Alessio Quaglino
a891782553
Do not allow a mix of `elastic2d != none` with `dof = trilinear` since the latter assumes 3d elasticity. Also, do not assume that `flex_interp > 0` in the engine. This will enable to use, e.g., `flex_interp = -1` to mean a linear surface finite element instead of a 3d finite element which is currently identified with `flex_interp = 1`. PiperOrigin-RevId: 903852035 Change-Id: Ia6290b4a05e9e510ffb7f36d141cd525b40d3110
1918 lines
59 KiB
C
1918 lines
59 KiB
C
// Copyright 2022 DeepMind Technologies Limited
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "engine/engine_derivative.h"
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#include <mujoco/mjdata.h>
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#include <mujoco/mjmodel.h>
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#include <mujoco/mjsan.h> // IWYU pragma: keep
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#include "engine/engine_core_util.h"
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#include "engine/engine_crossplatform.h"
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#include "engine/engine_memory.h"
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#include "engine/engine_passive.h"
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#include "engine/engine_sleep.h"
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#include "engine/engine_support.h"
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#include "engine/engine_util_blas.h"
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#include "engine/engine_util_errmem.h"
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#include "engine/engine_util_misc.h"
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#include "engine/engine_util_spatial.h"
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#include "engine/engine_util_sparse.h"
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//------------------------- derivatives of spatial algebra -----------------------------------------
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// derivatives of cross product, Da and Db are 3x3
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static void mjd_cross(const mjtNum a[3], const mjtNum b[3],
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mjtNum* restrict Da, mjtNum* restrict Db) {
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// derivative w.r.t a
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if (Da) {
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mju_zero(Da, 9);
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Da[1] = b[2];
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Da[2] = -b[1];
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Da[3] = -b[2];
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Da[5] = b[0];
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Da[6] = b[1];
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Da[7] = -b[0];
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}
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// derivative w.r.t b
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if (Db) {
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mju_zero(Db, 9);
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Db[1] = -a[2];
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Db[2] = a[1];
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Db[3] = a[2];
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Db[5] = -a[0];
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Db[6] = -a[1];
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Db[7] = a[0];
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}
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}
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// derivative of mju_crossMotion w.r.t velocity
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static void mjd_crossMotion_vel(mjtNum D[36], const mjtNum v[6]) {
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mju_zero(D, 36);
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// res[0] = -vel[2]*v[1] + vel[1]*v[2]
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D[0 + 2] = -v[1];
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D[0 + 1] = v[2];
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// res[1] = vel[2]*v[0] - vel[0]*v[2]
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D[6 + 2] = v[0];
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D[6 + 0] = -v[2];
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// res[2] = -vel[1]*v[0] + vel[0]*v[1]
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D[12 + 1] = -v[0];
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D[12 + 0] = v[1];
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// res[3] = -vel[2]*v[4] + vel[1]*v[5] - vel[5]*v[1] + vel[4]*v[2]
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D[18 + 2] = -v[4];
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D[18 + 1] = v[5];
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D[18 + 5] = -v[1];
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D[18 + 4] = v[2];
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// res[4] = vel[2]*v[3] - vel[0]*v[5] + vel[5]*v[0] - vel[3]*v[2]
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D[24 + 2] = v[3];
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D[24 + 0] = -v[5];
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D[24 + 5] = v[0];
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D[24 + 3] = -v[2];
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// res[5] = -vel[1]*v[3] + vel[0]*v[4] - vel[4]*v[0] + vel[3]*v[1]
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D[30 + 1] = -v[3];
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D[30 + 0] = v[4];
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D[30 + 4] = -v[0];
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D[30 + 3] = v[1];
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}
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// derivative of mju_crossForce w.r.t. velocity
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static void mjd_crossForce_vel(mjtNum D[36], const mjtNum f[6]) {
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mju_zero(D, 36);
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// res[0] = -vel[2]*f[1] + vel[1]*f[2] - vel[5]*f[4] + vel[4]*f[5]
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D[0 + 2] = -f[1];
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D[0 + 1] = f[2];
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D[0 + 5] = -f[4];
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D[0 + 4] = f[5];
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// res[1] = vel[2]*f[0] - vel[0]*f[2] + vel[5]*f[3] - vel[3]*f[5]
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D[6 + 2] = f[0];
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D[6 + 0] = -f[2];
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D[6 + 5] = f[3];
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D[6 + 3] = -f[5];
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// res[2] = -vel[1]*f[0] + vel[0]*f[1] - vel[4]*f[3] + vel[3]*f[4]
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D[12 + 1] = -f[0];
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D[12 + 0] = f[1];
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D[12 + 4] = -f[3];
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D[12 + 3] = f[4];
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// res[3] = -vel[2]*f[4] + vel[1]*f[5]
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D[18 + 2] = -f[4];
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D[18 + 1] = f[5];
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// res[4] = vel[2]*f[3] - vel[0]*f[5]
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D[24 + 2] = f[3];
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D[24 + 0] = -f[5];
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// res[5] = -vel[1]*f[3] + vel[0]*f[4]
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D[30 + 1] = -f[3];
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D[30 + 0] = f[4];
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}
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// derivative of mju_crossForce w.r.t. force
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static void mjd_crossForce_frc(mjtNum D[36], const mjtNum vel[6]) {
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mju_zero(D, 36);
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// res[0] = -vel[2]*f[1] + vel[1]*f[2] - vel[5]*f[4] + vel[4]*f[5]
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D[0 + 1] = -vel[2];
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D[0 + 2] = vel[1];
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D[0 + 4] = -vel[5];
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D[0 + 5] = vel[4];
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// res[1] = vel[2]*f[0] - vel[0]*f[2] + vel[5]*f[3] - vel[3]*f[5]
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D[6 + 0] = vel[2];
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D[6 + 2] = -vel[0];
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D[6 + 3] = vel[5];
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D[6 + 5] = -vel[3];
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// res[2] = -vel[1]*f[0] + vel[0]*f[1] - vel[4]*f[3] + vel[3]*f[4]
