KatanaKinematics6M90T.cpp

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/***************************************************************************
 *   Copyright (C) 2006 by Tiziano Mueller   *
 *   tiziano.mueller@neuronics.ch   *
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#include "KNI_InvKin/KatanaKinematics6M90T.h"
#include "common/MathHelperFunctions.h"
#include <algorithm>

namespace KNI {

const double KatanaKinematics6M90T::_tolerance = 0.001;
const int KatanaKinematics6M90T::_nrOfPossibleSolutions = 8;

void
KatanaKinematics6M90T::DK(coordinates& solution, encoders const& current_encoders) const {
        using namespace KNI_MHF;
        // numering the angles starting by 0-5

        double x0, x1, x2, x3;
        double y0, y1, y2, y3;
        double z0, z1, z2, z3;

        angles current_angles(current_encoders.size());
        for(unsigned int z = 0; z < current_angles.size(); ++z) {
                current_angles[z] = enc2rad(current_encoders[z], _parameters[z].angleOffset, _parameters[z].epc, _parameters[z].encOffset, _parameters[z].rotDir);
        }

        // needs refactoring:
        current_angles[1] = current_angles[1] - M_PI/2.0;
        current_angles[2] = current_angles[2] - M_PI;
        current_angles[3] = M_PI - current_angles[3];
        current_angles[5] = -current_angles[5];

        coordinates pose(6);

        angles cx(current_angles.size()), sx(current_angles.size());
        angles::iterator cx_iter, sx_iter;

        angles angle = current_angles;

        angle[2] = angle[1]+angle[2];
        angle[3] = angle[2]+angle[3];

        cx_iter = cx.begin();
        sx_iter = sx.begin();
        std::transform(angle.begin(), angle.end(), sx_iter, unary_precalc_sin<double>() );
        std::transform(angle.begin(), angle.end(), cx_iter, unary_precalc_cos<double>() );


        //x
        x0 =  cx[0]*sx[1];
        x1 =  cx[0]*sx[2];
        x2 =  cx[0]*sx[3];
        x3 = -cx[0]*cx[3]*cx[4]-sx[0]*sx[4];
        pose[0] = x0*_length[0]+x1*_length[1]+x2*_length[2]+x3*_length[3];

        //y
        y0 = sx[0]*sx[1];
        y1 = sx[0]*sx[2];
        y2 = sx[0]*sx[3];
        y3 = -sx[0]*cx[3]*cx[4]+cx[0]*sx[4];
        pose[1] = y0*_length[0]+y1*_length[1]+y2*_length[2]+y3*_length[3];

        //z
        z0 = cx[1];
        z1 = cx[2];
        z2 = cx[3];
        z3 = cx[4]*sx[3];
        pose[2] = z0*_length[0]+z1*_length[1]+z2*_length[2]+z3*_length[3];


        //theta
        pose[4] = acos(cx[4]*sx[3]);

        // phi & psi


        const double theta1 = angle[0];
        const double theta5 = angle[4];
        const double theta6 = angle[5];
        const double theta234 = angle[3];

        if( std::abs(pose[4])<_tolerance || std::abs(pose[4]-M_PI)<_tolerance ) { // catch the case where theta=0, resp. theta=180
                //phi
                angles v1(2), v2(2);

                double R11 = -sin(theta1)*cos(theta5)  *sin(theta6) + cos(theta1)*(sin(theta234)*cos(theta6)+cos(theta234)*sin(theta5)*sin(theta6));
                double R21 =  sin(theta1)*sin(theta234)*cos(theta6) + sin(theta6)*(cos(theta1)  *cos(theta5)+cos(theta234)*sin(theta1)*sin(theta5));

                v1[0] = acos( R11 );
                v1[1] = -v1[0];
                v2[0] = asin( R21 );
                v2[1] = M_PI - v2[0];

                pose[3] = anglereduce(findFirstEqualAngle(v1, v2));

                //psi
                pose[5] = 0;
        } else {
                //phi
                const double R13 = -cos(theta1)*cos(theta234)*cos(theta5) - sin(theta1)*sin(theta5);
                const double R23 = -sin(theta1)*cos(theta234)*cos(theta5) + cos(theta1)*sin(theta5);
                pose[3] = atan2(R13, -R23);

