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🦾 Makes embedded kinematics kinda work

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This commit is contained in:
Rune Harlyk
2024-05-21 14:57:38 +02:00
committed by Rune Harlyk
parent 68d319e022
commit d2d1c85f50
5 changed files with 195 additions and 127 deletions
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esp32/lib/ESP32-sveltekit/Kinematics.h
+117 -103
View File
@@ -4,14 +4,55 @@
#include <cmath>
#include <esp_dsp.h>
static esp_err_t inverse(float a[4][4], float b[4][4])
{
float s0 = a[0][0] * a[1][1] - a[1][0] * a[0][1];
float s1 = a[0][0] * a[1][2] - a[1][0] * a[0][2];
float s2 = a[0][0] * a[1][3] - a[1][0] * a[0][3];
float s3 = a[0][1] * a[1][2] - a[1][1] * a[0][2];
float s4 = a[0][1] * a[1][3] - a[1][1] * a[0][3];
float s5 = a[0][2] * a[1][3] - a[1][2] * a[0][3];
float c5 = a[2][2] * a[3][3] - a[3][2] * a[2][3];
float c4 = a[2][1] * a[3][3] - a[3][1] * a[2][3];
float c3 = a[2][1] * a[3][2] - a[3][1] * a[2][2];
float c2 = a[2][0] * a[3][3] - a[3][0] * a[2][3];
float c1 = a[2][0] * a[3][2] - a[3][0] * a[2][2];
float c0 = a[2][0] * a[3][1] - a[3][0] * a[2][1];
// Should check for 0 determinant
float det = (s0 * c5 - s1 * c4 + s2 * c3 + s3 * c2 - s4 * c1 + s5 * c0);
if (det == 0.0) return ESP_FAIL;
float invdet = 1.0 / det;
b[0][0] = ( a[1][1] * c5 - a[1][2] * c4 + a[1][3] * c3) * invdet;
b[0][1] = (-a[0][1] * c5 + a[0][2] * c4 - a[0][3] * c3) * invdet;
b[0][2] = ( a[3][1] * s5 - a[3][2] * s4 + a[3][3] * s3) * invdet;
b[0][3] = (-a[2][1] * s5 + a[2][2] * s4 - a[2][3] * s3) * invdet;
b[1][0] = (-a[1][0] * c5 + a[1][2] * c2 - a[1][3] * c1) * invdet;
b[1][1] = ( a[0][0] * c5 - a[0][2] * c2 + a[0][3] * c1) * invdet;
b[1][2] = (-a[3][0] * s5 + a[3][2] * s2 - a[3][3] * s1) * invdet;
b[1][3] = ( a[2][0] * s5 - a[2][2] * s2 + a[2][3] * s1) * invdet;
b[2][0] = ( a[1][0] * c4 - a[1][1] * c2 + a[1][3] * c0) * invdet;
b[2][1] = (-a[0][0] * c4 + a[0][1] * c2 - a[0][3] * c0) * invdet;
b[2][2] = ( a[3][0] * s4 - a[3][1] * s2 + a[3][3] * s0) * invdet;
b[2][3] = (-a[2][0] * s4 + a[2][1] * s2 - a[2][3] * s0) * invdet;
b[3][0] = (-a[1][0] * c3 + a[1][1] * c1 - a[1][2] * c0) * invdet;
b[3][1] = ( a[0][0] * c3 - a[0][1] * c1 + a[0][2] * c0) * invdet;
b[3][2] = (-a[3][0] * s3 + a[3][1] * s1 - a[3][2] * s0) * invdet;
b[3][3] = ( a[2][0] * s3 - a[2][1] * s1 + a[2][2] * s0) * invdet;
return ESP_OK;
}
typedef struct {
float omega;
float phi;
float psi;
float xm;
float ym;
float zm;
bool set;
float omega, phi, psi, xm, ym, zm;
} position_t;
@@ -21,18 +62,26 @@ typedef struct {
class Kinematics
{
private:
dspm::Mat Tlf;
dspm::Mat Trf;
dspm::Mat Tlb;
dspm::Mat Trb;
float Trb[4][4] = {0,};
float Trf[4][4] = {0,};
float Tlb[4][4] = {0,};
float Tlf[4][4] = {0,};
float inverse[4][4];
const float Ix[4][4] = {{-1,0,0,0},{0,1,0,0},{0,0,1,0},{0,0,0,1}};
float inv[4][4];
float point[4];
float Q1[4][4];
dspm::Mat Ix;
const float sHp = sin(PI / 2);
const float cHp = cos(PI / 2);
float point_lf[4][4];
public:
float l1, l2, l3, l4;
float L, W;
Kinematics(){
l1 = 50;
l2 = 20;
@@ -45,31 +94,29 @@ public:
~Kinematics(){}
esp_err_t calculate_inverse_kinematics(float lp[4][4], position_t p, float result[12]) {
esp_err_t ret = ESP_OK;
Tlf.clear();
Trf.clear();
Tlb.clear();
Trb.clear();
ret = bodyIK(p);
float Ix_data[] = {-1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1};
dspm::Mat Ix(Ix_data, 4, 4);
esp_err_t res = bodyIK(p);
ret += inverse(Tlf, inv);
dspm_mult_f32_ae32((float*) inv, (float*) lp[0], (float*) point, 4, 4, 1);
legIK((float*) point, result);
dspm::Mat result_vec(4, 4);
result_vec = (Tlf.inverse() * dspm::Mat(lp[0], 4, 1));
legIK(result_vec.data, result);
ret += inverse(Trf, inv);
dspm_mult_f32_ae32((float*) Ix, (float*) inv, (float*) Q1, 4, 4, 4);
dspm_mult_f32_ae32((float*) Q1, (float*) lp[1], (float*) point, 4, 4, 1);
legIK((float*) point, result + 3);
result_vec = Ix * (Trf.inverse() * dspm::Mat(lp[1], 4, 1));
legIK(result_vec.data, result + 3);
ret += inverse(Tlb, inv);
dspm_mult_f32_ae32((float*) inv, (float*) lp[2], (float*) point, 4, 4, 1);
legIK((float*) point, result + 6);
result_vec = (Tlb.inverse() * dspm::Mat(lp[2], 4, 1));
legIK(result_vec.data, result + 6);
ret += inverse(Trb, inv);
dspm_mult_f32_ae32((float*) Ix, (float*) inv, (float*) Q1, 4, 4, 4);
dspm_mult_f32_ae32((float*) Q1, (float*) lp[3], (float*) point, 4, 4, 1);
legIK((float*) point, result + 9);
result_vec = Ix * (Trb.inverse() * dspm::Mat(lp[3], 4, 1));
legIK(result_vec.data, result + 9);
return res;
return ret;
}
esp_err_t bodyIK(position_t p) {
@@ -79,97 +126,64 @@ public:
float sin_phi = sin(p.phi*DEGREES2RAD);
float cos_psi = cos(p.psi*DEGREES2RAD);
float sin_psi = sin(p.psi*DEGREES2RAD);
float Rx_data[] = {
1, 0, 0, 0,
0, cos_omega, -sin_omega, 0,
0, sin_omega, cos_omega, 0,
0, 0, 0, 1
float Tm[4][4] = {
{cos_phi * cos_psi, -sin_psi * cos_phi, sin_phi, p.xm},
{sin_omega * sin_phi * cos_psi + sin_psi * cos_omega, -sin_omega * sin_phi * sin_psi + cos_omega * cos_psi, -sin_omega * cos_phi, p.ym},
{sin_omega * sin_psi - sin_phi * cos_omega * cos_psi, sin_omega * cos_psi + sin_phi * sin_psi * cos_omega, cos_omega * cos_phi, p.zm},
{0, 0, 0, 1}
};
dspm::Mat Rx(Rx_data, 4, 4);
