empty, nv = m->nv, nefc = d->nefc;
int *nnz = d->efc_J_rownnz, *adr = d->efc_J_rowadr, *ind = d->efc_J_colind;
mjtNum *J = d->efc_J;
// init empty guard for constraints other than contact
if (type == mjCNSTR_CONTACT_FRICTIONLESS ||
type == mjCNSTR_CONTACT_PYRAMIDAL ||
type == mjCNSTR_CONTACT_ELLIPTIC) {
empty = 0;
} else {
empty = 1;
}
// dense: copy entire Jacobian
if (!mj_isSparse(m)) {
// make sure jac is not empty
if (empty) {
for (int i=0; i < size*nv; i++) {
if (jac[i]) {
empty = 0;
break;
}
}
}
// copy if not empty
if (!empty) {
mju_copy(J + nefc*nv, jac, size*nv);
}
}
// sparse: copy chain
else {
// clamp NV (in case -1 was used in constraint construction)
NV = mjMAX(0, NV);
if (NV) {
empty = 0;
} else if (empty) {
// all rows are empty, return early
return;
}
// chain required in sparse mode
if (NV && !chain) {
mjERROR("called with dense arguments");
}
// process size elements
for (int i=0; i < size; i++) {
// set row address
adr[nefc+i] = (nefc+i ? adr[nefc+i-1]+nnz[nefc+i-1] : 0);
// set row descriptor
nnz[nefc+i] = NV;
// copy if not empty
if (NV) {
mju_copyInt(ind + adr[nefc+i], chain, NV);
mju_copy(J + adr[nefc+i], jac + i*NV, NV);
}
}
}
// all rows empty: skip constraint
if (empty) {
return;
}
// set constraint pos, margin, frictionloss, type, id
for (int i=0; i < size; i++) {
d->efc_pos[nefc+i] = (pos ? pos[i] : 0);
d->efc_margin[nefc+i] = (margin ? margin[i] : 0);
d->efc_frictionloss[nefc+i] = frictionloss;
d->efc_type[nefc+i] = type;
d->efc_id[nefc+i] = id;
}
// increase counters
d->nefc += size;
if (type == mjCNSTR_EQUALITY) {
d->ne += size;
} else if (type == mjCNSTR_FRICTION_DOF || type == mjCNSTR_FRICTION_TENDON) {
d->nf += size;
} else if (type == mjCNSTR_LIMIT_JOINT || type == mjCNSTR_LIMIT_TENDON) {
d->nl += size;
}
}
// multiply Jacobian by vector
void mj_mulJacVec(const mjModel* m, const mjData* d, mjtNum* res, const mjtNum* vec) {
// exit if no constraints
if (!d->nefc) {
return;
}
// sparse Jacobian
if (mj_isSparse(m))
mju_mulMatVecSparse(res, d->efc_J, vec, d->nefc,
d->efc_J_rownnz, d->efc_J_rowadr,
d->efc_J_colind, d->efc_J_rowsuper);
// dense Jacobian
else {
mju_mulMatVec(res, d->efc_J, vec, d->nefc, m->nv);
}
}
// multiply JacobianT by vector
void mj_mulJacTVec(const mjModel* m, const mjData* d, mjtNum* res, const mjtNum* vec) {
// exit if no constraints
if (!d->nefc) {
return;
}
// sparse Jacobian
if (mj_isSparse(m))
mju_mulMatVecSparse(res, d->efc_JT, vec, m->nv,
d->efc_JT_rownnz, d->efc_JT_rowadr,
d->efc_JT_colind, d->efc_JT_rowsuper);
// dense Jacobian
else {
mju_mulMatTVec(res, d->efc_J, vec, d->nefc, m->nv);
}
}
//--------------------- instantiate constraints by type --------------------------------------------
// equality constraints
void mj_instantiateEquality(const mjModel* m, mjData* d) {
int issparse = mj_isSparse(m), nv = m->nv;
int id[2], size, NV, NV2, *chain = NULL, *chain2 = NULL, *buf_ind = NULL;
int flex_edgeadr, flex_edgenum;
mjtNum cpos[6], pos[2][3], ref[2], dif, deriv;
mjtNum quat[4], quat1[4], quat2[4], quat3[4], axis[3];
mjtNum *jac[2], *jacdif, *data, *sparse_buf = NULL;
// disabled or no equality constraints: return
if (mjDISABLED(mjDSBL_EQUALITY) || m->nemax == 0) {
return;
}
mj_markStack(d);
// allocate space
jac[0] = mjSTACKALLOC(d, 6*nv, mjtNum);
jac[1] = mjSTACKALLOC(d, 6*nv, mjtNum);
jacdif = mjSTACKALLOC(d, 6*nv, mjtNum);
if (issparse) {
chain = mjSTACKALLOC(d, nv, int);
chain2 = mjSTACKALLOC(d, nv, int);
buf_ind = mjSTACKALLOC(d, nv, int);
sparse_buf = mjSTACKALLOC(d, nv, mjtNum);
}
// find active equality constraints
for (int i=0; i < m->neq; i++) {
if (!d->eq_active[i]) {
continue;
}
// get constraint data
data = m->eq_data + mjNEQDATA*i;
id[0] = m->eq_obj1id[i];
id[1] = m->eq_obj2id[i];
size = 0;
NV = 0;
NV2 = 0;
int body_id[2];
// process according to type
switch ((mjtEq) m->eq_type[i]) {
case mjEQ_CONNECT: // connect bodies with ball joint
// find global points, body semantic
if (m->eq_objtype[i] == mjOBJ_BODY) {
for (int j=0; j < 2; j++) {
mju_mulMatVec3(pos[j], d->xmat + 9*id[j], data + 3*j);
mju_addTo3(pos[j], d->xpos + 3*id[j]);
body_id[j] = id[j];
}
}
// find global points, site semantic
else {
for (int j=0; j < 2; j++) {
mju_copy3(pos[j], d->site_xpos + 3*id[j]);
body_id[j] = m->site_bodyid[id[j]];
}
}
// compute position error
mju_sub3(cpos, pos[0], pos[1]);
// compute Jacobian difference (opposite of contact: 0 - 1)
NV = mj_jacDifPair(m, d, chain, body_id[1], body_id[0], pos[1], pos[0],
jac[1], jac[0], jacdif, NULL, NULL, NULL);
// copy difference into jac[0]
mju_copy(jac[0], jacdif, 3*NV);
size = 3;
break;
case mjEQ_WELD: // fix relative position and orientation
// find global points, body semantic
if (m->eq_objtype[i] == mjOBJ_BODY) {
for (int j=0; j < 2; j++) {
mjtNum* anchor = data + 3*(1-j);
mju_mulMatVec3(pos[j], d->xmat + 9*id[j], anchor);
mju_addTo3(pos[j], d->xpos + 3*id[j]);
body_id[j] = id[j];
}
}
// find global points, site semantic
else {
for (int j=0; j < 2; j++) {
mju_copy3(pos[j], d->site_xpos + 3*id[j]);
body_id[j] = m->site_bodyid[id[j]];
}
}
// compute position error
mju_sub3(cpos, pos[0], pos[1]);
// get torquescale coefficient
mjtNum torquescale = data[10];
// compute error Jacobian (opposite of contact: 0 - 1)
NV = mj_jacDifPair(m, d, chain, body_id[1], body_id[0], pos[1], pos[0],
jac[1], jac[0], jacdif,
jac[1]+3*nv, jac[0]+3*nv, jacdif+3*nv);
// copy difference into jac[0], compress translation:rotation if sparse
mju_copy(jac[0], jacdif, 3*NV);
mju_copy(jac[0]+3*NV, jacdif+3*nv, 3*NV);
// orientation, body semantic
if (m->eq_objtype[i] == mjOBJ_BODY) {
// compute orientation error: neg(q1) * q0 * relpose (axis components only)
mjtNum* relpose = data+6;
mju_mulQuat(quat, d->xquat+4*id[0], relpose); // quat = q0*relpose
mju_negQuat(quat1, d->xquat+4*id[1]); // quat1 = neg(q1)
}
// orientation, site semantic
else {
mjtNum quat_site1[4];
mju_mulQuat(quat, d->xquat+4*body_id[0], m->site_quat+4*id[0]);
mju_mulQuat(quat_site1, d->xquat+4*body_id[1], m->site_quat+4*id[1]);
mju_negQuat(quat1, quat_site1);
}
mju_mulQuat(quat2, quat1, quat);
mju_scl3(cpos+3, quat2+1, torquescale); // scale axis components by torquescale
// correct rotation Jacobian: 0.5 * neg(q1) * (jac0-jac1) * q0 * relpose
for (int j=0; j < NV; j++) {
// axis = [jac0-jac1]_col(j)
axis[0] = jac[0][3*NV+j];
axis[1] = jac[0][4*NV+j];
axis[2] = jac[0][5*NV+j];
// apply formula
