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interpolate.cc
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interpolate.cc
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/*
* @Author: your name
* @Date: 2023-08-12 20:17:37
* @LastEditTime: 2023-08-12 20:17:37
* @LastEditors: LAPTOP-GLMMQRJB
* @Description: In User Settings Edit
* @FilePath: \UR_RTDE_Dynamics\interpolate.cc
*/
#include "interpolate.h"
namespace rocos
{
double PULSE::pos( double time )
{
double ret = 0;
int n = time / _cycle; // 第几个周期
double m = time - n * _cycle; // 减去正周期整数倍的剩余时间
switch ( _type )
{
case VEL: // 速度方波，则位移三角波
if ( m > _cycle * _ratio ) // 剩余时间超过半个周期
{
ret = n * ( _amp * ( _cycle * ( 2.0 * _ratio - 1.0 ) ) ) + _amp * ( _cycle * _ratio ) -
_amp * ( m - _cycle * _ratio );
}
else
{
ret = n * ( _amp * ( _cycle * ( _ratio * 2.0 - 1.0 ) ) ) + _amp * m;
}
return ret;
break;
case ACC: // 加速度方波,速度是三角波，位移是递增
double v0 = 0;
for ( int i = 0; i < n; i++ )
{
double t = _cycle * _ratio;
ret = ret + v0 * t + 0.5 * _amp * t * t;
v0 = v0 + _amp * t;
t = _cycle - _cycle * _ratio;
ret = ret + v0 * t - 0.5 * _amp * t * t;
v0 = v0 - _amp * t;
}
if ( m > _cycle * _ratio )
{
ret = ret + v0 * _cycle * _ratio + 0.5 * _amp * ( _cycle * _ratio ) * ( _cycle * _ratio );
v0 = v0 + _amp * ( _cycle * _ratio );
ret = ret + v0 * ( _cycle * ( m - _cycle * _ratio ) ) -
0.5 * _amp * ( _cycle * ( m - _cycle * _ratio ) ) * ( _cycle * ( m - _cycle * _ratio ) );
v0 = v0 - _amp * ( _cycle * ( m - _cycle * _ratio ) );
}
else
{
ret = ret + v0 * ( _cycle * m ) + 0.5 * _amp * ( m ) * ( m );
}
return ret;
break;
}
return ret;
}
double PULSE::vel( double time )
{
double ret = 0;
int n = time / _cycle; // 第几个周期
double m = time - n * _cycle; // 减去正周期整数倍的剩余时间
switch ( _type )
{
case VEL:
if ( m > _cycle * _ratio )
{
return -_amp;
}
else
{
return _amp;
}
break;
case ACC:
PULSE temp( VEL, _cycle, _ratio, _amp );
return temp.pos( time );
return ret;
break;
}
return ret;
}
// 通用插补
#pragma region universel
bool R_INTERP::planProfile( )
{
if ( _pTarget == _pStart )
{
printf( "please input valid target!\n" );
}
if ( _v_limit == 0.0 || _a_limit == 0.0 )
{
printf( "please input valid velocity or acceleration limit!\n" );
}
//TODO 改动二：new->std::make_shared
switch ( _pType )
{
case trapezoid:
if ( _trapezoid == nullptr )
{
_trapezoid = std::make_shared< Trapezoid >( );
}
_pCurProfileType = _trapezoid;
_trapezoid->planTrapezoidProfile( _tStart, _pStart, _pTarget, _vStart, _vTarget, _v_limit, _a_limit );
break;
case doubleS:
if ( _doubleS == nullptr )
{
_doubleS = std::make_shared< DoubleS >( );
}
_pCurProfileType = _doubleS;
_doubleS->planDoubleSProfile( _tStart, _pStart, _pTarget, _vStart, _vTarget, _v_limit, _a_limit,
_j_limit );
break;
case polynomial_3rd_T:
if ( _tTerminal == 0 || _tTerminal <= _tStart )
{