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D[12 + 0] = -vel[1];
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D[12 + 1] = vel[0];
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D[12 + 3] = -vel[4];
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D[12 + 4] = vel[3];
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// res[3] = -vel[2]*f[4] + vel[1]*f[5]
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D[18 + 4] = -vel[2];
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D[18 + 5] = vel[1];
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// res[4] = vel[2]*f[3] - vel[0]*f[5]
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D[24 + 3] = vel[2];
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D[24 + 5] = -vel[0];
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// res[5] = -vel[1]*f[3] + vel[0]*f[4]
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D[30 + 3] = -vel[1];
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D[30 + 4] = vel[0];
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}
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// derivative of mju_mulInertVec w.r.t vel
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static void mjd_mulInertVec_vel(mjtNum D[36], const mjtNum i[10]) {
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mju_zero(D, 36);
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// res[0] = i[0]*v[0] + i[3]*v[1] + i[4]*v[2] - i[8]*v[4] + i[7]*v[5]
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D[0 + 0] = i[0];
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D[0 + 1] = i[3];
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D[0 + 2] = i[4];
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D[0 + 4] = -i[8];
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D[0 + 5] = i[7];
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// res[1] = i[3]*v[0] + i[1]*v[1] + i[5]*v[2] + i[8]*v[3] - i[6]*v[5]
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D[6 + 0] = i[3];
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D[6 + 1] = i[1];
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D[6 + 2] = i[5];
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D[6 + 3] = i[8];
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D[6 + 5] = -i[6];
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// res[2] = i[4]*v[0] + i[5]*v[1] + i[2]*v[2] - i[7]*v[3] + i[6]*v[4]
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D[12 + 0] = i[4];
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D[12 + 1] = i[5];
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D[12 + 2] = i[2];
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D[12 + 3] = -i[7];
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D[12 + 4] = i[6];
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// res[3] = i[8]*v[1] - i[7]*v[2] + i[9]*v[3]
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D[18 + 1] = i[8];
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D[18 + 2] = -i[7];
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D[18 + 3] = i[9];
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// res[4] = i[6]*v[2] - i[8]*v[0] + i[9]*v[4]
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D[24 + 2] = i[6];
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D[24 + 0] = -i[8];
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D[24 + 4] = i[9];
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// res[5] = i[7]*v[0] - i[6]*v[1] + i[9]*v[5]
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D[30 + 0] = i[7];
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D[30 + 1] = -i[6];
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D[30 + 5] = i[9];
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}
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// derivative of mju_subQuat w.r.t inputs
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void mjd_subQuat(const mjtNum qa[4], const mjtNum qb[4], mjtNum Da[9], mjtNum Db[9]) {
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// no outputs, quick return
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if (!Da && !Db) {
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return;
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}
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// compute axis-angle quaternion difference
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mjtNum axis[3];
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mju_subQuat(axis, qa, qb);
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// normalize axis, get half-angle
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mjtNum half_angle = 0.5 * mju_normalize3(axis);
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// identity
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mjtNum Da_tmp[9] = {
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1, 0, 0,
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0, 1, 0,
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0, 0, 1
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};
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// add term linear in cross product matrix K
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mjtNum K[9] = {
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0, -axis[2], axis[1],
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axis[2], 0, -axis[0],
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-axis[1], axis[0], 0
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};
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mju_addToScl(Da_tmp, K, half_angle, 9);
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// add term linear in K * K
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mjtNum KK[9];
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mju_mulMatMat3(KK, K, K);
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mjtNum coef = 1.0 - (half_angle < 6e-8 ? 1.0 : half_angle / mju_tan(half_angle));
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mju_addToScl(Da_tmp, KK, coef, 9);
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if (Da) {
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mju_copy9(Da, Da_tmp);
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}
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if (Db) { // Db = -Da^T
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mju_transpose(Db, Da_tmp, 3, 3);
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mju_scl(Db, Db, -1.0, 9);
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}
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}
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// derivative of mju_quatIntegrate w.r.t scaled velocity
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// reference: https://arxiv.org/abs/1711.02508, Eq. 183
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void mjd_quatIntegrate(const mjtNum vel[3], mjtNum scale,
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mjtNum Dquat[9], mjtNum Dvel[9], mjtNum Dscale[3]) {
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// scaled velocity
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mjtNum s[3] = {scale*vel[0], scale*vel[1], scale*vel[2]};
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// 3 basis matrices
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mjtNum eye[9] = {
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1, 0, 0,
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0, 1, 0,
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0, 0, 1
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};
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mjtNum cross[9] = {
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0, s[2], -s[1],
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-s[2], 0, s[0],
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s[1], -s[0], 0
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};
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mjtNum outer[9] = {
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s[0]*s[0], s[0]*s[1], s[0]*s[2],
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s[1]*s[0], s[1]*s[1], s[1]*s[2],
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s[2]*s[0], s[2]*s[1], s[2]*s[2]
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};
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// squared norm, norm of s
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mjtNum xx = mju_dot3(s, s);
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mjtNum x = mju_sqrt(xx);
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// 4 coefficients: a=cos(x), b=sin(x)/x, c=(1-cos(x))/x^2, d=(x-sin(x))/x^3
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mjtNum a = mju_cos(x);
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mjtNum b, c, d;
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// x is not small: use full expressions
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if (mju_abs(x) > 1.0/32) {
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b = mju_sin(x) / x;
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c = (1.0 - a) / xx;
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d = (1.0 - b) / xx;
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}
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// |x| <= 1/32: use 6th order Taylor expansion (Horner form)
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else {
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b = 1 + xx/6 * (xx/20 * (1 - xx/42) - 1);