mju_mulQuatAxis(quat2, quat1, axis); // quat2 = neg(q1)*(jac0-jac1)
mju_mulQuat(quat3, quat2, quat); // quat3 = neg(q1)*(jac0-jac1)*q0*relpose
// correct Jacobian
jac[0][3*NV+j] = 0.5*quat3[1];
jac[0][4*NV+j] = 0.5*quat3[2];
jac[0][5*NV+j] = 0.5*quat3[3];
}
// scale rotational jacobian by torquescale
mju_scl(jac[0]+3*NV, jac[0]+3*NV, torquescale, 3*NV);
size = 6;
break;
case mjEQ_JOINT: // couple joint values with cubic
case mjEQ_TENDON: // couple tendon lengths with cubic
// get scalar positions and their Jacobians
for (int j=0; j < 1+(id[1] >= 0); j++) {
if (m->eq_type[i] == mjEQ_JOINT) { // joint object
pos[j][0] = d->qpos[m->jnt_qposadr[id[j]]];
ref[j] = m->qpos0[m->jnt_qposadr[id[j]]];
// make Jacobian: sparse or dense
if (issparse) {
// add first or second joint
if (j == 0) {
NV = 1;
chain[0] = m->jnt_dofadr[id[j]];
jac[j][0] = 1;
} else {
NV2 = 1;
chain2[0] = m->jnt_dofadr[id[j]];
jac[j][0] = 1;
}
} else {
mju_zero(jac[j], nv);
jac[j][m->jnt_dofadr[id[j]]] = 1;
}
} else { // tendon object
pos[j][0] = d->ten_length[id[j]];
ref[j] = m->tendon_length0[id[j]];
// set tendon_efcadr
if (d->tendon_efcadr[id[j]] == -1) {
d->tendon_efcadr[id[j]] = i;
}
// copy Jacobian: sparse or dense
if (issparse) {
// add first or second chain
if (j == 0) {
NV = d->ten_J_rownnz[id[j]];
mju_copyInt(chain, d->ten_J_colind+d->ten_J_rowadr[id[j]], NV);
mju_copy(jac[j], d->ten_J+d->ten_J_rowadr[id[j]], NV);
} else {
NV2 = d->ten_J_rownnz[id[j]];
mju_copyInt(chain2, d->ten_J_colind+d->ten_J_rowadr[id[j]], NV2);
mju_copy(jac[j], d->ten_J+d->ten_J_rowadr[id[j]], NV2);
}
} else {
mju_copy(jac[j], d->ten_J+id[j]*nv, nv);
}
}
}
// both objects defined
if (id[1] >= 0) {
// compute position error
dif = pos[1][0] - ref[1];
cpos[0] = pos[0][0] - ref[0] - data[0] -
(data[1]*dif + data[2]*dif*dif + data[3]*dif*dif*dif + data[4]*dif*dif*dif*dif);
// compute derivative
deriv = data[1] + 2*data[2]*dif + 3*data[3]*dif*dif + 4*data[4]*dif*dif*dif;
// compute Jacobian: sparse or dense
if (issparse) {
NV = mju_combineSparse(jac[0], jac[1], 1, -deriv, NV, NV2, chain,
chain2, sparse_buf, buf_ind);
} else {
mju_addToScl(jac[0], jac[1], -deriv, nv);
}
}
// only one object defined
else {
// compute position error
cpos[0] = pos[0][0] - ref[0] - data[0];
// jac[0] already has the correct Jacobian
}
size = 1;
break;
case mjEQ_FLEX:
flex_edgeadr = m->flex_edgeadr[id[0]];
flex_edgenum = m->flex_edgenum[id[0]];
// add one constraint per non-rigid edge
for (int e=flex_edgeadr; e < flex_edgeadr+flex_edgenum; e++) {
// skip rigid
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+d->flexedge_J_rowadr[e], cpos, 0, 0,
1, mjCNSTR_EQUALITY, i,
d->flexedge_J_rownnz[e],
d->flexedge_J_colind+d->flexedge_J_rowadr[e]);
} else {
mj_addConstraint(m, d, d->flexedge_J+e*nv, cpos, 0, 0,
1, mjCNSTR_EQUALITY, i,
0, NULL);
}
}
break;
default: // SHOULD NOT OCCUR
mjERROR("invalid equality constraint type %d", m->eq_type[i]);
}
// add constraint
if (size) {
mj_addConstraint(m, d, jac[0], cpos, 0, 0,
size, mjCNSTR_EQUALITY, i,
issparse ? NV : 0,
issparse ? chain : NULL);
}
}
mj_freeStack(d);
}
// frictional dofs and tendons
void mj_instantiateFriction(const mjModel* m, mjData* d) {
int nv = m->nv, issparse = mj_isSparse(m);
mjtNum* jac;
// disabled: return
if (mjDISABLED(mjDSBL_FRICTIONLOSS)) {
return;
}
mj_markStack(d);
// allocate Jacobian
jac = mjSTACKALLOC(d, nv, mjtNum);
// find frictional dofs
for (int i=0; i < nv; i++) {
if (m->dof_frictionloss[i] > 0) {
// prepare Jacobian: sparse or dense
if (issparse) {
jac[0] = 1;
} else {
mju_zero(jac, nv);
jac[i] = 1;
}
// add constraint
mj_addConstraint(m, d, jac, 0, 0, m->dof_frictionloss[i],
1, mjCNSTR_FRICTION_DOF, i,
issparse ? 1 : 0,
issparse ? &i : NULL);
}
}
// find frictional tendons
for (int i=0; i < m->ntendon; i++) {
if (m->tendon_frictionloss[i] > 0) {
int efcadr = d->nefc;
// add constraint
mj_addConstraint(m, d, d->ten_J + (issparse ? d->ten_J_rowadr[i] : i*nv),
0, 0, m->tendon_frictionloss[i],
1, mjCNSTR_FRICTION_TENDON, i,
issparse ? d->ten_J_rownnz[i] : 0,
issparse ? d->ten_J_colind+d->ten_J_rowadr[i] : NULL);
// set tendon_efcadr
if (d->tendon_efcadr[i] == -1) {
d->tendon_efcadr[i] = efcadr;
}
}
}
mj_freeStack(d);
}
// joint and tendon limits
void mj_instantiateLimit(const mjModel* m, mjData* d) {
int side, nv = m->nv, issparse = mj_isSparse(m);
mjtNum margin, value, dist, angleAxis[3];
mjtNum *jac;
// disabled: return
if (mjDISABLED(mjDSBL_LIMIT)) {
return;
}
mj_markStack(d);
// allocate Jacobian
jac = mjSTACKALLOC(d, nv, mjtNum);
// find joint limits
for (int i=0; i < m->njnt; i++) {
if (m->jnt_limited[i]) {
// get margin
margin = m->jnt_margin[i];
// HINGE or SLIDE joint
if (m->jnt_type[i] == mjJNT_SLIDE || m->jnt_type[i] == mjJNT_HINGE) {
// get joint value
value = d->qpos[m->jnt_qposadr[i]];
// process lower and upper limits
for (side=-1; side <= 1; side+=2) {
// compute distance (negative: penetration)
dist = side * (m->jnt_range[2*i+(side+1)/2] - value);
// detect joint limit
if (dist < margin) {
// prepare Jacobian: sparse or dense
if (issparse) {
jac[0] = -(mjtNum)side;
} else {
mju_zero(jac, nv);
jac[m->jnt_dofadr[i]] = -(mjtNum)side;
}
// add constraint
mj_addConstraint(m, d, jac, &dist, &margin, 0,
1, mjCNSTR_LIMIT_JOINT, i,
issparse ? 1 : 0,
issparse ? m->jnt_dofadr+i : NULL);
}
}
}
// BALL joint
else if (m->jnt_type[i] == mjJNT_BALL) {
// convert joint quaternion to axis-angle
int adr = m->jnt_qposadr[i];
mjtNum quat[4] = {d->qpos[adr], d->qpos[adr+1], d->qpos[adr+2], d->qpos[adr+3]};
mju_normalize4(quat);
mju_quat2Vel(angleAxis, quat, 1);
// get rotation angle, normalize
value = mju_normalize3(angleAxis);
// compute distance, using max of range (negative: penetration)
dist = mju_max(m->jnt_range[2*i], m->jnt_range[2*i+1]) - value;
// detect joint limit
if (dist < margin) {
// sparse
if (issparse) {
// prepare dof index array
int chain[3] = {
m->jnt_dofadr[i],
m->jnt_dofadr[i] + 1,
m->jnt_dofadr[i] + 2
};
// prepare Jacobian
mju_scl3(jac, angleAxis, -1);
// add constraint
mj_addConstraint(m, d, jac, &dist, &margin, 0,
1, mjCNSTR_LIMIT_JOINT, i, 3, chain);
}
// dense
else {
// prepare Jacobian
mju_zero(jac, nv);
mju_scl3(jac + m->jnt_dofadr[i], angleAxis, -1);
// add constraint
mj_addConstraint(m, d, jac, &dist, &margin, 0,
1, mjCNSTR_LIMIT_JOINT, i, 0, 0);
}
}
}
}
}
// find tendon limits
for (int i=0; i < m->ntendon; i++) {