printf( "please input valid terminal time!\n" );
}
if ( _polynomial == nullptr )
{
_polynomial = std::make_shared< Polynomial >( );
}
_pCurProfileType = _polynomial;
_polynomial->plan3rdProfileT( _tStart, _tTerminal, _pStart, _pTarget, _vStart, _vTarget );
break;
case polynomial_5th_T:
if ( _tTerminal == 0 || _tTerminal <= _tStart )
{
printf( "please input valid terminal time!\n" );
}
if ( _polynomial == nullptr )
{
_polynomial = std::make_shared< Polynomial >( );
}
_pCurProfileType = _polynomial;
_polynomial->plan5thProfileT( _tStart, _tTerminal, _pStart, _pTarget, _vStart, _vTarget, _aStart,
_aTarget );
break;
case harmonic_T:
if ( _tTerminal == 0 || _tTerminal <= _tStart )
{
printf( "please input valid terminal time!\n" );
}
if ( _trigonometric == nullptr )
{
_trigonometric = std::make_shared< Trigonometric >( );
}
_pCurProfileType = _trigonometric;
_trigonometric->planHarmonicProfileT( _pStart, _pTarget, _tStart, _tTerminal );
break;
case cycloidal_T:
if ( _tTerminal == 0 || _tTerminal <= _tStart )
{
printf( "please input valid terminal time!\n" );
}
if ( _trigonometric == nullptr )
{
_trigonometric = std::make_shared< Trigonometric >( );
}
_pCurProfileType = _trigonometric;
_trigonometric->planCycloidalProfileT( _pStart, _pTarget, _tStart, _tTerminal );
break;
case elliptic_T:
if ( _tTerminal == 0 || _tTerminal <= _tStart )
{
printf( "please input valid terminal time!\n" );
}
if ( _trigonometric == nullptr )
{
_trigonometric = std::make_shared< Trigonometric >( );
}
_pCurProfileType = _trigonometric;
_trigonometric->planEllipticProfileT( _pStart, _pTarget, _tStart, _tTerminal, 1.5 );
break;
case unDefine:
_pType = doubleS;
planProfile( );
if ( !_pCurProfileType->isValidMovement( ) )
{
_pType = trapezoid;
planProfile( );
}
break;
}
return isValidMovement( );
}
bool R_INTERP::planDoubleSPorfile( double t0, double p0, double pf,
double v0, double vf, double v_limit, double a_limit, double j_limit )
{
setStartTime( t0 );
setStart( p0, v0 );
setTarget( pf, vf );
setLimit( v_limit, a_limit, j_limit );
if ( _doubleS == nullptr )
{
//TODO 改动三:new ->std::make_shared
_doubleS = std::make_shared< DoubleS >( );
}
_pCurProfileType = _doubleS;
_doubleS->planDoubleSProfile( t0, p0, pf, v0, vf, v_limit, a_limit, j_limit );
return _doubleS->isValidMovement( );
}
bool R_INTERP::planTrapezoidProfile( double t0, double p0, double pf,
double v0, double vf, double v_limit, double a_limit )
{
setStart( p0, v0 );
setTarget( pf, vf );
setStartTime( t0 );
setLimit( v_limit, a_limit );
if ( _trapezoid == nullptr )
{ //TODO 改动四:new ->std::make_shared
_trapezoid = std::make_shared< Trapezoid >( );
}
_pCurProfileType = _trapezoid;
_trapezoid->planTrapezoidProfile( t0, p0, pf, v0, vf, v_limit, a_limit );
return _trapezoid->isValidMovement( );
}
bool R_INTERP::plan3rdProfileT( double t0, double tf, double p0,