                //psi
                const double R31 =  cos(theta234)*cos(theta6) - sin(theta234)*sin(theta5)*sin(theta6);
                const double R32 = -cos(theta234)*sin(theta6) - sin(theta234)*sin(theta5)*cos(theta6);
                pose[5] = atan2(R31, R32);
        }

        std::swap(solution, pose);
}

void
KatanaKinematics6M90T::init( metrics const& length, parameter_container const& parameters ) {
        assert( (length.size() == 4) && "You have to provide the metrics for exactly 4 links" ); // we have 4 links
        assert( (parameters.size() == 6) && "You have to provide exactly 5 motor parameters" ); // 5 motors are used for IK calculations
        _setLength( length );
        _setParameters ( parameters );
}


void
KatanaKinematics6M90T::IK_theta234theta5(angles_calc& angle, const position &p_gr) const {
        using namespace KNI_MHF;

        if(p_gr.z==0) {
                angle.theta234=0;
                angle.theta5=angle.theta1-atan1(-p_gr.x,-p_gr.y);
        } else {
                angle.theta234 = -acotan( (  (p_gr.x * p_gr.z * cos(angle.theta1) ) -
                                     sqrt( ( -pow2(p_gr.z) ) *
                                           ( -pow2(_length[3]) + pow2(p_gr.x) + pow2(p_gr.z) ) * pow2(sin(angle.theta1))
                                         )
                                  ) / pow2(p_gr.z)
                                );
                angle.theta5   = acos( p_gr.z/(_length[3]*sin(angle.theta234)) );
        }

        bool griptest;
        griptest = GripperTest(p_gr, angle);
        if(!griptest) {
                angle.theta5=-angle.theta5;
                griptest=GripperTest(p_gr, angle);
                if(!griptest) {
                        angle.theta234 = -acotan( (   ( p_gr.x * p_gr.z * cos(angle.theta1) ) +
                                                      sqrt( ( -pow2(p_gr.z) ) *
                                                            ( -pow2(_length[3]) + pow2(p_gr.x) + pow2(p_gr.z) ) * pow2(sin(angle.theta1))
                                                          )
                                                  ) / pow2(p_gr.z)
                                                );
                        angle.theta5 =  acos( p_gr.z / (_length[3]*sin(angle.theta234)) );
                        if(p_gr.z==0) {
                                angle.theta234=-M_PI;
                                angle.theta5=atan1(p_gr.x,p_gr.y) - angle.theta1;
                        }

                        griptest=GripperTest(p_gr, angle);
                        if(!griptest) {
                                angle.theta5=-angle.theta5;
                        }
                }
        }

}

bool
KatanaKinematics6M90T::GripperTest(const position &p_gr, const angles_calc &angle) const {
        using namespace KNI_MHF;
        double xgr2, ygr2, zgr2;

        xgr2 = -_length[3]*(cos(angle.theta1)*cos(angle.theta234)*cos(angle.theta5)+sin(angle.theta1)*sin(angle.theta5));
        ygr2 = -_length[3]*(sin(angle.theta1)*cos(angle.theta234)*cos(angle.theta5)-cos(angle.theta1)*sin(angle.theta5));
        zgr2 =  _length[3]*sin(angle.theta234)*cos(angle.theta5);

        if((pow2(p_gr.x-xgr2)+pow2(p_gr.y-ygr2)+pow2(p_gr.z-zgr2))>=_tolerance)
                return false;

        return true;
}

void
KatanaKinematics6M90T::IK_b1b2costh3_6MS(angles_calc &angle, const position &p) const {
        using namespace KNI_MHF;

        double xg, yg, zg;
        double d5 = _length[2] + _length[3];
        xg = p.x + ( _length[3] * cos(angle.theta1) * sin(angle.theta234) );
        yg = p.y + ( _length[3] * sin(angle.theta1) * sin(angle.theta234) );
        zg = p.z + ( _length[3]                     * cos(angle.theta234) );


        angle.b1 = xg*cos(angle.theta1) + yg*sin(angle.theta1) - d5*sin(angle.theta234);
        angle.b2 = zg - d5*cos(angle.theta234);
        angle.costh3 = -( pow2(angle.b1) + pow2(angle.b2) - pow2(_length[0]) - pow2(_length[1]) ) / ( 2.0*_length[0]*_length[1] );