float Ry_data[] = {
cos_phi, 0, sin_phi, 0,
0, 1, 0, 0,
-sin_phi, 0, cos_phi, 0,
0, 0, 0, 1
float point_lf[4][4] = {
{cHp, 0, sHp, L / 2},
{0, 1, 0, 0},
{-sHp, 0, cHp, W / 2},
{0, 0, 0, 1}
};
dspm::Mat Ry(Ry_data, 4, 4);
float Rz_data[] = {
cos_psi, -sin_psi, 0, 0,
sin_psi, cos_psi, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
float point_rf[4][4] = {
{cHp, 0, sHp, L / 2},
{0, 1, 0, 0},
{-sHp, 0, cHp, -W / 2},
{0, 0, 0, 1}
};
dspm::Mat Rz(Rz_data, 4, 4);
dspm::Mat Rxyz = Rx * Ry * Rz;
float T_data[] = {
0, 0, 0, p.xm,
0, 0, 0, p.ym,
0, 0, 0, p.zm,
0, 0, 0, 0
float point_lb[4][4] = {
{cHp, 0, sHp, -L / 2},
{0, 1, 0, 0},
{-sHp, 0, cHp, W / 2},
{0, 0, 0, 1}
};
dspm::Mat T(T_data, 4, 4);
dspm::Mat Tm = T + Rxyz;
float sHp = sin(M_PI / 2);
float cHp = cos(M_PI / 2);
float points_lf[] = {
cHp, 0, sHp, L / 2,
0, 1, 0, 0,
-sHp, 0, cHp, W / 2,
0, 0, 0, 1
float point_rb[4][4] = {
{cHp, 0, sHp, -L / 2},
{0, 1, 0, 0},
{-sHp, 0, cHp, -W / 2},
{0, 0, 0, 1}
};
Tlf = Tm * dspm::Mat(points_lf, 4, 4);
float points_rf[] = {
cHp, 0, sHp, L / 2,
0, 1, 0, 0,
-sHp, 0, cHp, -W / 2,
0, 0, 0, 1
};
Trf = Tm * dspm::Mat(points_rf, 4, 4);
float points_lb[] = {
cHp, 0, sHp, -L / 2,
0, 1, 0, 0,
-sHp, 0, cHp, W / 2,
0, 0, 0, 1
};
Tlb = Tm * dspm::Mat(points_lb, 4, 4);
float points_rb[] = {
cHp, 0, sHp, -L / 2,
0, 1, 0, 0,
-sHp, 0, cHp, -W / 2,
0, 0, 0, 1
};
Trb = Tm * dspm::Mat(points_rb, 4, 4);
dspm_mult_f32_ae32((float*) Tm, (float*) point_lf, (float*) Trb, 4, 4, 4);
dspm_mult_f32_ae32((float*) Tm, (float*) point_rf, (float*) Trf, 4, 4, 4);
dspm_mult_f32_ae32((float*) Tm, (float*) point_lb, (float*) Tlf, 4, 4, 4);
dspm_mult_f32_ae32((float*) Tm, (float*) point_rb, (float*) Tlb, 4, 4, 4);
return ESP_OK;
}
void legIK(float point[4], float result[3]) {
float x = point[0];
float y = point[1];
float z = point[2];
float x = point[0], y = point[1], z = point[2];
float F = sqrt(x * x + y * y - l1 * l1);
if (isnan(F)) F = l1;
float G = F - l2;
float H = sqrt(G * G + z * z);
result[0] = -atan2(y, x) - atan2(F, -l1);
result[2] = acos((H * H - l3 * l3 - l4 * l4) / (2 * l3 * l4));
if (isnan(result[2])) result[2] = 0;
result[1] = atan2(z, G) - atan2(l4 * sin(result[2]), l3 + l4 * cos(result[2]));
result[0] *= RAD2DEGREES;
result[1] *= RAD2DEGREES;
result[2] *= RAD2DEGREES;
float theta1 = -atan2(y, x) - atan2(F, -l1);
float theta3 = acos((H * H - l3 * l3 - l4 * l4) / (2 * l3 * l4));
if (isnan(theta3)) theta3 = 0;
float theta2 = atan2(z, G) - atan2(l4 * sin(theta3), l3 + l4 * cos(theta3));
result[0] = theta1 * RAD2DEGREES;
result[1] = theta2 * RAD2DEGREES;
result[2] = theta3 * RAD2DEGREES;
}
};