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Mujoco_WASM/src/engine/engine_util_misc.c
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Alessio Quaglino ff7c94de8a Add quadratic interpolation to mju_interpolate3D. 
PiperOrigin-RevId: 820252349
Change-Id: I983175eb51d7e1a81da06c0911326fcb8f5fe764
2025-10-16 08:48:20 -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_util_misc.h"
#include <ctype.h>
#include <math.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <mujoco/mjdata.h>
#include <mujoco/mjmacro.h>
#include <mujoco/mjmodel.h>
#include "engine/engine_array_safety.h"
#include "engine/engine_macro.h"
#include "engine/engine_util_blas.h"
#include "engine/engine_util_errmem.h"
#include "engine/engine_util_spatial.h"
//------------------------------ tendon wrapping ---------------------------------------------------
// check for intersection of two 2D line segments
static mjtByte is_intersect(const mjtNum* p1, const mjtNum* p2,
const mjtNum* p3, const mjtNum* p4) {
mjtNum a, b;
// compute determinant, check
mjtNum det = (p4[1]-p3[1])*(p2[0]-p1[0]) - (p4[0]-p3[0])*(p2[1]-p1[1]);
if (mju_abs(det) < mjMINVAL) {
return 0;
}
// compute intersection point on each line
a = ((p4[0]-p3[0])*(p1[1]-p3[1]) - (p4[1]-p3[1])*(p1[0]-p3[0])) / det;
b = ((p2[0]-p1[0])*(p1[1]-p3[1]) - (p2[1]-p1[1])*(p1[0]-p3[0])) / det;
return ((a >= 0 && a <= 1 && b >= 0 && b <= 1) ? 1 : 0);
}
// curve length along circle
static mjtNum length_circle(const mjtNum* p0, const mjtNum* p1, int ind, mjtNum radius) {
mjtNum p0n[2] = {p0[0], p0[1]};
mjtNum p1n[2] = {p1[0], p1[1]};
// compute angle between 0 and pi
mju_normalize(p0n, 2);
mju_normalize(p1n, 2);
mjtNum angle = mju_acos(mju_dot(p0n, p1n, 2));
// flip if necessary
mjtNum cross = p0[1]*p1[0]-p0[0]*p1[1];
if ((cross > 0 && ind) || (cross < 0 && !ind)) {
angle = 2*mjPI - angle;
}
return radius*angle;
}
// 2D circle wrap
// input: pair of 2D endpoints in end[4], optional 2D side point in side[2], radius
// output: return length of circular wrap or -1
// pair of 2D points in pnt[4]
static mjtNum wrap_circle(mjtNum pnt[4], const mjtNum end[4], const mjtNum* side, mjtNum radius) {
mjtNum sqlen0 = end[0]*end[0] + end[1]*end[1];
mjtNum sqlen1 = end[2]*end[2] + end[3]*end[3];
mjtNum sqrad = radius*radius;
// either point inside circle or circle too small: no wrap
if (sqlen0 < sqrad || sqlen1 < sqrad || radius < mjMINVAL) {
return -1;
}
// points too close: no wrap
mjtNum dif[2] = {end[2]-end[0], end[3]-end[1]};
mjtNum dd = dif[0]*dif[0] + dif[1]*dif[1];
if (dd < mjMINVAL) {
return -1;
}
// find nearest point on line segment to origin: a*dif + d0
mjtNum a = -(dif[0]*end[0]+dif[1]*end[1])/dd;
if (a < 0) {
a = 0;
} else if (a > 1) {
a = 1;
}
// check for intersection and side
mjtNum tmp[2] = {a*dif[0] + end[0], a*dif[1] + end[1]};
if (tmp[0]*tmp[0]+tmp[1]*tmp[1] > sqrad && (!side || mju_dot(side, tmp, 2) >= 0)) {
return -1;
}
mjtNum sqrt0 = mju_sqrt(sqlen0 - sqrad);
mjtNum sqrt1 = mju_sqrt(sqlen1 - sqrad);
// construct the two solutions, compute goodness
mjtNum sol[2][2][2], good[2];
for (int i=0; i < 2; i++) {
int sgn = (i == 0 ? 1 : -1);
sol[i][0][0] = (end[0]*sqrad + sgn*radius*end[1]*sqrt0)/sqlen0;
sol[i][0][1] = (end[1]*sqrad - sgn*radius*end[0]*sqrt0)/sqlen0;
sol[i][1][0] = (end[2]*sqrad - sgn*radius*end[3]*sqrt1)/sqlen1;
sol[i][1][1] = (end[3]*sqrad + sgn*radius*end[2]*sqrt1)/sqlen1;
// goodness: close to sd, or shorter path
if (side) {
mju_add(tmp, sol[i][0], sol[i][1], 2);
mju_normalize(tmp, 2);
good[i] = mju_dot(tmp, side, 2);
} else {
mju_sub(tmp, sol[i][0], sol[i][1], 2);
good[i] = -mju_dot(tmp, tmp, 2);
}
// penalize for intersection
if (is_intersect(end, sol[i][0], end+2, sol[i][1])) {
good[i] = -10000;
}
}
// select the better solution
int i = (good[0] > good[1] ? 0 : 1);
pnt[0] = sol[i][0][0];
pnt[1] = sol[i][0][1];
pnt[2] = sol[i][1][0];
pnt[3] = sol[i][1][1];
// check for intersection
if (is_intersect(end, pnt, end+2, pnt+2)) {
return -1;
}
// return curve length
return length_circle(sol[i][0], sol[i][1], i, radius);
}
// 2D inside wrap
// input: pair of 2D endpoints in end[4], radius
// output: pair of 2D points in pnt[4]; return 0 if wrap, -1 if no wrap
static mjtNum wrap_inside(mjtNum pnt[4], const mjtNum end[4], mjtNum radius) {
// algorithm parameters
const int maxiter = 20;
const mjtNum zinit = 1 - 1e-7;
const mjtNum tolerance = 1e-6;
// constants
mjtNum len0 = mju_norm(end, 2);
mjtNum len1 = mju_norm(end+2, 2);
mjtNum dif[2] = {end[2]-end[0], end[3]-end[1]};
mjtNum dd = dif[0]*dif[0] + dif[1]*dif[1];