double pf, double v0, double vf )
{
setStartTime( t0 );
setTargetTime( tf );
setStart( p0, v0 );
setTarget( pf, vf );
if ( _polynomial == nullptr )
{ //TODO 改动5:new ->std::make_shared
_polynomial = std::make_shared< Polynomial >( );
}
_pCurProfileType = _polynomial;
_polynomial->plan3rdProfileT( t0, tf, p0, pf, v0, vf );
return _polynomial->isValidMovement( );
}
bool R_INTERP::plan5thProfileT( double t0, double tf, double p0,
double pf, double v0, double vf, double a0, double af )
{
setStartTime( t0 );
setTargetTime( tf );
setStart( p0, v0, a0 );
setTarget( pf, vf, af );
if ( _polynomial == nullptr )
{ //TODO 改动6:new ->std::make_shared
_polynomial = std::make_shared< Polynomial >( );
}
_pCurProfileType = _polynomial;
_polynomial->plan5thProfileT( t0, tf, p0, pf, v0, vf, a0, af );
return _polynomial->isValidMovement( );
}
#pragma endregion universel
// T型波
#pragma region TRAPEZOID
void Trapezoid::planProfile( double t0, double p0, double pf, double v0, double vf, double v_limit, double a_limit,
double j_limit )
{
planTrapezoidProfile( t0, p0, pf, v0, vf, v_limit, a_limit );
}
void Trapezoid::planTrapezoidProfile( double t0, double p0, double pf,
double v0, double vf, double v_limit, double a_limit )
{
_plannedProfile = false;
_direction = sign( pf - p0 );
if ( _direction == 0 )
{
// std::cerr<<("target and start points are the same!\n");
return;
}
double p0_z = _direction * p0;
double pf_z = _direction * pf;
double v0_z = _direction * v0;
double vf_z = _direction * vf;
double vmax = fabs( v_limit );
double amax = fabs( a_limit );
double vmin = -vmax;
double amin = -amax;
double v_limit_z = ( _direction + 1.0 ) / 2.0 * vmax + ( _direction - 1.0 ) / 2.0 * vmin;
double a_limit_z = ( _direction + 1.0 ) / 2.0 * amax + ( _direction - 1.0 ) / 2.0 * amin;
trapezoid_check_T( t0, p0_z, pf_z, v0_z, vf_z, v_limit_z, a_limit_z );
}
void Trapezoid::trapezoid_check_T( double t0, double p0, double pf,
double v0, double vf, double v_limit, double a_limit )
{
// the 'trapezoid' profile trajectory looks like :
//
// v | _________
// | / \
// |/ \
// | \
// | |
// 0-1--------2---3--> t
// let Ta Tv Td be the acceleration cursing and deceleration time interval
// so, pf - p0 = v0*Ta +0.5*_a[1]*Ta*Ta + _v[1]*Tv + vf*Td - 0.5*_a[3]*Td*Td
// Ta = (_v[1] - _v[0])/_a[1]; // here, _a[1],acceleration, bigger than zero
// Td = (_v[3] - _v[2])/_a[3]; // here, _a[3],deceleration, samller than zero,
// Tv = ((pf-p0) - (_v[0]*Ta + 0.5*_a[1]*Ta*Ta) - (_v[3]*Td - 0.5*_a[3]*Td*Td))/_v[1];
_t[ 0 ] = t0; // start time
_x[ 0 ] = p0;
_x[ 3 ] = pf;
_v[ 0 ] = v0;
_v[ 3 ] = vf;
_a[ 0 ] = 0;
_a[ 2 ] = 0;
double amax = a_limit; // a_limit: acceleration in phase #1;
_a[ 1 ] = a_limit; // plan the trajectory with the limited acceleration
double amin = -a_limit; //amin: acceleration in phase #3, be deceleration.