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c = (1 + xx/12 * (xx/30 * (1 - xx/56) - 1)) / 2;
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d = (1 + xx/20 * (xx/42 * (1 - xx/72) - 1)) / 6;
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}
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// derivatives
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mjtNum Dvel_[9];
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for (int i=0; i < 9; i++) {
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if (Dquat) Dquat[i] = a*eye[i] + b*cross[i] + c*outer[i];
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if (Dvel || Dscale) Dvel_[i] = b*eye[i] + c*cross[i] + d*outer[i];
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}
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if (Dvel) mju_copy9(Dvel, Dvel_);
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if (Dscale) mju_mulMatVec3(Dscale, Dvel_, vel);
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}
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//------------------------- dense derivatives of component functions -------------------------------
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// no longer used, except in tests
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// derivative of cvel, cdof_dot w.r.t qvel (dense version)
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static void mjd_comVel_vel_dense(const mjModel* m, mjData* d, mjtNum* Dcvel, mjtNum* Dcdofdot) {
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int nv = m->nv, nbody = m->nbody;
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mjtNum mat[36];
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// clear Dcvel
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mju_zero(Dcvel, nbody*6*nv);
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// forward pass over bodies: accumulate Dcvel, set Dcdofdot
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for (int i=1; i < nbody; i++) {
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// Dcvel = Dcvel_parent
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mju_copy(Dcvel+i*6*nv, Dcvel+m->body_parentid[i]*6*nv, 6*nv);
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// Dcvel += D(cdof * qvel), Dcdofdot = D(cvel x cdof)
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for (int j=m->body_dofadr[i]; j < m->body_dofadr[i]+m->body_dofnum[i]; j++) {
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switch ((mjtJoint) m->jnt_type[m->dof_jntid[j]]) {
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case mjJNT_FREE:
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// Dcdofdot = 0
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mju_zero(Dcdofdot+j*6*nv, 18*nv);
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// Dcvel += cdof * (D qvel)
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for (int k=0; k < 6; k++) {
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Dcvel[i*6*nv + k*nv + j+0] += d->cdof[(j+0)*6 + k];
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Dcvel[i*6*nv + k*nv + j+1] += d->cdof[(j+1)*6 + k];
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Dcvel[i*6*nv + k*nv + j+2] += d->cdof[(j+2)*6 + k];
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}
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// continue with rotations
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j += 3;
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mjFALLTHROUGH;
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case mjJNT_BALL:
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// Dcdofdot = D crossMotion(cvel, cdof)
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for (int k=0; k < 3; k++) {
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mjd_crossMotion_vel(mat, d->cdof+6*(j+k));
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mju_mulMatMat(Dcdofdot+(j+k)*6*nv, mat, Dcvel+i*6*nv, 6, 6, nv);
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}
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// Dcvel += cdof * (D qvel)
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for (int k=0; k < 6; k++) {
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Dcvel[i*6*nv + k*nv + j+0] += d->cdof[(j+0)*6 + k];
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Dcvel[i*6*nv + k*nv + j+1] += d->cdof[(j+1)*6 + k];
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Dcvel[i*6*nv + k*nv + j+2] += d->cdof[(j+2)*6 + k];
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}
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// adjust for 3-dof joint
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j += 2;
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break;
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default:
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// Dcdofdot = D crossMotion(cvel, cdof) * Dcvel
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mjd_crossMotion_vel(mat, d->cdof+6*j);
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mju_mulMatMat(Dcdofdot+j*6*nv, mat, Dcvel+i*6*nv, 6, 6, nv);
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// Dcvel += cdof * (D qvel)
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for (int k=0; k < 6; k++) {
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Dcvel[i*6*nv + k*nv + j] += d->cdof[j*6 + k];
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}
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}
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}
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}
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}
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// subtract (d qfrc_bias / d qvel) from qDeriv (dense version)
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void mjd_rne_vel_dense(const mjModel* m, mjData* d) {
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int nv = m->nv, nbody = m->nbody;
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mjtNum mat[36], mat1[36], mat2[36], dmul[36], tmp[6];
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mj_markStack(d);
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mjtNum* Dcvel = mjSTACKALLOC(d, nbody*6*nv, mjtNum);
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mjtNum* Dcdofdot = mjSTACKALLOC(d, nv*6*nv, mjtNum);
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mjtNum* Dcacc = mjSTACKALLOC(d, nbody*6*nv, mjtNum);
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mjtNum* Dcfrcbody = mjSTACKALLOC(d, nbody*6*nv, mjtNum);
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mjtNum* row = mjSTACKALLOC(d, nv, mjtNum);
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// compute Dcvel and Dcdofdot
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mjd_comVel_vel_dense(m, d, Dcvel, Dcdofdot);
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// clear Dcacc
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mju_zero(Dcacc, nbody*6*nv);
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// forward pass over bodies: accumulate Dcacc, set Dcfrcbody
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for (int i=1; i < nbody; i++) {
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// Dcacc = Dcacc_parent
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mju_copy(Dcacc + i*6*nv, Dcacc + m->body_parentid[i]*6*nv, 6*nv);
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// Dcacc += D(cdofdot * qvel)
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for (int j=m->body_dofadr[i]; j < m->body_dofadr[i]+m->body_dofnum[i]; j++) {
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// Dcacc += cdofdot * (D qvel)
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for (int k=0; k < 6; k++) {
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Dcacc[i*6*nv + k*nv + j] += d->cdof_dot[j*6 + k];
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}
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// Dcacc += (D cdofdot) * qvel
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mju_addToScl(Dcacc+i*6*nv, Dcdofdot+j*6*nv, d->qvel[j], 6*nv);
|
|
}
|
|
|
|
//---------- Dcfrcbody = D(cinert * cacc + cvel x (cinert * cvel))
|
|
|
|
// Dcfrcbody = (D mul / D cacc) * Dcacc
|
|
mjd_mulInertVec_vel(dmul, d->cinert+10*i);
|
|
mju_mulMatMat(Dcfrcbody+i*6*nv, dmul, Dcacc+i*6*nv, 6, 6, nv);
|
|
|
|
// mat = (D cross / D cvel) + (D cross / D mul) * (D mul / D cvel)
|
|
mju_mulInertVec(tmp, d->cinert+10*i, d->cvel+i*6);
|
|
mjd_crossForce_vel(mat, tmp);
|
|
mjd_crossForce_frc(mat1, d->cvel+i*6);
|
|
mju_mulMatMat(mat2, mat1, dmul, 6, 6, 6);
|
|
mju_addTo(mat, mat2, 36);
|
|
|
|
// Dcfrcbody += mat * Dcvel (use body 0 as temp)
|
|
mju_mulMatMat(Dcfrcbody, mat, Dcvel+i*6*nv, 6, 6, nv);
|
|
mju_addTo(Dcfrcbody+i*6*nv, Dcfrcbody, 6*nv);
|
|
}
|
|
|
|
// clear world Dcfrcbody, for style
|
|
mju_zero(Dcfrcbody, 6*nv);
|
|
|
|
// backward pass over bodies: accumulate Dcfrcbody
|
|
for (int i=nbody-1; i > 0; i--) {
|
|
if (m->body_parentid[i]) {
|
|
mju_addTo(Dcfrcbody+m->body_parentid[i]*6*nv, Dcfrcbody+i*6*nv, 6*nv);
|
|
}
|
|
}
|
|
|
|
// qDeriv -= D(cdof * cfrc_body)
|
|
for (int i=0; i < nv; i++) {
|
|
for (int k=0; k < 6; k++) {
|
|
// compute D(cdof * cfrc_body), store in row
|
|
mju_scl(row, Dcfrcbody + (m->dof_bodyid[i]*6+k)*nv, d->cdof[i*6+k], nv);
|
|
|
|
// dense to sparse: qDeriv -= row
|
|
int end = m->D_rowadr[i] + m->D_rownnz[i];
|
|