}

double
KatanaKinematics6M90T::findFirstEqualAngle(const angles& v1, const angles& v2) const {
        using namespace KNI_MHF;
        for(angles::const_iterator i = v1.begin(); i != v1.end(); ++i) {
                for(angles::const_iterator j = v2.begin(); j != v2.end(); ++j) {
                        if(std::abs(anglereduce(*j) - anglereduce(*i)) < _tolerance)
                                return *i;
                }
        }
        assert(!"precondition for findFirstEqualAngle failed -> no equal angles found");
        return 0;
}


void
KatanaKinematics6M90T::thetacomp(angles_calc &angle, const position &p_m, const coordinates& pose) const {
        using namespace KNI_MHF;

        const double theta1   = angle.theta1;
        double theta2   = 0;
        const double theta3   = angle.theta3;
        double theta4   = 0;
        const double theta5   = angle.theta5;
        double theta6   = 0;
        const double theta234 = angle.theta234;
        const double b1       = angle.b1;
        const double b2       = angle.b2;

        const double phi   = pose[3];
        const double theta = pose[4];
        const double psi   = pose[5];


        theta2 = -M_PI/2.0 - ( atan0(b1, b2)+atan0(_length[0]+_length[1]*cos(theta3),_length[1]*sin(theta3)) );
        theta4 = theta234 - theta2 - theta3;

        if(!PositionTest6MS(theta1, theta2, theta3, theta234 ,p_m)) {
                theta2 = theta2+M_PI;
                theta4 = theta234 - theta2 - theta3;
        }

        const double R11 = cos(phi)*cos(psi) - sin(phi)*cos(theta)*sin(psi);
        const double R21 = sin(phi)*cos(psi) + cos(phi)*cos(theta)*sin(psi);

        std::vector<double> theta16c(2), theta16s(2);

        if(std::abs(theta234 + M_PI/2) < _tolerance) {
                if(std::abs(theta5) < _tolerance) {
                        theta16c[0] = acos(-R11);
                        theta16c[1] = -theta16c[0];
                        theta16s[0] = asin(-R21);
                        theta16s[1] = M_PI - theta16s[0];

                        theta6 = theta1 - findFirstEqualAngle(theta16c, theta16s);

                } else if(std::abs(theta5-M_PI) < _tolerance) {
                        theta16c[0] = acos(-R11);
                        theta16c[1] = -theta16c[0];
                        theta16s[0] = asin(-R21);
                        theta16s[1] = M_PI - theta16s[0];

                        theta6 = findFirstEqualAngle(theta16c, theta16s) - theta1;

                } else {
                        assert(!"Special case \"|theta234+(1/2)*pi| = 0\" detected, but no solution found");
                }

        } else if(std::abs(theta234 + 3*M_PI/2) < _tolerance) {
                if(std::abs(theta5) < _tolerance) {
                        theta16c[0] = acos(R11);
                        theta16c[1] = -theta16c[0];
                        theta16s[0] = asin(R21);
                        theta16s[1] = M_PI - theta16s[0];

                        theta6  = findFirstEqualAngle(theta16c, theta16s) - theta1;

                } else if(std::abs(theta5-M_PI ) < _tolerance) {
                        theta16c[0] = acos(R11);
                        theta16c[1] = -theta16c[0];
                        theta16s[0] = asin(R21);
                        theta16s[1] = M_PI -theta16s[0];

                        theta6  = - theta1 - findFirstEqualAngle(theta16c, theta16s);
                } else {
                        assert(!"Special case \"|theta234+(3/2)*pi| = 0\" detected, but no solution found");
                }

        } else {

                const double R31 = sin(theta)*sin(psi);
                const double R32 = sin(theta)*cos(psi);

                const double temp1 =  cos(theta234);
                const double temp2 = -sin(theta234)*sin(theta5);

                const double c = ( R31*temp1 + R32*temp2 ) / ( pow2(temp1) + pow2(temp2) );
                const double s = ( R31*temp2 - R32*temp1 ) / ( pow2(temp1) + pow2(temp2) );

                theta16c[0] = acos(c);
                theta16c[1] = -theta16c[0];
                theta16s[0] = asin(s);
                theta16s[1] = M_PI - theta16s[0];

                theta6 = findFirstEqualAngle(theta16c, theta16s);
        }


        angle.theta2 = theta2;
        angle.theta4 = theta4;
        angle.theta6 = theta6;
}