_a[ 3 ] = amin; // by default, deceleration equals to minus acceleration
// it is necessary to check whether the trajectory is feasible or not by
if ( a_limit * ( pf - p0 ) < fabs( v0 * v0 - vf * vf ) / 2.0 )
{
std::cerr << ( "trapezoid trajectory is not feasible\n" );
_plannedProfile = false;
return;
}
else
{
double Ta, Tv, Td;
if ( ( pf - p0 ) * a_limit > v_limit * v_limit - ( v0 * v0 + vf * vf ) / 2.0 )
{
// Case 1: _v[1] = v_limit
_v[ 1 ] = v_limit;
}
else
{
// Case 2: _v[1] < v_limit
_v[ 1 ] = sqrt( ( pf - p0 ) * a_limit + ( v0 * v0 + vf * vf ) / 2.0 );
}
_v[ 2 ] = _v[ 1 ];
Ta = ( _v[ 1 ] - _v[ 0 ] ) / _a[ 1 ];
Td = ( _v[ 3 ] - _v[ 2 ] ) / _a[ 3 ];
Tv = ( ( pf - p0 ) - ( _v[ 0 ] * Ta + 0.5 * _a[ 1 ] * Ta * Ta ) - ( _v[ 3 ] * Td - 0.5 * _a[ 3 ] * Td * Td ) ) / _v[ 1 ];
_t[ 1 ] = _t[ 0 ] + Ta;
_t[ 2 ] = _t[ 1 ] + Tv;
_t[ 3 ] = _t[ 2 ] + Td;
_x[ 1 ] = _x[ 0 ] + _v[ 0 ] * Ta / 2.0 + _v[ 1 ] * ( Ta - Ta / 2.0 );
_x[ 2 ] = _x[ 0 ] + _v[ 0 ] * Ta / 2.0 + _v[ 1 ] * ( Tv - Ta / 2.0 );
}
_plannedProfile = true;
}
double Trapezoid::scaleToDuration( double newDuration )
{
if ( newDuration < ( _t[ 3 ] - _t[ 0 ] ) )
{
// std::cerr<<("New duration must be longer!\n");
return _t[ 3 ] - _t[ 0 ];
}
double p0 = _x[ 0 ];
double pf = _x[ 3 ];
double v0 = _v[ 0 ];
double vf = _v[ 3 ];
double h = pf - p0;
double T = _t[ 3 ] - _t[ 0 ];
double Ta = _t[ 1 ] - _t[ 0 ];
double Tv = _t[ 2 ] - _t[ 1 ];
double Td = _t[ 3 ] - _t[ 2 ];
Ta = Ta * newDuration / T;
Tv = Tv * newDuration / T;
Td = Td * newDuration / T;
// 3 equations to get new _v[1] _a[1] and _a[3]
// Ta = (_v[1] - v0)/_a[1];
// Tv = ((pf-p0) - (_v[0]*Ta + 0.5*_a[1]*Ta*Ta) - (_v[3]*Td - 0.5*_a[3]*Td*Td))/_v[1];
// Td = (_v[3] - _v[1])/_a[3];
_a[ 1 ] = -( 1.0 * ( 2.0 * p0 - 2.0 * pf + 2.0 * Ta * v0 + Td * v0 + 2.0 * Tv * v0 + Td * vf ) ) /
( Ta * ( Ta + Td + 2.0 * Tv ) );
_a[ 3 ] = ( 2.0 * p0 - 2.0 * pf + Ta * v0 + Ta * vf + 2.0 * Td * vf + 2.0 * Tv * vf ) / ( Td * ( Ta + Td + 2.0 * Tv ) );
_v[ 1 ] = -( 1.0 * ( 2.0 * p0 - 2.0 * pf + Ta * v0 + Td * vf ) ) / ( Ta + Td + 2.0 * Tv );
_v[ 2 ] = _v[ 1 ];
Ta = ( _v[ 1 ] - _v[ 0 ] ) / _a[ 1 ];
Td = ( _v[ 3 ] - _v[ 2 ] ) / _a[ 3 ];
Tv = ( ( pf - p0 ) - ( _v[ 0 ] * Ta + 0.5 * _a[ 1 ] * Ta * Ta ) - ( _v[ 3 ] * Td - 0.5 * _a[ 3 ] * Td * Td ) ) / _v[ 1 ];
_t[ 1 ] = _t[ 0 ] + Ta;
_t[ 2 ] = _t[ 1 ] + Tv;
_t[ 3 ] = _t[ 2 ] + Td;
_x[ 1 ] = _x[ 0 ] + _v[ 0 ] * Ta / 2.0 + _v[ 1 ] * ( Ta - Ta / 2.0 );
_x[ 2 ] = _x[ 0 ] + _v[ 0 ] * Ta / 2.0 + _v[ 1 ] * ( Tv - Ta / 2.0 );