for (int adr=m->D_rowadr[i]; adr < end; adr++) {
|
|
d->qDeriv[adr] -= row[m->D_colind[adr]];
|
|
}
|
|
}
|
|
}
|
|
|
|
mj_freeStack(d);
|
|
}
|
|
|
|
|
|
//------------------------- sparse derivatives of component functions ------------------------------
|
|
// internal sparse format: dense body/dof x sparse dof x 6 (inner size is 6)
|
|
|
|
// copy sparse B-row from parent, shared ancestors only
|
|
static void copyFromParent(const mjModel* m, mjData* d, mjtNum* mat, int n) {
|
|
// return if this is world or parent is world
|
|
if (n == 0 || m->body_weldid[m->body_parentid[n]] == 0) {
|
|
return;
|
|
}
|
|
|
|
// count dofs in ancestors
|
|
int ndof = 0;
|
|
int np = m->body_weldid[m->body_parentid[n]];
|
|
while (np > 0) {
|
|
// add self dofs
|
|
ndof += m->body_dofnum[np];
|
|
|
|
// advance to parent
|
|
np = m->body_weldid[m->body_parentid[np]];
|
|
}
|
|
|
|
// copy: guaranteed to be at beginning of sparse array, due to sorting
|
|
mju_copy(mat + 6*m->B_rowadr[n], mat + 6*m->B_rowadr[m->body_parentid[n]], 6*ndof);
|
|
}
|
|
|
|
|
|
// add sparse B-row to parent, all overlapping nonzeros
|
|
static void addToParent(const mjModel* m, mjData* d, mjtNum* mat, int n) {
|
|
// return if this is world or parent is world
|
|
if (n == 0 || m->body_weldid[m->body_parentid[n]] == 0) {
|
|
return;
|
|
}
|
|
|
|
// find matching nonzeros
|
|
int np = m->body_parentid[n];
|
|
int i = 0, ip = 0;
|
|
while (i < m->B_rownnz[n] && ip < m->B_rownnz[np]) {
|
|
// columns match
|
|
if (m->B_colind[m->B_rowadr[n] + i] == m->B_colind[m->B_rowadr[np] + ip]) {
|
|
mju_addTo(mat + 6*(m->B_rowadr[np] + ip), mat + 6*(m->B_rowadr[n] + i), 6);
|
|
|
|
// advance both
|
|
i++;
|
|
ip++;
|
|
}
|
|
|
|
// mismatch columns: advance parent
|
|
else if (m->B_colind[m->B_rowadr[n] + i] > m->B_colind[m->B_rowadr[np] + ip]) {
|
|
ip++;
|
|
}
|
|
|
|
// child nonzeroes must be subset of parent; SHOULD NOT OCCUR
|
|
else {
|
|
mjERROR("child nonzeroes must be subset of parent");
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// derivative of cvel, cdof_dot w.r.t qvel
|
|
static void mjd_comVel_vel(const mjModel* m, mjData* d, mjtNum* Dcvel, mjtNum* Dcdofdot) {
|
|
int nv = m->nv, nM = m->nM;
|
|
int sleep_filter = mjENABLED(mjENBL_SLEEP) && d->nbody_awake < m->nbody;
|
|
int nbody = sleep_filter ? d->nbody_awake : m->nbody;
|
|
int* Badr = m->B_rowadr, * Dadr = m->D_rowadr;
|
|
mjtNum mat[36], matT[36]; // 6x6 matrices
|
|
|
|
// forward pass over bodies: accumulate Dcvel, set Dcdofdot
|
|
for (int b=1; b < nbody; b++) {
|
|
int i = sleep_filter ? d->body_awake_ind[b] : b;
|
|
|
|
// Dcvel = Dcvel_parent
|
|
copyFromParent(m, d, Dcvel, i);
|
|
|
|
// process all dofs of this body
|
|
int doflast = m->body_dofadr[i] + m->body_dofnum[i];
|
|
for (int j = m->body_dofadr[i]; j < doflast; j++) {
|
|
// number of dof ancestors of dof j
|
|
int Jadr = (j < nv - 1 ? m->dof_Madr[j + 1] : nM) - (m->dof_Madr[j] + 1);
|
|
|
|
// Dcvel += D(cdof * qvel), Dcdofdot = D(cvel x cdof)
|
|
switch ((mjtJoint) m->jnt_type[m->dof_jntid[j]]) {
|
|
case mjJNT_FREE:
|
|
// Dcdofdot = 0 (already cleared)
|
|
|
|
// Dcvel += cdof * D(qvel)
|
|
mju_addTo(Dcvel + 6*(Badr[i] + Jadr + 0), d->cdof + 6*(j + 0), 6);
|
|
mju_addTo(Dcvel + 6*(Badr[i] + Jadr + 1), d->cdof + 6*(j + 1), 6);
|
|
mju_addTo(Dcvel + 6*(Badr[i] + Jadr + 2), d->cdof + 6*(j + 2), 6);
|
|
|
|
// continue with rotations
|
|
j += 3;
|
|
Jadr += 3;
|
|
mjFALLTHROUGH;
|
|
|
|
case mjJNT_BALL:
|
|
// Dcdofdot = Dcvel * D crossMotion(cvel, cdof)
|
|
for (int dj=0; dj < 3; dj++) {
|
|
mjd_crossMotion_vel(mat, d->cdof + 6 * (j + dj));
|
|
mju_transpose(matT, mat, 6, 6);
|
|
mju_mulMatMat(Dcdofdot + 6*Dadr[j + dj], Dcvel + 6*Badr[i], matT, Jadr + dj, 6, 6);
|
|
}
|
|
|
|
// Dcvel += cdof * (D qvel)
|
|
mju_addTo(Dcvel + 6*(Badr[i] + Jadr + 0), d->cdof + 6*(j + 0), 6);
|
|
mju_addTo(Dcvel + 6*(Badr[i] + Jadr + 1), d->cdof + 6*(j + 1), 6);
|
|
mju_addTo(Dcvel + 6*(Badr[i] + Jadr + 2), d->cdof + 6*(j + 2), 6);
|
|
|
|
// adjust for 3-dof joint
|
|
j += 2;
|
|
break;
|
|
|
|
case mjJNT_HINGE:
|
|
case mjJNT_SLIDE:
|
|
// Dcdofdot = D crossMotion(cvel, cdof) * Dcvel
|
|
mjd_crossMotion_vel(mat, d->cdof + 6 * j);
|
|
mju_transpose(matT, mat, 6, 6);
|
|
mju_mulMatMat(Dcdofdot + 6*Dadr[j], Dcvel + 6*Badr[i], matT, Jadr, 6, 6);
|
|
|
|
// Dcvel += cdof * (D qvel)
|
|
mju_addTo(Dcvel + 6*(Badr[i] + Jadr), d->cdof + 6*j, 6);
|
|
break;
|
|
|
|
default:
|
|
mjERROR("unknown joint type");
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// subtract d qfrc_bias / d qvel from qDeriv
|
|
static void mjd_rne_vel(const mjModel* m, mjData* d) {
|
|
int nM = m->nM;
|
|
int sleep_filter = mjENABLED(mjENBL_SLEEP) && d->nbody_awake < m->nbody;
|
|
int nbody = sleep_filter ? d->nbody_awake : m->nbody;
|
|
int nparent = sleep_filter ? d->nparent_awake : m->nbody;
|
|
int mnv = m->nv;
|
|
int nv = sleep_filter ? d->nv_awake : mnv;
|
|
|
|
const int* Badr = m->B_rowadr;
|
|
const int* Dadr = m->D_rowadr;
|
|
const int* Bnnz = m->B_rownnz;
|
|
|
|
mjtNum mat[36], mat1[36], mat2[36], dmul[36], tmp[6];
|
|
|
|
mj_markStack(d);
|
|
mjtNum* Dcdofdot = mjSTACKALLOC(d, 6*m->nD, mjtNum);
|
|
mjtNum* Dcvel = mjSTACKALLOC(d, 6*m->nB, mjtNum);
|
|
mjtNum* Dcacc = mjSTACKALLOC(d, 6*m->nB, mjtNum);
|
|
mjtNum* Dcfrcbody = mjSTACKALLOC(d, 6*m->nB, mjtNum);
|
|
mjtNum* row = mjSTACKALLOC(d, m->nv, mjtNum);
|
|
|
|
// clear
|
|
if (!sleep_filter) {
|
|
mju_zero(Dcdofdot, 6*m->nD);
|
|
mju_zero(Dcvel, 6*m->nB);
|
|
mju_zero(Dcacc, 6*m->nB);
|
|
mju_zero(Dcfrcbody, 6*m->nB);
|
|
} else {
|
|
for (int i = 0; i < nv; i++) {
|
|
int dof = d->dof_awake_ind[i];
|
|
mju_zero(Dcdofdot + 6*m->D_rowadr[dof], 6*m->D_rownnz[dof]);
|
|
}
|
|
|
|
for (int i = 0; i < nbody; i++) {
|
|
int body = d->body_awake_ind[i];
|
|
int adr = 6*m->B_rowadr[body];
|
|
int nnz = 6*m->B_rownnz[body];
|
|
mju_zero(Dcvel + adr, nnz);
|
|
mju_zero(Dcacc + adr, nnz);
|
|
mju_zero(Dcfrcbody + adr, nnz);
|
|
}
|
|
}
|
|
|
|
// compute Dcvel and Dcdofdot
|
|
mjd_comVel_vel(m, d, Dcvel, Dcdofdot);
|
|
|
|
// forward pass over bodies: accumulate Dcacc, set Dcfrcbody
|
|
for (int b=1; b < nbody; b++) {
|
|
int i = sleep_filter ? d->body_awake_ind[b] : b;
|
|
|
|
// Dcacc = Dcacc_parent
|
|
copyFromParent(m, d, Dcacc, i);
|
|
|
|
// process all dofs of this body
|
|
int doflast = m->body_dofadr[i] + m->body_dofnum[i];
|
|
for (int j=m->body_dofadr[i]; j < doflast; j++) {
|
|
// number of dof ancestors of dof j
|
|
int Jadr = (j < mnv - 1 ? m->dof_Madr[j + 1] : nM) - (m->dof_Madr[j] + 1);
|
|
|
|
// Dcacc += cdofdot * (D qvel)
|
|
mju_addTo(Dcacc + 6*(Badr[i] + Jadr), d->cdof_dot + 6*j, 6);
|
|
|
|
// Dcacc += (D cdofdot) * qvel
|
|
// Dcacc[row i] and Dcdofdot[row j] have identical sparsity
|
|
mju_addToScl(Dcacc + 6*Badr[i], Dcdofdot + 6*Dadr[j], d->qvel[j], 6*Bnnz[i]);
|
|
}
|
|
|
|
//---------- Dcfrcbody = D(cinert * cacc + cvel x (cinert * cvel))
|
|
|
|
// Dcfrcbody = (D mul / D cacc) * Dcacc
|
|
mjd_mulInertVec_vel(dmul, d->cinert + 10*i);
|
|
mju_transpose(mat1, dmul, 6, 6);
|
|
mju_mulMatMat(Dcfrcbody + 6*Badr[i], Dcacc + 6*Badr[i], mat1, Bnnz[i], 6, 6);
|
|
|
|
// mat = (D cross / D cvel) + (D cross / D mul) * (D mul / D cvel)
|
|
mju_mulInertVec(tmp, d->cinert + 10*i, d->cvel + i*6);
|
|
mjd_crossForce_vel(mat, tmp);
|
|
mjd_crossForce_frc(mat1, d->cvel + i*6);
|
|
mju_mulMatMat(mat2, mat1, dmul, 6, 6, 6);
|
|
mju_addTo(mat, mat2, 36);
|
|
|
|
// Dcfrcbody += mat * Dcvel (use worldbody as temp)
|
|
mju_transpose(mat1, mat, 6, 6);
|
|
mju_mulMatMat(Dcfrcbody, Dcvel + 6*Badr[i], mat1, Bnnz[i], 6, 6);
|
|
mju_addTo(Dcfrcbody + 6*Badr[i], Dcfrcbody, 6*Bnnz[i]);
|
|
}
|
|
|
|
// clear worldbody Dcfrcbody
|
|
mju_zero(Dcfrcbody, 6*Bnnz[0]);
|
|
|
|
// backward pass over bodies: accumulate Dcfrcbody
|
|
for (int b=nparent-1; b > 0; b--) {
|
|
int i = sleep_filter ? d->parent_awake_ind[b] : b;
|
|
addToParent(m, d, Dcfrcbody, i);
|
|
}
|
|
|
|
// process all dofs, update qDeriv
|
|
for (int v=0; v < nv; v++) {
|
|
int j = sleep_filter ? d->dof_awake_ind[v] : v;
|
|
|
|
// get body index
|
|
int i = m->dof_bodyid[j];
|
|
|
|
// qDeriv -= D(cdof * cfrc_body)
|
|
mju_mulMatVec(row, Dcfrcbody + 6*Badr[i], d->cdof + 6*j, Bnnz[i], 6);
|
|
mju_subFrom(d->qDeriv + Dadr[j], row, Bnnz[i]);
|
|
}
|
|
|
|
mj_freeStack(d);
|
|
}
|
|
|
|
|
|
//--------------------- utility functions for (d force / d vel) Jacobians --------------------------
|
|
|
|
// add J'*B*J to qDeriv
|
|
static void addJTBJ(const mjModel* m, mjData* d, const mjtNum* J, const mjtNum* B, int n) {
|
|
int nv = m->nv;
|
|
|
|
// allocate dense row
|
|
mj_markStack(d);
|
|
mjtNum* row = mjSTACKALLOC(d, nv, mjtNum);
|
|
|
|
// process non-zero elements of B
|
|
for (int i=0; i < n; i++) {
|
|
for (int j=0; j < n; j++) {
|
|
if (!B[i*n+j]) {
|
|
continue;
|
|
}
|
|
// process non-zero elements of J(i,:)
|
|
for (int k=0; k < nv; k++) {
|
|
if (J[i*nv+k]) {
|
|
// row = J(i,k)*B(i,j)*J(j,:)
|
|
mju_scl(row, J+j*nv, J[i*nv+k] * B[i*n+j], nv);
|
|
|
|
// add row to qDeriv(k,:)
|
|
int rownnz_k = m->D_rownnz[k];
|
|
for (int s=0; s < rownnz_k; s++) {
|
|
int adr = m->D_rowadr[k] + s;
|
|
d->qDeriv[adr] += row[m->D_colind[adr]];
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
mj_freeStack(d);
|
|
}
|
|
|
|
|
|
// add J'*B*J to qDeriv, sparse version
|
|
static void addJTBJSparse(
|
|
const mjModel* m, mjData* d, const mjtNum* J,
|
|
const mjtNum* B, int n, int offset,
|
|
const int* J_rownnz, const int* J_rowadr, const int* J_colind) {
|
|
|
|