// either point inside circle or circle too small: no wrap
if (len0 <= radius || len1 <= radius || radius < mjMINVAL || len0 < mjMINVAL || len1 < mjMINVAL) {
return -1;
}
// segment-circle intersection: no wrap
if (dd > mjMINVAL) {
// find nearest point on line segment to origin: d0 + a*dif
mjtNum a = -(dif[0]*end[0] + dif[1]*end[1]) / dd;
// in segment
if (a > 0 && a < 1) {
mjtNum tmp[2];
mju_addScl(tmp, end, dif, a, 2);
if (mju_norm(tmp, 2) <= radius) {
return -1;
}
}
}
// prepare default in case of numerical failure: average
pnt[0] = 0.5*(end[0] + end[2]);
pnt[1] = 0.5*(end[1] + end[3]);
mju_normalize(pnt, 2);
mju_scl(pnt, pnt, radius, 2);
pnt[2] = pnt[0];
pnt[3] = pnt[1];
// compute function parameters: asin(A*z) + asin(B*z) - 2*asin(z) + G = 0
mjtNum A = radius/len0;
mjtNum B = radius/len1;
mjtNum cosG = (len0*len0 + len1*len1 - dd) / (2*len0*len1);
if (cosG < -1+mjMINVAL) {
return -1;
} else if (cosG > 1-mjMINVAL) {
return 0;
}
mjtNum G = mju_acos(cosG);
// init
mjtNum z = zinit;
mjtNum f = mju_asin(A*z) + mju_asin(B*z) - 2*mju_asin(z) + G;
// make sure init is not on the other side
if (f > 0) {
return 0;
}
// Newton method
int iter;
for (iter=0; iter < maxiter && mju_abs(f) > tolerance; iter++) {
// derivative
mjtNum df = A/mju_max(mjMINVAL, mju_sqrt(1-z*z*A*A)) +
B/mju_max(mjMINVAL, mju_sqrt(1-z*z*B*B)) -
2/mju_max(mjMINVAL, mju_sqrt(1-z*z));
// check sign; SHOULD NOT OCCUR
if (df > -mjMINVAL) {
return 0;
}
// new point
mjtNum z1 = z - f/df;
// make sure we are moving to the left; SHOULD NOT OCCUR
if (z1 > z) {
return 0;
}
// update solution
z = z1;
f = mju_asin(A*z) + mju_asin(B*z) - 2*mju_asin(z) + G;
// exit if positive; SHOULD NOT OCCUR
if (f > tolerance) {
return 0;
}
}
// check convergence
if (iter >= maxiter) {
return 0;
}
// finalize: rotation by ang from vec = a or b, depending on cross(a,b) sign
mjtNum vec[2];
mjtNum ang;
if (end[0]*end[3] - end[1]*end[2] > 0) {
mju_copy(vec, end, 2);
ang = mju_asin(z) - mju_asin(A*z);
} else {
mju_copy(vec, end+2, 2);
ang = mju_asin(z) - mju_asin(B*z);
}
mju_normalize(vec, 2);
pnt[0] = radius*(mju_cos(ang)*vec[0] - mju_sin(ang)*vec[1]);
pnt[1] = radius*(mju_sin(ang)*vec[0] + mju_cos(ang)*vec[1]);
pnt[2] = pnt[0];
pnt[3] = pnt[1];
return 0;
}
// wrap tendons around spheres and cylinders
// input: x0, x1: pair of 3D endpoints
// xpos, xmat, radius: position, orientation and radius of geom
// type: wrap type (mjtWrap)
// side: 3D position of sidesite
// output: return wrap length, -1 if no wrap
// wpnt: pair of 3D wrap points
mjtNum mju_wrap(mjtNum wpnt[6], const mjtNum x0[3], const mjtNum x1[3],
const mjtNum xpos[3], const mjtNum xmat[9], mjtNum radius,
int type, const mjtNum side[3]) {
// check object type; SHOULD NOT OCCUR
if (type != mjWRAP_SPHERE && type != mjWRAP_CYLINDER) {
mjERROR("unknown wrapping object type %d", type);
}
// map sites to wrap object's local frame
mjtNum tmp[3];
mju_sub3(tmp, x0, xpos);
mjtNum p[2][3];
mju_mulMatTVec3(p[0], xmat, tmp);
mju_sub3(tmp, x1, xpos);
mju_mulMatTVec3(p[1], xmat, tmp);
// too close to origin: return
if (mju_norm3(p[0]) < mjMINVAL || mju_norm3(p[1]) < mjMINVAL) {
return -1;
}
// construct 2D frame for circle wrap
mjtNum axis[2][3];
if (type == mjWRAP_SPHERE) {
// 1st axis = p0
mju_copy3(axis[0], p[0]);
mju_normalize3(axis[0]);
// normal to p0-0-p1 plane = cross(p0, p1)
mjtNum normal[3];
mju_cross(normal, p[0], p[1]);
mjtNum nrm = mju_normalize3(normal);
// if (p0, p1) parallel: different normal
if (nrm < mjMINVAL) {
// find max component of axis0
int i = 0;
if (mju_abs(axis[0][1]) > mju_abs(axis[0][0]) &&
mju_abs(axis[0][1]) > mju_abs(axis[0][2])) {
i = 1;
}
if (mju_abs(axis[0][2]) > mju_abs(axis[0][0]) &&
mju_abs(axis[0][2]) > mju_abs(axis[0][1])) {
i = 2;
}
// init second axis: 0 at i; 1 elsewhere
axis[1][0] = 1;
axis[1][1] = 1;
axis[1][2] = 1;
axis[1][i] = 0;
// recompute normal
mju_cross(normal, axis[0], axis[1]);
mju_normalize3(normal);
}
// 2nd axis = cross(normal, p0)
mju_cross(axis[1], normal, axis[0]);
mju_normalize3(axis[1]);
} else {
// 1st axis = x
axis[0][0] = 1;
axis[0][1] = axis[0][2] = 0;
// 2nd axis = y
axis[1][1] = 1;
axis[1][0] = axis[1][2] = 0;
}
// project points in 2D frame: p => d
mjtNum s[3], d[4], sd[2];
d[0] = mju_dot3(p[0], axis[0]);
d[1] = mju_dot3(p[0], axis[1]);
d[2] = mju_dot3(p[1], axis[0]);
d[3] = mju_dot3(p[1], axis[1]);
// handle sidesite
if (side) {
// side point: apply same projection as x0, x1
mju_sub3(tmp, side, xpos);
mju_mulMatTVec3(s, xmat, tmp);
// side point: project and rescale
sd[0] = mju_dot3(s, axis[0]);
