src/modules/robot/arm_solutions/RotatableDeltaSolution.cpp

   1 #include "RotatableDeltaSolution.h"
   2 #include "checksumm.h"
   3 #include "ConfigValue.h"
   4 #include "ConfigCache.h"
   5 #include "libs/Kernel.h"
   6 #include "libs/nuts_bolts.h"
   7 #include "libs/Config.h"
   8 #include "libs/utils.h"
   9 #include "StreamOutputPool.h"
  10 #include <fastmath.h>
  11
  12 #define delta_e_checksum                        CHECKSUM("delta_e_checksum")
  13 #define delta_f_checksum                        CHECKSUM("delta_f_checksum")
  14 #define delta_re_checksum                       CHECKSUM("delta_re_checksum")
  15 #define delta_rf_checksum                       CHECKSUM("delta_rf_checksum")
  16 #define delta_z_offset_checksum                 CHECKSUM("delta_z_offset_checksum")
  17
  18 #define delta_ee_offs_checksum                  CHECKSUM("delta_ee_offs_checksum")
  19 #define tool_offset_checksum                    CHECKSUM("tool_offset_checksum")
  20
  21 const static float pi     = 3.14159265358979323846;    // PI
  22 const static float two_pi = 2 * pi;
  23 const static float sin120 = 0.86602540378443864676372317075294; //sqrt3/2.0
  24 const static float cos120 = -0.5;
  25 const static float tan60  = 1.7320508075688772935274463415059; //sqrt3;
  26 const static float sin30  = 0.5;
  27 const static float tan30  = 0.57735026918962576450914878050196; //1/sqrt3
  28
  29 RotatableDeltaSolution::RotatableDeltaSolution(Config* config)
  30 {
  31         // End effector length
  32         delta_e = config->value(delta_e_checksum)->by_default(131.636F)->as_number();
  33
  34         // Base length
  35         delta_f = config->value(delta_f_checksum)->by_default(190.526F)->as_number();
  36
  37         // Carbon rod length
  38         delta_re = config->value(delta_re_checksum)->by_default(270.000F)->as_number();
  39
  40         // Servo horn length
  41         delta_rf = config->value(delta_rf_checksum)->by_default(90.000F)->as_number();
  42
  43         // Distance from delta 8mm rod/pulley to table/bed,
  44         // NOTE: For OpenPnP, set the zero to be about 25mm above the bed..
  45         delta_z_offset = config->value(delta_z_offset_checksum)->by_default(290.700F)->as_number();
  46
  47         // Ball joint plane to bottom of end effector surface
  48         delta_ee_offs = config->value(delta_ee_offs_checksum)->by_default(15.000F)->as_number();
  49
  50         // Distance between end effector ball joint plane and tip of tool (PnP)
  51         tool_offset = config->value(tool_offset_checksum)->by_default(30.500F)->as_number();
  52
  53         init();
  54 }
  55
  56 // inverse kinematics
  57 // helper functions, calculates angle theta1 (for YZ-pane)
  58 int RotatableDeltaSolution::delta_calcAngleYZ(float x0, float y0, float z0, float &theta)
  59 {
  60     float y1 = -0.5F * tan30 * delta_f; // f/2 * tan 30
  61     y0      -=  0.5F * tan30 * delta_e; // shift center to edge
  62     // z = a + b*y
  63     float a = (x0*x0 + y0*y0 + z0*z0 + delta_rf*delta_rf - delta_re*delta_re - y1*y1) / (2.0F*z0);
  64     float b = (y1-y0)/z0;
  65
  66     float d = -(a+b*y1)*(a+b*y1) + delta_rf*(b*b*delta_rf+delta_rf); // discriminant
  67     if (d < 0.0F) return -1;                                            // non-existing point
  68
