// 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 #include #include #include #include #include #include #include #include #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 (fabs(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 rad) { mjtNum angle, cross; 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); angle = mju_acos(mju_dot(p0n, p1n, 2)); // flip if necessary cross = p0[1]*p1[0]-p0[0]*p1[1]; if ((cross > 0 && ind) || (cross < 0 && !ind)) { angle = 2*mjPI - angle; } return rad*angle; } // 2D circle wrap // input: pair of 2D points in d[4], optional 2D side point in sd[2], radius // output: pair of 2D points in pnt[4], length of circular wrap or -1 static mjtNum wrap_circle(mjtNum* pnt, const mjtNum* d, const mjtNum* sd, mjtNum rad) { mjtNum sqlen0 = d[0]*d[0]+d[1]*d[1]; mjtNum sqlen1 = d[2]*d[2]+d[3]*d[3]; mjtNum sqrad = rad*rad; mjtNum dif[2] = {d[2]-d[0], d[3]-d[1]}; mjtNum a, tmp[2], dd, sqrt0, sqrt1; mjtNum sol[2][2][2], good[2], wlen; int sgn; // either point inside circle or circle too small: no wrap if (sqlen0 < sqrad || sqlen1 < sqrad || rad < mjMINVAL) { return -1; } // points too close: no wrap 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 a = -(dif[0]*d[0]+dif[1]*d[1])/dd; if (a < 0) { a = 0; } else if (a > 1) { a = 1; } tmp[0] = a*dif[0] + d[0]; tmp[1] = a*dif[1] + d[1]; // check for intersection and side if (tmp[0]*tmp[0]+tmp[1]*tmp[1] > sqrad && (!sd || mju_dot(sd, tmp, 2) >= 0)) { return -1; } // construct the two solutions, compute goodness for (int i=0; i < 2; i++) { sqrt0 = mju_sqrt(sqlen0 - sqrad); sqrt1 = mju_sqrt(sqlen1 - sqrad); sgn = (i == 0 ? 1 : -1); sol[i][0][0] = (d[0]*sqrad + sgn*rad*d[1]*sqrt0)/sqlen0; sol[i][0][1] = (d[1]*sqrad - sgn*rad*d[0]*sqrt0)/sqlen0; sol[i][1][0] = (d[2]*sqrad - sgn*rad*d[3]*sqrt1)/sqlen1; sol[i][1][1] = (d[3]*sqrad + sgn*rad*d[2]*sqrt1)/sqlen1; // goodness: close to sd, or shorter path if (sd) { mju_add(tmp, sol[i][0], sol[i][1], 2); mju_normalize(tmp, 2); good[i] = mju_dot(tmp, sd, 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(d, sol[i][0], d+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(d, pnt, d+2, pnt+2)) { return -1; } // compute curve length wlen = length_circle(sol[i][0], sol[i][1], i, rad); return wlen; } // 2D inside wrap // input: pair of 2D points in d[4], radius // output: pair of 2D points in pnt[4]; return 0 if wrap, -1 if no wrap static mjtNum wrap_inside(mjtNum* pnt, const mjtNum* d, mjtNum rad) { // algorithm parameters const int maxiter = 20; const mjtNum zinit = 1 - 1e-7; const mjtNum tolerance = 1e-6; // constants mjtNum len0 = mju_norm(d, 2); mjtNum len1 = mju_norm(d+2, 2); mjtNum dif[2] = {d[2]-d[0], d[3]-d[1]}; mjtNum dd = dif[0]*dif[0] + dif[1]*dif[1]; // either point inside circle or circle too small: no wrap if (len0 <= rad || len1 <= rad || rad < 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]*d[0]+dif[1]*d[1])/dd; // in segment if (a > 0 && a < 1) { mjtNum tmp[2]; mju_addScl(tmp, d, dif, a, 2); if (mju_norm(tmp, 2) <= rad) { return -1; } } } // prepare default in case of numerical failure: average pnt[0] = 0.5*(d[0] + d[2]); pnt[1] = 0.5*(d[1] + d[3]); mju_normalize(pnt, 2); mju_scl(pnt, pnt, rad, 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 = rad/len0; mjtNum B = rad/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 (d[0]*d[3] - d[1]*d[2] > 0) { mju_copy(vec, d, 2); ang = mju_asin(z) - mju_asin(A*z); } else { mju_copy(vec, d+2, 2); ang = mju_asin(z) - mju_asin(B*z); } mju_normalize(vec, 2); pnt[0] = rad*(mju_cos(ang)*vec[0] - mju_sin(ang)*vec[1]); pnt[1] = rad*(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 mjtNum mju_wrap(mjtNum* wpnt, const mjtNum* x0, const mjtNum* x1, const mjtNum* xpos, const mjtNum* xmat, const mjtNum* size, int type, const mjtNum* side) { mjtNum tmp[3], normal[3], axis[2][3], p[2][3], s[3], d[4], sd[2], pnt[4]; mjtNum res[6], wlen, height; mjtNum L0, L1; // 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 mju_sub3(tmp, x0, xpos); mju_mulMatTVec(p[0], xmat, tmp, 3, 3); mju_sub3(tmp, x1, xpos); mju_mulMatTVec(p[1], xmat, tmp, 3, 3); // too close to origin: return if (mju_norm3(p[0]) < mjMINVAL || mju_norm3(p[1]) < mjMINVAL) { return -1; } // construct 2D frame for circle wrap 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) 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 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]); 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, size[0], 2); } // apply inside wrap if (side && mju_norm3(s) < size[0]) { wlen = wrap_inside(pnt, d, size[0]); } // apply circle wrap else { wlen = wrap_circle(pnt, d, (side ? sd : 0), size[0]); } // no wrap if (wlen < 0) { return -1; } // reconstruct 3D points in local frame: res 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 L0 = mju_sqrt((p[0][0]-res[0])*(p[0][0]-res[0]) + (p[0][1]-res[1])*(p[0][1]-res[1])); 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 height = mju_abs(res[5] - res[2]); wlen = mju_sqrt(wlen*wlen + height*height); } // map back to global frame: wpnt mju_mulMatVec(wpnt, xmat, res, 3, 3); mju_mulMatVec(wpnt+3, xmat, res+3, 3, 3); mju_addTo3(wpnt, xpos); mju_addTo3(wpnt+3, xpos); return wlen; } // all 3 semi-axes of a geom void mju_geomSemiAxes(const mjModel* m, int geom_id, mjtNum semiaxes[3]) { mjtNum* size = m->geom_size + 3*geom_id; switch ((mjtGeom) m->geom_type[geom_id]) { 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]; } } //------------------------------ 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 timscale mjtNum tau_deact = prm[1] / (0.5 + 1.5*actclamp); // deactivation timscale 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. Either the arena memory is full, or nconmax is specified and is " "exceeded. Increase arena memory allocation, or increase/remove nconmax. " "(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(mjtNum* vec, int n) { for (int i=0; i < n; i++) { if (vec[i] != 0) { return 0; } } return 1; } // set integer vector to 0 void mju_zeroInt(int* res, int n) { memset(res, 0, n*sizeof(int)); } void mju_zeroSizeT(size_t* res, size_t n) { memset(res, 0, n*sizeof(size_t)); } // 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]; } } // 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); }