sd[1] = mju_dot3(s, axis[1]);
mju_normalize(sd, 2);
mju_scl(sd, sd, radius, 2);
}
// apply inside wrap
mjtNum wlen;
mjtNum pnt[4];
if (side && mju_norm3(s) < radius) {
wlen = wrap_inside(pnt, d, radius);
}
// apply circle wrap
else {
wlen = wrap_circle(pnt, d, (side ? sd : NULL), radius);
}
// no wrap: return
if (wlen < 0) {
return -1;
}
// reconstruct 3D points in local frame: res
mjtNum res[6];
for (int i=0; i < 2; i++) {
// res = axis0*d0 + axis1*d1
mju_scl3(res+3*i, axis[0], pnt[2*i]);
mju_scl3(tmp, axis[1], pnt[2*i+1]);
mju_addTo3(res+3*i, tmp);
}
// cylinder: correct along z
if (type == mjWRAP_CYLINDER) {
// set vertical coordinates
mjtNum L0 = mju_sqrt((p[0][0]-res[0])*(p[0][0]-res[0]) + (p[0][1]-res[1])*(p[0][1]-res[1]));
mjtNum L1 = mju_sqrt((p[1][0]-res[3])*(p[1][0]-res[3]) + (p[1][1]-res[4])*(p[1][1]-res[4]));
res[2] = p[0][2] + (p[1][2] - p[0][2])*L0 / (L0+wlen+L1);
res[5] = p[0][2] + (p[1][2] - p[0][2])*(L0+wlen) / (L0+wlen+L1);
// correct wlen for height
mjtNum height = mju_abs(res[5] - res[2]);
wlen = mju_sqrt(wlen*wlen + height*height);
}
// map back to global frame: wpnt
mju_mulMatVec3(wpnt, xmat, res);
mju_mulMatVec3(wpnt+3, xmat, res+3);
mju_addTo3(wpnt, xpos);
mju_addTo3(wpnt+3, xpos);
return wlen;
}
// all 3 semi-axes of a geom
void mju_geomSemiAxes(mjtNum semiaxes[3], const mjtNum size[3], mjtGeom type) {
switch (type) {
case mjGEOM_SPHERE:
semiaxes[0] = size[0];
semiaxes[1] = size[0];
semiaxes[2] = size[0];
break;
case mjGEOM_CAPSULE:
semiaxes[0] = size[0];
semiaxes[1] = size[0];
semiaxes[2] = size[1] + size[0];
break;
case mjGEOM_CYLINDER:
semiaxes[0] = size[0];
semiaxes[1] = size[0];
semiaxes[2] = size[1];
break;
default:
semiaxes[0] = size[0];
semiaxes[1] = size[1];
semiaxes[2] = size[2];
}
}
// return 1 if point is inside a primitive geom, 0 otherwise
int mju_insideGeom(const mjtNum pos[3], const mjtNum mat[9], const mjtNum size[3], mjtGeom type,
const mjtNum point[3]) {
// vector from geom to point
mjtNum vec[3];
mju_sub3(vec, point, pos);
// quick return for spheres, frame rotation not required
if (type == mjGEOM_SPHERE) {
return mju_dot3(vec, vec) < size[0]*size[0];
}
// rotate into local frame
mjtNum plocal[3];
mju_mulMatTVec3(plocal, mat, vec);
// handle other geom types
switch (type) {
case mjGEOM_CAPSULE: {
mjtNum z = plocal[2];
mjtNum z_clamped = mju_clip(z, -size[1], size[1]);
mjtNum z_dist_sq = (z - z_clamped) * (z - z_clamped);
return (plocal[0]*plocal[0] + plocal[1]*plocal[1] + z_dist_sq < size[0]*size[0]);
}
case mjGEOM_ELLIPSOID:
return (plocal[0]*plocal[0]/(size[0]*size[0]) +
plocal[1]*plocal[1]/(size[1]*size[1]) +
plocal[2]*plocal[2]/(size[2]*size[2]) < 1);
case mjGEOM_CYLINDER:
return (mju_abs(plocal[2]) < size[1] &&
plocal[0]*plocal[0] + plocal[1]*plocal[1] < size[0]*size[0]);
case mjGEOM_BOX:
return (mju_abs(plocal[0]) < size[0] &&
mju_abs(plocal[1]) < size[1] &&
mju_abs(plocal[2]) < size[2]);
case mjGEOM_PLANE:
return plocal[2] < 0;
default:
return 0;
}
}
// ----------------------------- Flex interpolation ------------------------------------------------
mjtNum static inline phi(mjtNum s, int i, int order) {
if (order == 1) {
return i == 0 ? 1 - s : s;
} else if (order == 2) {
switch (i) {
case 0:
return 2 * s * s - 3 * s + 1;
case 1:
return 4 * (s - s * s);
case 2:
return 2 * s * s - s;
default:
mjERROR("invalid index %d", i);
return 0;
}
} else {
mjERROR("order must be 1 or 2");
return 0;
}
}
mjtNum static inline dphi(mjtNum s, int i, int order) {
if (order == 1) {
return i == 0 ? -1 : 1;
} else if (order == 2) {
switch (i) {
case 0:
return 4 * s - 3;
case 1:
return 4 * (1 - 2 * s);
case 2:
return 4 * s - 1;
default:
mjERROR("invalid index %d, must be 0, 1, or 2", i);
return 0;
}
} else {
mjERROR("order must be 1 or 2");
return 0;
}
}
// evaluate the deformation gradient at p using the nodal dof values
void mju_defGradient(mjtNum res[9], const mjtNum p[3], const mjtNum* dof, int order) {
int idx = 0;
mjtNum gradient[3];
mju_zero(res, 9);
for (int i = 0; i <= order; i++) {
for (int j = 0; j <= order; j++) {
for (int k = 0; k <= order; k++) {
gradient[0] = dphi(p[0], i, order) * phi(p[1], j, order) * phi(p[2], k, order);
gradient[1] = phi(p[0], i, order) * dphi(p[1], j, order) * phi(p[2], k, order);
gradient[2] = phi(p[0], i, order) * phi(p[1], j, order) * dphi(p[2], k, order);
res[0] += dof[3*idx+0] * gradient[0];
res[1] += dof[3*idx+0] * gradient[1];
res[2] += dof[3*idx+0] * gradient[2];
res[3] += dof[3*idx+1] * gradient[0];
res[4] += dof[3*idx+1] * gradient[1];
res[5] += dof[3*idx+1] * gradient[2];