  69     float yj = (y1 - a*b - sqrtf(d))/(b*b + 1.0F);                     // choosing outer point
  70     float zj = a + b*yj;
  71
  72     theta = 180.0F*atanf(-zj/(y1 - yj))/pi + ((yj>y1)?180.0F:0.0F);
  73     return 0;
  74 }
  75
  76 // forward kinematics: (theta1, theta2, theta3) -> (x0, y0, z0)
  77 // returned status: 0=OK, -1=non-existing position
  78 int RotatableDeltaSolution::delta_calcForward(float theta1, float theta2, float theta3, float &x0, float &y0, float &z0)
  79 {
  80      float t = (delta_f-delta_e)*tan30/2.0F;
  81      float degrees_to_radians = pi/180.0F;
  82
  83      theta1 *= degrees_to_radians;
  84      theta2 *= degrees_to_radians;
  85      theta3 *= degrees_to_radians;
  86
  87      float y1 = -(t + delta_rf*cosf(theta1));
  88      float z1 = -delta_rf*sinf(theta1);
  89
  90      float y2 = (t + delta_rf*cosf(theta2))*sin30;
  91      float x2 = y2*tan60;
  92      float z2 = -delta_rf*sinf(theta2);
  93
  94      float y3 = (t + delta_rf*cosf(theta3))*sin30;
  95      float x3 = -y3*tan60;
  96      float z3 = -delta_rf*sinf(theta3);
  97
  98      float dnm = (y2-y1)*x3-(y3-y1)*x2;
  99
 100      float w1 = y1*y1 + z1*z1;
 101      float w2 = x2*x2 + y2*y2 + z2*z2;
 102      float w3 = x3*x3 + y3*y3 + z3*z3;
 103
 104      // x = (a1*z + b1)/dnm
 105      float a1 = (z2-z1)*(y3-y1)-(z3-z1)*(y2-y1);
 106      float b1 = -((w2-w1)*(y3-y1)-(w3-w1)*(y2-y1))/2.0F;
 107
 108      // y = (a2*z + b2)/dnm;
 109      float a2 = -(z2-z1)*x3+(z3-z1)*x2;
 110      float b2 = ((w2-w1)*x3 - (w3-w1)*x2)/2.0F;
 111
 112      // a*z^2 + b*z + c = 0
 113      float a = a1*a1 + a2*a2 + dnm*dnm;
 114      float b = 2.0F*(a1*b1 + a2*(b2-y1*dnm) - z1*dnm*dnm);
 115      float c = (b2-y1*dnm)*(b2-y1*dnm) + b1*b1 + dnm*dnm*(z1*z1 - delta_re*delta_re);
 116
 117      // discriminant
 118      float d = b*b - (float)4.0F*a*c;
 119      if (d < 0.0F) return -1; // non-existing point
 120
 121      z0 = -(float)0.5F*(b+sqrtf(d))/a;
 122      x0 = (a1*z0 + b1)/dnm;
 123      y0 = (a2*z0 + b2)/dnm;
 124
 125      z0 += z_calc_offset; //nj
 126      return 0;
 127 }
 128
 129
 130 void RotatableDeltaSolution::init() {
 131
 132         //these are calculated here and not in the config() as these variables can be fine tuned by the user.
 133         z_calc_offset  = (delta_z_offset - tool_offset - delta_ee_offs)*-1.0F;
 134
 135         // This is calculated from the Z_HOME_ANGLE angles after applying forward kinematics, and adding the Z calc offset to it.
 136         z_home_offs    = (((delta_z_offset - tool_offset - delta_ee_offs) - 182.002F) - 0.5F);
 137
 138 }
 139
 140 void RotatableDeltaSolution::cartesian_to_actuator( float cartesian_mm[], float actuator_mm[] )
 141 {
 142         //We need to translate the Cartesian coordinates in mm to the actuator position required in mm so the stepper motor  functions
 143         float alpha_theta = 0.0F;
 144         float beta_theta  = 0.0F;
 145         float gamma_theta = 0.0F;
 146
 147         //Code from Trossen Robotics tutorial, note we put the X axis at the back and not the front of the robot.
 148
 149         float x0 = cartesian_mm[X_AXIS];
 150         float y0 = cartesian_mm[Y_AXIS];
 151         float z_with_offset = cartesian_mm[Z_AXIS] + z_calc_offset; //The delta calculation below places zero at the top.  Subtract the Z offset to make zero at the bottom.