bool
KatanaKinematics6M90T::PositionTest6MS(const double& theta1, const double& theta2, const double& theta3, const double& theta234, const position &p) const {
        using namespace KNI_MHF;
        double temp, xm2, ym2, zm2;

        temp = _length[0]*sin(theta2) + _length[1]*sin(theta2+theta3) + _length[2]*sin(theta234);
        xm2  = cos(theta1)*temp;
        ym2  = sin(theta1)*temp;
        zm2  = _length[0]*cos(theta2) + _length[1]*cos(theta2+theta3) + _length[2]*cos(theta234);

        if((pow2(p.x-xm2)+pow2(p.y-ym2)+pow2(p.z-zm2))>=_tolerance)
                return false;

        return true;
}

bool
KatanaKinematics6M90T::angledef(angles_calc &a) const {
        using namespace KNI_MHF;

        // constants here. needs refactoring:
        a.theta2=anglereduce(a.theta2+M_PI/2.0);
        a.theta3=anglereduce(a.theta3+M_PI);
        a.theta4=anglereduce(M_PI-a.theta4);
        a.theta5=anglereduce(a.theta5);
        a.theta6=-a.theta6;

        if(a.theta1>_parameters[0].angleStop) {
                a.theta1=a.theta1-2.0*M_PI;
        }
        if(a.theta2>M_PI) {
                a.theta2=a.theta2-2.0*M_PI;
        }
        if(a.theta6<_parameters[5].angleOffset) {
                a.theta6=a.theta6+2.0*M_PI;
        } else if(a.theta6>_parameters[5].angleStop) {
                a.theta6=a.theta6-2.0*M_PI;
        }
        if(a.theta5<_parameters[4].angleOffset) {
                a.theta5 += 2.0*M_PI;
        }

        return AnglePositionTest(a);

}

bool
KatanaKinematics6M90T::AnglePositionTest(const angles_calc &a) const {

        if( (a.theta1+0.0087<_parameters[0].angleOffset)||(a.theta1>_parameters[0].angleStop) ) {
                return false;
        }
        if( (a.theta2-0.0087>_parameters[1].angleOffset)||(a.theta2<_parameters[1].angleStop) ) {
                return false;
        }
        if( (a.theta3<_parameters[2].angleOffset)||(a.theta3>_parameters[2].angleStop) ) {
                return false;
        }

        if( (a.theta4<_parameters[3].angleOffset)||(a.theta4>_parameters[3].angleStop) ) {
                return false;
        }

        if( (a.theta5<_parameters[4].angleOffset)||(a.theta5>_parameters[4].angleStop) ) {
                return false;
        }
        if( (a.theta6<_parameters[5].angleOffset)||(a.theta6>_parameters[5].angleStop) ) {
                return false;
        }

        return true;
}




void
KatanaKinematics6M90T::IK(encoders::iterator solution, coordinates const& pose, encoders const& current_encoders) const {
        using namespace KNI_MHF;

        // pose: Winkel Deg->Rad
        // Alle 8 Loeungen werden in einem Array angle, welches aus 8 Structs besteht, gespeichert:
        // 0-3 fr theta1_1
        // 4-7 fr theta1_2

        // Declaration
        position p_gr;
        position p_m;
        angles_container angle(_nrOfPossibleSolutions);

        // calculation of the gripper vector
        p_gr.x = _length[3]*sin(pose[4])*sin(pose[3]);
        p_gr.y = -_length[3]*sin(pose[4])*cos(pose[3]);
        p_gr.z = _length[3]*cos(pose[4]);

        p_m.x = pose[0]-p_gr.x;
        p_m.y = pose[1]-p_gr.y;
        p_m.z = pose[2]-p_gr.z;

        // calculate theta1_1 and theta1_2
        angle[0].theta1 = atan1(p_m.x,p_m.y);
        angle[4].theta1 = angle[0].theta1+M_PI;


        // check the borders according to the settings
        if(angle[0].theta1>_parameters[0].angleStop)
                angle[0].theta1=angle[0].theta1-2.0*M_PI;

        if(angle[0].theta1<_parameters[0].angleOffset)
                angle[0].theta1=angle[0].theta1+2.0*M_PI;

        if(angle[4].theta1>_parameters[0].angleStop)
                angle[4].theta1=angle[4].theta1-2.0*M_PI;

        if(angle[4].theta1<_parameters[0].angleOffset)
                angle[4].theta1=angle[4].theta1+2.0*M_PI;


