春雨哥开源六自由度机械臂逆解算法"/>
为春雨哥开源六自由度机械臂逆解算法
六自由度机械臂是大学生学习舵机控制很好的练习，由于当时比赛的需求，做了简单一个机械臂逆解算法，原理不做过多解释，只是为我春雨哥方便使用，由于我们fpga使用的办卡无法处理浮点数，因此自定义了许多超越函数。
#include <stdint.h>
#include <errno.h>
#include <unistd.h>
#include <sys/types.h>#include <stdio.h>#include "math.h"#define PI 3.1415926535898#define eps 1e-7
#define RAD2ANG (3.1415926535898/180.0)
#define ANG2RAD(N) ( (N) * (180.0/3.1415926535898) )#define TAN_MAP_RES 0.003921569f
#define RAD_PER_DEG 0.017453293f
#define TAN_MAP_SIZE 256float fac(float n); //阶乘
float kvat(float n,float ci); //次方
float sinus(float x);
float fcos(float x);
float my_acos(float x);
float my_asin(float in);
float my_abs(float f);
float fast_atan2(float y, float x);
double fsqrt(int n);
void inverseKinematics(float x, float y, float z);float fast_atan_table[257] =
{0.000000e+00, 3.921549e-03, 7.842976e-03, 1.176416e-02,1.568499e-02, 1.960533e-02, 2.352507e-02, 2.744409e-02,3.136226e-02, 3.527947e-02, 3.919560e-02, 4.311053e-02,4.702413e-02, 5.093629e-02, 5.484690e-02, 5.875582e-02,6.266295e-02, 6.656816e-02, 7.047134e-02, 7.437238e-02,7.827114e-02, 8.216752e-02, 8.606141e-02, 8.995267e-02,9.384121e-02, 9.772691e-02, 1.016096e-01, 1.054893e-01,1.093658e-01, 1.132390e-01, 1.171087e-01, 1.209750e-01,1.248376e-01, 1.286965e-01, 1.325515e-01, 1.364026e-01,1.402496e-01, 1.440924e-01, 1.479310e-01, 1.517652e-01,1.555948e-01, 1.594199e-01, 1.632403e-01, 1.670559e-01,1.708665e-01, 1.746722e-01, 1.784728e-01, 1.822681e-01,1.860582e-01, 1.898428e-01, 1.936220e-01, 1.973956e-01,2.011634e-01, 2.049255e-01, 2.086818e-01, 2.124320e-01,2.161762e-01, 2.199143e-01, 2.236461e-01, 2.273716e-01,2.310907e-01, 2.348033e-01, 2.385093e-01, 2.422086e-01,2.459012e-01, 2.495869e-01, 2.532658e-01, 2.569376e-01,2.606024e-01, 2.642600e-01, 2.679104e-01, 2.715535e-01,2.751892e-01, 2.788175e-01, 2.824383e-01, 2.860514e-01,2.896569e-01, 2.932547e-01, 2.968447e-01, 3.004268e-01,3.040009e-01, 3.075671e-01, 3.111252e-01, 3.146752e-01,3.182170e-01, 3.217506e-01, 3.252758e-01, 3.287927e-01,3.323012e-01, 3.358012e-01, 3.392926e-01, 3.427755e-01,3.462497e-01, 3.497153e-01, 3.531721e-01, 3.566201e-01,3.600593e-01, 3.634896e-01, 3.669110e-01, 3.703234e-01,3.737268e-01, 3.771211e-01, 3.805064e-01, 3.838825e-01,3.872494e-01, 3.906070e-01, 3.939555e-01, 3.972946e-01,4.006244e-01, 4.039448e-01, 4.072558e-01, 4.105574e-01,4.138496e-01, 4.171322e-01, 4.204054e-01, 4.236689e-01,4.269229e-01, 4.301673e-01, 4.334021e-01, 4.366272e-01,4.398426e-01, 4.430483e-01, 4.462443e-01, 4.494306e-01,4.526070e-01, 4.557738e-01, 4.589307e-01, 4.620778e-01,4.652150e-01, 4.683424e-01, 4.714600e-01, 4.745676e-01,4.776654e-01, 4.807532e-01, 4.838312e-01, 4.868992e-01,4.899573e-01, 4.930055e-01, 4.960437e-01, 4.990719e-01,5.020902e-01, 5.050985e-01, 5.080968e-01, 5.110852e-01,5.140636e-01, 5.170320e-01, 5.199904e-01, 5.229388e-01,5.258772e-01, 