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6dof-kinematic.cpp
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6dof-kinematic.cpp
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#include <cmath>
#include <cstring>
#include "6dof-kinematic.h"
inline float cosf(float x)
{
return cos(x);
}
inline float sinf(float x)
{
return sin(x);
}
static void MatMultiply(const float* _matrix1, const float* _matrix2, float* _matrixOut,
const int _m, const int _l, const int _n)
{
float tmp;
int i, j, k;
for (i = 0; i < _m; i++)
{
for (j = 0; j < _n; j++)
{
tmp = 0.0f;
for (k = 0; k < _l; k++)
{
tmp += _matrix1[_l * i + k] * _matrix2[_n * k + j];
}
_matrixOut[_n * i + j] = tmp;
}
}
}
static void RotMatToEulerAngle(const float* _rotationM, float* _eulerAngles)
{
float A, B, C, cb;
if (fabs(_rotationM[6]) >= 1.0 - 0.0001)
{
if (_rotationM[6] < 0)
{
A = 0.0f;
B = (float) M_PI_2;
C = atan2f(_rotationM[1], _rotationM[4]);
} else
{
A = 0.0f;
B = -(float) M_PI_2;
C = -atan2f(_rotationM[1], _rotationM[4]);
}
} else
{
B = atan2f(-_rotationM[6], sqrtf(_rotationM[0] * _rotationM[0] + _rotationM[3] * _rotationM[3]));
cb = cosf(B);
A = atan2f(_rotationM[3] / cb, _rotationM[0] / cb);
C = atan2f(_rotationM[7] / cb, _rotationM[8] / cb);
}
_eulerAngles[0] = C;
_eulerAngles[1] = B;
_eulerAngles[2] = A;
}
static void EulerAngleToRotMat(const float* _eulerAngles, float* _rotationM)
{
float ca, cb, cc, sa, sb, sc;
cc = cosf(_eulerAngles[0]);
cb = cosf(_eulerAngles[1]);
ca = cosf(_eulerAngles[2]);
sc = sinf(_eulerAngles[0]);
sb = sinf(_eulerAngles[1]);
sa = sinf(_eulerAngles[2]);
_rotationM[0] = ca * cb;
_rotationM[1] = ca * sb * sc - sa * cc;
_rotationM[2] = ca * sb * cc + sa * sc;
_rotationM[3] = sa * cb;
_rotationM[4] = sa * sb * sc + ca * cc;
_rotationM[5] = sa * sb * cc - ca * sc;
_rotationM[6] = -sb;
_rotationM[7] = cb * sc;
_rotationM[8] = cb * cc;
}
DOF6Kinematic::DOF6Kinematic(float L_BS, float D_BS, float L_AM, float L_FA, float D_EW, float L_WT)
: armConfig(ArmConfig_t{L_BS, D_BS, L_AM, L_FA, D_EW, L_WT})
{
float tmp_DH_matrix[6][4] = {
{0.0f, armConfig.L_BASE, armConfig.D_BASE, -(float) M_PI_2},
{-(float) M_PI_2, 0.0f, armConfig.L_ARM, 0.0f},
{(float) M_PI_2, armConfig.D_ELBOW, 0.0f, (float) M_PI_2},
{0.0f, armConfig.L_FOREARM, 0.0f, -(float) M_PI_2},
{0.0f, 0.0f, 0.0f, (float) M_PI_2},
{0.0f, armConfig.L_WRIST, 0.0f, 0.0f}
};
memcpy(DH_matrix, tmp_DH_matrix, sizeof(tmp_DH_matrix));
float tmp_L1_bs[3] = {armConfig.D_BASE, -armConfig.L_BASE, 0.0f};
memcpy(L1_base, tmp_L1_bs, sizeof(tmp_L1_bs));