return getDuration( );
}
bool Trapezoid::isValidMovement( ) const
{
return _plannedProfile;
}
double Trapezoid::getDuration( ) const
{
return ( _t[ 3 ] - _t[ 0 ] );
}
double Trapezoid::pos( double t ) const
{
double p;
double dt = ( t - _t[ 0 ] );
double ta = _t[ 1 ] - _t[ 0 ];
double tv = _t[ 2 ] - _t[ 1 ];
double td = _t[ 3 ] - _t[ 2 ];
double T = _t[ 3 ] - _t[ 0 ];
if ( dt < 0 )
{
p = _x[ 0 ];
}
if ( dt < ta && dt >= 0 )
{
p = _x[ 0 ] + _v[ 0 ] * dt + ( _v[ 1 ] - _v[ 0 ] ) / 2.0 / ta * dt * dt;
}
if ( ta <= dt && dt < ta + tv )
{
p = _x[ 0 ] + _v[ 0 ] * ta / 2.0 + _v[ 1 ] * ( dt - ta / 2.0 );
}
if ( ta + tv <= dt && dt < T )
{
p = _x[ 3 ] - _v[ 3 ] * ( T - dt ) - ( _v[ 2 ] - _v[ 3 ] ) / 2.0 / td * ( T - dt ) * ( T - dt );
}
if ( dt >= T )
{
dt = T;
p = _x[ 3 ] - _v[ 3 ] * ( T - dt ) - ( _v[ 2 ] - _v[ 3 ] ) / 2.0 / td * ( T - dt ) * ( T - dt );
}
p = p * _direction;
return p;
}
double Trapezoid::vel( double t ) const
{
double v;
double dt = ( t - _t[ 0 ] );
double ta = _t[ 1 ] - _t[ 0 ];
double tv = _t[ 2 ] - _t[ 1 ];
double td = _t[ 3 ] - _t[ 2 ];
double T = _t[ 3 ] - _t[ 0 ];
if ( dt < 0 )
{
v = _v[ 0 ];
}
if ( dt < ta && dt >= 0 )
{
v = _v[ 0 ] + ( _v[ 1 ] - _v[ 0 ] ) / ta * dt;
}
if ( ta <= dt && dt < ta + tv )
{
v = _v[ 1 ];
}
if ( ta + tv <= dt && dt < T )
{
v = _v[ 3 ] + ( _v[ 2 ] - _v[ 3 ] ) / td * ( T - dt );
}
if ( dt >= T )
{
dt = T;
v = _v[ 3 ] + ( _v[ 2 ] - _v[ 3 ] ) / td * ( T - dt );
}
v = v * _direction;
return v;
}
double Trapezoid::acc( double t ) const
{
double a;
double dt = ( t - _t[ 0 ] );
double ta = _t[ 1 ] - _t[ 0 ];
double tv = _t[ 2 ] - _t[ 1 ];
double td = _t[ 3 ] - _t[ 2 ];
double T = _t[ 3 ] - _t[ 0 ];
if ( dt < 0 )
{
a = 0.0;
}
if ( dt < ta && dt >= 0 )
{
a = _a[ 1 ];
}
if ( ta <= dt && dt < ta + tv )
{
a = _a[ 2 ];
}
if ( ta + tv <= dt && dt < T )
{
a = _a[ 3 ];
}
if ( dt >= T )
{
a = 0.0;
}
a = a * _direction;
return a;
}
double Trapezoid::jerk( double t ) const
{
return 0;
}
double Trapezoid::max_vel( ) const
{
double v = 0;
for ( int i = 0; i < 4; i++ )
{
v = fmax( fabs( v ), fabs( _v[ i ] ) );
}
for ( int i = 0; i < 4; i++ )
{
if ( v == fabs( _v[ i ] ) )
{
v = _v[ i ] * _direction;
}
}
return v;
}
double Trapezoid::max_acc( ) const
{
double a = 0;
for ( int i = 0; i < 4; i++ )
{
a = fmax( fabs( a ), fabs( _a[ i ] ) );
}
for ( int i = 0; i < 4; i++ )
{
if ( fabs( a ) == fabs( _a[ i ] ) )
{
a = _a[ i ] * _direction;
}
}
return a;
}
#pragma endregion TRAPEZOID
// S型波
#pragma region DOUBLES