// compute qDeriv(k,p) += sum_{i,j} ( J(i,k)*B(i,j)*J(j,p) )
|
|
for (int i = 0; i < n; i++) {
|
|
for (int j = 0; j < n; j++) {
|
|
if (!B[i*n+j]) {
|
|
continue;
|
|
}
|
|
|
|
// loop over non-zero elements of J(i,:)
|
|
int nnz_i = J_rownnz[offset+i];
|
|
int adr_i = J_rowadr[offset+i];
|
|
int nnz_j = J_rownnz[offset+j];
|
|
int adr_j = J_rowadr[offset+j];
|
|
for (int k = 0; k < nnz_i; k++) {
|
|
int ik = adr_i + k;
|
|
int colik = J_colind[ik];
|
|
|
|
// qDeriv(k,:) += J(j,:) * J(i,k)*B(i,j)
|
|
mju_addToSclSparseInc(d->qDeriv + m->D_rowadr[colik], J + adr_j,
|
|
m->D_rownnz[colik], m->D_colind + m->D_rowadr[colik],
|
|
nnz_j, J_colind + adr_j,
|
|
J[ik]*B[i*n+j]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
//----------------------------- derivatives of actuator forces -------------------------------------
|
|
|
|
// derivative of mju_muscleGain w.r.t velocity
|
|
static mjtNum mjd_muscleGain_vel(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 / mju_max(mjMINVAL, acc0);
|
|
}
|
|
|
|
// optimum length
|
|
mjtNum L0 = (lengthrange[1]-lengthrange[0]) / mju_max(mjMINVAL, range[1]-range[0]);
|
|
|
|
// normalized length and velocity
|
|
mjtNum L = range[0] + (len-lengthrange[0]) / mju_max(mjMINVAL, L0);
|
|
mjtNum V = vel / mju_max(mjMINVAL, L0*vmax);
|
|
|
|
// length curve
|
|
mjtNum FL = mju_muscleGainLength(L, lmin, lmax);
|
|
|
|
// velocity curve
|
|
mjtNum dFV;
|
|
mjtNum y = fvmax-1;
|
|
if (V <= -1) {
|
|
// FV = 0
|
|
dFV = 0;
|
|
} else if (V <= 0) {
|
|
// FV = (V+1)*(V+1)
|
|
dFV = 2*V + 2;
|
|
} else if (V <= y) {
|
|
// FV = fvmax - (y-V)*(y-V) / mju_max(mjMINVAL, y)
|
|
dFV = (-2*V + 2*y) / mju_max(mjMINVAL, y);
|
|
} else {
|
|
// FV = fvmax
|
|
dFV = 0;
|
|
}
|
|
|
|
// compute FVL and scale, make it negative
|
|
return -force*FL*dFV/mju_max(mjMINVAL, L0*vmax);
|
|
}
|
|
|
|
|
|
//--------------------- utility functions for (d force / d pos) * vec Jacobians --------------------
|
|
|
|
// add J'*B*J*vec to res, sparse version
|
|
static void addJTBJ_mulSparse(const mjModel* m, mjData* d, mjtNum* res, const mjtNum* vec,
|
|
const int* J_rownnz, const int* J_rowadr, const int* J_colind,
|
|
const mjtNum* J, const mjtNum* B, int n) {
|
|
// allocate temp vectors
|
|
mj_markStack(d);
|
|
mjtNum* Jv = mjSTACKALLOC(d, n, mjtNum);
|
|
mjtNum* BJv = mjSTACKALLOC(d, n, mjtNum);
|
|
|
|
// Jv = J*vec (Sparse Matrix-Vector Multiplication)
|
|
mju_zero(Jv, n);
|
|
for (int i=0; i < n; i++) {
|
|
int nnz = J_rownnz[i];
|
|
int adr = J_rowadr[i];
|
|
for (int k=0; k < nnz; k++) {
|
|
Jv[i] += J[adr + k] * vec[J_colind[adr + k]];
|
|
}
|
|
}
|
|
|
|
// BJv = B*Jv (Dense Matrix-Vector Multiplication)
|
|
mju_mulMatVec(BJv, B, Jv, n, n);
|
|
|
|
// res += J'*BJv (Sparse Transpose Matrix-Vector Multiplication)
|
|
for (int i=0; i < n; i++) {
|
|
int nnz = J_rownnz[i];
|
|
int adr = J_rowadr[i];
|
|
mjtNum val = BJv[i];
|
|
for (int k=0; k < nnz; k++) {
|
|
res[J_colind[adr + k]] += J[adr + k] * val;
|
|
}
|
|
}
|
|
|
|
mj_freeStack(d);
|
|
}
|
|
|
|
|
|
// operation type for flex interpolation derivative kernel
|
|
typedef enum {
|
|
mjFLEXOP_VEC, // res += J'*K*J*vec
|
|
mjFLEXOP_ADDH // H -= J'*K*J to H (dense)
|
|
} mjtFlexOp;
|
|
|
|
// shared kernel for flex interpolation derivatives, scale = s1 + s2*damping
|
|
// op: operation type (VEC, or ADDH)
|
|
// res: output vector (VEC) or banded H matrix (ADDH)
|
|
// vec: input vector for VEC operation, NULL otherwise
|
|
// dof_indices, ndof, nband: DOF mapping and band width for ADDH, ignored otherwise
|
|
static void mjd_flexInterp_kernel(const mjModel* m, mjData* d, mjtFlexOp op,
|
|
mjtNum* res, const mjtNum* vec, mjtNum s1, mjtNum s2,
|
|
const int* dof_indices, int ndof, int nband) {
|
|
int nv = m->nv;
|
|
|
|
// compute upper bounds across all interpolated flexes
|
|
int max_nodenum = 0;
|
|
int max_npc = 0;
|
|
for (int f = 0; f < m->nflex; f++) {
|
|
if (!m->flex_interp[f]) continue;
|
|
if (m->flex_rigid[f]) continue;
|
|
int order = m->flex_interp[f];
|
|
order = order < 0 ? -order : order;
|
|
int npc = (order+1)*(order+1)*(order+1);
|
|
if (npc > max_npc) max_npc = npc;
|
|
if (m->flex_nodenum[f] > max_nodenum) max_nodenum = m->flex_nodenum[f];
|
|
}
|
|
|
|
// nothing to do
|
|
if (max_npc == 0) {
|
|
return;
|
|
}
|
|
|
|
int max_dim_c = 3 * max_npc;
|
|
|
|
// single unconditional markStack
|
|
mj_markStack(d);
|
|
|
|
// global2local map for ADDH
|
|
int* global2local = mjSTACKALLOC(d, nv, int);
|
|
if (op == mjFLEXOP_ADDH) {
|
|
mju_fillInt(global2local, -1, nv);
|
|
for (int i=0; i<ndof; i++) {
|
|
global2local[dof_indices[i]] = i;
|
|
}
|
|
}
|
|
|
|
// per-flex node positions (upper bound)
|
|
mjtNum* xpos = mjSTACKALLOC(d, 3*max_nodenum, mjtNum);
|
|
|
|
// per-cell arrays (upper bound)
|
|
mjtNum* xpos_c = mjSTACKALLOC(d, 3*max_npc, mjtNum);
|
|
mjtNum* K_rot_cell = mjSTACKALLOC(d, max_dim_c*max_dim_c, mjtNum);
|
|
|
|
// sparse Jacobian for one cell (upper bound)
|
|
int* J_rownnz = mjSTACKALLOC(d, max_dim_c, int);
|
|
int* J_rowadr = mjSTACKALLOC(d, max_dim_c, int);
|
|
mjtNum* J_val = mjSTACKALLOC(d, max_dim_c*nv, mjtNum);
|
|
int* J_colind = mjSTACKALLOC(d, max_dim_c*nv, int);
|
|
|
|
// temp allocations for chain
|
|
int* chain_colind = mjSTACKALLOC(d, nv, int);
|
|
mjtNum* blk_jac = mjSTACKALLOC(d, 3*nv, mjtNum);
|
|
|
|
// ADDH-specific allocations (upper bound)
|
|
mjtNum* J_reduced = NULL;
|
|
mjtNum* KJ = NULL;
|
|
if (op == mjFLEXOP_ADDH) {
|
|
J_reduced = mjSTACKALLOC(d, max_dim_c*ndof, mjtNum);
|
|
KJ = mjSTACKALLOC(d, max_dim_c*ndof, mjtNum);
|
|
}
|
|
|
|
// loop over flexes
|
|
for (int f=0; f < m->nflex; f++) {
|
|
// only process flex_interp
|
|
if (!m->flex_interp[f]) {
|
|
continue;
|
|
}
|
|
|
|
// get stiffness and damping
|
|
mjtNum* K = m->flex_stiffness + m->flex_stiffnessadr[f];
|
|
|
|
// skip if rigid or no stiffness
|
|
if (m->flex_rigid[f] || K[0] == 0) {
|
|
continue;
|
|
}
|
|
|
|
// skip if strain constraints present (stiffness handled by constraint solver)
|
|
if (m->flex_edgeequality[f] == 3) {
|
|
continue;
|
|
}
|
|
|
|
// compute scale
|
|
mjtNum damping = m->flex_damping[f];
|
|
mjtNum scale = s1 + s2 * damping;
|
|
|
|
// skip if scale is zero
|
|
if (scale == 0) {
|
|
continue;
|
|
}
|
|
|
|
int order = m->flex_interp[f];
|
|
order = order < 0 ? -order : order;
|
|
int npc = (order+1)*(order+1)*(order+1);
|
|
int cx = m->flex_cellnum[3*f+0];
|
|
int cy = m->flex_cellnum[3*f+1];
|
|
int cz = m->flex_cellnum[3*f+2];
|
|
|
|
int* bodyid = m->flex_nodebodyid + m->flex_nodeadr[f];
|
|
|
|
int dim_c = 3 * npc;
|
|
|
|
// gather raw node positions (unrotated)
|
|
mju_flexGatherState(m, d, f, xpos, NULL);
|
|
|
|
// loop over cells
|
|
int cell_idx = 0;
|
|
for (int ci = 0; ci < cx; ci++) {
|
|
for (int cj = 0; cj < cy; cj++) {
|
|
for (int ck = 0; ck < cz; ck++) {
|
|
// get cell stiffness
|
|
mjtNum* k_cell = K + cell_idx * 3*npc * 3*npc;
|
|
|
|
// skip empty cells: stiffness buffer is zero-initialized at compile time
|
|
// (user_model.cc), and non-empty cells have strictly positive diagonal
|
|
if (k_cell[0] == 0) {
|
|
cell_idx++;
|
|
continue;
|
|
}
|
|
|
|
// gather cell-local node positions
|
|
int gindices[125]; // max npc = 125 for quadratic
|
|
mjtNum quat[4];
|
|
mju_flexGatherCellState(order, cy, cz, ci, cj, ck, xpos, NULL, NULL,
|
|
xpos_c, NULL, NULL, gindices, quat);
|
|
|
|
// R = R_global2local, RT = R_local2global
|
|
mjtNum R[9], RT[9];
|
|
mju_quat2Mat(R, quat);
|
|
mju_transpose(RT, R, 3, 3);
|
|
|
|
// compute K_rot_cell = RT * K_cell * R (block-wise)
|
|
mju_zero(K_rot_cell, dim_c*dim_c);
|
|
for (int a = 0; a < npc; a++) {
|
|
for (int b = 0; b < npc; b++) {
|
|
mjtNum blk[9], tmp[9];
|
|
|
|
// get K_cell(a,b) 3x3 block
|
|
int adr_cell = (3*a)*(3*npc) + 3*b;
|
|
for (int r = 0; r < 3; r++) {
|
|
for (int c = 0; c < 3; c++) {
|
|
blk[3*r+c] = k_cell[adr_cell + r*(3*npc) + c];
|
|
}
|
|
}
|
|
|
|
// tmp = K * R
|
|
mju_mulMatMat3(tmp, blk, R);
|
|
// blk = RT * tmp = RT * K * R
|
|
mju_mulMatMat3(blk, RT, tmp);
|
|
|
|
// store in K_rot_cell at (a, b)
|
|
int adr_out = (3*a)*dim_c + 3*b;
|
|
for (int r = 0; r < 3; r++) {
|
|
for (int c = 0; c < 3; c++) {
|
|
K_rot_cell[adr_out + r*dim_c + c] = scale * blk[3*r+c];
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// construct sparse Jacobian for this cell's nodes
|
|
int current_adr = 0;
|
|
for (int n = 0; n < npc; n++) {
|
|
int bid = bodyid[gindices[n]];
|
|
int chain_nnz = mj_bodyChain(m, bid, chain_colind);
|
|
mj_jacSparse(m, d, blk_jac, NULL, xpos+3*gindices[n], bid,
|
|
chain_nnz, chain_colind, /*flg_skipcommon=*/0);
|
|
|
|
for (int r = 0; r < 3; r++) {
|
|
int row_idx = 3*n + r;
|
|
J_rownnz[row_idx] = chain_nnz;
|
|
J_rowadr[row_idx] = current_adr;
|
|
|
|
for (int idx = 0; idx < chain_nnz; idx++) {
|
|
J_colind[current_adr] = chain_colind[idx];
|
|
J_val[current_adr] = blk_jac[r*chain_nnz + idx];
|
|
current_adr++;
|
|
}
|
|
}
|
|
}
|
|
|
|
// apply operation with cell's K_rot and J
|
|
if (op == mjFLEXOP_VEC) {
|
|
addJTBJ_mulSparse(m, d, res, vec, J_rownnz, J_rowadr, J_colind,
|
|
J_val, K_rot_cell, dim_c);
|
|
} else if (op == mjFLEXOP_ADDH) {
|
|
// H -= J_cell^T * K_rot_cell * J_cell (banded format)
|
|
mju_zero(J_reduced, dim_c*ndof);
|
|
|
|
for (int i = 0; i < dim_c; i++) {
|
|
int nnz = J_rownnz[i];
|
|
int adr = J_rowadr[i];
|
|
for (int idx = 0; idx < nnz; idx++) {
|
|
int global_col = J_colind[adr + idx];
|
|
int local_idx = global2local[global_col];
|
|
if (local_idx >= 0) {
|
|
J_reduced[i*ndof + local_idx] = J_val[adr + idx];
|
|
