ik.cpp

/* Inverse kinetics, Nick Moriarty May 2014
This code is provided under the terms of the MIT license.

The MIT License (MIT)

Copyright (c) 2014 Nick Moriarty

Permission is hereby granted, free of charge, to any person obtaining a copy 
of this software and associated documentation files (the "Software"), to deal 
in the Software without restriction, including without limitation the rights 
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 
copies of the Software, and to permit persons to whom the Software is 
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in 
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 
SOFTWARE.
 */
#include "math.h"
#include "ik.h"

const float PI=3.14159265359;
float L1=80; //Shoulder to elbow length
float L2=80; //Elbow to wrise length
float L3=68; //Length from wrist to hand PLUS base centre to shoulder

// Get polar coords from cartesian ones
void cart2polar(float a, float b, float& r, float& theta)
{
    // Determine magnitude of cartesian coords
    r = sqrt(a*a + b*b);

    // Don't try to calculate zero-magnitude vectors' angles
    if(r == 0) return;

    float c = a / r;
    float s = b / r;

    // Safety!
    if(s > 1) s = 1;
    if(c > 1) c = 1;
    if(s < -1) s = -1;
    if(c < -1) c = -1;

    // Calculate angle in 0..PI
    theta = acos(c);

    // Convert to full range
    if(s < 0) theta *= -1;
}

// Get angle from a triangle using cosine rule
bool cosangle(float opp, float adj1, float adj2, float& theta)
{
    // Cosine rule:
    // C^2 = A^2 + B^2 - 2*A*B*cos(angle_AB)
    // cos(angle_AB) = (A^2 + B^2 - C^2)/(2*A*B)
    // C is opposite
    // A, B are adjacent
    float den = 2*adj1*adj2;

    if(den==0) return false;
    float c = (adj1*adj1 + adj2*adj2 - opp*opp)/den;

    if(c>1 || c<-1) return false;

    theta = acos(c);

    return true;
}

// Solve angles!
bool solve(float x, float y, float z, float& a0, float& a1, float& a2)
{
    // Solve top-down view
    float r, th0;
    cart2polar(y, x, r, th0);

    // Account for the wrist length!
    r -= L3;

    // In arm plane, convert to polar
    float ang_P, R;
    cart2polar(r, z, R, ang_P);

    // Solve arm inner angles as required
    float B, C;
    if(!cosangle(L2, L1, R, B)) return false;
    if(!cosangle(R, L1, L2, C)) return false;

    // Solve for servo angles from horizontal
    a0 = th0;
    a1 = ang_P + B;
    a2 = C + a1 - PI;

    return true;
}