frames.cpp

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/***************************************************************************
                        frames.cxx -  description
                       -------------------------
    begin                : June 2006
    copyright            : (C) 2006 Erwin Aertbelien
    email                : firstname.lastname@mech.kuleuven.ac.be

 History (only major changes)( AUTHOR-Description ) :

 ***************************************************************************
 *   This library is free software; you can redistribute it and/or         *
 *   modify it under the terms of the GNU Lesser General Public            *
 *   License as published by the Free Software Foundation; either          *
 *   version 2.1 of the License, or (at your option) any later version.    *
 *                                                                         *
 *   This library is distributed in the hope that it will be useful,       *
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU     *
 *   Lesser General Public License for more details.                       *
 *                                                                         *
 *   You should have received a copy of the GNU Lesser General Public      *
 *   License along with this library; if not, write to the Free Software   *
 *   Foundation, Inc., 51 Franklin Street,                                    *
 *   Fifth Floor, Boston, MA 02110-1301, USA.                               *
 *                                                                         *
 ***************************************************************************/

#include "frames.hpp"

namespace KDL {

#ifndef KDL_INLINE
#include "frames.inl"
#endif

void Frame::Make4x4(double * d)
{
    int i;
    int j;
    for (i=0;i<3;i++) {
        for (j=0;j<3;j++)
            d[i*4+j]=M(i,j);
        d[i*4+3] = p(i)/1000;
    }
    for (j=0;j<3;j++)
        d[12+j] = 0.;
    d[15] = 1;
}

Frame Frame::DH_Craig1989(double a,double alpha,double d,double theta)
// returns Modified Denavit-Hartenberg parameters (According to Craig)
{
    double ct,st,ca,sa;
    ct = cos(theta);
    st = sin(theta);
    sa = sin(alpha);
    ca = cos(alpha);
    return Frame(Rotation(
                    ct,       -st,     0,
                    st*ca,  ct*ca,   -sa,
                    st*sa,  ct*sa,    ca   ),
                 Vector(
                    a,      -sa*d,  ca*d   )
            );
}

Frame Frame::DH(double a,double alpha,double d,double theta)
// returns Denavit-Hartenberg parameters (Non-Modified DH)
{
    double ct,st,ca,sa;
    ct = cos(theta);
    st = sin(theta);
    sa = sin(alpha);
    ca = cos(alpha);
    return Frame(Rotation(
                    ct,    -st*ca,   st*sa,
                    st,     ct*ca,  -ct*sa,
                     0,        sa,      ca   ),
                 Vector(
                    a*ct,      a*st,  d   )
            );
}

double Vector2::Norm() const
{
    double tmp0 = fabs(data[0]);
    double tmp1 = fabs(data[1]);
    if (tmp0 >= tmp1) {
        if (tmp1 == 0)
            return 0;
        return tmp0*sqrt(1+sqr(tmp1/tmp0));
    } else {
        return tmp1*sqrt(1+sqr(tmp0/tmp1));
    }
}
// makes v a unitvector and returns the norm of v.
// if v is smaller than eps, Vector(1,0,0) is returned with norm 0.
// if this is not good, check the return value of this method.
double Vector2::Normalize(double eps) {
    double v = this->Norm();
    if (v < eps) {
        *this = Vector2(1,0);
        return v;
    } else {
        *this = (*this)/v;
        return v;
    }
}


// do some effort not to lose precision
double Vector::Norm() const
{
    double tmp1;
    double tmp2;
    tmp1 = fabs(data[0]);
    tmp2 = fabs(data[1]);
    if (tmp1 >= tmp2) {
        tmp2=fabs(data[2]);
        if (tmp1 >= tmp2) {
            if (tmp1 == 0) {
                // only to everything exactly zero case, all other are handled correctly
                return 0;
            }
            return tmp1*sqrt(1+sqr(data[1]/data[0])+sqr(data[2]/data[0]));
        } else {
            return tmp2*sqrt(1+sqr(data[0]/data[2])+sqr(data[1]/data[2]));
        }
    } else {
        tmp1=fabs(data[2]);
        if (tmp2 > tmp1) {
            return tmp2*sqrt(1+sqr(data[0]/data[1])+sqr(data[2]/data[1]));
        } else {
            return tmp1*sqrt(1+sqr(data[0]/data[2])+sqr(data[1]/data[2]));
        }
    }
}