void DoubleS::planProfile( double t0, double p0, double pf, double v0, double vf, double v_limit, double a_limit,
double j_limit )
{
planDoubleSProfile( t0, p0, pf, v0, vf, v_limit, a_limit, j_limit );
}
void DoubleS::planDoubleSProfile( double t0, double p0, double pf,
double v0, double vf, double v_limit, double a_limit, double j_limit )
{
_plannedProfile = false;
_direction = sign( pf - p0 );
if ( _direction == 0 )
{
_t[ 0 ] = t0;
_t[ 7 ] = t0;
std::cerr << ( "target and start points are the same!\n" );
return;
}
double p0_z = _direction * p0;
double pf_z = _direction * pf;
double v0_z = _direction * v0;
double vf_z = _direction * vf;
double vmax = fabs( v_limit );
double amax = fabs( a_limit );
double jmax = fabs( j_limit );
double vmin = -vmax;
double amin = -amax;
double jmin = -jmax;
double v_limit_z = ( _direction + 1.0 ) / 2.0 * vmax + ( _direction - 1.0 ) / 2.0 * vmin;
double a_limit_z = ( _direction + 1.0 ) / 2.0 * amax + ( _direction - 1.0 ) / 2.0 * amin;
double j_limit_z = ( _direction + 1.0 ) / 2.0 * jmax + ( _direction - 1.0 ) / 2.0 * jmin;
doubleS_check_T( t0, p0_z, pf_z, v0_z, vf_z, v_limit_z, a_limit_z, j_limit );
}
void DoubleS::doubleS_check_T( double t0, double p0, double pf,
double v0, double vf, double v_limit, double a_limit, double j_limit )
{
// the 'doubleS' has acceleration phase, cursing phase and deceleration phase
// in acceleration phase and deceleration phase, the acceleration has three phases:
// acc acceleration phase, acc cursing phase and acc deceleration phase
// a | _________
// | / \
// |/ \
// 0--1- -----2--3-------4--5------6--7-----------> t
// \ /
// \ /
// ---------
// the time interval between 0~1 is: Ta_acc
// the time interval between 1~2 is: Tv_acc
// the time interval between 2~3 is: Td_acc
// the time interval between 0~3 is: Ta
// the time interval between 3~4 is: Tv
// the time interval between 4~5 is: Ta_dec
// the time interval between 5~6 is: Tv_dec
// the time interval between 6~7 is: Td_dec
// the time interval between 4~7 is: Td
// by default, Td_acc = Ta_acc, and Ta_dec = Td_dec
_t[ 0 ] = t0; // start time
_x[ 0 ] = p0;
_x[ 7 ] = pf;
_v[ 0 ] = v0;
_v[ 7 ] = vf;
_a[ 0 ] = 0;
_a[ 4 ] = 0;
_a[ 3 ] = 0;
_a[ 7 ] = 0;
_j[ 0 ] = 0;
_j[ 2 ] = 0;
_j[ 4 ] = 0;
_j[ 6 ] = 0;
double r = 1; // scale factor for re-planning doubleS profile
// It is necessary to check if it is possible to perform the trajectory
// with a double jerk impulse(one positive and one negative) only.