if (m->tendon_limited[i]) {
// get value = length, margin
value = d->ten_length[i];
margin = m->tendon_margin[i];
// process lower and upper limits
for (side=-1; side <= 1; side+=2) {
// compute distance (negative: penetration)
dist = side * (m->tendon_range[2*i+(side+1)/2] - value);
// detect tendon limit
if (dist < margin) {
// prepare Jacobian: sparse or dense
if (issparse) {
mju_scl(jac, d->ten_J+d->ten_J_rowadr[i], -side, d->ten_J_rownnz[i]);
} else {
mju_scl(jac, d->ten_J+i*nv, -side, nv);
}
// add constraint
int efcadr = d->nefc;
mj_addConstraint(m, d, jac, &dist, &margin, 0,
1, mjCNSTR_LIMIT_TENDON, i,
issparse ? d->ten_J_rownnz[i] : 0,
issparse ? d->ten_J_colind+d->ten_J_rowadr[i] : NULL);
// set tendon_efcadr
if (d->tendon_efcadr[i] == -1) {
d->tendon_efcadr[i] = efcadr;
}
}
}
}
}
mj_freeStack(d);
}
// frictionless and frictional contacts
void mj_instantiateContact(const mjModel* m, mjData* d) {
int ispyramid = mj_isPyramidal(m), issparse = mj_isSparse(m), ncon = d->ncon;
int dim, NV, nv = m->nv, *chain = NULL;
mjContact* con;
mjtNum cpos[6], cmargin[6], *jac, *jacdif, *jacdifp, *jacdifr, *jac1p, *jac2p, *jac1r, *jac2r;
if (mjDISABLED(mjDSBL_CONTACT) || ncon == 0 || nv == 0) {
return;
}
mj_markStack(d);
// allocate Jacobian
jac = mjSTACKALLOC(d, 6*nv, mjtNum);
jacdif = mjSTACKALLOC(d, 6*nv, mjtNum);
jacdifp = jacdif;
jacdifr = jacdif + 3*nv;
jac1p = mjSTACKALLOC(d, 3*nv, mjtNum);
jac2p = mjSTACKALLOC(d, 3*nv, mjtNum);
jac1r = mjSTACKALLOC(d, 3*nv, mjtNum);
jac2r = mjSTACKALLOC(d, 3*nv, mjtNum);
if (issparse) {
chain = mjSTACKALLOC(d, nv, int);
}
// find contacts to be included
for (int i=0; i < ncon; i++) {
if (!d->contact[i].exclude) {
// get contact info, safe efc_address
con = d->contact + i;
dim = con->dim;
con->efc_address = d->nefc;
// special case: single body on each side
if ((con->geom[0] >= 0 || (con->vert[0] >= 0 && m->flex_interp[con->flex[0]] == 0)) &&
(con->geom[1] >= 0 || (con->vert[1] >= 0 && m->flex_interp[con->flex[1]] == 0))) {
// get bodies
int bid[2];
for (int side=0; side < 2; side++) {
bid[side] = (con->geom[side] >= 0) ?
m->geom_bodyid[con->geom[side]] :
m->flex_vertbodyid[m->flex_vertadr[con->flex[side]] + con->vert[side]];
}
// compute Jacobian differences
if (dim > 3) {
NV = mj_jacDifPair(m, d, chain, bid[0], bid[1], con->pos, con->pos,
jac1p, jac2p, jacdifp, jac1r, jac2r, jacdifr);
} else {
NV = mj_jacDifPair(m, d, chain, bid[0], bid[1], con->pos, con->pos,
jac1p, jac2p, jacdifp, NULL, NULL, NULL);
}
}
// general case: flex elements involved
else {
// get bodies and weights
int nb = 0;
int bid[64];
mjtNum bweight[64];
for (int side=0; side < 2; side++) {
int nw = 0;
int vid[4];
mjtNum bw[4];
// geom
if (con->geom[side] >= 0) {
bid[nb] = m->geom_bodyid[con->geom[side]];
bweight[nb] = side ? +1 : -1;
nb++;
}
// flex vert
else if (con->vert[side] >= 0) {
vid[0] = m->flex_vertadr[con->flex[side]] + con->vert[side];
bw[0] = side ? +1 : -1;
nw = 1;
}
// flex elem
else {
nw = mj_elemBodyWeight(m, d, con->flex[side], con->elem[side],
con->vert[1-side], con->pos, vid, bw);
// negative sign for first side of contact
if (side == 0) {
mju_scl(bw, bw, -1, nw);
}
}
// get body or node ids and weights
for (int k=0; k < nw; k++) {
if (m->flex_interp[con->flex[side]] == 0) {
bid[nb] = m->flex_vertbodyid[vid[k]];
bweight[nb] = bw[k];
nb++;
} else {
nb += mj_vertBodyWeight(m, d, con->flex[side], vid[k],
con->pos, bid+nb, bweight+nb, bw[k]);
}
}
}
// combine weighted Jacobians
NV = mj_jacSum(m, d, chain, nb, bid, bweight, con->pos, jacdif, dim > 3);
}
// skip contact if no DOFs affected
if (NV == 0) {
con->efc_address = -1;
con->exclude = 3;
continue;
}
// rotate Jacobian differences to contact frame
mju_mulMatMat(jac, con->frame, jacdifp, dim > 1 ? 3 : 1, 3, NV);
if (dim > 3) {
mju_mulMatMat(jac + 3*NV, con->frame, jacdifr, dim-3, 3, NV);
}
// make frictionless contact
if (dim == 1) {
// add constraint
mj_addConstraint(m, d, jac, &(con->dist), &(con->includemargin), 0,
1, mjCNSTR_CONTACT_FRICTIONLESS, i,
issparse ? NV : 0,
issparse ? chain : NULL);
}
// make pyramidal friction cone
else if (ispyramid) {
// pos = dist
cpos[0] = cpos[1] = con->dist;
cmargin[0] = cmargin[1] = con->includemargin;
// one pair per friction dimension
for (int k=1; k < con->dim; k++) {
// Jacobian for pair of opposing pyramid edges
mju_addScl(jacdifp, jac, jac + k*NV, con->friction[k-1], NV);
mju_addScl(jacdifp + NV, jac, jac + k*NV, -con->friction[k-1], NV);
// add constraint
mj_addConstraint(m, d, jacdifp, cpos, cmargin, 0,
2, mjCNSTR_CONTACT_PYRAMIDAL, i,
issparse ? NV : 0,
issparse ? chain : NULL);
}
}
// make elliptic friction cone
else {
// normal pos = dist, all others 0
mju_zero(cpos, con->dim);
mju_zero(cmargin, con->dim);
cpos[0] = con->dist;
cmargin[0] = con->includemargin;
// add constraint
mj_addConstraint(m, d, jac, cpos, cmargin, 0,
con->dim, mjCNSTR_CONTACT_ELLIPTIC, i,
issparse ? NV : 0,
issparse ? chain : NULL);
}
}
}
mj_freeStack(d);
}
//------------------------ compute constraint parameters -------------------------------------------
// compute diagApprox
void mj_diagApprox(const mjModel* m, mjData* d) {
int id, dim, b1, b2, f, weldcnt = 0;
int nefc = d->nefc;
mjtNum tran, rot, fri, *dA = d->efc_diagApprox;
mjContact* con = NULL;
// loop over all constraints, compute approximate inverse inertia
for (int i=0; i < nefc; i++) {
// get constraint id
id = d->efc_id[i];
// process according to constraint type
switch ((mjtConstraint) d->efc_type[i]) {
case mjCNSTR_EQUALITY:
// process according to equality-constraint type
switch (m->eq_type[id]) {
case mjEQ_CONNECT:
b1 = m->eq_obj1id[id];
b2 = m->eq_obj2id[id];
// get body ids if using site semantics
if (m->eq_objtype[id] == mjOBJ_SITE) {
b1 = m->site_bodyid[b1];
b2 = m->site_bodyid[b2];
}
// body translation
dA[i] = m->body_invweight0[2*b1] + m->body_invweight0[2*b2];
break;
case mjEQ_WELD: // distinguish translation and rotation inertia
b1 = m->eq_obj1id[id];
b2 = m->eq_obj2id[id];
// get body ids if using site semantics
if (m->eq_objtype[id] == mjOBJ_SITE) {
b1 = m->site_bodyid[b1];
b2 = m->site_bodyid[b2];
}
// body translation or rotation depending on weldcnt
dA[i] = m->body_invweight0[2*b1 + (weldcnt > 2)] +
m->body_invweight0[2*b2 + (weldcnt > 2)];
weldcnt = (weldcnt + 1) % 6;
break;
case mjEQ_JOINT:
case mjEQ_TENDON:
// object 1 contribution
dA[i] = (m->eq_type[id] == mjEQ_JOINT ?