float tmp_L2_se[3] = {armConfig.L_ARM, 0.0f, 0.0f};
memcpy(L2_arm, tmp_L2_se, sizeof(tmp_L2_se));
float tmp_L3_ew[3] = {-armConfig.D_ELBOW, 0.0f, armConfig.L_FOREARM};
memcpy(L3_elbow, tmp_L3_ew, sizeof(tmp_L3_ew));
float tmp_L6_wt[3] = {0.0f, 0.0f, armConfig.L_WRIST};
memcpy(L6_wrist, tmp_L6_wt, sizeof(tmp_L6_wt));
l_se_2 = armConfig.L_ARM * armConfig.L_ARM;
l_se = armConfig.L_ARM;
l_ew_2 = armConfig.L_FOREARM * armConfig.L_FOREARM + armConfig.D_ELBOW * armConfig.D_ELBOW;
l_ew = 0;
atan_e = 0;
}
bool
DOF6Kinematic::SolveFK(const DOF6Kinematic::Joint6D_t &_inputJoint6D, DOF6Kinematic::Pose6D_t &_outputPose6D)
{
float q_in[6];
float q[6];
float cosq, sinq;
float cosa, sina;
float P06[6];
float R06[9];
float R[6][9];
float R02[9];
float R03[9];
float R04[9];
float R05[9];
float L0_bs[3];
float L0_se[3];
float L0_ew[3];
float L0_wt[3];
for (int i = 0; i < 6; i++)
q_in[i] = _inputJoint6D.a[i] / RAD_TO_DEG;
for (int i = 0; i < 6; i++)
{
q[i] = q_in[i] + DH_matrix[i][0];
cosq = cosf(q[i]);
sinq = sinf(q[i]);
cosa = cosf(DH_matrix[i][3]);
sina = sinf(DH_matrix[i][3]);
R[i][0] = cosq;
R[i][1] = -cosa * sinq;
R[i][2] = sina * sinq;
R[i][3] = sinq;
R[i][4] = cosa * cosq;
R[i][5] = -sina * cosq;
R[i][6] = 0.0f;
R[i][7] = sina;
R[i][8] = cosa;
}
MatMultiply(R[0], R[1], R02, 3, 3, 3);
MatMultiply(R02, R[2], R03, 3, 3, 3);
MatMultiply(R03, R[3], R04, 3, 3, 3);
MatMultiply(R04, R[4], R05, 3, 3, 3);
MatMultiply(R05, R[5], R06, 3, 3, 3);
MatMultiply(R[0], L1_base, L0_bs, 3, 3, 1);
MatMultiply(R02, L2_arm, L0_se, 3, 3, 1);
MatMultiply(R03, L3_elbow, L0_ew, 3, 3, 1);
MatMultiply(R06, L6_wrist, L0_wt, 3, 3, 1);
for (int i = 0; i < 3; i++)
P06[i] = L0_bs[i] + L0_se[i] + L0_ew[i] + L0_wt[i];
RotMatToEulerAngle(R06, &(P06[3]));
_outputPose6D.X = P06[0];
_outputPose6D.Y = P06[1];
_outputPose6D.Z = P06[2];
_outputPose6D.A = P06[3] * RAD_TO_DEG;
_outputPose6D.B = P06[4] * RAD_TO_DEG;
_outputPose6D.C = P06[5] * RAD_TO_DEG;
memcpy(_outputPose6D.R, R06, 9 * sizeof(float));
return true;
}
bool DOF6Kinematic::SolveIK(const DOF6Kinematic::Pose6D_t &_inputPose6D, const Joint6D_t &_lastJoint6D,
DOF6Kinematic::IKSolves_t &_outputSolves)
{
float qs[2];
float qa[2][2];
float qw[2][3];
float cosqs, sinqs;
float cosqa[2], sinqa[2];
float cosqw, sinqw;
float P06[6];
float R06[9];
float P0_w[3];
float P1_w[3];
float L0_wt[3];
float L1_sw[3];
float R10[9];
float R31[9];
float R30[9];
float R36[9];
float l_sw_2, l_sw, atan_a, acos_a, acos_e;
int ind_arm, ind_elbow, ind_wrist;
int i;
if (0 == l_ew)
{
l_ew = sqrtf(l_ew_2);