// makes v a unitvector and returns the norm of v.
// if v is smaller than eps, Vector(1,0,0) is returned with norm 0.
// if this is not good, check the return value of this method.
double Vector::Normalize(double eps) {
    double v = this->Norm();
    if (v < eps) {
        *this = Vector(1,0,0);
        return v;
    } else {
        *this = (*this)/v;
        return v;
    }
}


bool Equal(const Rotation& a,const Rotation& b,double eps) {
    return (Equal(a.data[0],b.data[0],eps) &&
            Equal(a.data[1],b.data[1],eps) &&
            Equal(a.data[2],b.data[2],eps) &&
            Equal(a.data[3],b.data[3],eps) &&
            Equal(a.data[4],b.data[4],eps) &&
            Equal(a.data[5],b.data[5],eps) &&
            Equal(a.data[6],b.data[6],eps) &&
            Equal(a.data[7],b.data[7],eps) &&
            Equal(a.data[8],b.data[8],eps)    );
}

void Rotation::Ortho()
{
    double n;
    n=sqrt(sqr(data[0])+sqr(data[3])+sqr(data[6]));n=(n>1e-10)?1.0/n:0.0;data[0]*=n;data[3]*=n;data[6]*=n; 
    n=sqrt(sqr(data[1])+sqr(data[4])+sqr(data[7]));n=(n>1e-10)?1.0/n:0.0;data[1]*=n;data[4]*=n;data[7]*=n; 
    n=sqrt(sqr(data[2])+sqr(data[5])+sqr(data[8]));n=(n>1e-10)?1.0/n:0.0;data[2]*=n;data[5]*=n;data[8]*=n; 
}

Rotation operator *(const Rotation& lhs,const Rotation& rhs)
// Complexity : 27M+27A
{
    return Rotation(
        lhs.data[0]*rhs.data[0]+lhs.data[1]*rhs.data[3]+lhs.data[2]*rhs.data[6],
        lhs.data[0]*rhs.data[1]+lhs.data[1]*rhs.data[4]+lhs.data[2]*rhs.data[7],
        lhs.data[0]*rhs.data[2]+lhs.data[1]*rhs.data[5]+lhs.data[2]*rhs.data[8],
        lhs.data[3]*rhs.data[0]+lhs.data[4]*rhs.data[3]+lhs.data[5]*rhs.data[6],
        lhs.data[3]*rhs.data[1]+lhs.data[4]*rhs.data[4]+lhs.data[5]*rhs.data[7],
        lhs.data[3]*rhs.data[2]+lhs.data[4]*rhs.data[5]+lhs.data[5]*rhs.data[8],
        lhs.data[6]*rhs.data[0]+lhs.data[7]*rhs.data[3]+lhs.data[8]*rhs.data[6],
        lhs.data[6]*rhs.data[1]+lhs.data[7]*rhs.data[4]+lhs.data[8]*rhs.data[7],
        lhs.data[6]*rhs.data[2]+lhs.data[7]*rhs.data[5]+lhs.data[8]*rhs.data[8]
    );

}


Rotation Rotation::RPY(double roll,double pitch,double yaw)
    {
        double ca1,cb1,cc1,sa1,sb1,sc1;
        ca1 = cos(yaw); sa1 = sin(yaw);
        cb1 = cos(pitch);sb1 = sin(pitch);
        cc1 = cos(roll);sc1 = sin(roll);
        return Rotation(ca1*cb1,ca1*sb1*sc1 - sa1*cc1,ca1*sb1*cc1 + sa1*sc1,
                   sa1*cb1,sa1*sb1*sc1 + ca1*cc1,sa1*sb1*cc1 - ca1*sc1,
                   -sb1,cb1*sc1,cb1*cc1);
    }

// Gives back a rotation matrix specified with RPY convention
void Rotation::GetRPY(double& roll,double& pitch,double& yaw) const
    {
        if (fabs(data[6]) > 1.0 - epsilon ) {
            roll = -sign(data[6]) * atan2(data[1], data[4]);
            pitch= -sign(data[6]) * PI / 2;
            yaw  = 0.0 ;
        } else {
            roll  = atan2(data[7], data[8]);
            pitch = atan2(-data[6], sqrt( sqr(data[0]) +sqr(data[3]) )  );
            yaw   = atan2(data[3], data[0]);
        }
    }

Rotation Rotation::EulerZYZ(double Alfa,double Beta,double Gamma) {
        double sa,ca,sb,cb,sg,cg;
        sa  = sin(Alfa);ca = cos(Alfa);
        sb  = sin(Beta);cb = cos(Beta);
        sg  = sin(Gamma);cg = cos(Gamma);
        return Rotation( ca*cb*cg-sa*sg,     -ca*cb*sg-sa*cg,        ca*sb,
                 sa*cb*cg+ca*sg,     -sa*cb*sg+ca*cg,        sa*sb,
                 -sb*cg ,                sb*sg,              cb
                );

     }


void Rotation::GetEulerZYZ(double& alfa,double& beta,double& gamma) const {
        if (fabs(data[6]) < epsilon ) {
            alfa=0.0;
            if (data[8]>0) {
                beta = 0.0;
                gamma= atan2(-data[1],data[0]);
            } else {
                beta = PI;
                gamma= atan2(data[1],-data[0]);
            }
        } else {
            alfa=atan2(data[5], data[2]);
            beta=atan2(sqrt( sqr(data[6]) +sqr(data[7]) ),data[8]);
            gamma=atan2(data[7], -data[6]);
        }
 }