5.288056e-01, 5.317241e-01, 5.346325e-01,5.375310e-01, 5.404195e-01, 5.432980e-01, 5.461666e-01,5.490251e-01, 5.518738e-01, 5.547124e-01, 5.575411e-01,5.603599e-01, 5.631687e-01, 5.659676e-01, 5.687566e-01,5.715357e-01, 5.743048e-01, 5.770641e-01, 5.798135e-01,5.825531e-01, 5.852828e-01, 5.880026e-01, 5.907126e-01,5.934128e-01, 5.961032e-01, 5.987839e-01, 6.014547e-01,6.041158e-01, 6.067672e-01, 6.094088e-01, 6.120407e-01,6.146630e-01, 6.172755e-01, 6.198784e-01, 6.224717e-01,6.250554e-01, 6.276294e-01, 6.301939e-01, 6.327488e-01,6.352942e-01, 6.378301e-01, 6.403565e-01, 6.428734e-01,6.453808e-01, 6.478788e-01, 6.503674e-01, 6.528466e-01,6.553165e-01, 6.577770e-01, 6.602282e-01, 6.626701e-01,6.651027e-01, 6.675261e-01, 6.699402e-01, 6.723452e-01,6.747409e-01, 6.771276e-01, 6.795051e-01, 6.818735e-01,6.842328e-01, 6.865831e-01, 6.889244e-01, 6.912567e-01,6.935800e-01, 6.958943e-01, 6.981998e-01, 7.004964e-01,7.027841e-01, 7.050630e-01, 7.073330e-01, 7.095943e-01,7.118469e-01, 7.140907e-01, 7.163258e-01, 7.185523e-01,7.207701e-01, 7.229794e-01, 7.251800e-01, 7.273721e-01,7.295557e-01, 7.317307e-01, 7.338974e-01, 7.360555e-01,7.382053e-01, 7.403467e-01, 7.424797e-01, 7.446045e-01,7.467209e-01, 7.488291e-01, 7.509291e-01, 7.530208e-01,7.551044e-01, 7.571798e-01, 7.592472e-01, 7.613064e-01,7.633576e-01, 7.654008e-01, 7.674360e-01, 7.694633e-01,7.714826e-01, 7.734940e-01, 7.754975e-01, 7.774932e-01,7.794811e-01, 7.814612e-01, 7.834335e-01, 7.853983e-01,7.853983e-01
};
const float sinetable[8193] = {
0.000000,0.000767,0.001534,0.002301,0.003068,0.003835,0.004602,0.005369,0.006136,0.006903,0.007670,0.008437,0.009204,0.009971,0.010738,0.011505,0.012272,0.013038,0.013805,0.014572,0.015339,0.016106,0.016873,0.017640,0.018407,0.019174,0.019940,0.020707,0.021474,0.022241,0.023008,0.023774,0.024541,
0.025308,0.026075,0.026841,0.027608,0.028375,0.029142,0.029908,0.030675,0.031441,0.032208,0.032975,0.033741,0.034508,0.035274,0.036041,0.036807,0.037574,0.038340,0.039107,0.039873,0.040639,0.041406,0.042172,0.042938,0.043705,0.044471,0.045237,0.046003,0.046769,0.047535,0.048302,0.049068,
0.049834,0.050600,0.051366,0.052132,0.052898,0.053664,0.054429,0.055195,0.055961,0.056727,0.057493,0.058258,0.059024,0.059790,0.060555,0.061321,0.062086,0.062852,0.063617,0.064383,0.065148,0.065913,0.066679,0.067444,0.068209,0.068974,0.069739,0.070505,0.071270,0.072035,0.072800,0.073565,
0.074329,0.075094,0.075859,0.076624,0.077389,0.078153,0.078918,0.079682,0.080447,0.081211,0.081976,0.082740,0.083505,0.084269,0.085033,0.085797,0.086561,0.087326,0.088090,0.088854,0.089617,0.090381,0.091145,0.091909,0.092673,0.093436,0.094200,0.094963,0.095727,0.096490,0.097254,0.098017,
0.098780,0.099544,0.100307,0.101070,0.101833,0.102596,0.103359,0.104122,0.104884,0.105647,0.106410,0.107172,0.107935,0.108697,0.109460,0.110222,0.110984,0.111747,0.112509,0.113271,0.114033,0.114795,0.115557,0.116319,0.117080,0.117842,0.118604,0.119365,0.120127,0.120888,0.121649,0.122411,