res[6] += dof[3*idx+2] * gradient[0];
res[7] += dof[3*idx+2] * gradient[1];
res[8] += dof[3*idx+2] * gradient[2];
idx++;
}
}
}
}
// evaluate the basis function at x for the i-th node
mjtNum mju_evalBasis(const mjtNum x[3], int i, int order) {
if (order == 1) {
return phi(x[2], i&1, order) * phi(x[1], i&2, order) * phi(x[0], i&4, order);
} else if (order == 2) {
return phi(x[2], i % 3, order) * phi(x[1], (i / 3) % 3, order) * phi(x[0], i / 9, order);
} else {
return -1;
}
}
// interpolate a function at x with given interpolation coefficients and order n
void mju_interpolate3D(mjtNum res[3], const mjtNum x[3], const mjtNum* coeff, int order) {
int npoint = (order + 1) * (order + 1) * (order + 1);
for (int j=0; j < npoint; j++) {
mju_addToScl3(res, coeff+3*j, mju_evalBasis(x, j, order));
}
}
//------------------------------ actuator models ---------------------------------------------------
// normalized muscle length-gain curve
mjtNum mju_muscleGainLength(mjtNum length, mjtNum lmin, mjtNum lmax) {
if (lmin <= length && length <= lmax) {
// mid-ranges (maximum is at 1.0)
mjtNum a = 0.5*(lmin+1);
mjtNum b = 0.5*(1+lmax);
if (length <= a) {
mjtNum x = (length-lmin) / mjMAX(mjMINVAL, a-lmin);
return 0.5*x*x;
} else if (length <= 1) {
mjtNum x = (1-length) / mjMAX(mjMINVAL, 1-a);
return 1 - 0.5*x*x;
} else if (length <= b) {
mjtNum x = (length-1) / mjMAX(mjMINVAL, b-1);
return 1 - 0.5*x*x;
} else {
mjtNum x = (lmax-length) / mjMAX(mjMINVAL, lmax-b);
return 0.5*x*x;
}
}
return 0.0;
}
// muscle active force, prm = (range[2], force, scale, lmin, lmax, vmax, fpmax, fvmax)
mjtNum mju_muscleGain(mjtNum len, mjtNum vel, const mjtNum lengthrange[2],
mjtNum acc0, const mjtNum prm[9]) {
// unpack parameters
mjtNum range[2] = {prm[0], prm[1]};
mjtNum force = prm[2];
mjtNum scale = prm[3];
mjtNum lmin = prm[4];
mjtNum lmax = prm[5];
mjtNum vmax = prm[6];
mjtNum fvmax = prm[8];
// scale force if negative
if (force < 0) {
force = scale / mjMAX(mjMINVAL, acc0);
}
// optimum length
mjtNum L0 = (lengthrange[1]-lengthrange[0]) / mjMAX(mjMINVAL, range[1]-range[0]);
// normalized length and velocity
mjtNum L = range[0] + (len-lengthrange[0]) / mjMAX(mjMINVAL, L0);
mjtNum V = vel / mjMAX(mjMINVAL, L0*vmax);
// length curve
mjtNum FL = mju_muscleGainLength(L, lmin, lmax);
// velocity curve
mjtNum FV;
mjtNum y = fvmax-1;
if (V <= -1) {
FV = 0;
} else if (V <= 0) {
FV = (V+1)*(V+1);
} else if (V <= y) {
FV = fvmax - (y-V)*(y-V) / mjMAX(mjMINVAL, y);
} else {
FV = fvmax;
}
// compute FVL and scale, make it negative
return -force*FL*FV;
}
// muscle passive force, prm = (range[2], force, scale, lmin, lmax, vmax, fpmax, fvmax)
mjtNum mju_muscleBias(mjtNum len, const mjtNum lengthrange[2],
mjtNum acc0, const mjtNum prm[9]) {
// unpack parameters
mjtNum range[2] = {prm[0], prm[1]};
mjtNum force = prm[2];
mjtNum scale = prm[3];
mjtNum lmax = prm[5];
mjtNum fpmax = prm[7];
// scale force if negative
if (force < 0) {
force = scale / mjMAX(mjMINVAL, acc0);
}
// optimum length
mjtNum L0 = (lengthrange[1]-lengthrange[0]) / mjMAX(mjMINVAL, range[1]-range[0]);
// normalized length
mjtNum L = range[0] + (len-lengthrange[0]) / mjMAX(mjMINVAL, L0);
// half-quadratic to (L0+lmax)/2, linear beyond
mjtNum b = 0.5*(1+lmax);
if (L <= 1) {
return 0;
} else if (L <= b) {
mjtNum x = (L-1) / mjMAX(mjMINVAL, b-1);
return -force*fpmax*0.5*x*x;
} else {
mjtNum x = (L-b) / mjMAX(mjMINVAL, b-1);
return -force*fpmax*(0.5 + x);
}
}
// muscle time constant with optional smoothing
mjtNum mju_muscleDynamicsTimescale(mjtNum dctrl, mjtNum tau_act, mjtNum tau_deact,
mjtNum smoothing_width) {
mjtNum tau;
// hard switching
if (smoothing_width < mjMINVAL) {
tau = dctrl > 0 ? tau_act : tau_deact;
}
// smooth switching
else {
// scale by width, center around 0.5 midpoint, rescale to bounds
tau = tau_deact + (tau_act-tau_deact)*mju_sigmoid(dctrl/smoothing_width + 0.5);
}
return tau;
}
// muscle activation dynamics, prm = (tau_act, tau_deact, smoothing_width)
mjtNum mju_muscleDynamics(mjtNum ctrl, mjtNum act, const mjtNum prm[3]) {
// clamp control
mjtNum ctrlclamp = mju_clip(ctrl, 0, 1);
// clamp activation
mjtNum actclamp = mju_clip(act, 0, 1);
// compute timescales as in Millard et al. (2013) https://doi.org/10.1115/1.4023390
mjtNum tau_act = prm[0] * (0.5 + 1.5*actclamp); // activation timescale
mjtNum tau_deact = prm[1] / (0.5 + 1.5*actclamp); // deactivation timescale
mjtNum smoothing_width = prm[2]; // width of smoothing sigmoid
mjtNum dctrl = ctrlclamp - act; // excess excitation
mjtNum tau = mju_muscleDynamicsTimescale(dctrl, tau_act, tau_deact, smoothing_width);