 152
 153         int status =              delta_calcAngleYZ(x0,                    y0,                  z_with_offset, alpha_theta);
 154         if (status == 0) status = delta_calcAngleYZ(x0*cos120 + y0*sin120, y0*cos120-x0*sin120, z_with_offset, beta_theta);  // rotate co-ordinates to +120 deg
 155         if (status == 0) status = delta_calcAngleYZ(x0*cos120 - y0*sin120, y0*cos120+x0*sin120, z_with_offset, gamma_theta);  // rotate co-ordinates to -120 deg
 156
 157         if (status == -1)  //something went wrong,
 158         {
 159             //force to actuator FPD home position as we know this is a valid position
 160             actuator_mm[ALPHA_STEPPER] = 0;
 161             actuator_mm[BETA_STEPPER ] = 0;
 162             actuator_mm[GAMMA_STEPPER] = 0;
 163
 164 //DEBUG CODE, uncomment the following to help determine what may be happening if you are trying to adapt this to your own different roational delta.
 165 //          THEKERNEL->streams->printf("ERROR: Delta calculation fail!  Unable to move to:\n");
 166 //          THEKERNEL->streams->printf("    x= %f\n",cartesian_mm[X_AXIS]);
 167 //          THEKERNEL->streams->printf("    y= %f\n",cartesian_mm[Y_AXIS]);
 168 //          THEKERNEL->streams->printf("    z= %f\n",cartesian_mm[Z_AXIS]);
 169 //          THEKERNEL->streams->printf(" CalcZ= %f\n",z_calc_offset);
 170 //          THEKERNEL->streams->printf(" Offz= %f\n",z_with_offset);
 171           }
 172           else
 173           {
 174             actuator_mm[ALPHA_STEPPER] = alpha_theta;
 175             actuator_mm[BETA_STEPPER ] = beta_theta;
 176             actuator_mm[GAMMA_STEPPER] = gamma_theta;
 177
 178 //                THEKERNEL->streams->printf("cartesian x= %f\n\r",cartesian_mm[X_AXIS]);
 179 //                THEKERNEL->streams->printf(" y= %f\n\r",cartesian_mm[Y_AXIS]);
 180 //                THEKERNEL->streams->printf(" z= %f\n\r",cartesian_mm[Z_AXIS]);
 181 //                THEKERNEL->streams->printf(" Offz= %f\n\r",z_with_offset);
 182 //                THEKERNEL->streams->printf(" delta x= %f\n\r",delta[X_AXIS]);
 183 //                THEKERNEL->streams->printf(" y= %f\n\r",delta[Y_AXIS]);
 184 //                THEKERNEL->streams->printf(" z= %f\n\r",delta[Z_AXIS]);
 185           }
 186
 187 }
 188
 189 void RotatableDeltaSolution::actuator_to_cartesian( float actuator_mm[], float cartesian_mm[] )
 190 {
 191     //Use forward kinematics
 192     delta_calcForward(actuator_mm[ALPHA_STEPPER], actuator_mm[BETA_STEPPER ], actuator_mm[GAMMA_STEPPER], cartesian_mm[X_AXIS], cartesian_mm[Y_AXIS], cartesian_mm[Z_AXIS]);
 193 }
 194
 195 bool RotatableDeltaSolution::set_optional(const arm_options_t& options) {
 196
 197     for(auto &i : options) {
 198         switch(i.first) {
 199             case 'A': delta_e                   = i.second; break;
 200             case 'B': delta_f                   = i.second; break;
 201             case 'C': delta_re                  = i.second; break;
 202             case 'D': delta_rf                  = i.second; break;
 203             case 'E': delta_z_offset            = i.second; break;
 204             case 'F': delta_ee_offs             = i.second; break;
 205             case 'H': tool_offset               = i.second; break;
 206         }
 207     }
 208     init();
 209     return true;
 210 }
 211
 212 bool RotatableDeltaSolution::get_optional(arm_options_t& options) {
 213
 214     // don't report these if none of them are set
 215     if(this->delta_e     != 0.0F || this->delta_f        != 0.0F || this->delta_re               != 0.0F ||
 216        this->delta_rf    != 0.0F || this->delta_z_offset != 0.0F || this->delta_ee_offs          != 0.0F ||
 217        this->tool_offset != 0.0F) {
 218
 219         options['A'] = this->delta_e;
 220         options['B'] = this->delta_f;
 221         options['C'] = this->delta_re;
 222         options['D'] = this->delta_rf;
 223         options['E'] = this->delta_z_offset;
 224         options['F'] = this->delta_ee_offs;
 225         options['H'] = this->tool_offset;
 226     }
 227
 228     return true;
 229 };
 230