0.123172,0.123933,0.124694,0.125455,0.126216,0.126977,0.127737,0.128498,0.129259,0.130019,0.130780,0.131540,0.132300,0.133061,0.133821,0.134581,0.135341,0.136101,0.136860,0.137620,0.138380,0.139139,0.139899,0.140658,0.141418,0.142177,0.142936,0.143695,0.144454,0.145213,0.145972,0.146730,
0.147489,0.148248,0.149006,0.149765,0.150523,0.151281,0.152039,0.152797,0.153555,0.154313,0.155071,0.155828,0.156586,0.157343,0.158101,0.158858,0.159615,0.160372,0.161129,0.161886,0.162643,0.163400,0.164157,0.164913,0.165670,0.166426,0.167182,0.167938,0.168694,0.169450,0.170206,0.170962,
0.171718,0.172473,0.173229,0.173984,0.174739,0.175494,0.176249,0.177004,0.177759,0.178514,0.179268,0.180023,0.180777,0.181532,0.182286,0.183040,0.183794,0.184548,0.185301,0.186055,0.186809,0.187562,0.188315,0.189069,0.189822,0.190575,0.191328,0.192080,0.192833,0.193586,0.194338,0.195090,
0.195843,0.196595,0.197347,0.198098,0.198850,0.199602,0.200353,0.201105,0.201856,0.202607,0.203358,0.204109,0.204860,0.205610,0.206361,0.207111,0.207862,0.208612,0.209362,0.210112,0.210862,0.211611,0.212361,0.213110,0.213860,0.214609,0.215358,0.216107,0.216856,0.217604,0.218353,0.219101,
0.219850,0.220598,0.221346,0.222094,0.222841,0.223589,0.224337,0.225084,0.225831,0.226578,0.227325,0.228072,0.228819,0.229565,0.230312,0.231058,0.231804,0.232550,0.233296,0.234042,0.234788,0.235533,0.236278,0.237024,0.237769,0.238514,0.239258,0.240003,0.240748,0.241492,0.242236,0.242980,
0.243724,0.244468,0.245212,0.245955,0.246698,0.247442,0.248185,0.248928,0.249670,0.250413,0.251155,0.251898,0.252640,0.253382,0.254124,0.254866,0.255607,0.256349,0.257090,0.257831,0.258572,0.259313,0.260054,0.260794,0.261534,0.262275,0.263015,0.263755,0.264494,0.265234,0.265973,0.266713,
0.267452,0.268191,0.268930,0.269668,0.270407,0.271145,0.271883,0.272621,0.273359,0.274097,0.274834,0.275572,0.276309,0.277046,0.277783,0.278520,0.279256,0.279993,0.280729,0.281465,0.282201,0.282937,0.283672,0.284408,0.285143,0.285878,0.286613,0.287347,0.288082,0.288816,0.289551,0.290285,
0.291019,0.291752,0.292486,0.293219,0.293952,0.294685,0.295418,0.296151,0.296883,0.297616,0.298348,0.299080,0.299812,0.300543,0.301275,0.302006,0.302737,0.303468,0.304199,0.304929,0.305660,0.306390,0.307120,0.307850,0.308579,0.309309,0.310038,0.310767,0.311496,0.312225,0.312953,0.313682,
0.314410,0.315138,0.315866,0.316593,0.317321,0.318048,0.318775,0.319502,0.320229,0.320955,0.321682,0.322408,0.323134,0.323859,0.324585,0.325310,0.326035,0.326760,0.327485,0.328210,0.328934,0.329658,0.330382,0.331106,0.331830,0.332553,0.333277,0.334000,0.334722,0.335445,0.336168,0.336890,