atan_e = atanf(armConfig.D_ELBOW / armConfig.L_FOREARM);
}
P06[0] = _inputPose6D.X / 1000.0f;
P06[1] = _inputPose6D.Y / 1000.0f;
P06[2] = _inputPose6D.Z / 1000.0f;
if (!_inputPose6D.hasR)
{
P06[3] = _inputPose6D.A / RAD_TO_DEG;
P06[4] = _inputPose6D.B / RAD_TO_DEG;
P06[5] = _inputPose6D.C / RAD_TO_DEG;
EulerAngleToRotMat(&(P06[3]), R06);
} else
{
memcpy(R06, _inputPose6D.R, 9 * sizeof(float));
}
for (i = 0; i < 2; i++)
{
qs[i] = _lastJoint6D.a[0];
qa[i][0] = _lastJoint6D.a[1];
qa[i][1] = _lastJoint6D.a[2];
qw[i][0] = _lastJoint6D.a[3];
qw[i][1] = _lastJoint6D.a[4];
qw[i][2] = _lastJoint6D.a[5];
}
MatMultiply(R06, L6_wrist, L0_wt, 3, 3, 1);
for (i = 0; i < 3; i++)
{
P0_w[i] = P06[i] - L0_wt[i];
}
if (sqrt(P0_w[0] * P0_w[0] + P0_w[1] * P0_w[1]) <= 0.000001)
{
qs[0] = _lastJoint6D.a[0];
qs[1] = _lastJoint6D.a[0];
for (i = 0; i < 4; i++)
{
_outputSolves.solFlag[0 + i][0] = -1;
_outputSolves.solFlag[4 + i][0] = -1;
}
} else
{
qs[0] = atan2f(P0_w[1], P0_w[0]);
qs[1] = atan2f(-P0_w[1], -P0_w[0]);
for (i = 0; i < 4; i++)
{
_outputSolves.solFlag[0 + i][0] = 1;
_outputSolves.solFlag[4 + i][0] = 1;
}
}
for (ind_arm = 0; ind_arm < 2; ind_arm++)
{
cosqs = cosf(qs[ind_arm] + DH_matrix[0][0]);
sinqs = sinf(qs[ind_arm] + DH_matrix[0][0]);
R10[0] = cosqs;
R10[1] = sinqs;
R10[2] = 0.0f;
R10[3] = 0.0f;
R10[4] = 0.0f;
R10[5] = -1.0f;
R10[6] = -sinqs;
R10[7] = cosqs;
R10[8] = 0.0f;
MatMultiply(R10, P0_w, P1_w, 3, 3, 1);
for (i = 0; i < 3; i++)
{
L1_sw[i] = P1_w[i] - L1_base[i];
}
l_sw_2 = L1_sw[0] * L1_sw[0] + L1_sw[1] * L1_sw[1];
l_sw = sqrtf(l_sw_2);
if (fabs(l_se + l_ew - l_sw) <= 0.000001)
{
qa[0][0] = atan2f(L1_sw[1], L1_sw[0]);
qa[1][0] = qa[0][0];
qa[0][1] = 0.0f;
qa[1][1] = 0.0f;
if (l_sw > l_se + l_ew)
{
for (i = 0; i < 2; i++)
{
_outputSolves.solFlag[4 * ind_arm + 0 + i][1] = 0;
_outputSolves.solFlag[4 * ind_arm + 2 + i][1] = 0;
}
} else
{
for (i = 0; i < 2; i++)
{
_outputSolves.solFlag[4 * ind_arm + 0 + i][1] = 1;
_outputSolves.solFlag[4 * ind_arm + 2 + i][1] = 1;
}
}
} else if (fabs(l_sw - fabs(l_se - l_ew)) <= 0.000001)
{
qa[0][0] = atan2f(L1_sw[1], L1_sw[0]);
qa[1][0] = qa[0][0];
if (0 == ind_arm)
{
qa[0][1] = (float) M_PI;
qa[1][1] = -(float) M_PI;
} else
{
qa[0][1] = -(float) M_PI;
qa[1][1] = (float) M_PI;
}
if (l_sw < fabs(l_se - l_ew))
{
for (i = 0; i < 2; i++)
{
_outputSolves.solFlag[4 * ind_arm + 0 + i][1] = 0;
_outputSolves.solFlag[4 * ind_arm + 2 + i][1] = 0;
}
} else
{
for (i = 0; i < 2; i++)
{
_outputSolves.solFlag[4 * ind_arm + 0 + i][1] = 1;
_outputSolves.solFlag[4 * ind_arm + 2 + i][1] = 1;