}
|
|
}
|
|
}
|
|
|
|
// KJ = K_rot_cell * J_reduced (dim_c x ndof)
|
|
mju_mulMatMat(KJ, K_rot_cell, J_reduced, dim_c, dim_c, ndof);
|
|
|
|
// H[i,j] -= J_reduced[k,i] * KJ[k,j], store lower triangle in banded format
|
|
for (int i = 0; i < ndof; i++) {
|
|
for (int j = mjMAX(0, i-nband+1); j <= i; j++) {
|
|
mjtNum val = 0;
|
|
for (int dim_idx = 0; dim_idx < dim_c; dim_idx++) {
|
|
val += J_reduced[dim_idx*ndof + i] * KJ[dim_idx*ndof + j];
|
|
}
|
|
res[i*nband + nband-1-(i-j)] -= val;
|
|
}
|
|
}
|
|
}
|
|
|
|
cell_idx++;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
mj_freeStack(d);
|
|
}
|
|
|
|
|
|
|
|
// compute res += (h^2 + h*damping) * J'*K*J * vec, for all interpolated flexes
|
|
void mjd_flexInterp_mulKD(const mjModel* m, mjData* d, mjtNum* res, const mjtNum* vec, mjtNum h) {
|
|
// s1=h*h, s2=h => scale = h*h + h*damping
|
|
mjd_flexInterp_kernel(m, d, mjFLEXOP_VEC, res, vec, h * h, h, NULL, 0, 0);
|
|
}
|
|
|
|
|
|
// add (h^2 + h*damping) * J'*K*J to banded matrix H, for all interpolated flexes
|
|
// H: banded ndof x nband matrix (lower triangle, band storage)
|
|
// dof_indices: maps local indices to global DOFs
|
|
void mjd_flexInterp_addH(const mjModel* m, mjData* d, mjtNum* H, const int* dof_indices,
|
|
int ndof, int nband, mjtNum h) {
|
|
mjd_flexInterp_kernel(m, d, mjFLEXOP_ADDH, H, NULL, h * h, h, dof_indices, ndof, nband);
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
// add (d qfrc_actuator / d qvel) to qDeriv
|
|
void mjd_actuator_vel(const mjModel* m, mjData* d) {
|
|
int nu = m->nu;
|
|
int sleep_filter = mjENABLED(mjENBL_SLEEP) && d->ntree_awake < m->ntree;
|
|
|
|
// disabled: nothing to add
|
|
if (mjDISABLED(mjDSBL_ACTUATION)) {
|
|
return;
|
|
}
|
|
|
|
// process actuators
|
|
for (int i=0; i < nu; i++) {
|
|
// skip if disabled
|
|
if (mj_actuatorDisabled(m, i)) {
|
|
continue;
|
|
}
|
|
|
|
// skip if sleeping
|
|
if (sleep_filter && mj_sleepState(m, d, mjOBJ_ACTUATOR, i) == mjS_ASLEEP) {
|
|
continue;
|
|
}
|
|
|
|
// skip if force is clamped by forcerange
|
|
if (m->actuator_forcelimited[i]) {
|
|
mjtNum force = d->actuator_force[i];
|
|
mjtNum* range = m->actuator_forcerange + 2*i;
|
|
if (force <= range[0] || force >= range[1]) {
|
|
continue;
|
|
}
|
|
}
|
|
|
|
mjtNum bias_vel = 0, gain_vel = 0;
|
|
|
|
// affine bias
|
|
if (m->actuator_biastype[i] == mjBIAS_AFFINE) {
|
|
// extract bias info: prm = [const, kp, kv]
|
|
bias_vel = (m->actuator_biasprm + mjNBIAS*i)[2];
|
|
}
|
|
|
|
// DC motor bias (back-EMF)
|
|
else if (m->actuator_biastype[i] == mjBIAS_DCMOTOR) {
|
|
const mjtNum* dynprm = m->actuator_dynprm + mjNDYN*i;
|
|
const mjtNum* gainprm = m->actuator_gainprm + mjNGAIN*i;
|
|
if (dynprm[0] <= 0) {
|
|
mjtNum R = mju_max(mjMINVAL, gainprm[0]);
|
|
mjtNum K = gainprm[1];
|
|
bias_vel -= K * K / R;
|
|
}
|
|
}
|
|
|
|
// affine gain
|
|
if (m->actuator_gaintype[i] == mjGAIN_AFFINE) {
|
|
// extract bias info: prm = [const, kp, kv]
|
|
gain_vel = (m->actuator_gainprm + mjNGAIN*i)[2];
|
|
}
|
|
|
|
// muscle gain
|
|
else if (m->actuator_gaintype[i] == mjGAIN_MUSCLE) {
|
|
gain_vel = mjd_muscleGain_vel(d->actuator_length[i],
|
|
d->actuator_velocity[i],
|
|
m->actuator_lengthrange+2*i,
|
|
m->actuator_acc0[i],
|
|
m->actuator_gainprm + mjNGAIN*i);
|
|
}
|
|
|
|
// DC motor controller damping and LuGre micro-damping
|
|
else if (m->actuator_gaintype[i] == mjGAIN_DCMOTOR) {
|
|
const mjtNum* dynprm = m->actuator_dynprm + mjNDYN*i;
|
|
const mjtNum* gainprm = m->actuator_gainprm + mjNGAIN*i;
|
|
mjtNum te = dynprm[0];
|
|
|
|
// controller velocity derivative: dV/dω
|
|
int input_mode = (int)gainprm[8];
|
|
mjtNum dVdw = 0;
|
|
if (input_mode == 1) dVdw = -gainprm[6]; // position: -kd
|
|
else if (input_mode == 2) dVdw = -gainprm[4]; // velocity: -kp
|
|
|
|
if (te > 0) {
|
|
// stateful current with actearly: d(K*next_act)/dω
|
|
// includes both back-EMF (-K) and controller (dVdw) through act_dot
|
|
mjtNum R = mju_max(mjMINVAL, gainprm[0]);
|
|
mjtNum K = gainprm[1];
|
|
mjtNum s = 1 - mju_exp(-m->opt.timestep / te);
|
|
bias_vel += K * (dVdw - K) * s / R;
|
|
} else if (dVdw != 0) {
|
|
// stateless: controller terms only (back-EMF handled in bias block)
|
|
mjtNum R = mju_max(mjMINVAL, gainprm[0]);
|
|
mjtNum K = gainprm[1];
|
|
bias_vel += K * dVdw / R;
|
|
}
|
|
|
|
// LuGre: force includes -sigma1*z_dot, z_dot = a*z + v
|
|
// d(sigma1*z_dot)/dv = sigma1*(da/dv*z + 1), ignoring higher-order da/dv*z
|
|
mjtNum sigma1 = dynprm[6];
|
|
if (sigma1 > 0) {
|
|
bias_vel -= sigma1;
|
|
}
|
|
}
|
|
|
|
// force = gain .* [ctrl/act]
|
|
if (gain_vel != 0) {
|
|
if (m->actuator_dyntype[i] == mjDYN_NONE) {
|
|
bias_vel += gain_vel * d->ctrl[i];
|
|
} else {
|
|
int act_adr = m->actuator_actadr[i] + m->actuator_actnum[i] - 1;
|
|
mjtNum act = d->act[act_adr];
|
|
|
|
// use next activation if actearly is set (matching forward pass)
|
|
if (m->actuator_actearly[i]) {
|
|
act = mj_nextActivation(m, d, i, act_adr, d->act_dot[act_adr]);
|
|
}
|
|
|
|
bias_vel += gain_vel * act;
|
|
}
|
|
}
|
|
|
|
// add
|
|
if (bias_vel != 0) {
|
|
addJTBJSparse(m, d, d->actuator_moment, &bias_vel, 1, i,
|
|
d->moment_rownnz, d->moment_rowadr, d->moment_colind);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
//----------------- utilities for ellipsoid-based fluid force derivatives --------------------------
|
|
|
|
static inline mjtNum pow2(const mjtNum val) {
|
|
return val*val;
|
|
}
|
|
|
|
|
|
static inline mjtNum ellipsoid_max_moment(const mjtNum size[3], const int dir) {
|
|
const mjtNum d0 = size[dir];
|
|
const mjtNum d1 = size[(dir+1) % 3];
|
|
const mjtNum d2 = size[(dir+2) % 3];
|
|
return 8.0/15.0 * mjPI * d0 * pow2(pow2(mju_max(d1, d2)));
|
|
}
|
|
|
|
|
|
// add 3x3 matrix D to one of the four quadrants of the 6x6 matrix B
|
|
// row_quad and col_quad should be either 0 or 1 (not checked)
|
|
static void addToQuadrant(mjtNum* restrict B, const mjtNum D[9], int col_quad, int row_quad) {
|
|
int r = 3*row_quad, c = 3*col_quad;
|
|
B[6*(c+0) + r+0] += D[0];
|
|
B[6*(c+0) + r+1] += D[1];
|
|
B[6*(c+0) + r+2] += D[2];
|
|
B[6*(c+1) + r+0] += D[3];
|
|
B[6*(c+1) + r+1] += D[4];
|
|
B[6*(c+1) + r+2] += D[5];
|
|
B[6*(c+2) + r+0] += D[6];
|
|
B[6*(c+2) + r+1] += D[7];
|
|
B[6*(c+2) + r+2] += D[8];
|
|
}
|
|
|
|
|
|
//----------------- components of ellipsoid-based fluid force derivatives --------------------------
|
|
|
|
// forces due to fluid mass moving with the body, B is 6x6
|
|
static void mjd_addedMassForces(
|
|
mjtNum* restrict B, const mjtNum local_vels[6], const mjtNum fluid_density,
|
|
const mjtNum virtual_mass[3], const mjtNum virtual_inertia[3]) {
|
|
const mjtNum lin_vel[3] = {local_vels[3], local_vels[4], local_vels[5]};
|
|
const mjtNum ang_vel[3] = {local_vels[0], local_vels[1], local_vels[2]};
|
|
const mjtNum virtual_lin_mom[3] = {
|
|
fluid_density * virtual_mass[0] * lin_vel[0],
|
|
fluid_density * virtual_mass[1] * lin_vel[1],
|
|
fluid_density * virtual_mass[2] * lin_vel[2]
|
|
};
|
|
const mjtNum virtual_ang_mom[3] = {
|
|
fluid_density * virtual_inertia[0] * ang_vel[0],
|
|
fluid_density * virtual_inertia[1] * ang_vel[1],
|
|
fluid_density * virtual_inertia[2] * ang_vel[2]
|
|
};
|
|
mjtNum Da[9];
|
|
mjtNum Db[9];
|
|
|
|
// force[:3] += cross(virtual_ang_mom, ang_vel)
|
|
mjd_cross(virtual_ang_mom, ang_vel, Da, Db);
|
|
addToQuadrant(B, Db, 0, 0);
|
|
for (int i=0; i < 9; ++i) {
|
|
Da[i] *= fluid_density * virtual_inertia[i % 3];
|
|
}
|
|
addToQuadrant(B, Da, 0, 0);
|
|
|
|
// force[:3] += cross(virtual_lin_mom, lin_vel)
|
|
mjd_cross(virtual_lin_mom, lin_vel, Da, Db);
|
|
addToQuadrant(B, Db, 0, 1);
|
|
for (int i=0; i < 9; ++i) {
|
|
Da[i] *= fluid_density * virtual_mass[i % 3];
|
|
}
|
|
addToQuadrant(B, Da, 0, 1);
|
|
|
|
// force[3:] += cross(virtual_lin_mom, ang_vel)
|
|
mjd_cross(virtual_lin_mom, ang_vel, Da, Db);
|
|
addToQuadrant(B, Db, 1, 0);
|
|
for (int i=0; i < 9; ++i) {
|
|
Da[i] *= fluid_density * virtual_mass[i % 3];
|
|
}
|
|
addToQuadrant(B, Da, 1, 1);
|
|
}
|
|
|
|
|
|
// torque due to motion in the fluid, D is 3x3
|
|
static inline void mjd_viscous_torque(
|
|
mjtNum* restrict D, const mjtNum lvel[6], const mjtNum fluid_density,
|
|
const mjtNum fluid_viscosity, const mjtNum size[3],
|
|
const mjtNum slender_drag_coef, const mjtNum ang_drag_coef) {
|
|
const mjtNum d_max = mju_max(mju_max(size[0], size[1]), size[2]);
|
|
const mjtNum d_min = mju_min(mju_min(size[0], size[1]), size[2]);
|
|
const mjtNum d_mid = size[0] + size[1] + size[2] - d_max - d_min;
|
|
// viscous force and torque in Stokes flow, analytical for spherical bodies
|
|
const mjtNum eq_sphere_D = 2.0/3.0 * (size[0] + size[1] + size[2]);
|
|
const mjtNum lin_visc_torq_coef = mjPI * eq_sphere_D*eq_sphere_D*eq_sphere_D;
|
|
|
|
// moments of inertia used to compute angular quadratic drag
|
|
const mjtNum I_max = 8.0/15.0 * mjPI * d_mid * (d_max*d_max)*(d_max*d_max);
|
|
const mjtNum II[3] = {
|
|
ellipsoid_max_moment(size, 0),
|
|
ellipsoid_max_moment(size, 1),
|
|
ellipsoid_max_moment(size, 2)
|
|
};
|
|
const mjtNum x = lvel[0], y = lvel[1], z = lvel[2];
|
|
const mjtNum mom_coef[3] = {
|
|
ang_drag_coef*II[0] + slender_drag_coef*(I_max - II[0]),
|
|
ang_drag_coef*II[1] + slender_drag_coef*(I_max - II[1]),
|
|
ang_drag_coef*II[2] + slender_drag_coef*(I_max - II[2])
|
|
};
|
|
const mjtNum mom_visc[3] = {
|
|
x * mom_coef[0],
|
|
y * mom_coef[1],
|
|
z * mom_coef[2]
|
|
};
|
|
const mjtNum density = fluid_density / mju_max(mjMINVAL, mju_norm3(mom_visc));
|
|
|
|