m->dof_invweight0[m->jnt_dofadr[m->eq_obj1id[id]]] :
m->tendon_invweight0[m->eq_obj1id[id]]);
// add object 2 contribution if present
if (m->eq_obj2id[id] >= 0)
dA[i] += (m->eq_type[id] == mjEQ_JOINT ?
m->dof_invweight0[m->jnt_dofadr[m->eq_obj2id[id]]] :
m->tendon_invweight0[m->eq_obj2id[id]]);
break;
case mjEQ_FLEX:
// process all non-rigid edges for this flex
f = m->eq_obj1id[id];
int flex_edgeadr = m->flex_edgeadr[f];
int flex_edgenum = m->flex_edgenum[f];
for (int e=flex_edgeadr; e<flex_edgeadr+flex_edgenum; e++) {
if (!m->flexedge_rigid[e]) {
dA[i++] = m->flexedge_invweight0[e];
}
}
// adjust constraint counter
i--;
break;
default:
mjERROR("unknown constraint type type %d", d->efc_type[i]); // SHOULD NOT OCCUR
}
break;
case mjCNSTR_FRICTION_DOF:
dA[i] = m->dof_invweight0[id];
break;
case mjCNSTR_LIMIT_JOINT:
dA[i] = m->dof_invweight0[m->jnt_dofadr[id]];
break;
case mjCNSTR_FRICTION_TENDON:
case mjCNSTR_LIMIT_TENDON:
dA[i] = m->tendon_invweight0[id];
break;
case mjCNSTR_CONTACT_FRICTIONLESS:
case mjCNSTR_CONTACT_PYRAMIDAL:
case mjCNSTR_CONTACT_ELLIPTIC:
// get contact info
con = d->contact + id;
dim = con->dim;
// add the average translation and rotation components from both sides
tran = rot = 0;
for (int side=0; side < 2; side++) {
// get bodies and weights
int nb = 0, bid[32], vid[4], nw = 0;
mjtNum bweight[32], bw[4];
// geom
if (con->geom[side] >= 0) {
bid[0] = m->geom_bodyid[con->geom[side]];
bweight[0] = 1;
nb = 1;
}
// flex vert
else if (con->vert[side] >= 0) {
vid[0] = m->flex_vertadr[con->flex[side]] + con->vert[side];
bw[0] = 1;
nw = 1;
}
// flex elem
else {
nw = mj_elemBodyWeight(m, d, con->flex[side], con->elem[side],
con->vert[1-side], con->pos, vid, bw);
}
// get body or node ids and weights
for (int k=0; k < nw; k++) {
if (m->flex_interp[con->flex[side]] == 0) {
bid[k] = m->flex_vertbodyid[vid[k]];
bweight[k] = bw[k];
nb++;
} else {
nb = mj_vertBodyWeight(m, d, con->flex[side], vid[k],
con->pos, bid, bweight, bw[k]);
}
}
// add weighted average over bodies
for (int k=0; k < nb; k++) {
tran += m->body_invweight0[2*bid[k]] * bweight[k];
rot += m->body_invweight0[2*bid[k]+1] * bweight[k];
}
}
// set frictionless
if (d->efc_type[i] == mjCNSTR_CONTACT_FRICTIONLESS) {
dA[i] = tran;
}
// set elliptical
else if (d->efc_type[i] == mjCNSTR_CONTACT_ELLIPTIC) {
for (int j=0; j < dim; j++) {
dA[i+j] = (j < 3 ? tran : rot);
}
// processed dim elements in one i-loop iteration; advance counter
i += (dim-1);
}
// set pyramidal
else {
for (int j=0; j < dim-1; j++) {
fri = con->friction[j];
dA[i+2*j] = dA[i+2*j+1] = tran + fri*fri*(j < 2 ? tran : rot);
}
// processed 2*dim-2 elements in one i-loop iteration; advance counter
i += (2*dim-3);
}
}
}
}
// get solref, solimp for specified constraint
static void getsolparam(const mjModel* m, const mjData* d, int i,
mjtNum* solref, mjtNum* solreffriction, mjtNum* solimp) {
// get constraint id
int id = d->efc_id[i];
// clear solreffriction (applies only to contacts)
mju_zero(solreffriction, mjNREF);
// extract solver parameters from corresponding model element
switch ((mjtConstraint) d->efc_type[i]) {
case mjCNSTR_EQUALITY:
mju_copy(solref, m->eq_solref+mjNREF*id, mjNREF);
mju_copy(solimp, m->eq_solimp+mjNIMP*id, mjNIMP);
break;
case mjCNSTR_LIMIT_JOINT:
mju_copy(solref, m->jnt_solref+mjNREF*id, mjNREF);
mju_copy(solimp, m->jnt_solimp+mjNIMP*id, mjNIMP);
break;
case mjCNSTR_FRICTION_DOF:
mju_copy(solref, m->dof_solref+mjNREF*id, mjNREF);
mju_copy(solimp, m->dof_solimp+mjNIMP*id, mjNIMP);
break;
case mjCNSTR_LIMIT_TENDON:
mju_copy(solref, m->tendon_solref_lim+mjNREF*id, mjNREF);
mju_copy(solimp, m->tendon_solimp_lim+mjNIMP*id, mjNIMP);
break;
case mjCNSTR_FRICTION_TENDON:
mju_copy(solref, m->tendon_solref_fri+mjNREF*id, mjNREF);
mju_copy(solimp, m->tendon_solimp_fri+mjNIMP*id, mjNIMP);
break;
case mjCNSTR_CONTACT_FRICTIONLESS:
case mjCNSTR_CONTACT_PYRAMIDAL:
case mjCNSTR_CONTACT_ELLIPTIC:
mju_copy(solref, d->contact[id].solref, mjNREF);
mju_copy(solreffriction, d->contact[id].solreffriction, mjNREF);
mju_copy(solimp, d->contact[id].solimp, mjNIMP);
}
// check reference format: standard or direct, cannot be mixed
if ((solref[0] > 0) ^ (solref[1] > 0)) {
mju_warning("mixed solref format, replacing with default");
mj_defaultSolRefImp(solref, NULL);
}
// integrator safety: impose ref[0]>=2*timestep for standard format
if (!mjDISABLED(mjDSBL_REFSAFE) && solref[0] > 0) {
solref[0] = mju_max(solref[0], 2*m->opt.timestep);
}
// check reference format: standard or direct, cannot be mixed
if ((solreffriction[0] > 0) ^ (solreffriction[1] > 0)) {
mju_warning("solreffriction values should have the same sign, replacing with default");
mju_zero(solreffriction, mjNREF); // default solreffriction is (0, 0)
}
// integrator safety: impose ref[0]>=2*timestep for standard format
if (!mjDISABLED(mjDSBL_REFSAFE) && solreffriction[0] > 0) {
solreffriction[0] = mju_max(solreffriction[0], 2*m->opt.timestep);
}
// enforce constraints on solimp
solimp[0] = mju_min(mjMAXIMP, mju_max(mjMINIMP, solimp[0]));
solimp[1] = mju_min(mjMAXIMP, mju_max(mjMINIMP, solimp[1]));
solimp[2] = mju_max(0, solimp[2]);
solimp[3] = mju_min(mjMAXIMP, mju_max(mjMINIMP, solimp[3]));
solimp[4] = mju_max(1, solimp[4]);
}
// get pos and dim for specified constraint
static void getposdim(const mjModel* m, const mjData* d, int i, mjtNum* pos, int* dim) {
// get id of constraint-related object
int id = d->efc_id[i];
// set (dim, pos) for common case
*dim = 1;
*pos = d->efc_pos[i];
// change (dim, distance) for special cases
switch ((mjtConstraint) d->efc_type[i]) {
case mjCNSTR_CONTACT_ELLIPTIC:
*dim = d->contact[id].dim;
break;
case mjCNSTR_CONTACT_PYRAMIDAL:
*dim = 2*(d->contact[id].dim-1);
break;
case mjCNSTR_EQUALITY:
if (m->eq_type[id] == mjEQ_WELD) {
*dim = 6;
*pos = mju_norm(d->efc_pos+i, 6);
} else if (m->eq_type[id] == mjEQ_CONNECT) {
*dim = 3;
*pos = mju_norm(d->efc_pos+i, 3);
}
break;
default:
// already handled
break;
}
}
// return a to the power of b, quick return for powers 1 and 2
// solimp[4] == 2 is the default, so these branches are common
static mjtNum power(mjtNum a, mjtNum b) {
if (b == 1) {
return a;
} else if (b == 2) {
return a*a;
}
return mju_pow(a, b);
}
// compute impedance and derivative for one constraint