0.337612,0.338334,0.339055,0.339777,0.340498,0.341219,0.341940,0.342661,0.343381,0.344101,0.344821,0.345541,0.346261,0.346980,0.347700,0.348419,0.349138,0.349856,0.350575,0.351293,0.352011,0.352729,0.353446,0.354164,0.354881,0.355598,0.356314,0.357031,0.357747,0.358463,0.359179,0.359895,
0.360611,0.361326,0.362041,0.362756,0.363470,0.364185,0.364899,0.365613,0.366327,0.367040,0.367754,0.368467,0.369180,0.369892,0.370605,0.371317,0.372029,0.372741,0.373453,0.374164,0.374875,0.375586,0.376297,0.377007,0.377718,0.378428,0.379138,0.379847,0.380557,0.381266,0.381975,0.382683,
0.383392,0.384100,0.384808,0.385516,0.386224,0.386931,0.387638,0.388345,0.389052,0.389758,0.390464,0.391170,0.391876,0.392582,0.393287,0.393992,0.394697,0.395401,0.396106,0.396810,0.397514,0.398218,0.398921,0.399624,0.400327,0.401030,0.401732,0.402435,0.403137,0.403838,0.404540,0.405241,
0.405942,0.406643,0.407344,0.408044,0.408744,0.409444,0.410144,0.410843,0.411542,0.412241,0.412940,0.413638,0.414336,0.415034,0.415732,0.416430,0.417127,0.417824,0.418520,0.419217,0.419913,0.420609,0.421305,0.422000,0.422695,0.423390,0.424085,0.424780,0.425474,0.426168,0.426862,0.427555,
0.428248,0.428941,0.429634,0.430326,0.431019,0.431711,0.432402,0.433094,0.433785,0.434476,0.435167,0.435857,0.436547,0.437237,0.437927,0.438616,0.439305,0.439994,0.440683,0.441371,0.442059,0.442747,0.443435,0.444122,0.444809,0.445496,0.446183,0.446869,0.447555,0.448241,0.448926,0.449611,
0.450296,0.450981,0.451665,0.452350,0.453033,0.453717,0.454400,0.455084,0.455766,0.456449,0.457131,0.457813,0.458495,0.459177,0.459858,0.460539,0.461219,0.461900,0.462580,0.463260,0.463939,0.464619,0.465298,0.465976,0.466655,0.467333,0.468011,0.468689,0.469366,0.470043,0.470720,0.471397,
0.472073,0.472749,0.473425,0.474100,0.474775,0.475450,0.476125,0.476799,0.477473,0.478147,0.478821,0.479494,0.480167,0.480839,0.481512,0.482184,0.482856,0.483527,0.484198,0.484869,0.485540,0.486210,0.486880,0.487550,0.488220,0.488889,0.489558,0.490226,0.490895,0.491563,0.492231,0.492898,
0.493565,0.494232,0.494899,0.495565,0.496231,0.496897,0.497563,0.498228,0.498893,0.499557,0.500221,0.500885,0.501549,0.502212,0.502876,0.503538,0.504201,0.504863,0.505525,0.506187,0.506848,0.507509,0.508170,0.508830,0.509490,0.510150,0.510810,0.511469,0.512128,0.512786,0.513445,0.514103,
0.514760,0.515418,0.516075,0.516732,0.517388,0.518045,0.518700,0.519356,0.520011,0.520666,0.521321,0.521975,0.522629,0.523283,0.523937,0.524590,0.525243,0.525895,0.526547,0.527199,0.527851,0.528502,0.529153,0.529804,0.530454,0.531104,0.531754,0.532403,0.533052,0.533701,0.534349,0.534998,
0.535645,0.536293,0.536940,0.537587,0.538234,0.538880,0.539526,0.540171,0.540817,0.541462,0.542106,0.542751,0.543395,0.544039,0.544682,0.545325,0.545968,0.546610,0.547252,0.547894,0.548536,0.549177,0.549817,0.550458,0.551098,0.551738,0.552378,0.553017,0.553656,0.554294,0.554932,0.555570,