// For this purpose, let us define
double Tjx = fmin( sqrt( fabs( vf - v0 ) / j_limit ), a_limit / j_limit );
if ( Tjx == a_limit / j_limit )
{
if ( pf - p0 <= 0.5 * ( v0 + vf ) * ( Tjx + fabs( vf - v0 ) / a_limit ) )
{
_plannedProfile = false;
std::cerr << ( "The two points are two close! DoubleS trajectory is not feasible!\n" );
return;
}
}
else
{
if ( pf - p0 <= Tjx * ( vf + v0 ) )
{
_plannedProfile = false;
std::cerr << ( "The two points are two close! DoubleS trajectory is not feasible!\n" );
return;
}
}
// In this case, by defining the maximum value of the velocity during
// the motion as vmax = max(v(t)), there are two possibilities:
// Case 1: vmax = v_limit
// Case 2: vmax < v_limit
// In both Case 1 and Case 2, it is possible that the limited
// acceleration(positive or negative) is not reached. This may happen if
// the displacement is small, if the limited allowed acceleration a_limit is high.
// Let us define:
// Ta: acceleration period;
// Tv: constant velocity period;
// Td: deceleration period;
// T: total duration of the trajectory (=Ta+Tv+Td);
// Ta_acc: acceleration increasing time-interval during acceleration peroid;
// Tv_acc: acceleration keep constant time-interval during acceleration period;
// Td_acc: acceleration decreasing time-interval during acceleration peroid;
// Ta_dec: deceleration increasing time-interval during deceleration peroid;
// Tv_dec: deceleration keep constant time-interval during decelration peroid;
// Td_dec: deceleration decreasing time-interval during deceleration period.
double Ta, Tv, Td, T, Ta_acc, Tv_acc, Td_acc, Ta_dec, Tv_dec, Td_dec;
double jmax_a, jmin_a, jmax_d, jmin_d, amax_a, amin_d, vmax;
// Case 1: vmax = v_limit
if ( ( v_limit - v0 ) * j_limit < a_limit * a_limit ) // acceleration phase
{
// a_limit is not reached
Ta_acc = sqrt( ( v_limit - v0 ) / j_limit );
Ta = 2 * Ta_acc;
}
else
{
// a_limit is reached
Ta_acc = a_limit / j_limit;
Ta = Ta_acc + ( v_limit - v0 ) / a_limit;
}
if ( ( v_limit - vf ) * j_limit < a_limit * a_limit ) // deceleration phase
{
// a_limit is not reached
Ta_dec = sqrt( ( v_limit - vf ) / j_limit );
Td = 2 * Ta_dec;
}
else
{
// a_limit is reached
Ta_dec = a_limit / j_limit;
Td = Ta_dec + ( v_limit - vf ) / a_limit;
}
// Finally, it is possible to determine the time duration of the
// constant velocity segments as
Tv = ( pf - p0 ) / v_limit - Ta / 2.0 * ( 1.0 + v0 / v_limit ) - Td / 2.0 * ( 1.0 + vf / v_limit );
if ( Tv <= 0 )
{
// Case 2: vmax < v_max
// In this case, the constant velocity segment is not present(Tv=0),
// and the duration of the acceleration and deceleration segments
// can be easily computed if the limited accelerations are reached
// in both segments. In this case
double temp = 0;
while ( 1 )
{
Ta_acc = a_limit / j_limit;
Ta_dec = a_limit / j_limit;
temp = ( a_limit * a_limit * a_limit * a_limit ) / ( j_limit * j_limit ) + 2.0 * ( v0 * v0 + vf * vf ) + a_limit * ( 4.0 * ( pf - p0 ) - 2.0 * a_limit / j_limit * ( v0 + vf ) );
Ta = ( ( a_limit * a_limit ) / j_limit - 2.0 * v0 + sqrt( temp ) ) / 2.0 / a_limit;
Td = ( ( a_limit * a_limit ) / j_limit - 2.0 * vf + sqrt( temp ) ) / 2.0 / a_limit;
Tv = 0;
// if Ta<2*Ta_acc or Td<2*Ta_dec, then the limited acceleration is
// not reached in at least one of the two segments, and therefore it
// is not possible to use above eq. In this case(indeed rather
// unusual), the determination of parameters is quite difficult, and
// it may be more convenient to find an approximated solution that,
// although not optimal, results acceptable from a computational
// point of view. A possible way to determine this solution is to
// progressively decrease the value of a_limit (e.g. by assuming
// a_limit=r*a_limit, with 0<r<1) and compute the duration of the
// segments by means of above eq. until the condition Ta>2*Ta_acc and
// Td>2*Ta_dec are both true.