static void getimpedance(const mjtNum* solimp, mjtNum pos, mjtNum margin,
mjtNum* imp, mjtNum* impP) {
// flat function
if (solimp[0] == solimp[1] || solimp[2] <= mjMINVAL) {
*imp = 0.5*(solimp[0] + solimp[1]);
*impP = 0;
return;
}
// x = abs((pos-margin) / width)
mjtNum x = (pos-margin) / solimp[2];
mjtNum sgn = 1;
if (x < 0) {
x = -x;
sgn = -1;
}
// fully saturated
if (x >= 1 || x <= 0) {
*imp = (x >= 1 ? solimp[1] : solimp[0]);
*impP = 0;
return;
}
// linear
mjtNum y, yP;
if (solimp[4] == 1) {
y = x;
yP = 1;
}
// y(x) = a*x^p if x<=midpoint
else if (x <= solimp[3]) {
mjtNum a = 1/power(solimp[3], solimp[4]-1);
y = a*power(x, solimp[4]);
yP = solimp[4] * a*power(x, solimp[4]-1);
}
// y(x) = 1-b*(1-x)^p if x>midpoint
else {
mjtNum b = 1/power(1-solimp[3], solimp[4]-1);
y = 1-b*power(1-x, solimp[4]);
yP = solimp[4] * b*power(1-x, solimp[4]-1);
}
// scale
*imp = solimp[0] + y*(solimp[1]-solimp[0]);
*impP = yP * sgn * (solimp[1]-solimp[0]) / solimp[2];
}
// compute efc_R, efc_D, efc_KBIP, adjust efc_diagApprox
void mj_makeImpedance(const mjModel* m, mjData* d) {
int dim, nefc = d->nefc;
mjtNum *R = d->efc_R, *KBIP = d->efc_KBIP;
mjtNum pos, imp, impP, Rpy, solref[mjNREF], solreffriction[mjNREF], solimp[mjNIMP];
// set efc_R, efc_KBIP
for (int i=0; i < nefc; i++) {
// get solref and solimp
getsolparam(m, d, i, solref, solreffriction, solimp);
// get pos and dim
getposdim(m, d, i, &pos, &dim);
// get imp and impP
getimpedance(solimp, pos, d->efc_margin[i], &imp, &impP);
// set R and KBIP for all constraint dimensions
for (int j=0; j < dim; j++) {
// R = (1-imp)/imp * diagApprox
R[i+j] = mju_max(mjMINVAL, (1-imp)*d->efc_diagApprox[i+j]/imp);
// constraint type
int tp = d->efc_type[i+j];
// elliptic contacts use solreffriction in non-normal directions, if non-zero
int elliptic_friction = (tp == mjCNSTR_CONTACT_ELLIPTIC) && (j > 0);
mjtNum* ref = elliptic_friction && (solreffriction[0] || solreffriction[1]) ?
solreffriction : solref;
// friction: K = 0
if (tp == mjCNSTR_FRICTION_DOF || tp == mjCNSTR_FRICTION_TENDON || elliptic_friction) {
KBIP[4*(i+j)] = 0;
}
// standard: K = 1 / (dmax^2 * timeconst^2 * dampratio^2)
else if (ref[0] > 0)
KBIP[4*(i+j)] = 1 / mju_max(mjMINVAL, solimp[1]*solimp[1] * ref[0]*ref[0] * ref[1]*ref[1]);
// direct: K = -solref[0] / dmax^2
else {
KBIP[4*(i+j)] = -ref[0] / mju_max(mjMINVAL, solimp[1]*solimp[1]);
}
// standard: B = 2 / (dmax*timeconst)
if (ref[1] > 0) {
KBIP[4*(i+j)+1] = 2 / mju_max(mjMINVAL, solimp[1]*ref[0]);
}
// direct: B = -solref[1] / dmax
else {
KBIP[4*(i+j)+1] = -ref[1] / mju_max(mjMINVAL, solimp[1]);
}
// I = imp, P = imp'
KBIP[4*(i+j)+2] = imp;
KBIP[4*(i+j)+3] = impP;
}
// skip the rest of this constraint
i += (dim-1);
}
// frictional contacts: adjust R in friction dimensions, set contact master mu
for (int i=d->ne+d->nf; i < nefc; i++) {
if (d->efc_type[i] == mjCNSTR_CONTACT_PYRAMIDAL ||
d->efc_type[i] == mjCNSTR_CONTACT_ELLIPTIC) {
// extract id, dim, mu
int id = d->efc_id[i];
dim = d->contact[id].dim;
mjtNum* friction = d->contact[id].friction;
// set R[1] = R[0]/impratio
R[i+1] = R[i]/mju_max(mjMINVAL, m->opt.impratio);
// set mu of regularized cone = mu[1]*sqrt(R[1]/R[0])
d->contact[id].mu = friction[0] * mju_sqrt(R[i+1]/R[i]);
// elliptic
if (d->efc_type[i] == mjCNSTR_CONTACT_ELLIPTIC) {
// set remaining R's such that R[j]*mu[j]^2 = R[1]*mu[1]^2
for (int j=1; j < dim-1; j++) {
R[i+j+1] = R[i+1]*friction[0]*friction[0]/(friction[j]*friction[j]);
}
// skip the rest of this contact
i += (dim-1);
}
// pyramidal: common R matching friction impedance of elliptic model
else {
// D0_el = 2*(dim-1)*D_py : normal match
// D0_el = 2*mu^2*D_py : friction match
Rpy = 2*d->contact[id].mu*d->contact[id].mu*R[i];
// assign Rpy to all pyramidal R
for (int j=0; j < 2*(dim-1); j++) {
R[i+j] = Rpy;
}
// skip the rest of this contact
i += 2*(dim-1) - 1;
}
}
}
// set D = 1 / R
for (int i=0; i < nefc; i++) {
d->efc_D[i] = 1 / R[i];
}
// adjust diagApprox so that R = (1-imp)/imp * diagApprox
for (int i=0; i < nefc; i++) {
d->efc_diagApprox[i] = R[i] * KBIP[4*i+2] / (1-KBIP[4*i+2]);
}
}
//------------------------------------- constraint counting ----------------------------------------
// count the non-zero columns in the Jacobian difference of two bodies
static int mj_jacDifPairCount(const mjModel* m, int* chain,
int b1, int b2, int issparse) {
if (!m->nv) {
return 0;
}
if (issparse) {
if (m->body_simple[b1] && m->body_simple[b2]) {
return mj_mergeChainSimple(m, chain, b1, b2);
}
return mj_mergeChain(m, chain, b1, b2);
}
return m->nv;
}
// count the non-zero columns of the Jacobian returned by mj_jacSum
static int mj_jacSumCount(const mjModel* m, mjData* d, int* chain,
int n, const int* body) {
int nv = m->nv, NV;
mj_markStack(d);
int* bodychain = mjSTACKALLOC(d, nv, int);
int* tempchain = mjSTACKALLOC(d, nv, int);
// set first
NV = mj_bodyChain(m, body[0], chain);
// accumulate remaining
for (int i=1; i < n; i++) {
// get body chain
int bodyNV = mj_bodyChain(m, body[i], bodychain);
if (!bodyNV) {
continue;
}
// accumulate chains
NV = mju_addChains(tempchain, nv, NV, bodyNV, chain, bodychain);
if (NV) {
mju_copyInt(chain, tempchain, NV);
}
}
mj_freeStack(d);
return NV;
}
// return number of constraint non-zeros, handle dense and dof-less cases
static inline int mj_addConstraintCount(const mjModel* m, int size, int NV) {
// over count for dense allocation
if (!mj_isSparse(m)) {
return m->nv ? size : 0;
}
return mjMAX(0, NV) ? size : 0;
}
// count equality constraints, count Jacobian nonzeros if nnz is not NULL
static int mj_ne(const mjModel* m, mjData* d, int* nnz) {
int ne = 0, nnze = 0;
int nv = m->nv, neq = m->neq;
int id[2], size, NV, NV2, *chain = NULL, *chain2 = NULL;
int issparse = (nnz != NULL);
int flex_edgeadr, flex_edgenum;
// disabled or no equality constraints: return
if (mjDISABLED(mjDSBL_EQUALITY) || m->nemax == 0) {
return 0;
}
mj_markStack(d);
if (nnz) {
chain = mjSTACKALLOC(d, nv, int);
chain2 = mjSTACKALLOC(d, nv, int);
}
// find active equality constraints
for (int i=0; i < neq; i++) {
if (d->eq_active[i]) {
id[0] = m->eq_obj1id[i];
id[1] = m->eq_obj2id[i];
size = 0;
NV = 0;
NV2 = 0;
// process according to type
switch ((mjtEq) m->eq_type[i]) {
case mjEQ_CONNECT:
size = 3;
if (!nnz) {
break;
}
// get body ids if using site semantics