}
}
} else
{
atan_a = atan2f(L1_sw[1], L1_sw[0]);
acos_a = 0.5f * (l_se_2 + l_sw_2 - l_ew_2) / (l_se * l_sw);
if (acos_a >= 1.0f) acos_a = 0.0f;
else if (acos_a <= -1.0f) acos_a = (float) M_PI;
else acos_a = acosf(acos_a);
acos_e = 0.5f * (l_se_2 + l_ew_2 - l_sw_2) / (l_se * l_ew);
if (acos_e >= 1.0f) acos_e = 0.0f;
else if (acos_e <= -1.0f) acos_e = (float) M_PI;
else acos_e = acosf(acos_e);
if (0 == ind_arm)
{
qa[0][0] = atan_a - acos_a + (float) M_PI_2;
qa[0][1] = atan_e - acos_e + (float) M_PI;
qa[1][0] = atan_a + acos_a + (float) M_PI_2;
qa[1][1] = atan_e + acos_e - (float) M_PI;
} else
{
qa[0][0] = atan_a + acos_a + (float) M_PI_2;
qa[0][1] = atan_e + acos_e - (float) M_PI;
qa[1][0] = atan_a - acos_a + (float) M_PI_2;
qa[1][1] = atan_e - acos_e + (float) M_PI;
}
for (i = 0; i < 2; i++)
{
_outputSolves.solFlag[4 * ind_arm + 0 + i][1] = 1;
_outputSolves.solFlag[4 * ind_arm + 2 + i][1] = 1;
}
}
for (ind_elbow = 0; ind_elbow < 2; ind_elbow++)
{
cosqa[0] = cosf(qa[ind_elbow][0] + DH_matrix[1][0]);
sinqa[0] = sinf(qa[ind_elbow][0] + DH_matrix[1][0]);
cosqa[1] = cosf(qa[ind_elbow][1] + DH_matrix[2][0]);
sinqa[1] = sinf(qa[ind_elbow][1] + DH_matrix[2][0]);
R31[0] = cosqa[0] * cosqa[1] - sinqa[0] * sinqa[1];
R31[1] = cosqa[0] * sinqa[1] + sinqa[0] * cosqa[1];
R31[2] = 0.0f;
R31[3] = 0.0f;
R31[4] = 0.0f;
R31[5] = 1.0f;
R31[6] = cosqa[0] * sinqa[1] + sinqa[0] * cosqa[1];
R31[7] = -cosqa[0] * cosqa[1] + sinqa[0] * sinqa[1];
R31[8] = 0.0f;
MatMultiply(R31, R10, R30, 3, 3, 3);
MatMultiply(R30, R06, R36, 3, 3, 3);
if (R36[8] >= 1.0 - 0.000001)
{
cosqw = 1.0f;
qw[0][1] = 0.0f;
qw[1][1] = 0.0f;
} else if (R36[8] <= -1.0 + 0.000001)
{
cosqw = -1.0f;
if (0 == ind_arm)
{
qw[0][1] = (float) M_PI;
qw[1][1] = -(float) M_PI;
} else
{
qw[0][1] = -(float) M_PI;
qw[1][1] = (float) M_PI;
}
} else
{
cosqw = R36[8];
if (0 == ind_arm)
{
qw[0][1] = acosf(cosqw);
qw[1][1] = -acosf(cosqw);
} else
{
qw[0][1] = -acosf(cosqw);
qw[1][1] = acosf(cosqw);
}
}
if (1.0f == cosqw || -1.0f == cosqw)
{
if (0 == ind_arm)
{
qw[0][0] = _lastJoint6D.a[3];
cosqw = cosf(_lastJoint6D.a[3] + DH_matrix[3][0]);
sinqw = sinf(_lastJoint6D.a[3] + DH_matrix[3][0]);
qw[0][2] = atan2f(cosqw * R36[3] - sinqw * R36[0], cosqw * R36[0] + sinqw * R36[3]);
qw[1][2] = _lastJoint6D.a[5];
cosqw = cosf(_lastJoint6D.a[5] + DH_matrix[5][0]);
sinqw = sinf(_lastJoint6D.a[5] + DH_matrix[5][0]);
qw[1][0] = atan2f(cosqw * R36[3] - sinqw * R36[0], cosqw * R36[0] + sinqw * R36[3]);
} else
{
qw[0][2] = _lastJoint6D.a[5];
cosqw = cosf(_lastJoint6D.a[5] + DH_matrix[5][0]);
