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// SCARA_Arms library
// Code to compute the shoulder angles required to move a Dual-Arm SCARA robot to required x,y position
// More information at http://robdobson.com/scara-arm-calculations
// Copyright (C) Rob Dobson 2013-2015, MIT License

#include "mbed.h"
#include "math.h"
#include "ScaraArms.h"

const double PI =  3.14159;

// Description of a Dual-Arm SCARA robot
// The two arms of the robot are akin to two human arms with the hands permanently clasped together
// The arms are always in the same plane (generally horizontal) and the hands hold a stick (also in the same plane)
// On the end of the stick is the tool (pen/actuayor/nozzle/laser etc)

// Constructor
// The measurements required to describe a Dual-Arm SCARA robot of the kind described above are:
// 1) Distance between shoulders
// 2) Distance from shoulder to elbow
// 3) Distance from elbow to hand
// 4) Distance from hand to tool (length of stick holding the tool)

ScaraArms::ScaraArms(double betweenShouldersMM, double shoulderToElbowMM, double elbowToHandMM, double handToToolMM)
{
    _betweenShouldersMM = betweenShouldersMM;
    _shoulderToElbowMM = shoulderToElbowMM;
    _elbowToHandMM = elbowToHandMM;
    _handToToolMM = handToToolMM;
}

// Compute the angles at the shoulders given the required XY position of the tool in radians
// Note that the way the angles are measured is that theta1 (the left arm angle) is measured counter-clockwise from 3 O'Clock
// theta2 (the right arm angle) is measured clockwise from 9 O'Clock
// To calculate both clockwise from 9 O'Clock use PI-theta2
// To convert the angles to degrees multiply by 180/PI
// The XY position has it's origin (0,0) at the left shoulder
void ScaraArms::ConvertXYtoScara(double x, double y, double &theta1, double &theta2)
{
    double L1 = _shoulderToElbowMM;
    double L2 = _elbowToHandMM;
    double L3 = _handToToolMM;
    double alpha = PI/4;
    double C = _betweenShouldersMM;
    double L4 = sqrt(L2*L2+L3*L3-2*L2*L3*cos(PI-alpha));
    double eta = acos((L3*L3+L4*L4-L2*L2)/(2*L3*L4));    

//    printf("L1 %f, L2 %f, L3 %f, L4 %f, eta %f, alpha %f\r\n", L1, L2, L3, L4, eta*180/PI, alpha*180/PI);

    double d3 = sqrt((C-x)*(C-x)+y*y);
    double theta2c = atan2(y, (C-x));
    double theta2d = acos((d3*d3+L1*L1-L4*L4) / (2*L1*d3));
    theta2 = theta2c+theta2d;
    
    double x4 = C+L1*cos(PI-theta2);
    double y4 = L1*sin(PI-theta2);
    
    double delta = atan2(x4-x,y-y4);
    double x1 = x + L3*sin(delta - eta);
    double y1 = y - L3*cos(delta - eta);

    double d1 = sqrt(x1*x1+y1*y1);
    double theta1a = atan2(y1, x1);
    double theta1b = acos((d1*d1+L1*L1-L2*L2) / (2*L1*d1));
    
    theta1 = theta1a+theta1b;
}

// Compute the XY position of the tool given the angles at the shoulders
// See the comments above for the reverse calculation concerning the way the angles are measured and the origin 
// of the XY coordinates
// These calculations use a different mathematical model as the conversion in this direction is simpler and
// it provides a useful cross check
void ScaraArms::ConvertScaratoXY(double theta1, double theta2, double &x, double &y)
{
    double L1 = _shoulderToElbowMM;
    double L2 = _elbowToHandMM;
    double L3 = _handToToolMM;
    double alpha = PI/4;
    double C = _betweenShouldersMM;

    // Uses different maths as a cross check
    double theta1rev = theta1;
    double theta2rev = PI - theta2;
    double xh1 = L1 * cos(theta1rev);
    double yh1 = sin(theta1rev) * L1;
    double xh2 = C + L1 * cos(theta2rev);
    double yh2 = sin(theta2rev) * L1;
    double gamma = atan2((yh1-yh2), (xh1-xh2));
    double l = sqrt(pow(xh1-xh2,2)+pow(yh1-yh2,2));
    double h = sqrt(pow(L2,2)-pow(l/2,2));
    double xi = (xh1+xh2)/2 + (h * sin(gamma));
    double yi = (yh1+yh2)/2 + fabs(h * cos(gamma));

    double psichk = atan2((yi-yh2),(xh2-xi));
    x = xi - L3 * cos(psichk+alpha);
    y = yi + L3 * sin(psichk+alpha);    
}