// -density * [x, y, z] * mom_coef^2
|
|
const mjtNum mom_sq[3] = {
|
|
-density * x * mom_coef[0] * mom_coef[0],
|
|
-density * y * mom_coef[1] * mom_coef[1],
|
|
-density * z * mom_coef[2] * mom_coef[2]
|
|
};
|
|
const mjtNum lin_coef = fluid_viscosity * lin_visc_torq_coef;
|
|
|
|
// initialize
|
|
mju_zero(D, 9);
|
|
|
|
// set diagonal
|
|
D[0] = D[4] = D[8] = x*mom_sq[0] + y*mom_sq[1] + z*mom_sq[2] - lin_coef;
|
|
|
|
// add outer product
|
|
mju_addToScl3(D, mom_sq, x);
|
|
mju_addToScl3(D+3, mom_sq, y);
|
|
mju_addToScl3(D+6, mom_sq, z);
|
|
}
|
|
|
|
|
|
// drag due to motion in the fluid, D is 3x3
|
|
static inline void mjd_viscous_drag(
|
|
mjtNum* restrict D, const mjtNum lvel[6], const mjtNum fluid_density,
|
|
const mjtNum fluid_viscosity, const mjtNum size[3],
|
|
const mjtNum blunt_drag_coef, const mjtNum slender_drag_coef) {
|
|
const mjtNum d_max = mju_max(mju_max(size[0], size[1]), size[2]);
|
|
const mjtNum d_min = mju_min(mju_min(size[0], size[1]), size[2]);
|
|
const mjtNum d_mid = size[0] + size[1] + size[2] - d_max - d_min;
|
|
// viscous force and torque in Stokes flow, analytical for spherical bodies
|
|
const mjtNum eq_sphere_D = 2.0/3.0 * (size[0] + size[1] + size[2]);
|
|
const mjtNum A_max = mjPI * d_max * d_mid;
|
|
|
|
const mjtNum a = pow2(size[1] * size[2]);
|
|
const mjtNum b = pow2(size[2] * size[0]);
|
|
const mjtNum c = pow2(size[0] * size[1]);
|
|
const mjtNum aa = a*a, bb = b*b, cc = c*c;
|
|
|
|
const mjtNum x = lvel[3], y = lvel[4], z = lvel[5];
|
|
const mjtNum xx = x*x, yy = y*y, zz = z*z, xy=x*y, yz=y*z, xz=x*z;
|
|
|
|
const mjtNum proj_denom = aa*xx + bb*yy + cc*zz;
|
|
const mjtNum proj_num = a*xx + b*yy + c*zz;
|
|
const mjtNum dA_coef = mjPI / mju_max(mjMINVAL,
|
|
mju_sqrt(proj_num*proj_num*proj_num * proj_denom));
|
|
|
|
const mjtNum A_proj = mjPI * mju_sqrt(proj_denom/mju_max(mjMINVAL, proj_num));
|
|
|
|
const mjtNum norm = mju_sqrt(xx + yy + zz);
|
|
const mjtNum inv_norm = 1.0 / mju_max(mjMINVAL, norm);
|
|
|
|
const mjtNum lin_coef = fluid_viscosity * 3.0 * mjPI * eq_sphere_D;
|
|
const mjtNum quad_coef = fluid_density * (
|
|
A_proj*blunt_drag_coef + slender_drag_coef*(A_max - A_proj));
|
|
const mjtNum Aproj_coef = fluid_density * norm * (blunt_drag_coef - slender_drag_coef);
|
|
|
|
const mjtNum dAproj_dv[3] = {
|
|
Aproj_coef * dA_coef * a * x * (b * yy * (a - b) + c * zz * (a - c)),
|
|
Aproj_coef * dA_coef * b * y * (a * xx * (b - a) + c * zz * (b - c)),
|
|
Aproj_coef * dA_coef * c * z * (a * xx * (c - a) + b * yy * (c - b))
|
|
};
|
|
|
|
// outer product
|
|
D[0] = xx; D[1] = xy; D[2] = xz;
|
|
D[3] = xy; D[4] = yy; D[5] = yz;
|
|
D[6] = xz; D[7] = yz; D[8] = zz;
|
|
|
|
// diag(D) += dot([x y z], [x y z])
|
|
mjtNum inner = xx + yy + zz;
|
|
D[0] += inner;
|
|
D[4] += inner;
|
|
D[8] += inner;
|
|
|
|
// scale by -quad_coef*inv_norm
|
|
mju_scl(D, D, -quad_coef*inv_norm, 9);
|
|
|
|
// D += outer_product(-[x y z], dAproj_dv)
|
|
mju_addToScl3(D+0, dAproj_dv, -x);
|
|
mju_addToScl3(D+3, dAproj_dv, -y);
|
|
mju_addToScl3(D+6, dAproj_dv, -z);
|
|
|
|
// diag(D) -= lin_coef
|
|
D[0] -= lin_coef;
|
|
D[4] -= lin_coef;
|
|
D[8] -= lin_coef;
|
|
}
|
|
|
|
|
|
// Kutta lift due to motion in the fluid, D is 3x3
|
|
static inline void mjd_kutta_lift(
|
|
mjtNum* restrict D, const mjtNum lvel[6], const mjtNum fluid_density,
|
|
const mjtNum size[3], const mjtNum kutta_lift_coef) {
|
|
const mjtNum a = pow2(size[1] * size[2]);
|
|
const mjtNum b = pow2(size[2] * size[0]);
|
|
const mjtNum c = pow2(size[0] * size[1]);
|
|
const mjtNum aa = a*a, bb = b*b, cc = c*c;
|
|
const mjtNum x = lvel[3], y = lvel[4], z = lvel[5];
|
|
const mjtNum xx = x*x, yy = y*y, zz = z*z, xy=x*y, yz=y*z, xz=x*z;
|
|
|
|
const mjtNum proj_denom = aa * xx + bb * yy + cc * zz;
|
|
const mjtNum proj_num = a * xx + b * yy + c * zz;
|
|
const mjtNum norm2 = xx + yy + zz;
|
|
const mjtNum df_denom = mjPI * kutta_lift_coef * fluid_density / mju_max(
|
|
mjMINVAL, mju_sqrt(proj_denom * proj_num * norm2));
|
|
|
|
const mjtNum dfx_coef = yy * (a - b) + zz * (a - c);
|
|
const mjtNum dfy_coef = xx * (b - a) + zz * (b - c);
|
|
const mjtNum dfz_coef = xx * (c - a) + yy * (c - b);
|
|
const mjtNum proj_term = proj_num / mju_max(mjMINVAL, proj_denom);
|
|
const mjtNum cos_term = proj_num / mju_max(mjMINVAL, norm2);
|
|
|
|
// cosA = proj_num/(norm*proj_denom), A_proj = pi*sqrt(proj_denom/proj_num)
|
|
// F = cosA * A_proj * (([a,b,c] * vel) \times vel) \times vel
|
|
// derivative obtained with SymPy
|
|
|
|
D[0] = a-a; D[1] = b-a; D[2] = c-a;
|
|
D[3] = a-b; D[4] = b-b; D[5] = c-b;
|
|
D[6] = a-c; D[7] = b-c; D[8] = c-c;
|
|
mju_scl(D, D, 2 * proj_num, 9);
|
|
|
|
const mjtNum inner_term[3] = {
|
|
aa * proj_term - a + cos_term,
|
|
bb * proj_term - b + cos_term,
|
|
cc * proj_term - c + cos_term
|
|
};
|
|
mju_addToScl3(D + 0, inner_term, dfx_coef);
|
|
mju_addToScl3(D + 3, inner_term, dfy_coef);
|
|
mju_addToScl3(D + 6, inner_term, dfz_coef);
|
|
|
|
D[0] *= xx; D[1] *= xy; D[2] *= xz;
|
|
D[3] *= xy; D[4] *= yy; D[5] *= yz;
|
|
D[6] *= xz; D[7] *= yz; D[8] *= zz;
|
|
|
|
D[0] -= dfx_coef * proj_num;
|
|
D[4] -= dfy_coef * proj_num;
|
|
D[8] -= dfz_coef * proj_num;
|
|
|
|
mju_scl(D, D, df_denom, 9);
|
|
}
|
|
|
|
|
|
// Magnus force due to motion in the fluid, B is 6x6
|
|
static inline void mjd_magnus_force(
|
|
mjtNum* restrict B, const mjtNum lvel[6], const mjtNum fluid_density,
|
|
const mjtNum size[3], const mjtNum magnus_lift_coef) {
|
|
const mjtNum volume = 4.0/3.0 * mjPI * size[0] * size[1] * size[2];
|
|
|
|
// magnus_coef = magnus_lift_coef * fluid_density * volume
|
|
const mjtNum magnus_coef = magnus_lift_coef * fluid_density * volume;
|
|
|
|
mjtNum D_lin[9], D_ang[9];
|
|
|
|
// premultiply by magnus_coef
|
|
const mjtNum lin_vel[3] = {
|
|
magnus_coef * lvel[3], magnus_coef * lvel[4], magnus_coef * lvel[5]
|
|
};
|
|
const mjtNum ang_vel[3] = {
|
|
magnus_coef * lvel[0], magnus_coef * lvel[1], magnus_coef * lvel[2]
|
|
};
|
|
|
|
// force[3:] += magnus_coef * cross(ang_vel, lin_vel)
|
|
mjd_cross(ang_vel, lin_vel, D_ang, D_lin);
|
|
|
|
addToQuadrant(B, D_ang, 1, 0);
|
|
addToQuadrant(B, D_lin, 1, 1);
|
|
}
|
|
|
|
|
|
//----------------- fluid force derivatives, ellipsoid and inertia-box models ----------------------
|
|
|
|
// fluid forces based on ellipsoid approximation
|
|
void mjd_ellipsoidFluid(const mjModel* m, mjData* d, int bodyid) {
|
|
mj_markStack(d);
|
|
|
|
int nv = m->nv;
|
|
int nnz = nv;
|
|
int rownnz[6], rowadr[6];
|
|
mjtNum* J = mjSTACKALLOC(d, 6*nv, mjtNum);
|
|
mjtNum* tmp = mjSTACKALLOC(d, 3*nv, mjtNum);
|
|
int* colind = mjSTACKALLOC(d, 6*nv, int);
|
|
int* colind_compressed = mjSTACKALLOC(d, 6*nv, int);
|
|
|
|
mjtNum lvel[6], wind[6], lwind[6];
|
|
mjtNum geom_interaction_coef, magnus_lift_coef, kutta_lift_coef;
|
|
mjtNum semiaxes[3], virtual_mass[3], virtual_inertia[3];
|
|
mjtNum blunt_drag_coef, slender_drag_coef, ang_drag_coef;
|
|
|
|
if (mj_isSparse(m)) {
|
|
// get sparse body Jacobian structure
|
|
nnz = mj_bodyChain(m, bodyid, colind);
|
|
|
|
// prepare rownnz, rowadr, colind for all 6 rows
|
|
for (int i=0; i < 6; i++) {
|
|
rownnz[i] = nnz;
|
|
rowadr[i] = i == 0 ? 0 : rowadr[i-1] + nnz;
|
|
for (int k=0; k < nnz; k++) {
|
|
colind_compressed[i*nnz+k] = colind[k];
|
|
}
|
|
}
|
|
}
|
|
|
|
for (int j=0; j < m->body_geomnum[bodyid]; j++) {
|
|
const int geomid = m->body_geomadr[bodyid] + j;
|
|
|
|
mju_geomSemiAxes(semiaxes, m->geom_size + 3*geomid, m->geom_type[geomid]);
|
|
|
|
readFluidGeomInteraction(
|
|
m->geom_fluid + mjNFLUID*geomid, &geom_interaction_coef,
|
|
&blunt_drag_coef, &slender_drag_coef, &ang_drag_coef,
|
|
&kutta_lift_coef, &magnus_lift_coef,
|
|
virtual_mass, virtual_inertia);
|
|
|
|
// scales all forces, read from MJCF as boolean (0.0 or 1.0)
|
|
if (geom_interaction_coef == 0.0) {
|
|
continue;
|
|
}
|
|
|
|
// map from CoM-centered to local body-centered 6D velocity
|
|
mj_objectVelocity(m, d, mjOBJ_GEOM, geomid, lvel, 1);
|
|
// compute wind in local coordinates
|
|
mju_zero(wind, 6);
|
|
mju_copy3(wind+3, m->opt.wind);
|
|
mju_transformSpatial(lwind, wind, 0,
|
|
d->geom_xpos + 3*geomid, // Frame of ref's origin.
|
|
d->subtree_com + 3*m->body_rootid[bodyid],
|
|
d->geom_xmat + 9*geomid); // Frame of ref's orientation.
|
|
// subtract translational component from grom velocity
|
|
mju_subFrom3(lvel+3, lwind+3);
|
|
|
|
// get geom global Jacobian: rotation then translation
|
|
if (mj_isSparse(m)) {
|
|
mj_jacSparse(m, d, J+3*nnz, J, d->geom_xpos+3*geomid, m->geom_bodyid[geomid], nnz, colind,
|
|
/*flg_skipcommon=*/0);
|
|
} else {
|
|
mj_jacGeom(m, d, J+3*nv, J, geomid);
|
|
}
|
|
|
|
// rotate (compressed) Jacobian to local frame
|
|
mju_mulMatTMat(tmp, d->geom_xmat+9*geomid, J, 3, 3, nnz);
|
|
mju_copy(J, tmp, 3*nnz);
|
|
mju_mulMatTMat(tmp, d->geom_xmat+9*geomid, J+3*nnz, 3, 3, nnz);
|
|
mju_copy(J+3*nnz, tmp, 3*nnz);
|
|
|
|
mjtNum B[36], D[9];
|
|
mju_zero(B, 36);
|
|
mjd_magnus_force(B, lvel, m->opt.density, semiaxes, magnus_lift_coef);
|
|
|
|
mjd_kutta_lift(D, lvel, m->opt.density, semiaxes, kutta_lift_coef);
|
|
addToQuadrant(B, D, 1, 1);
|
|
|
|
mjd_viscous_drag(D, lvel, m->opt.density, m->opt.viscosity, semiaxes,
|
|
blunt_drag_coef, slender_drag_coef);
|
|
addToQuadrant(B, D, 1, 1);
|
|
|
|
mjd_viscous_torque(D, lvel, m->opt.density, m->opt.viscosity, semiaxes,
|
|
slender_drag_coef, ang_drag_coef);
|
|
addToQuadrant(B, D, 0, 0);
|
|
|
|
mjd_addedMassForces(B, lvel, m->opt.density, virtual_mass, virtual_inertia);
|
|