0.556208,0.556845,0.557482,0.558119,0.558755,0.559391,0.560026,0.560662,0.561297,0.561931,0.562565,0.563199,0.563833,0.564466,0.565099,0.565732,0.566364,0.566996,0.567628,0.568259,0.568890,0.569521,0.570151,0.570781,0.571410,0.572040,0.572669,0.573297,0.573925,0.574553,0.575181,0.575808,
0.576435,0.577062,0.577688,0.578314,0.578939,0.579565,0.580189,0.580814,0.581438,0.582062,0.582685,0.583309,0.583931,0.584554,0.585176,0.585798,0.586419,0.587040,0.587661,0.588282,0.588902,0.589521,0.590141,0.590760,0.591378,0.591997,0.592615,0.593232,0.593850,0.594466,0.595083,0.595699,
0.596315,0.596931,0.597546,0.598161,0.598775,0.599389,0.600003,0.600616,0.601230,0.601842,0.602455,0.603067,0.603678,0.604290,0.604900,0.605511,0.606121,0.606731,0.607341,0.607950,0.608559,0.609167,0.609775,0.610383,0.610990,0.611597,0.612204,0.612810,0.613416,0.614022,0.614627,0.615232,
0.615836,0.616440,0.617044,0.617647,0.618250,0.618853,0.619455,0.620057,0.620659,0.621260,0.621861,0.622461,0.623061,0.623661,0.624260,0.624859,0.625458,0.626056,0.626654,0.627252,0.627849,0.628446,0.629042,0.629638,0.630234,0.630829,0.631424,0.632019,0.632613,0.633207,0.633800,0.634393,
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};
int abs(int f)
{if (f >= 0){return f;}return -f;
}int main (void)
{ inverseKinematics(0,18,0);}
//先定义一个阶乘函数
float fac(float n){float f=0;if(n == 1 || n==0)f =1;elsef = fac(n-1)*n;return f;
}
//一个指数函数(次方)
float kvat(float n,float ci){float chengf=1;int i;for (i=1; i<=ci; i++) {chengf = chengf*n;}return chengf;
}
float sinus(float x)
{int z =-1;int j =1;float sin= x;for (j =3;fabs( kvat(x,j)/fac(j) )>0.00001 ; j+=2) {
// printf("%lf\n",kvat(x, j));sin =sin + z*(kvat(x,j)/fac(j));z = -z;}return sin;
}float fcos(float x)
{float temp=0.0,t=5;int i=0;while(x>=2*PI) x=x-2*PI; //最多只有2π个弧度while(t>=0.00001){t=(kvat(x,2*i))/fac(2*i);temp+=kvat(-1,i)*t;i++;//printf("%.5lf\n",temp);}return temp;
}float my_acos(float x)
{unsigned char i;float ans = x,t1 = 1,t2 = x;x *= x;for(i = 3;i < 51;i += 2){t1 *= (float)(i - 2) / (float)(i - 1);t2 *= x;ans += (t1 * t2 / (float)i);}return ans = 1.5708 - ans;
}
float my_asin(float in)
{float a = PI/2 - my_acos(in);return a;
}
float my_abs(float f)
{if (f >= 0.0f){return f;}return -f;
}
float fast_atan2(float y, float x)
{float x_abs, y_abs, z;float alpha, angle, base_angle;int index;/* don't divide by zero! */if ((y == 0.0f) || (x == 0.0f))//if ((y == 0.0f) && (x == 0.0f))angle = 1.5707963705;else{/* normalize to +/- 45 degree range */y_abs = my_abs(y);x_abs = my_abs(x);//z = (y_abs < x_abs ? y_abs / x_abs : x_abs / y_abs);if (y_abs < x_abs)z = y_abs / x_abs;elsez = x_abs / y_abs;/* when ratio approaches the table resolution, the angle is *//* best approximated with the argument itself... */if (z < TAN_MAP_RES)base_angle = z;else{/* find index and interpolation value */alpha = z * (float) TAN_MAP_SIZE - .5f;index = (int) alpha;alpha -= (float) index;/* determine base angle based