// filter output
return dctrl / mjMAX(mjMINVAL, tau);
}
//---------------------------------------- Base64 --------------------------------------------------
// decoding function for Base64
static uint32_t _decode(char ch) {
if (ch >= 'A' && ch <= 'Z') {
return ch - 'A';
}
if (ch >= 'a' && ch <= 'z') {
return (ch - 'a') + 26;
}
if (ch >= '0' && ch <= '9') {
return (ch - '0') + 52;
}
if (ch == '+') {
return 62;
}
if (ch == '/') {
return 63;
}
return 0;
}
// encode data as Base64 into buf (including padding and null char)
// returns number of chars written in buf: 4 * [(ndata + 2) / 3] + 1
size_t mju_encodeBase64(char* buf, const uint8_t* data, size_t ndata) {
static const char *table =
"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
int i = 0, j = 0;
// loop over 24 bit chunks
while (i + 3 <= ndata) {
// take next 24 bit chunk (3 bytes)
uint32_t byte_1 = data[i++];
uint32_t byte_2 = data[i++];
uint32_t byte_3 = data[i++];
// merge bytes into one 32 bit int
uint32_t k = (byte_1 << 16) | (byte_2 << 8) | byte_3;
// encode 6 bit chucks into four chars
buf[j++] = table[(k >> 18) & 63];
buf[j++] = table[(k >> 12) & 63];
buf[j++] = table[(k >> 6) & 63];
buf[j++] = table[(k >> 0) & 63];
}
// one byte left
if (i + 1 == ndata) {
uint32_t byte_1 = data[i];
uint32_t k = byte_1 << 16;
buf[j++] = table[(k >> 18) & 63];
buf[j++] = table[(k >> 12) & 63];
buf[j++] = '='; // padding
buf[j++] = '='; // padding
}
// two bytes left
if (i + 2 == ndata) {
uint32_t byte_1 = data[i++];
uint32_t byte_2 = data[i];
uint32_t k = (byte_1 << 16) + (byte_2 << 8);
buf[j++] = table[(k >> 18) & 63];
buf[j++] = table[(k >> 12) & 63];
buf[j++] = table[(k >> 6) & 63];
buf[j++] = '='; // padding
}
buf[j] = '\0';
return 4 * ((ndata + 2) / 3) + 1;
}
// return size in decoded bytes if s is a valid Base64 encoding
// return 0 if s is empty or invalid Base64 encoding
size_t mju_isValidBase64(const char* s) {
size_t i = 0;
int pad = 0; // 0, 1, or 2 zero padding at the end of s
// validate chars
for (; s[i] && s[i] != '='; i++) {
if (!isalnum(s[i]) && s[i] != '/' && s[i] != '+') {
return 0;
}
}
// padding at end
if (s[i] == '=') {
if (!s[i + 1]) {
pad = 1; // one '=' padding at end
} else if (s[i + 1] == '=' && !s[i + 2]) {
pad = 2; // two '=' padding at end
} else {
return 0;
}
}
// strlen(s) must be a multiple of 4
int len = i + pad;
return len % 4 ? 0 : 3 * (len / 4) - pad;
}
// decode valid Base64 in string s into buf, undefined behavior if s is not valid Base64
// returns number of bytes decoded (upper limit of 3 * (strlen(s) / 4))
size_t mju_decodeBase64(uint8_t* buf, const char* s) {
size_t i = 0, j = 0;
// loop over 24 bit chunks
while (s[i] != '\0') {
// take next 24 bit chuck (4 chars; 6 bits each)
uint32_t char_1 = _decode(s[i++]);
uint32_t char_2 = _decode(s[i++]);
uint32_t char_3 = _decode(s[i++]);
uint32_t char_4 = _decode(s[i++]);
// merge into 32 bit int
uint32_t k = (char_1 << 18) | (char_2 << 12) | (char_3 << 6) | char_4;
// write up to three bytes (exclude padding at end)
buf[j++] = (k >> 16) & 0xFF;
if (s[i - 2] != '=') {
buf[j++] = (k >> 8) & 0xFF;
}
if (s[i - 1] != '=') {
buf[j++] = k & 0xFF;
}
}
return j;
}
//------------------------------ miscellaneous -----------------------------------------------------
// convert contact force to pyramid representation
// the pyramid frame is: V0_i = N + mu_i*T_i
// V1_i = N - mu_i*T_i
void mju_encodePyramid(mjtNum* pyramid, const mjtNum* force, const mjtNum* mu, int dim) {
mjtNum a = force[0]/(dim-1), b;
// arbitrary redundancy resolution:
// pyramid0_i + pyramid1_i = force_normal/(dim-1) = a
// pyramid0_i - pyramid1_i = force_tangent_i/mu_i = b
for (int i=0; i < dim-1; i++) {
b = mju_min(a, force[i+1]/mu[i]);
pyramid[2*i] = 0.5*(a+b);
pyramid[2*i+1] = 0.5*(a-b);
}
}
// convert pyramid representation to contact force
void mju_decodePyramid(mjtNum* force, const mjtNum* pyramid, const mjtNum* mu, int dim) {
// special handling of frictionless contacts
if (dim == 1) {
force[0] = pyramid[0];
return;
}
// force_normal = sum(pyramid0_i + pyramid1_i)
force[0] = 0;
for (int i=0; i < 2*(dim-1); i++) {
force[0] += pyramid[i];
}
// force_tangent_i = (pyramid0_i - pyramid1_i) * mu_i
for (int i=0; i < dim-1; i++) {
force[i+1] = (pyramid[2*i] - pyramid[2*i+1]) * mu[i];
}
}
// integrate spring-damper analytically, return pos(t)
mjtNum mju_springDamper(mjtNum pos0, mjtNum vel0, mjtNum k, mjtNum b, mjtNum t) {
mjtNum det, c1, c2, r1, r2, w;
// determinant of characteristic equation
det = b*b - 4*k;