|
|
// make B symmetric if integrator is IMPLICITFAST
|
|
if (m->opt.integrator == mjINT_IMPLICITFAST) {
|
|
mju_symmetrize(B, B, 6);
|
|
}
|
|
|
|
if (mj_isSparse(m)) {
|
|
addJTBJSparse(m, d, J, B, 6, 0, rownnz, rowadr, colind_compressed);
|
|
} else {
|
|
addJTBJ(m, d, J, B, 6);
|
|
}
|
|
}
|
|
|
|
mj_freeStack(d);
|
|
}
|
|
|
|
|
|
// fluid forces based on inertia-box approximation
|
|
void mjd_inertiaBoxFluid(const mjModel* m, mjData* d, int i) {
|
|
mj_markStack(d);
|
|
|
|
int nv = m->nv;
|
|
int rownnz[6], rowadr[6];
|
|
mjtNum* J = mjSTACKALLOC(d, 6*nv, mjtNum);
|
|
mjtNum* tmp = mjSTACKALLOC(d, 3*nv, mjtNum);
|
|
int* colind = mjSTACKALLOC(d, 6*nv, int);
|
|
|
|
mjtNum lvel[6], wind[6], lwind[6], box[3], B;
|
|
mjtNum* inertia = m->body_inertia + 3*i;
|
|
|
|
// equivalent inertia box
|
|
box[0] = mju_sqrt(mju_max(mjMINVAL,
|
|
(inertia[1] + inertia[2] - inertia[0])) / m->body_mass[i] * 6.0);
|
|
box[1] = mju_sqrt(mju_max(mjMINVAL,
|
|
(inertia[0] + inertia[2] - inertia[1])) / m->body_mass[i] * 6.0);
|
|
box[2] = mju_sqrt(mju_max(mjMINVAL,
|
|
(inertia[0] + inertia[1] - inertia[2])) / m->body_mass[i] * 6.0);
|
|
|
|
// map from CoM-centered to local body-centered 6D velocity
|
|
mj_objectVelocity(m, d, mjOBJ_BODY, i, lvel, 1);
|
|
|
|
// compute wind in local coordinates
|
|
mju_zero(wind, 6);
|
|
mju_copy3(wind+3, m->opt.wind);
|
|
mju_transformSpatial(lwind, wind, 0, d->xipos+3*i,
|
|
d->subtree_com+3*m->body_rootid[i], d->ximat+9*i);
|
|
|
|
// subtract translational component from body velocity
|
|
mju_subFrom3(lvel+3, lwind+3);
|
|
|
|
// init with dense
|
|
int nnz = nv;
|
|
|
|
// sparse Jacobian
|
|
if (mj_isSparse(m)) {
|
|
// get sparse body Jacobian structure
|
|
nnz = mj_bodyChain(m, i, colind);
|
|
|
|
// get sparse jacBodyCom
|
|
mj_jacSparse(m, d, J+3*nnz, J, d->xipos+3*i, i, nnz, colind, /*flg_skipcommon=*/0);
|
|
|
|
// prepare rownnz, rowadr, colind for all 6 rows
|
|
rownnz[0] = nnz;
|
|
rowadr[0] = 0;
|
|
for (int j=1; j < 6; j++) {
|
|
rownnz[j] = nnz;
|
|
rowadr[j] = rowadr[j-1] + nnz;
|
|
for (int k=0; k < nnz; k++) {
|
|
colind[j*nnz+k] = colind[k];
|
|
}
|
|
}
|
|
}
|
|
|
|
// dense Jacobian
|
|
else {
|
|
mj_jacBodyCom(m, d, J+3*nv, J, i);
|
|
}
|
|
|
|
// rotate (compressed) Jacobian to local frame
|
|
mju_mulMatTMat(tmp, d->ximat+9*i, J, 3, 3, nnz);
|
|
mju_copy(J, tmp, 3*nnz);
|
|
mju_mulMatTMat(tmp, d->ximat+9*i, J+3*nnz, 3, 3, nnz);
|
|
mju_copy(J+3*nnz, tmp, 3*nnz);
|
|
|
|
// add viscous force and torque
|
|
if (m->opt.viscosity > 0) {
|
|
// diameter of sphere approximation
|
|
mjtNum diam = (box[0] + box[1] + box[2])/3.0;
|
|
|
|
// mju_scl3(lfrc, lvel, -mjPI*diam*diam*diam*m->opt.viscosity)
|
|
B = -mjPI*diam*diam*diam*m->opt.viscosity;
|
|
for (int j=0; j < 3; j++) {
|
|
if (mj_isSparse(m)) {
|
|
addJTBJSparse(m, d, J, &B, 1, j, rownnz, rowadr, colind);
|
|
} else {
|
|
addJTBJ(m, d, J+j*nv, &B, 1);
|
|
}
|
|
}
|
|
|
|
// mju_scl3(lfrc+3, lvel+3, -3.0*mjPI*diam*m->opt.viscosity);
|
|
B = -3.0*mjPI*diam*m->opt.viscosity;
|
|
for (int j=0; j < 3; j++) {
|
|
if (mj_isSparse(m)) {
|
|
addJTBJSparse(m, d, J, &B, 1, 3+j, rownnz, rowadr, colind);
|
|
} else {
|
|
addJTBJ(m, d, J+3*nv+j*nv, &B, 1);
|
|
}
|
|
}
|
|
}
|
|
|
|
// add lift and drag force and torque
|
|
if (m->opt.density > 0) {
|
|
// lfrc[0] -= m->opt.density*box[0]*(box[1]*box[1]*box[1]*box[1]+box[2]*box[2]*box[2]*box[2])*
|
|
// mju_abs(lvel[0])*lvel[0]/64.0;
|
|
B = -m->opt.density*box[0]*(box[1]*box[1]*box[1]*box[1]+box[2]*box[2]*box[2]*box[2])*
|
|
2*mju_abs(lvel[0])/64.0;
|
|
if (mj_isSparse(m)) {
|
|
addJTBJSparse(m, d, J, &B, 1, 0, rownnz, rowadr, colind);
|
|
} else {
|
|
addJTBJ(m, d, J, &B, 1);
|
|
}
|
|
|
|
// lfrc[1] -= m->opt.density*box[1]*(box[0]*box[0]*box[0]*box[0]+box[2]*box[2]*box[2]*box[2])*
|
|
// mju_abs(lvel[1])*lvel[1]/64.0;
|
|
B = -m->opt.density*box[1]*(box[0]*box[0]*box[0]*box[0]+box[2]*box[2]*box[2]*box[2])*
|
|
2*mju_abs(lvel[1])/64.0;
|
|
if (mj_isSparse(m)) {
|
|
addJTBJSparse(m, d, J, &B, 1, 1, rownnz, rowadr, colind);
|
|
} else {
|
|
addJTBJ(m, d, J+nv, &B, 1);
|
|
}
|
|
|
|
// lfrc[2] -= m->opt.density*box[2]*(box[0]*box[0]*box[0]*box[0]+box[1]*box[1]*box[1]*box[1])*
|
|
// mju_abs(lvel[2])*lvel[2]/64.0;
|
|
B = -m->opt.density*box[2]*(box[0]*box[0]*box[0]*box[0]+box[1]*box[1]*box[1]*box[1])*
|
|
2*mju_abs(lvel[2])/64.0;
|
|
if (mj_isSparse(m)) {
|
|
addJTBJSparse(m, d, J, &B, 1, 2, rownnz, rowadr, colind);
|
|
} else {
|
|
addJTBJ(m, d, J+2*nv, &B, 1);
|
|
}
|
|
|
|
// lfrc[3] -= 0.5*m->opt.density*box[1]*box[2]*mju_abs(lvel[3])*lvel[3];
|
|
B = -0.5*m->opt.density*box[1]*box[2]*2*mju_abs(lvel[3]);
|
|
if (mj_isSparse(m)) {
|
|
addJTBJSparse(m, d, J, &B, 1, 3, rownnz, rowadr, colind);
|
|
} else {
|
|
addJTBJ(m, d, J+3*nv, &B, 1);
|
|
}
|
|
|
|
// lfrc[4] -= 0.5*m->opt.density*box[0]*box[2]*mju_abs(lvel[4])*lvel[4];
|
|
B = -0.5*m->opt.density*box[0]*box[2]*2*mju_abs(lvel[4]);
|
|
if (mj_isSparse(m)) {
|
|
addJTBJSparse(m, d, J, &B, 1, 4, rownnz, rowadr, colind);
|
|
} else {
|
|
addJTBJ(m, d, J+4*nv, &B, 1);
|
|
}
|
|
|
|
// lfrc[5] -= 0.5*m->opt.density*box[0]*box[1]*mju_abs(lvel[5])*lvel[5];
|
|
B = -0.5*m->opt.density*box[0]*box[1]*2*mju_abs(lvel[5]);
|
|
if (mj_isSparse(m)) {
|
|
addJTBJSparse(m, d, J, &B, 1, 5, rownnz, rowadr, colind);
|
|
} else {
|
|
addJTBJ(m, d, J+5*nv, &B, 1);
|
|
}
|
|
}
|
|
|
|
mj_freeStack(d);
|
|
}
|
|
|
|
|
|
//------------------------- derivatives of passive forces ------------------------------------------
|
|
|
|
// add (d qfrc_passive / d qvel) to qDeriv
|
|
void mjd_passive_vel(const mjModel* m, mjData* d) {
|
|
// all disabled: nothing to add
|
|
if (mjDISABLED(mjDSBL_SPRING) && mjDISABLED(mjDSBL_DAMPER)) {
|
|
return;
|
|
}
|
|
|
|
int sleep_filter = mjENABLED(mjENBL_SLEEP) && d->ntree_awake < m->ntree;
|
|
int nbody = sleep_filter ? d->nbody_awake : m->nbody;
|
|
|
|
// fluid drag model, either body-level (inertia box) or geom-level (ellipsoid)
|
|
if (m->opt.viscosity > 0 || m->opt.density > 0) {
|
|
for (int b=0; b < nbody; b++) {
|
|
int i = sleep_filter ? d->body_awake_ind[b] : b;
|
|
|
|
if (m->body_mass[i] < mjMINVAL) {
|
|
continue;
|
|
}
|
|
|
|
int use_ellipsoid_model = 0;
|
|
// if any child geom uses the ellipsoid model, inertia-box model is disabled for parent body
|
|
for (int j=0; j < m->body_geomnum[i] && use_ellipsoid_model == 0; j++) {
|
|
const int geomid = m->body_geomadr[i] + j;
|
|
use_ellipsoid_model += (m->geom_fluid[mjNFLUID*geomid] > 0);
|
|
}
|
|
if (use_ellipsoid_model) {
|
|
mjd_ellipsoidFluid(m, d, i);
|
|
} else {
|
|
mjd_inertiaBoxFluid(m, d, i);
|
|
}
|
|
}
|
|
}
|
|
|
|
// disabled: nothing to add
|
|
if (mjDISABLED(mjDSBL_DAMPER)) {
|
|
return;
|
|
}
|
|
|
|
// dof damping
|
|
int nv = m->nv;
|
|
int nv_awake = sleep_filter ? d->nv_awake : nv;
|
|
for (int j = 0; j < nv_awake; j++) {
|
|
int i = sleep_filter ? d->dof_awake_ind[j] : j;
|
|
mjtNum v = d->qvel[i];
|
|
mjtNum poly[mjNPOLY];
|
|
mju_copy(poly, m->dof_dampingpoly + mjNPOLY*i, mjNPOLY);
|
|
mjtNum damping = m->dof_damping[i] + mj_actuatorDamping(m, mjOBJ_JOINT, m->dof_jntid[i], poly);
|
|
int adr = m->D_rowadr[i] + m->D_diag[i];
|
|
d->qDeriv[adr] -= mjd_xPolyForce(damping, poly, v, mjNPOLY, 1);
|
|
}
|
|
|
|
// flex edge damping
|
|
for (int f=0; f < m->nflex; f++) {
|
|
mjtNum B = -m->flex_edgedamping[f];
|
|
if (m->flex_rigid[f] || !B) {
|
|
continue;
|
|
}
|
|
|
|
int flex_edgeadr = m->flex_edgeadr[f];
|
|
int flex_edgenum = m->flex_edgenum[f];
|
|
|
|
// process non-rigid edges of this flex
|
|
for (int e=flex_edgeadr; e < flex_edgeadr+flex_edgenum; e++) {
|
|
// skip rigid
|
|
if (m->flexedge_rigid[e]) {
|
|
continue;
|
|
}
|
|
|
|
// always sparse
|
|
addJTBJSparse(m, d, d->flexedge_J, &B, 1, e,
|
|
m->flexedge_J_rownnz, m->flexedge_J_rowadr, m->flexedge_J_colind);
|
|
}
|
|
}
|
|
|
|
// tendon damping
|
|
int ntendon = m->ntendon;
|
|
for (int i=0; i < ntendon; i++) {
|
|
// skip tendon in one or two sleeping trees
|
|
if (sleep_filter) {
|
|
int treenum = m->tendon_treenum[i];
|
|
int id1 = m->tendon_treeid[2*i];
|
|
if (treenum == 1 && !d->tree_awake[id1]) continue;
|
|
int id2 = m->tendon_treeid[2*i+1];
|
|
if (treenum == 2 && !d->tree_awake[id1] && !d->tree_awake[id2]) continue;
|
|
}
|
|
|
|
mjtNum v = d->ten_velocity[i];
|
|
mjtNum poly[mjNPOLY];
|
|
mju_copy(poly, m->tendon_dampingpoly+mjNPOLY*i, mjNPOLY);
|
|
mjtNum damping = m->tendon_damping[i] + mj_actuatorDamping(m, mjOBJ_TENDON, i, poly);
|
|
mjtNum B = -mjd_xPolyForce(damping, poly, v, mjNPOLY, 1);
|
|
|
|
if (!B) {
|
|
continue;
|
|
}
|
|
|
|
// add sparse
|
|
addJTBJSparse(m, d, d->ten_J, &B, 1, i, m->ten_J_rownnz, m->ten_J_rowadr, m->ten_J_colind);
|
|
}
|
|
}
|
|
|
|
|
|
//------------------------- main entry points ------------------------------------------------------
|
|
|
|
// analytical derivative of smooth forces w.r.t velocities:
|
|
// d->qDeriv = d (qfrc_actuator + qfrc_passive - [qfrc_bias]) / d qvel
|
|
void mjd_smooth_vel(const mjModel* m, mjData* d, int flg_bias) {
|
|
int sleep_filter = mjENABLED(mjENBL_SLEEP) && d->nv_awake < m->nv;
|
|
|
|
// clear qDeriv
|
|
if (!sleep_filter) {
|
|
mju_zero(d->qDeriv, m->nD);
|
|
} else {
|
|
mju_zeroSparse(d->qDeriv, m->D_rownnz, m->D_rowadr, d->dof_awake_ind, d->nv_awake);
|
|
}
|
|
|
|
// qDeriv += d qfrc_actuator / d qvel
|
|
mjd_actuator_vel(m, d);
|
|
|
|
// qDeriv += d qfrc_passive / d qvel
|
|
mjd_passive_vel(m, d);
|
|
|
|
// qDeriv -= d qfrc_bias / d qvel; optional
|
|
if (flg_bias) {
|
|
mjd_rne_vel(m, d);
|
|
}
|
|
}
|