on quadrant and *//* add or subtract table value from base angle based on quadrant */base_angle = fast_atan_table[index];base_angle += (fast_atan_table[index + 1] - fast_atan_table[index]) * alpha;}if (x_abs > y_abs){ /* -45 -> 45 or 135 -> 225 */if (x >= 0.0f){ /* -45 -> 45 */if (y >= 0.0f)angle = base_angle; /* 0 -> 45, angle OK */elseangle = -base_angle; /* -45 -> 0, angle = -angle */}else{ /* 135 -> 180 or 180 -> -135 */angle = 3.14159265358979323846;if (y >= 0.0f)angle -= base_angle; /* 135 -> 180, angle = 180 - angle */elseangle = base_angle - angle; /* 180 -> -135, angle = angle - 180 */}}else{ /* 45 -> 135 or -135 -> -45 */if (y >= 0.0f){ /* 45 -> 135 */angle = 1.57079632679489661923;if (x >= 0.0f)angle -= base_angle; /* 45 -> 90, angle = 90 - angle */elseangle += base_angle; /* 90 -> 135, angle = 90 + angle */}else{ /* -135 -> -45 */angle = -1.57079632679489661923;if (x >= 0.0f)angle += base_angle; /* -90 -> -45, angle = -90 + angle */elseangle -= base_angle; /* -135 -> -90, angle = -90 - angle */}}}
#ifdef ZERO_TO_TWOPIif (angle < 0)return (angle + TWOPI);elsereturn (angle);
#elsereturn (angle);
#endif
}
double fsqrt(int n)
{double i=0,j=0;while(i*i<n){i++;//1 2 3}double left=i-1,right=i,mid;if(right*right==n){return right;}while(right-left>eps){mid=(left+right)/2;if(mid*mid>n){right=mid;}else{left=mid;}}return mid;
}void inverseKinematics(float x, float y, float z)
{ //printf("%f %f %f",x,y,z);float a, b, c; //临时变量float L1 = 10.5, L2 = 10, L3 = 12;//3节手臂的长度float m, n, t, q, p;//临时变量float j1, j2, j3, j0;//4个舵机的旋转角度float x1, y1, z1;//逆解后正解算出来的值，看是否与逆解值相等char i = 0;float m1,m2,m3,m4,m5,m6;float n1,n2;j0 = fast_atan2(y,x);n1 = sinus(j0);n2 = fcos(j0);a = x / n2;if (x == 0) a = y; //如果x为0，需要交换x，yb = z;for (j1 = 90; j1 > -90; j1--)//for(j1 = -90;j1 <90;j1++){j1 *= RAD2ANG;m1 = sinus(j1);m2 = fcos(j1);j3 = my_acos((kvat(a, 2) + kvat(b, 2) + kvat(L1, 2) - kvat(L2, 2) - kvat(L3, 2) - 2 * a*L1*m1 - 2 * b*L1*m2) / (2 * L2*L3));//j3 = my_acos((kvat(a, 2) + kvat(b, 2) + kvat(L1, 2) - kvat(L2, 2) - kvat(L3, 2) - 2 * a*L1*sinus(j1) - 2 * b*L1*fcos(j1)) / (2 * L2*L3));m3 = fcos(j3);m4 = sinus(j3);m = L2 * m1 + L3 * m1*m3 + L3 * m2*m4;n = L2 * m2 + L3 * m2*m3 - L3 * m1*m4;//m = L2 * sinus(j1) + L3 * sinus(j1)*fcos(j3) + L3 * fcos(j1)*sinus(j3);// n = L2 * fcos(j1) + L3 * fcos(j1)*fcos(j3) - L3 * sinus(j1)*sinus(j3);// t = a - L1 * sinus(j1);t = a - L1 * m1;// p = fsqrt(n*n + m*m);p = fsqrt(kvat(n, 2) + kvat(m, 2));q = my_asin(m / p);j2 = -(my_asin(t / p) - q);//if (abs(ANG2RAD(j2)) >= 135) { j1 = ANG2RAD(j1); continue; }//***************计算正解然后与目标解对比，看解是否正确**************//x1 = (L1 * sinus(j1) + L2 * sinus(j1 + j2) + L3 * sinus(j1 + j2 + j3))*fcos(j0);//y1 = (L1 * sinus(j1) + L2 * sinus(j1 + j2) + L3 * sinus(j1 + j2 + j3))*sinus(j0);//z1 = L1 * fcos(j1) + L2 * fcos(j1 + j2) + L3 * fcos(j1 + j2 + j3);m5 = sinus(j1 + j2);m6 = sinus(j1 + j2 + j3);x1 = (L1 * m1 + L2 * m5 + L3 * m6)*n2;y1 = (L1 * m1 + L2 * m5 + L3 * m6)*n1;z1 = L1 * m2 + L2 * fcos(j1 + j2) + L3 * fcos(j1 + j2 + j3);j1 = ANG2RAD(j1);j2 = ANG2RAD(j2);j3 = ANG2RAD(j3);// printf("%f\n",j3);if (x1<(x + 1) && x1 >(x - 1) && y1<(y + 1) && y1 >(y - 1) && z1<(z + 1) && z1 >(z - 1)){if(j3 <135){printf("j0:%f,j1:%f,j2:%f,j3:%f,x:%f,y:%f,z:%f\r\n", ANG2RAD(j0), j1, j2, j3, x1, y1, z1);break;}}}
}/*
void inverseKinematics(float x, float y, float z)
{float a, b, c; //临时变量float L1 = 10, L2 = 11, L3 = 14;//3节手臂的长度float m, n, t, q, p;//临时变量float j1, j2, j3, j0;//4个舵机的旋转角度float x1, y1, z1;//逆解后正解算出来的值，看是否与逆解值相等j0 = atan2(y, x);a = x / cos(j0);if (x == 0) a = y; //如果x为0，需要交换x，yb = z;for (j1 = -90; j1 < 90; j1++){j1 *= RAD2ANG;j3 = acos((pow(a, 2) + pow(b, 2) + pow(L1, 2) - pow(L2, 2) - pow(L3, 2) - 2 * a*L1*sin(j1) - 2 * b*L1*cos(j1)) / (2 * L2*L3));//if (abs(ANG2RAD(j3)) >= 135) { j1 = ANG2RAD(j1); continue; }m = L2 * sin(j1) + L3 * sin(j1)*cos(j3) + L3 * cos(j1)*sin(j3);n = L2 * cos(j1) + L3 * cos(j1)*cos(j3) - L3 * sin(j1)*sin(j3);t = a - L1 * sin(j1);p = pow(pow(n, 2) + pow(m, 2), 0.5);q = asin(m / p);j2 = asin(t / p) - q;//if (abs(ANG2RAD(j2)) >= 135) { j1 = ANG2RAD(j1); continue; }//***************计算正解然后与目标解对比，看解是否正确**************x1 = (L1 * sin(j1) + L2 * sin(j1 + j2) + L3 * sin(j1 + j2 + j3))*cos(j0);y1 = (L1 * sin(j1) + L2 * sin(j1 + j2) + L3 * sin(j1 + j2 + j3))*sin(j0);z1 = L1 * cos(j1) + L2 * cos(j1 + j2) + L3 * cos(j1 + j2 + j3);j1 = ANG2RAD(j1);j2 = ANG2RAD(j2);j3 = ANG2RAD(j3);if (x1<(x + 1) && x1 >(x - 1) && y1<(y + 1) && y1 >(y - 1) && z1<(z + 1) && z1 >(z - 1)){printf("j0:%f,j1:%f,j2:%f,j3:%f,x:%f,y:%f,z:%f\r\n", ANG2RAD(j0), j1, j2, j3, x1, y1, z1);}}for (j1 = -90; j1 < 90; j1++)//这个循环是为了求解另一组解，j2 = asin(t / p) - q;j2 = -(asin(t / p) - q);多了个负号{j1 *= RAD2ANG;j3 = acos((pow(a, 2) + pow(b, 2) + pow(L1, 2) - pow(L2, 2) - pow(L3, 2) - 2 * a*L1*sin(j1) - 2 * b*L1*cos(j1)) / (2 * L2*L3));//if (abs(ANG2RAD(j3)) >= 135) { j1 = ANG2RAD(j1); continue; }m = L2 * sin(j1) + L3 * sin(j1)*cos(j3) + L3 * cos(j1)*sin(j3);n = L2 * cos(j1) + L3 * cos(j1)*cos(j3) - L3 * sin(j1)*sin(j3);t = a - L1 * sin(j1);p = pow(pow(n, 2) + pow(m, 2), 0.5);q = asin(m / p);j2 = -(asin(t / p) - q);//if (abs(ANG2RAD(j2)) >= 135) { j1 = ANG2RAD(j1); continue; }x1 = (L1 * sin(j1) + L2 * sin(j1 + j2) + L3 * sin(j1 + j2 + j3))*cos(j0);y1 = (L1 * sin(j1) + L2 * sin(j1 + j2) + L3 * sin(j1 + j2 + j3))*sin(j0);z1 = L1 * cos(j1) + L2 * cos(j1 + j2) + L3 * cos(j1 + j2 + j3);j1 = ANG2RAD(j1);j2 = ANG2RAD(j2);j3 = ANG2RAD(j3);if (x1<(x + 1) && x1 >(x - 1) && y1<(y + 1) && y1 >(y - 1) && z1<(z + 1) && z1 >(z - 1)){printf("j0:%f,j1:%f,j2:%f,j3:%f,x:%f,y:%f,z:%f\r\n", ANG2RAD(j0), j1, j2, j3, x1, y1, z1);}}}
*/
可以观看，不可抄袭，如果比赛冲突，我们要追究责任！！！
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