sinqw = sinf(_lastJoint6D.a[5] + DH_matrix[5][0]);
qw[0][0] = atan2f(cosqw * R36[3] - sinqw * R36[0], cosqw * R36[0] + sinqw * R36[3]);
qw[1][0] = _lastJoint6D.a[3];
cosqw = cosf(_lastJoint6D.a[3] + DH_matrix[3][0]);
sinqw = sinf(_lastJoint6D.a[3] + DH_matrix[3][0]);
qw[1][2] = atan2f(cosqw * R36[3] - sinqw * R36[0], cosqw * R36[0] + sinqw * R36[3]);
}
_outputSolves.solFlag[4 * ind_arm + 2 * ind_elbow + 0][2] = -1;
_outputSolves.solFlag[4 * ind_arm + 2 * ind_elbow + 1][2] = -1;
} else
{
if (0 == ind_arm)
{
qw[0][0] = atan2f(R36[5], R36[2]);
qw[1][0] = atan2f(-R36[5], -R36[2]);
qw[0][2] = atan2f(R36[7], -R36[6]);
qw[1][2] = atan2f(-R36[7], R36[6]);
} else
{
qw[0][0] = atan2f(-R36[5], -R36[2]);
qw[1][0] = atan2f(R36[5], R36[2]);
qw[0][2] = atan2f(-R36[7], R36[6]);
qw[1][2] = atan2f(R36[7], -R36[6]);
}
_outputSolves.solFlag[4 * ind_arm + 2 * ind_elbow + 0][2] = 1;
_outputSolves.solFlag[4 * ind_arm + 2 * ind_elbow + 1][2] = 1;
}
for (ind_wrist = 0; ind_wrist < 2; ind_wrist++)
{
if (qs[ind_arm] > (float) M_PI)
_outputSolves.config[4 * ind_arm + 2 * ind_elbow + ind_wrist].a[0] =
qs[ind_arm] - (float) M_PI;
else if (qs[ind_arm] < -(float) M_PI)
_outputSolves.config[4 * ind_arm + 2 * ind_elbow + ind_wrist].a[0] =
qs[ind_arm] + (float) M_PI;
else
_outputSolves.config[4 * ind_arm + 2 * ind_elbow + ind_wrist].a[0] = qs[ind_arm];
for (i = 0; i < 2; i++)
{
if (qa[ind_elbow][i] > (float) M_PI)
_outputSolves.config[4 * ind_arm + 2 * ind_elbow + ind_wrist].a[1 + i] =
qa[ind_elbow][i] - (float) M_PI;
else if (qa[ind_elbow][i] < -(float) M_PI)
_outputSolves.config[4 * ind_arm + 2 * ind_elbow + ind_wrist].a[1 + i] =
qa[ind_elbow][i] + (float) M_PI;
else
_outputSolves.config[4 * ind_arm + 2 * ind_elbow + ind_wrist].a[1 + i] =
qa[ind_elbow][i];
}
for (i = 0; i < 3; i++)
{
if (qw[ind_wrist][i] > (float) M_PI)
_outputSolves.config[4 * ind_arm + 2 * ind_elbow + ind_wrist].a[3 + i] =
qw[ind_wrist][i] - (float) M_PI;
else if (qw[ind_wrist][i] < -(float) M_PI)
_outputSolves.config[4 * ind_arm + 2 * ind_elbow + ind_wrist].a[3 + i] =
qw[ind_wrist][i] + (float) M_PI;
else
_outputSolves.config[4 * ind_arm + 2 * ind_elbow + ind_wrist].a[3 + i] =
qw[ind_wrist][i];
}
}
}
}
for (i = 0; i < 8; i++)
for (float &j: _outputSolves.config[i].a)
j *= RAD_TO_DEG;
return true;
}
DOF6Kinematic::Joint6D_t
operator-(const DOF6Kinematic::Joint6D_t &_joints1, const DOF6Kinematic::Joint6D_t &_joints2)
{
DOF6Kinematic::Joint6D_t tmp{};
for (int i = 0; i < 6; i++)
tmp.a[i] = _joints1.a[i] - _joints2.a[i];
return tmp;
}