// overdamping
// pos(t) = c1*exp(r1*t) + c2*exp(r2*t); r12 = (-b +- sqrt(det))/2
if (det > mjMINVAL) {
// compute w = sqrt(det)/2
w = mju_sqrt(det)/2;
// compute r1,r2
r1 = -b/2 + w;
r2 = -b/2 - w;
// compute coefficients
c1 = (pos0*r2-vel0) / (r2-r1);
c2 = (pos0*r1-vel0) / (r1-r2);
// evaluate result
return c1*mju_exp(r1*t) + c2*mju_exp(r2*t);
}
// critical damping
// pos(t) = exp(-b*t/2) * (c1 + c2*t)
else if (det <= mjMINVAL && det >= -mjMINVAL) {
// compute coefficients
c1 = pos0;
c2 = vel0 + b*c1/2;
// evaluate result
return mju_exp(-b*t/2) * (c1 + c2*t);
}
// underdamping
// pos(t) = exp(-b*t/2) * (c1*cos(w*t) + c2*sin(w*t)); w = sqrt(abs(det))/2
else {
// compute w
w = mju_sqrt(mju_abs(det))/2;
// compute coefficients
c1 = pos0;
c2 = (vel0 + b*c1/2)/w;
// evaluate result
return mju_exp(-b*t/2) * (c1*mju_cos(w*t) + c2*mju_sin(w*t));
}
}
// return 1 if point is outside box given by pos, mat, size * inflate
// return -1 if point is inside box given by pos, mat, size / inflate
// return 0 if point is between the inflated and deflated boxes
int mju_outsideBox(const mjtNum point[3], const mjtNum pos[3], const mjtNum mat[9],
const mjtNum size[3], mjtNum inflate) {
// check inflation coefficient
if (inflate < 1) {
mjERROR("inflation coefficient must be >= 1")
}
// vector from pos to point, projected to box frame
mjtNum vec[3] = {point[0]-pos[0], point[1]-pos[1], point[2]-pos[2]};
mju_mulMatTVec3(vec, mat, vec);
// big: inflated box
mjtNum big[3] = {size[0], size[1], size[2]};
if (inflate > 1) {
mju_scl3(big, big, inflate);
}
// check if outside big box
if (vec[0] > big[0] || vec[0] < -big[0] ||
vec[1] > big[1] || vec[1] < -big[1] ||
vec[2] > big[2] || vec[2] < -big[2]) {
return 1;
}
// quick return if no inflation
if (inflate == 1) {
return -1;
}
// check if inside small (deflated) box
mjtNum small[3] = {size[0]/inflate, size[1]/inflate, size[2]/inflate};
if (vec[0] < small[0] && vec[0] > -small[0] &&
vec[1] < small[1] && vec[1] > -small[1] &&
vec[2] < small[2] && vec[2] > -small[2]) {
return -1;
}
// within margin between small and big box
return 0;
}
// print matrix to screen
void mju_printMat(const mjtNum* mat, int nr, int nc) {
for (int r=0; r < nr; r++) {
for (int c=0; c < nc; c++) {
printf("%.8f ", mat[r*nc+c]);
}
printf("\n");
}
printf("\n");
}
// print sparse matrix to screen
void mju_printMatSparse(const mjtNum* mat, int nr,
const int* rownnz, const int* rowadr,
const int* colind) {
for (int r=0; r < nr; r++) {
for (int adr=rowadr[r]; adr < rowadr[r]+rownnz[r]; adr++) {
printf("(%d %d): %9.6f ", r, colind[adr], mat[adr]);
}
printf("\n");
}
printf("\n");
}
// min function, avoid re-evaluation
mjtNum mju_min(mjtNum a, mjtNum b) {
if (a <= b) {
return a;
} else {
return b;
}
}
// max function, avoid re-evaluation
mjtNum mju_max(mjtNum a, mjtNum b) {
if (a >= b) {
return a;
} else {
return b;
}
}
// clip x to the range [min, max]
mjtNum mju_clip(mjtNum x, mjtNum min, mjtNum max) {
if (x < min) {
return min;
} else if (x > max) {
return max;
} else {
return x;
}
}
// sign function
mjtNum mju_sign(mjtNum x) {
if (x < 0) {
return -1;
} else if (x > 0) {
return 1;
} else {
return 0;
}
}
// round to nearest integer
int mju_round(mjtNum x) {
mjtNum lower = floor(x);
mjtNum upper = ceil(x);
if (x-lower < upper-x) {
return (int)lower;
} else {
return (int)upper;
}
}
// convert type id to type name
const char* mju_type2Str(int type) {
switch ((mjtObj) type) {
case mjOBJ_BODY:
return "body";
case mjOBJ_XBODY:
return "xbody";
case mjOBJ_JOINT:
return "joint";
case mjOBJ_DOF:
return "dof";
case mjOBJ_GEOM:
return "geom";
case mjOBJ_SITE:
return "site";
case mjOBJ_CAMERA:
return "camera";
case mjOBJ_LIGHT:
return "light";
case mjOBJ_FLEX:
return "flex";
case mjOBJ_MESH:
return "mesh";
case mjOBJ_SKIN:
return "skin";
case mjOBJ_HFIELD:
return "hfield";
case mjOBJ_TEXTURE:
return "texture";
case mjOBJ_MATERIAL:
return "material";
case mjOBJ_PAIR:
return "pair";
case mjOBJ_EXCLUDE:
return "exclude";
case mjOBJ_EQUALITY:
return "equality";
case mjOBJ_TENDON:
return "tendon";
case mjOBJ_ACTUATOR:
return "actuator";
case mjOBJ_SENSOR:
return "sensor";
case mjOBJ_NUMERIC:
return "numeric";
case mjOBJ_TEXT:
return "text";
case mjOBJ_TUPLE:
return "tuple";
case mjOBJ_KEY:
return "key";
case mjOBJ_PLUGIN:
return "plugin";
case mjOBJ_FRAME:
return "frame";
default:
return 0;
}
}
// convert type id to type name
int mju_str2Type(const char* str) {
if (!strcmp(str, "body")) {
return mjOBJ_BODY;
}
else if (!strcmp(str, "xbody")) {
return mjOBJ_XBODY;
}
else if (!strcmp(str, "joint")) {