if (m->eq_objtype[i] == mjOBJ_SITE) {
id[0] = m->site_bodyid[id[0]];
id[1] = m->site_bodyid[id[1]];
}
NV = mj_jacDifPairCount(m, chain, id[1], id[0], issparse);
break;
case mjEQ_WELD:
size = 6;
if (!nnz) {
break;
}
// get body ids if using site semantics
if (m->eq_objtype[i] == mjOBJ_SITE) {
id[0] = m->site_bodyid[id[0]];
id[1] = m->site_bodyid[id[1]];
}
NV = mj_jacDifPairCount(m, chain, id[1], id[0], issparse);
break;
case mjEQ_JOINT:
case mjEQ_TENDON:
size = 1;
if (!nnz) {
break;
}
for (int j=0; j < 1+(id[1] >= 0); j++) {
if (m->eq_type[i] == mjEQ_JOINT) {
if (!j) {
NV = 1;
chain[0] = m->jnt_dofadr[id[j]];
} else {
NV2 = 1;
chain2[0] = m->jnt_dofadr[id[j]];
}
} else {
if (!j) {
NV = d->ten_J_rownnz[id[j]];
mju_copyInt(chain, d->ten_J_colind+d->ten_J_rowadr[id[j]], NV);
} else {
NV2 = d->ten_J_rownnz[id[j]];
mju_copyInt(chain2, d->ten_J_colind+d->ten_J_rowadr[id[j]], NV2);
}
}
}
if (id[1] >= 0) {
NV = mju_combineSparseCount(NV, NV2, chain, chain2);
}
break;
case mjEQ_FLEX:
flex_edgeadr = m->flex_edgeadr[id[0]];
flex_edgenum = m->flex_edgenum[id[0]];
// init with all edges, subract rigid later
size = flex_edgenum;
// process edges of this flex
for (int e=flex_edgeadr; e < flex_edgeadr+flex_edgenum; e++) {
// rigid: reduce size and skip
if (m->flexedge_rigid[e]) {
size--;
continue;
}
// accumulate NV if needed
if (nnz) {
int b1 = m->flex_vertbodyid[m->flex_vertadr[id[0]] + m->flex_edge[2*e]];
int b2 = m->flex_vertbodyid[m->flex_vertadr[id[0]] + m->flex_edge[2*e+1]];
NV += mj_jacDifPairCount(m, chain, b1, b2, issparse);
}
}
break;
default:
// might occur in case of the now-removed distance equality constraint
mjERROR("unknown constraint type type %d", m->eq_type[i]); // SHOULD NOT OCCUR
}
// accumulate counts; flex NV already accumulated
ne += mj_addConstraintCount(m, size, NV);
nnze += (m->eq_type[i] == mjEQ_FLEX) ? NV : size*NV;
}
}
if (nnz) {
*nnz += nnze;
}
mj_freeStack(d);
return ne;
}
// count frictional constraints, count Jacobian nonzeros if nnz is not NULL
static int mj_nf(const mjModel* m, const mjData* d, int *nnz) {
int nf = 0;
int nv = m->nv, ntendon = m->ntendon;
if (mjDISABLED(mjDSBL_FRICTIONLOSS)) {
return 0;
}
for (int i=0; i < nv; i++) {
if (m->dof_frictionloss[i] > 0) {
nf += mj_addConstraintCount(m, 1, 1);
if (nnz) *nnz += 1;
}
}
for (int i=0; i < ntendon; i++) {
if (m->tendon_frictionloss[i] > 0) {
nf += mj_addConstraintCount(m, 1, d->ten_J_rownnz[i]);
if (nnz) *nnz += d->ten_J_rownnz[i];
}
}
return nf;
}
// count limit constraints, count Jacobian nonzeros if nnz is not NULL
static int mj_nl(const mjModel* m, const mjData* d, int *nnz) {
int nl = 0;
int ntendon = m->ntendon;
int side;
mjtNum margin, value, dist;
// disabled: return
if (mjDISABLED(mjDSBL_LIMIT)) {
return 0;
}
for (int i=0; i < m->njnt; i++) {
if (!m->jnt_limited[i]) {
continue;
}
margin = m->jnt_margin[i];
// slider and hinge joint limits can be bilateral, check both sides
if (m->jnt_type[i] == mjJNT_SLIDE || m->jnt_type[i] == mjJNT_HINGE) {
value = d->qpos[m->jnt_qposadr[i]];
for (side=-1; side <= 1; side+=2) {
dist = side * (m->jnt_range[2*i+(side+1)/2] - value);
if (dist < margin) {
nl += mj_addConstraintCount(m, 1, 1);
if (nnz) *nnz += 1;
}
}
}
else if (m->jnt_type[i] == mjJNT_BALL) {
mjtNum angleAxis[3];
int adr = m->jnt_qposadr[i];
mjtNum quat[4] = {d->qpos[adr], d->qpos[adr+1], d->qpos[adr+2], d->qpos[adr+3]};
mju_normalize4(quat);
mju_quat2Vel(angleAxis, quat, 1);
value = mju_normalize3(angleAxis);
dist = mju_max(m->jnt_range[2*i], m->jnt_range[2*i+1]) - value;
if (dist < margin) {
nl += mj_addConstraintCount(m, 1, 3);
if (nnz) *nnz += 3;
}
}
}
for (int i=0; i < ntendon; i++) {
if (m->tendon_limited[i]) {
value = d->ten_length[i];
margin = m->tendon_margin[i];
// tendon limits can be bilateral, check both sides
for (side=-1; side <= 1; side+=2) {
dist = side * (m->tendon_range[2*i+(side+1)/2] - value);
if (dist < margin) {
nl += mj_addConstraintCount(m, 1, d->ten_J_rownnz[i]);
if (nnz) *nnz += d->ten_J_rownnz[i];
}
}
}
}
return nl;
}
// count contact constraints, count Jacobian nonzeros if nnz is not NULL
static int mj_nc(const mjModel* m, mjData* d, int* nnz) {
int nnzc = 0, nc = 0;
int ispyramid = mj_isPyramidal(m), ncon = d->ncon;
if (mjDISABLED(mjDSBL_CONTACT) || !ncon) {
return 0;
}
mj_markStack(d);
int *chain = mjSTACKALLOC(d, m->nv, int);
for (int i=0; i < ncon; i++) {
mjContact* con = d->contact + i;
// skip if excluded
if (con->exclude) {
continue;
}
// compute NV only if nnz requested
int NV = 0;
if (nnz) {
// get bodies
int nb = 0, bid[64];
for (int side=0; side < 2; side++) {
int nw = 0;
int vid[4];
// geom
if (con->geom[side] >= 0) {
bid[nb++] = m->geom_bodyid[con->geom[side]];
}
// flex vert
else if (con->vert[side] >= 0) {
vid[nw++] = m->flex_vertadr[con->flex[side]] + con->vert[side];
}
// flex elem
else {
int f = con->flex[side];
int fdim = m->flex_dim[f];
const int* edata = m->flex_elem + m->flex_elemdataadr[f] + con->elem[side]*(fdim+1);
for (int k=0; k <= fdim; k++) {
vid[nw++] = m->flex_vertadr[f] + edata[k];
}
}
// get body or node ids and weights
for (int k=0; k < nw; k++) {
if (m->flex_interp[con->flex[side]] == 0) {
bid[nb] = m->flex_vertbodyid[vid[k]];
nb++;
} else {
nb += mj_vertBodyWeight(m, d, con->flex[side], vid[k],
con->pos, bid+nb, NULL, 0);
}
}
}
// count non-zeros in merged chain
NV = mj_jacSumCount(m, d, chain, nb, bid);
if (!NV) {
continue;
}
}
// count according to friction type
int dim = con->dim;
if (dim == 1) {
nc++;
nnzc += NV;
} else if (ispyramid) {
nc += 2*(dim-1);
nnzc += 2*(dim-1)*NV;
} else {
nc += dim;
nnzc += dim*NV;
}
}
if (nnz) {
*nnz += nnzc;
}
mj_freeStack(d);
return nc;
}
//---------------------------- top-level API for constraint construction ---------------------------
// driver: call all functions above
void mj_makeConstraint(const mjModel* m, mjData* d) {
// clear sizes
d->ne = d->nf = d->nl = d->nefc = d->nJ = d->nA = 0;
// disabled or Jacobian not allocated: return
if (mjDISABLED(mjDSBL_CONSTRAINT)) {
return;
}
// precount sizes for constraint Jacobian matrices
int *nnz = mj_isSparse(m) ? &(d->nJ) : NULL;
int ne_allocated = mj_ne(m, d, nnz);
int nf_allocated = mj_nf(m, d, nnz);
int nl_allocated = mj_nl(m, d, nnz);
int nefc_allocated = ne_allocated + nf_allocated + nl_allocated + mj_nc(m, d, nnz);