Rotation Rotation::Rot(const Vector& rotaxis,double angle) {
    // The formula is
    // V.(V.tr) + st*[V x] + ct*(I-V.(V.tr))
    // can be found by multiplying it with an arbitrary vector p
    // and noting that this vector is rotated.
    double ct = cos(angle);
    double st = sin(angle);
    double vt = 1-ct;
    Vector rotvec = rotaxis;
    rotvec.Normalize();
    return Rotation(
        ct            +  vt*rotvec(0)*rotvec(0),
        -rotvec(2)*st +  vt*rotvec(0)*rotvec(1),
        rotvec(1)*st  +  vt*rotvec(0)*rotvec(2),
        rotvec(2)*st  +  vt*rotvec(1)*rotvec(0),
        ct            +  vt*rotvec(1)*rotvec(1),
        -rotvec(0)*st +  vt*rotvec(1)*rotvec(2),
        -rotvec(1)*st +  vt*rotvec(2)*rotvec(0),
        rotvec(0)*st  +  vt*rotvec(2)*rotvec(1),
        ct            +  vt*rotvec(2)*rotvec(2)
        );
    }

Rotation Rotation::Rot2(const Vector& rotvec,double angle) {
    // rotvec should be normalized !
    // The formula is
    // V.(V.tr) + st*[V x] + ct*(I-V.(V.tr))
    // can be found by multiplying it with an arbitrary vector p
    // and noting that this vector is rotated.
    double ct = cos(angle);
    double st = sin(angle);
    double vt = 1-ct;
    return Rotation(
        ct            +  vt*rotvec(0)*rotvec(0),
        -rotvec(2)*st +  vt*rotvec(0)*rotvec(1),
        rotvec(1)*st  +  vt*rotvec(0)*rotvec(2),
        rotvec(2)*st  +  vt*rotvec(1)*rotvec(0),
        ct            +  vt*rotvec(1)*rotvec(1),
        -rotvec(0)*st +  vt*rotvec(1)*rotvec(2),
        -rotvec(1)*st +  vt*rotvec(2)*rotvec(0),
        rotvec(0)*st  +  vt*rotvec(2)*rotvec(1),
        ct            +  vt*rotvec(2)*rotvec(2)
        );
}



Vector Rotation::GetRot() const
         // Returns a vector with the direction of the equiv. axis
         // and its norm is angle
     {
       Vector axis  = Vector((data[7]-data[5]),
                 (data[2]-data[6]),
                 (data[3]-data[1]) )/2;

       double sa    = axis.Norm();
       double ca    = (data[0]+data[4]+data[8]-1)/2.0;
       double alfa;
       if (sa > epsilon)
           alfa = ::atan2(sa,ca)/sa;
       else {
           if (ca < 0.0) {
               alfa = KDL::PI;
               axis.data[0] = 0.0;
               axis.data[1] = 0.0;
               axis.data[2] = 0.0;
               if (data[0] > 0.0) {
                   axis.data[0] = 1.0;
               } else if (data[4] > 0.0) {
                   axis.data[1] = 1.0;
               } else {
                   axis.data[2] = 1.0;
               }
           } else {
               alfa = 0.0;
           }
       }
       return axis * alfa;
     }

Vector2 Rotation::GetXZRot() const
{
    // [0,1,0] x Y
    Vector2 axis(data[7], -data[1]);
    double norm = axis.Normalize();
    if (norm < epsilon) {
        norm = (data[4] < 0.0) ? PI : 0.0;
    } else {
        norm = acos(data[4]);
    }
    return axis*norm;
}


double Rotation::GetRotAngle(Vector& axis,double eps) const {
    double ca    = (data[0]+data[4]+data[8]-1)/2.0;
    if (ca>1-eps) {
        // undefined choose the Z-axis, and angle 0
        axis = Vector(0,0,1);
        return 0;
    }
    if (ca < -1+eps) {
        // two solutions, choose a positive Z-component of the axis
        double z = sqrt( (data[8]+1)/2 );
        double x = (data[2])/2/z;
        double y = (data[5])/2/z;
        axis = Vector( x,y,z  );
        return PI;
    }
    double angle = acos(ca);
    double sa    = sin(angle);
    axis  = Vector((data[7]-data[5])/2/sa,
                       (data[2]-data[6])/2/sa,
                       (data[3]-data[1])/2/sa  );
    return angle;
}

bool operator==(const Rotation& a,const Rotation& b) {
#ifdef KDL_USE_EQUAL
    return Equal(a,b);
#else
    return ( a.data[0]==b.data[0] &&
             a.data[1]==b.data[1] &&
             a.data[2]==b.data[2] &&
             a.data[3]==b.data[3] &&
             a.data[4]==b.data[4] &&
             a.data[5]==b.data[5] &&
             a.data[6]==b.data[6] &&
             a.data[7]==b.data[7] &&
             a.data[8]==b.data[8]  );
#endif
}
}