return mjOBJ_JOINT;
}
else if (!strcmp(str, "dof")) {
return mjOBJ_DOF;
}
else if (!strcmp(str, "geom")) {
return mjOBJ_GEOM;
}
else if (!strcmp(str, "site")) {
return mjOBJ_SITE;
}
else if (!strcmp(str, "camera")) {
return mjOBJ_CAMERA;
}
else if (!strcmp(str, "light")) {
return mjOBJ_LIGHT;
}
else if (!strcmp(str, "flex")) {
return mjOBJ_FLEX;
}
else if (!strcmp(str, "mesh")) {
return mjOBJ_MESH;
}
else if (!strcmp(str, "skin")) {
return mjOBJ_SKIN;
}
else if (!strcmp(str, "hfield")) {
return mjOBJ_HFIELD;
}
else if (!strcmp(str, "texture")) {
return mjOBJ_TEXTURE;
}
else if (!strcmp(str, "material")) {
return mjOBJ_MATERIAL;
}
else if (!strcmp(str, "pair")) {
return mjOBJ_PAIR;
}
else if (!strcmp(str, "exclude")) {
return mjOBJ_EXCLUDE;
}
else if (!strcmp(str, "equality")) {
return mjOBJ_EQUALITY;
}
else if (!strcmp(str, "tendon")) {
return mjOBJ_TENDON;
}
else if (!strcmp(str, "actuator")) {
return mjOBJ_ACTUATOR;
}
else if (!strcmp(str, "sensor")) {
return mjOBJ_SENSOR;
}
else if (!strcmp(str, "numeric")) {
return mjOBJ_NUMERIC;
}
else if (!strcmp(str, "text")) {
return mjOBJ_TEXT;
}
else if (!strcmp(str, "tuple")) {
return mjOBJ_TUPLE;
}
else if (!strcmp(str, "key")) {
return mjOBJ_KEY;
}
else if (!strcmp(str, "plugin")) {
return mjOBJ_PLUGIN;
}
else {
return mjOBJ_UNKNOWN;
}
}
// return human readable number of bytes using standard letter suffix
const char* mju_writeNumBytes(size_t nbytes) {
int i;
static mjTHREADLOCAL char message[20];
static const char suffix[] = " KMGTPE";
for (i=0; i < 6; i++) {
const size_t bits = (size_t)(1) << (10*(6-i));
if (nbytes >= bits && !(nbytes & (bits - 1))) {
break;
}
}
if (i < 6) {
mjSNPRINTF(message, "%zu%c", nbytes >> (10*(6-i)), suffix[6-i]);
} else {
mjSNPRINTF(message, "%zu", nbytes >> (10*(6-i)));
}
return message;
}
// warning text
const char* mju_warningText(int warning, size_t info) {
static mjTHREADLOCAL char str[1000];
switch ((mjtWarning) warning) {
case mjWARN_INERTIA:
mjSNPRINTF(str, "Inertia matrix is too close to singular at DOF %zu. Check model.", info);
break;
case mjWARN_CONTACTFULL:
mjSNPRINTF(str,
"Too many contacts. The arena memory is full, increase arena memory allocation."
"(ncon = %zu)", info);
break;
case mjWARN_CNSTRFULL:
mjSNPRINTF(str,
"Insufficient arena memory for the number of constraints generated. "
"Increase arena memory allocation above %s bytes.", mju_writeNumBytes(info));
break;
case mjWARN_VGEOMFULL:
mjSNPRINTF(str, "Pre-allocated visual geom buffer is full. Increase maxgeom above %zu.", info);
break;
case mjWARN_BADQPOS:
mjSNPRINTF(str, "Nan, Inf or huge value in QPOS at DOF %zu. The simulation is unstable.", info);
break;
case mjWARN_BADQVEL:
mjSNPRINTF(str, "Nan, Inf or huge value in QVEL at DOF %zu. The simulation is unstable.", info);
break;
case mjWARN_BADQACC:
mjSNPRINTF(str, "Nan, Inf or huge value in QACC at DOF %zu. The simulation is unstable.", info);
break;
case mjWARN_BADCTRL:
mjSNPRINTF(str, "Nan, Inf or huge value in CTRL at ACTUATOR %zu. The simulation is unstable.",
info);
break;
default:
mjSNPRINTF(str, "Unknown warning type %d.", warning);
}
return str;
}
// return 1 if nan or abs(x)>mjMAXVAL, 0 otherwise
int mju_isBad(mjtNum x) {
return (x != x || x > mjMAXVAL || x < -mjMAXVAL);
}
// return 1 if all elements are 0
int mju_isZero(const mjtNum* vec, int n) {
for (int i=0; i < n; i++) {
if (vec[i] != 0) {
return 0;
}
}
return 1;
}
// return 1 if all elements are 0
int mju_isZeroByte(const unsigned char* vec, int n) {
if (!n || *vec) return !n;
return memcmp(vec, vec + 1, n - 1) == 0;
}
// set integer vector to 0
void mju_zeroInt(int* res, int n) {
memset(res, 0, n*sizeof(int));
}
// copy int vector vec into res
void mju_copyInt(int* res, const int* vec, int n) {
memcpy(res, vec, n*sizeof(int));
}
// standard normal random number generator (optional second number)
mjtNum mju_standardNormal(mjtNum* num2) {
const mjtNum scale = 2.0/((mjtNum)RAND_MAX);
mjtNum x1, x2, w;
do {
x1 = scale * (mjtNum)rand() - 1.0;
x2 = scale * (mjtNum)rand() - 1.0;
w = x1 * x1 + x2 * x2;
} while (w >= 1.0 || w == 0);
w = mju_sqrt((-2.0 * mju_log(w)) / w);
if (num2) {
*num2 = x2 * w;
}
return (x1 * w);
}
// convert from float to mjtNum
void mju_f2n(mjtNum* res, const float* vec, int n) {
for (int i=0; i < n; i++) {
res[i] = (mjtNum) vec[i];
}
}
// convert from mjtNum to float
void mju_n2f(float* res, const mjtNum* vec, int n) {
for (int i=0; i < n; i++) {
res[i] = (float) vec[i];
}
}
// convert from double to mjtNum
void mju_d2n(mjtNum* res, const double* vec, int n) {