if (!mj_isSparse(m)) {
d->nJ = nefc_allocated * m->nv;
}
d->nefc = nefc_allocated;
// allocate efc arrays on arena
if (!arenaAllocEfc(m, d)) {
return;
}
// clear tendon_efcadr
for (int i=0; i < m->ntendon; i++) {
d->tendon_efcadr[i] = -1;
}
// reset nefc for the instantiation functions,
// and instantiate all elements of Jacobian
d->nefc = 0;
mj_instantiateEquality(m, d);
mj_instantiateFriction(m, d);
mj_instantiateLimit(m, d);
mj_instantiateContact(m, d);
// check sparse allocation
if (mj_isSparse(m)) {
if (d->ne != ne_allocated) {
mjERROR("ne mis-allocation: found ne=%d but allocated %d", d->ne, ne_allocated);
}
if (d->nf != nf_allocated) {
mjERROR("nf mis-allocation: found nf=%d but allocated %d", d->nf, nf_allocated);
}
if (d->nl != nl_allocated) {
mjERROR("nl mis-allocation: found nl=%d but allocated %d", d->nl, nl_allocated);
}
// check that nefc was computed correctly
if (d->nefc != nefc_allocated) {
mjERROR("nefc mis-allocation: found nefc=%d but allocated %d", d->nefc, nefc_allocated);
}
// check that nJ was computed correctly
if (d->nefc > 0) {
int nJ = d->efc_J_rownnz[d->nefc - 1] + d->efc_J_rowadr[d->nefc - 1];
if (d->nJ != nJ) {
mjERROR("constraint Jacobian mis-allocation: found nJ=%d but allocated %d", nJ, d->nJ);
}
}
} else if (d->nefc > nefc_allocated) {
mjERROR("nefc under-allocation: found nefc=%d but allocated only %d",
d->nefc, nefc_allocated);
}
// collect memory use statistics
d->maxuse_con = mjMAX(d->maxuse_con, d->ncon);
d->maxuse_efc = mjMAX(d->maxuse_efc, d->nefc);
// no constraints: return
if (!d->nefc) {
return;
}
// transpose sparse Jacobian, make row supernodes
if (mj_isSparse(m)) {
// transpose
mju_transposeSparse(d->efc_JT, d->efc_J, d->nefc, m->nv,
d->efc_JT_rownnz, d->efc_JT_rowadr, d->efc_JT_colind, d->efc_JT_rowsuper,
d->efc_J_rownnz, d->efc_J_rowadr, d->efc_J_colind);
#ifdef mjUSEAVX
// compute supernodes of J; used by mju_mulMatVecSparse_avx
mju_superSparse(d->nefc, d->efc_J_rowsuper,
d->efc_J_rownnz, d->efc_J_rowadr, d->efc_J_colind);
#else
#ifdef MEMORY_SANITIZER
// tell msan to treat the entire J rowsuper as uninitialized
__msan_allocated_memory(d->efc_J_rowsuper, d->nefc);
#endif // MEMORY_SANITIZER
#endif // mjUSEAVX
}
// compute diagApprox
mj_diagApprox(m, d);
// compute KBIP, D, R, adjust diagApprox
mj_makeImpedance(m, d);
}
// compute efc_AR
void mj_projectConstraint(const mjModel* m, mjData* d) {
int nefc = d->nefc, nv = m->nv;
// nothing to do
if (nefc == 0 || !mj_isDual(m)) {
return;
}
mj_markStack(d);
// inverse square root of D from inertia LDL decomposition
mjtNum* sqrtInvD = mjSTACKALLOC(d, nv, mjtNum);
for (int i=0; i < nv; i++) {
int diag = d->M_rowadr[i] + d->M_rownnz[i] - 1;
sqrtInvD[i] = 1 / mju_sqrt(d->qLD[diag]);
}
// sparse
if (mj_isSparse(m)) {
// compute B = backsubM2(J')' and its transpose
// === pre-count B_rownnz, B_rowadr, nB (total nonzeros)
// allocate B rownnz and rowadr
int* B_rownnz = mjSTACKALLOC(d, nefc, int);
int* B_rowadr = mjSTACKALLOC(d, nefc, int);
// markers for merged dofs, initialized to -1
int* marker = mjSTACKALLOC(d, nv, int);
for (int i=0; i < nv; i++) {
marker[i] = -1;
}
B_rowadr[0] = 0;
for (int r=0; r < nefc; r++) {
int nnz = 0; // nonzeros in row r of B
// traverse row r of J in reverse, count unique nonzeros
int start = d->efc_J_rowadr[r];
int end = start + d->efc_J_rownnz[r];
for (int i=end-1; i >= start; i--) {
int j = d->efc_J_colind[i];
// if dof j is marked, it was already counted by a child dof: skip it
if (marker[j] == r) {
continue;
}
// traverse row j of C, marking new unique nonzeros
int nnzC = d->M_rownnz[j];
int adrC = d->M_rowadr[j];
for (int k=0; k < nnzC; k++) {
int c = d->M_colind[adrC + k];
if (marker[c] != r) {
marker[c] = r;
nnz++;
}
}
}
// update rownnz and rowadr
B_rownnz[r] = nnz;
if (r < nefc - 1) {
B_rowadr[r+1] = B_rowadr[r] + nnz;
}
}
// total non-zeros in B
int nB = B_rowadr[nefc-1] + B_rownnz[nefc-1];
// === fill in B column indices, copy values from J
// allocate values and column indices
mjtNum* B = mjSTACKALLOC(d, nB, mjtNum);
int* B_colind = mjSTACKALLOC(d, nB, int);
for (int r=0; r < nefc; r++) {
// init row
int end = B_rowadr[r] + B_rownnz[r];
int adrJ = d->efc_J_rowadr[r];
int remainJ = d->efc_J_rownnz[r];
int nnzB = 0;
// complete chain in reverse
while (1) {
// get previous dof in src and dst
int prev_src = (remainJ > 0 ? d->efc_J_colind[adrJ + remainJ - 1] : -1);
int prev_dst = (nnzB > 0 ? m->dof_parentid[B_colind[end - nnzB]] : -1);
// both finished: break
if (prev_src < 0 && prev_dst < 0) {
break;
}
// add src
else if (prev_src >= prev_dst) {
nnzB++;
remainJ--;
B_colind[end - nnzB] = prev_src;
B[end - nnzB] = d->efc_J[adrJ + remainJ];
}
// add dst
else {
nnzB++;
B_colind[end - nnzB] = prev_dst;
B[end - nnzB] = 0;
}
}
// compare with B_rownnz: SHOULD NOT OCCUR
if (nnzB != B_rownnz[r]) {
mjERROR("pre and post-count of B_rownnz are not equal on row %d", r);
}
}
// === in-place sparse back-substitution: B <- B * M^-1/2
// sparse backsubM2 (half of LD back-substitution)
for (int r=0; r < nefc; r++) {
int nnzB = B_rownnz[r];
int adrB = B_rowadr[r];
// B(r,:) <- inv(L') * B(r,:), exploit sparsity of input vector
for (int i=adrB + nnzB-1; i >= adrB; i--) {
mjtNum b = B[i];
if (b == 0) {
continue;
}
int j = B_colind[i];
int adrC = d->M_rowadr[j];
mju_addToSclSparseInc(B + adrB, d->qLD + adrC,
nnzB, B_colind + adrB,
d->M_rownnz[j]-1, d->M_colind + adrC, -b);
}
// B(r,:) <- sqrt(inv(D)) * B(r,:)
for (int i=adrB; i < adrB + nnzB; i++) {
int j = B_colind[i];
B[i] *= sqrtInvD[j];
}
}
// construct B supernodes
int* B_rowsuper = mjSTACKALLOC(d, nefc, int);
mju_superSparse(nefc, B_rowsuper, B_rownnz, B_rowadr, B_colind);
// construct B transposed
int* BT_rownnz = mjSTACKALLOC(d, nv, int);
int* BT_rowadr = mjSTACKALLOC(d, nv, int);
int* BT_colind = mjSTACKALLOC(d, nB, int);
mjtNum* BT = mjSTACKALLOC(d, nB, mjtNum);
mju_transposeSparse(BT, B, nefc, nv,
BT_rownnz, BT_rowadr, BT_colind, NULL,
B_rownnz, B_rowadr, B_colind);
// allocate AR row nonzeros and addresses on arena
d->efc_AR_rownnz = mj_arenaAllocByte(d, sizeof(int) * nefc, _Alignof(int));
d->efc_AR_rowadr = mj_arenaAllocByte(d, sizeof(int) * nefc, _Alignof(int));
if (!d->efc_AR_rownnz || !d->efc_AR_rowadr) {
mj_warning(d, mjWARN_CNSTRFULL, d->narena);