        //====THETA1_1==================
        //-------THETA234_1-------------
        IK_theta234theta5(angle[0], p_gr);
        IK_b1b2costh3_6MS(angle[0], p_m);

        angle[1]=angle[0];
        angle[0].theta3 =  acos(angle[0].costh3)-M_PI;
        thetacomp(angle[0], p_m, pose);
        angle[1].theta3 =  -acos(angle[1].costh3)+M_PI;
        thetacomp(angle[1], p_m, pose);

        //-------THETA234_2-------------
        angle[2].theta1=angle[0].theta1;
        angle[2].theta234=angle[0].theta234-M_PI;
        angle[2].theta5=M_PI-angle[0].theta5;

        IK_b1b2costh3_6MS(angle[2], p_m);
        angle[3]=angle[2];
        angle[2].theta3 =  acos(angle[2].costh3)-M_PI;
        thetacomp(angle[2], p_m, pose);
        angle[3].theta3 =  -acos(angle[3].costh3)+M_PI;
        thetacomp(angle[3], p_m, pose);


        //====THETA1_2==================
        //-------THETA234_1-------------
        IK_theta234theta5(angle[4], p_gr);
        IK_b1b2costh3_6MS(angle[4], p_m);

        angle[5]=angle[4];
        angle[4].theta3 =  acos(angle[4].costh3)-M_PI;
        thetacomp(angle[4], p_m, pose);
        angle[5].theta3 =  -acos(angle[5].costh3)+M_PI;
        thetacomp(angle[5], p_m, pose);

        //-------THETA234_2-------------
        angle[6].theta1=angle[4].theta1;
        angle[6].theta234=angle[4].theta234-M_PI;
        angle[6].theta5=M_PI-angle[4].theta5;
        IK_b1b2costh3_6MS(angle[6], p_m);
        angle[7]=angle[6];
        angle[6].theta3 =  acos(angle[6].costh3)-M_PI;
        thetacomp(angle[6], p_m, pose);
        angle[7].theta3 =  -acos(angle[7].costh3)+M_PI;
        thetacomp(angle[7], p_m, pose);

        for( ::std::vector<angles_calc>::iterator iter = angle.begin(); iter != angle.end(); /* do iter forward in body */ ) {
                if( pow2(iter->costh3) <= 1.0) {
                        if(!angledef(*iter))
                                iter = angle.erase(iter);
                        else
                                ++iter;
                        continue;
                }
                iter = angle.erase(iter);
        }


        if(angle.size() == 0) {
                throw NoSolutionException();
        }

        ::std::vector< ::std::vector<int> > PossibleTargetsInEncoders;
        for( ::std::vector<angles_calc>::iterator i = angle.begin(); i != angle.end(); ++i ) {
                ::std::vector<int> solution(6);

                solution[0] = rad2enc(i->theta1, _parameters[0].angleOffset, _parameters[0].epc, _parameters[0].encOffset, _parameters[0].rotDir);
                solution[1] = rad2enc(i->theta2, _parameters[1].angleOffset, _parameters[1].epc, _parameters[1].encOffset, _parameters[1].rotDir);
                solution[2] = rad2enc(i->theta3, _parameters[2].angleOffset, _parameters[2].epc, _parameters[2].encOffset, _parameters[2].rotDir);
                solution[3] = rad2enc(i->theta4, _parameters[3].angleOffset, _parameters[3].epc, _parameters[3].encOffset, _parameters[3].rotDir);
                solution[4] = rad2enc(i->theta5, _parameters[4].angleOffset, _parameters[4].epc, _parameters[4].encOffset, _parameters[4].rotDir);
                solution[5] = rad2enc(i->theta6, _parameters[5].angleOffset, _parameters[5].epc, _parameters[5].encOffset, _parameters[5].rotDir);
                PossibleTargetsInEncoders.push_back(solution);
        }


        ::std::vector< ::std::vector<int> >::const_iterator sol = KinematicsDefaultEncMinAlgorithm()(PossibleTargetsInEncoders.begin(), PossibleTargetsInEncoders.end(), current_encoders.begin(), current_encoders.end());

        assert( sol != PossibleTargetsInEncoders.end() && "All solutions are out of range");


        encoders::iterator gripper_encoder_iter = std::copy( (*sol).begin(), (*sol).end(), solution );

}



} // NAMESPACE: KNI