for (int i=0; i < n; i++) {
res[i] = (mjtNum) vec[i];
}
}
// convert from mjtNum to double
void mju_n2d(double* res, const mjtNum* vec, int n) {
for (int i=0; i < n; i++) {
res[i] = (double) vec[i];
}
}
// gather
void mju_gather(mjtNum* restrict res, const mjtNum* restrict vec, const int* restrict ind, int n) {
for (int i=0; i < n; i++) {
res[i] = vec[ind[i]];
}
}
// masked gather (set to 0 at negative indices)
void mju_gatherMasked(mjtNum* restrict res, const mjtNum* restrict vec,
const int* restrict ind, int n) {
for (int i=0; i < n; i++) {
res[i] = ind[i] >= 0 ? vec[ind[i]] : 0;
}
}
// scatter
void mju_scatter(mjtNum* restrict res, const mjtNum* restrict vec, const int* restrict ind, int n) {
for (int i=0; i < n; i++) {
res[ind[i]] = vec[i];
}
}
// gather integers
void mju_gatherInt(int* restrict res, const int* restrict vec, const int* restrict ind, int n) {
for (int i=0; i < n; i++) {
res[i] = vec[ind[i]];
}
}
// scatter integers
void mju_scatterInt(int* restrict res, const int* restrict vec, const int* restrict ind, int n) {
for (int i=0; i < n; i++) {
res[ind[i]] = vec[i];
}
}
// build gather indices mapping src to res, assumes pattern(res) \subseteq pattern(src)
void mju_sparseMap(int* map, int nr,
const int* res_rowadr, const int* res_rownnz, const int* res_colind,
const int* src_rowadr, const int* src_rownnz, const int* src_colind) {
for (int i = 0; i < nr; i++) {
int res_cursor = res_rowadr[i];
int res_end = res_cursor + res_rownnz[i];
int src_cursor = src_rowadr[i];
int src_end = src_cursor + src_rownnz[i];
while (res_cursor < res_end) {
int res_col = res_colind[res_cursor];
while (src_cursor < src_end && src_colind[src_cursor] < res_col) {
src_cursor++;
}
// found match, set index and advance cursors
map[res_cursor++] = src_cursor++;
}
}
}
// build masked-gather map to copy a lower-triangular src into symmetric res
// `cursor` is a preallocated buffer of size `nr`
void mju_lower2SymMap(int* map, int nr,
const int* res_rowadr, const int* res_rownnz, const int* res_colind,
const int* src_rowadr, const int* src_rownnz, const int* src_colind,
int* cursor) {
if (!nr) return;
// default all map entries to "no source"
int nnz = res_rowadr[nr-1] + res_rownnz[nr-1];
for (int i = 0; i < nnz; i++) {
map[i] = -1;
}
// initialize per-row cursor
for (int i = 0; i < nr; i++) {
cursor[i] = res_rowadr[i];
}
// sweep src rows; for each lower (i,j) set res(i,j) and res(j,i)
for (int i = 0; i < nr; i++) {
int src_start = src_rowadr[i];
int src_end = src_start + src_rownnz[i];
// sweep src row
for (int k = src_start; k < src_end; k++) {
int j = src_colind[k];
if (j > i) break; // use only lower triangle of src
// --- lower triangle: res(i, j)
int res_start = res_rowadr[i];
int res_end = res_start + res_rownnz[i];
int c = cursor[i];
// increment c until there is a match
while (c < res_end && res_colind[c] < j) c++;
// found match, set index, advance and save cursor
if (c < res_end && res_colind[c] == j) {
map[c] = k;
c++;
}
cursor[i] = c;
// --- upper mirror: res(j, i)
if (j != i) {
res_start = res_rowadr[j];
res_end = res_start + res_rownnz[j];
c = cursor[j];
// increment c until there is a match
while (c < res_end && res_colind[c] < i) c++;
// found match, set index and advance and save cursor
if (c < res_end && res_colind[c] == i) {
map[c] = k;
c++;
}
cursor[j] = c;
}
}
}
}
// insertion sort, increasing order
void mju_insertionSort(mjtNum* list, int n) {
for (int i=1; i < n; i++) {
mjtNum x = list[i];
int j = i-1;
while (j >= 0 && list[j] > x) {
list[j+1] = list[j];
j--;
}
list[j+1] = x;
}
}
// integer insertion sort, increasing order
void mju_insertionSortInt(int* list, int n) {
for (int i=1; i < n; i++) {
int x = list[i];
int j = i-1;
while (j >= 0 && list[j] > x) {
list[j+1] = list[j];
j--;
}
list[j+1] = x;
}
}
// Halton sequence
mjtNum mju_Halton(int index, int base) {
int n0 = index;
mjtNum b = (mjtNum)base;
mjtNum f = 1/b, hn = 0;
while (n0 > 0) {
int n1 = n0/base;
int r = n0 - n1*base;
hn += f*r;
f /= b;
n0 = n1;
}
return hn;
}
// Call strncpy, then set dst[n-1] = 0.
char* mju_strncpy(char *dst, const char *src, int n) {
if (dst && src && n > 0) {
strncpy(dst, src, n);
dst[n-1] = 0;
}
return dst;
}
// sigmoid function over 0<=x<=1 using quintic polynomial
mjtNum mju_sigmoid(mjtNum x) {
// fast return
if (x <= 0) {
return 0;
}
if (x >= 1) {
return 1;
}
// sigmoid: f(x) = 6*x^5 - 15*x^4 + 10*x^3
// solution of f(0) = f'(0) = f''(0) = 0, f(1) = 1, f'(1) = f''(1) = 0
return x*x*x * (3*x * (2*x - 5) + 10);
}
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