mj_clearEfc(d);
d->parena = d->ncon * sizeof(mjContact);
mj_freeStack(d);
return;
}
// pre-count A nonzeros (compute AR_rownnz, AR_rowadr)
d->nA = mju_sqrMatTDSparseCount(d->efc_AR_rownnz, d->efc_AR_rowadr, nefc,
BT_rownnz, BT_rowadr, BT_colind,
B_rownnz, B_rowadr, B_colind, B_rowsuper, d, /*flg_upper=*/1);
// allocate A values and column indices on arena
d->efc_AR = mj_arenaAllocByte(d, sizeof(mjtNum) * d->nA, _Alignof(mjtNum));
d->efc_AR_colind = mj_arenaAllocByte(d, sizeof(int) * d->nA, _Alignof(int));
if (!d->efc_AR || !d->efc_AR_colind) {
mj_warning(d, mjWARN_CNSTRFULL, d->narena);
mj_clearEfc(d);
d->parena = d->ncon * sizeof(mjContact);
mj_freeStack(d);
return;
}
// A = B * B'
int* diagind = mjSTACKALLOC(d, nefc, int);
mju_sqrMatTDSparse(d->efc_AR, BT, B, NULL, nv, nefc,
d->efc_AR_rownnz, d->efc_AR_rowadr, d->efc_AR_colind,
BT_rownnz, BT_rowadr, BT_colind, NULL,
B_rownnz, B_rowadr, B_colind, B_rowsuper, d, diagind);
// AR = A + diag(R)
for (int i=0; i < nefc; i++) {
d->efc_AR[diagind[i]] += d->efc_R[i];
}
}
// dense
else {
d->nA = nefc * nefc;
// arena-allocate efc_AR
d->efc_AR = mj_arenaAllocByte(d, sizeof(mjtNum) * d->nA, _Alignof(mjtNum));
if (!d->efc_AR) {
mj_warning(d, mjWARN_CNSTRFULL, d->narena);
mj_clearEfc(d);
d->parena = d->ncon * sizeof(mjContact);
mj_freeStack(d);
return;
}
// space for B = backsubM2(J')' and its transpose
mjtNum* B = mjSTACKALLOC(d, nefc*nv, mjtNum);
mjtNum* BT = mjSTACKALLOC(d, nv*nefc, mjtNum);
// B = backsubM2(J')'
mj_solveM2(m, d, B, d->efc_J, sqrtInvD, nefc);
// construct BT
mju_transpose(BT, B, nefc, nv);
// AR = B * B'
mju_sqrMatTD(d->efc_AR, BT, NULL, nv, nefc);
// add R to diagonal of AR
for (int r=0; r < nefc; r++) {
d->efc_AR[r*(nefc+1)] += d->efc_R[r];
}
}
mj_freeStack(d);
}
// compute efc_vel, efc_aref
void mj_referenceConstraint(const mjModel* m, mjData* d) {
int nefc = d->nefc;
mjtNum* KBIP = d->efc_KBIP;
// compute efc_vel
mj_mulJacVec(m, d, d->efc_vel, d->qvel);
// compute aref = -B*vel - K*I*(pos-margin)
for (int i=0; i < nefc; i++) {
d->efc_aref[i] = -KBIP[4*i+1]*d->efc_vel[i]
-KBIP[4*i]*KBIP[4*i+2]*(d->efc_pos[i]-d->efc_margin[i]);
}
}
//---------------------------- update constraint state ---------------------------------------------
// compute efc_state, efc_force
// optional: cost(qacc) = s_hat(jar); cone Hessians
void mj_constraintUpdate_impl(int ne, int nf, int nefc,
const mjtNum* D, const mjtNum* R, const mjtNum* floss,
const mjtNum* jar, const int* type, const int* id,
mjContact* contact, int* state, mjtNum* force, mjtNum cost[1],
int flg_coneHessian) {
mjtNum s = 0;
// no constraints: clear cost, return
if (!nefc) {
if (cost) {
*cost = 0;
}
return;
}
// compute unconstrained efc_force
for (int i=0; i < nefc; i++) {
force[i] = -D[i]*jar[i];
}
// update constraints
for (int i=0; i < nefc; i++) {
// ==== equality
if (i < ne) {
if (cost) {
s += 0.5*D[i]*jar[i]*jar[i];
}
state[i] = mjCNSTRSTATE_QUADRATIC;
continue;
}
// ==== friction
if (i < ne + nf) {
// linear negative
if (jar[i] <= -R[i]*floss[i]) {
if (cost) {
s += -0.5*R[i]*floss[i]*floss[i] - floss[i]*jar[i];
}
force[i] = floss[i];
state[i] = mjCNSTRSTATE_LINEARNEG;
}
// linear positive
else if (jar[i] >= R[i]*floss[i]) {
if (cost) {
s += -0.5*R[i]*floss[i]*floss[i] + floss[i]*jar[i];
}
force[i] = -floss[i];
state[i] = mjCNSTRSTATE_LINEARPOS;
}
// quadratic
else {
if (cost) {
s += 0.5*D[i]*jar[i]*jar[i];
}
state[i] = mjCNSTRSTATE_QUADRATIC;
}
continue;
}
// ==== contact
// non-negative constraint
if (type[i] != mjCNSTR_CONTACT_ELLIPTIC) {
// constraint is satisfied: no cost
if (jar[i] >= 0) {
force[i] = 0;
state[i] = mjCNSTRSTATE_SATISFIED;
}
// quadratic
else {
if (cost) {
s += 0.5*D[i]*jar[i]*jar[i];
}
state[i] = mjCNSTRSTATE_QUADRATIC;
}
}
// contact with elliptic cone
else {
// get contact
mjContact* con = contact + id[i];
mjtNum mu = con->mu, *friction = con->friction;
int dim = con->dim;
// map to regular dual cone space
mjtNum U[6];
U[0] = jar[i]*mu;
for (int j=1; j < dim; j++) {
U[j] = jar[i+j]*friction[j-1];
}
// decompose into normal and tangent
mjtNum N = U[0];
mjtNum T = mju_norm(U+1, dim-1);
// top zone
if (N >= mu*T || (T <= 0 && N >= 0)) {
mju_zero(force+i, dim);
state[i] = mjCNSTRSTATE_SATISFIED;
}
// bottom zone
else if (mu*N+T <= 0 || (T <= 0 && N < 0)) {
if (cost) {
for (int j=0; j < dim; j++) {
s += 0.5*D[i+j]*jar[i+j]*jar[i+j];
}
}
state[i] = mjCNSTRSTATE_QUADRATIC;
}
// middle zone
else {
// cost: 0.5*D0/(mu*mu*(1+mu*mu))*(N-mu*T)^2
mjtNum Dm = D[i]/(mu*mu*(1+mu*mu));
mjtNum NmT = N - mu*T;
if (cost) {
s += 0.5*Dm*NmT*NmT;
}
// force: - ds/djar = dU/djar * ds/dU (dU/djar = diag(mu, friction))
force[i] = -Dm*NmT*mu;
for (int j=1; j < dim; j++) {
force[i+j] = -force[i]/T*U[j]*friction[j-1];
}
// set state
state[i] = mjCNSTRSTATE_CONE;
// cone Hessian
if (flg_coneHessian) {
// get Hessian pointer
mjtNum* H = contact[id[i]].H;
// set first row: (1, -mu/T * U)
mjtNum scl = -mu/T;
H[0] = 1;
for (int j=1; j < dim; j++) {
H[j] = scl*U[j];
}
// set upper block: mu*N/T^3 * U*U'
scl = mu*N/(T*T*T);
for (int k=1; k < dim; k++) {
for (int j=k; j < dim; j++) {
H[k*dim+j] = scl*U[j]*U[k];
}
}
// add to diagonal: (mu^2 - mu*N/T) * I
scl = mu*mu - mu*N/T;
for (int j=1; j < dim; j++) {
H[j*(dim+1)] += scl;
}
// pre and post multiply by diag(mu, friction), scale by Dm
for (int k=0; k < dim; k++) {
scl = Dm * (k == 0 ? mu : friction[k-1]);
for (int j=k; j < dim; j++) {
H[k*dim+j] *= scl * (j == 0 ? mu : friction[j-1]);
}
}
// make symmetric: copy upper into lower
for (int k=0; k < dim; k++) {
for (int j=k+1; j < dim; j++) {
H[j*dim+k] = H[k*dim+j];
}
}
}
}
// replicate state in all cone dimensions
for (int j=1; j < dim; j++) {
state[i+j] = state[i];
}
// advance to end of contact
i += (dim-1);
}
}
// assign cost
if (cost) {
*cost = s;
}
}
// compute efc_state, efc_force, qfrc_constraint
// optional: cost(qacc) = s_hat(jar) where jar = Jac*qacc-aref; cone Hessians
void mj_constraintUpdate(const mjModel* m, mjData* d, const mjtNum* jar,
mjtNum cost[1], int flg_coneHessian) {
mj_constraintUpdate_impl(d->ne, d->nf, d->nefc, d->efc_D, d->efc_R, d->efc_frictionloss,
jar, d->efc_type, d->efc_id, d->contact, d->efc_state, d->efc_force,
cost, flg_coneHessian);
mj_mulJacTVec(m, d, d->qfrc_constraint, d->efc_force);
}