if ( Ta < 0 || Td < 0 )
{
// During this recursive computation,it may happen that Ta
// or Td became negative. In this case, only one of the
// acceleration or deceleration phase is necessary,
// depending on the values of the initial and final
// velocities. If Ta<0 (note that in this case necessarily
// v0>v1), the acceleration phase is not present. Then, Ta
// is set to 0 and the duration of the deceleration segment
// can be computed according to
if ( Ta < 0 )
{
Td = 2 * ( pf - p0 ) / ( vf + v0 );
Ta_dec = ( j_limit * ( pf - p0 ) - sqrt( j_limit * ( j_limit * ( pf - p0 ) * ( pf - p0 ) +
( vf + v0 ) * ( vf + v0 ) * ( vf - v0 ) ) ) ) /
( j_limit * ( vf + v0 ) );
Ta = 0.0;
Ta_acc = 0.0;
break;
}
// In the dual case, i.e. when Td<0 (this case is possible
// when v1>v0), the deceleration phase is not necessary
// (Td=0) and the duration of the acceleration period must
// be computed as
if ( Td < 0 )
{
Ta = 2 * ( pf - p0 ) / ( vf + v0 );
Ta_acc = ( j_limit * ( pf - p0 ) - sqrt( j_limit * ( j_limit * ( pf - p0 ) * ( pf - p0 ) -
( vf + v0 ) * ( vf + v0 ) * ( vf - v0 ) ) ) ) /
( j_limit * ( vf + v0 ) );
Td = 0;
Ta_dec = 0;
break;
}
}
else
{
if ( ( Ta < 2 * Ta_acc ) || ( Td < 2 * Ta_dec ) )
{
r = r - 0.01;
a_limit = r * a_limit;
//std::cerr<<("DoubleS re-planning: Ta<2*Tj1 or Td<2*Tj2\n");
}
else
{
break;
}
}
}
}
amax_a = j_limit * Ta_acc;
amin_d = -j_limit * Ta_dec;
vmax = v0 + ( Ta - Ta_acc ) * amax_a;
jmax_a = j_limit;
jmin_a = -j_limit;
jmax_d = -j_limit;
jmin_d = j_limit;
Td_acc = Ta_acc;
Tv_acc = Ta - 2.0 * Ta_acc;
Td_dec = Ta_dec;
Tv_dec = Td - 2.0 * Ta_dec;
T = Ta + Tv + Td;
_j[ 1 ] = jmax_a;
_j[ 3 ] = jmin_a;
_j[ 5 ] = jmax_d;
_j[ 7 ] = jmin_d;
_t[ 0 ] = t0;
_t[ 1 ] = _t[ 0 ] + Ta_acc;
_t[ 2 ] = _t[ 1 ] + Tv_acc;
_t[ 3 ] = _t[ 2 ] + Td_acc;
_t[ 4 ] = _t[ 3 ] + Tv;
_t[ 5 ] = _t[ 4 ] + Ta_dec;
_t[ 6 ] = _t[ 5 ] + Tv_dec;
_t[ 7 ] = _t[ 6 ] + Td_dec;
_a[ 1 ] = amax_a;
_a[ 2 ] = amax_a;
_a[ 5 ] = amin_d;
_a[ 6 ] = amin_d;
_v[ 3 ] = vmax;
_v[ 4 ] = vmax;
_v[ 1 ] = vel( _t[ 1 ] );
_v[ 2 ] = vel( _t[ 2 ] );
_v[ 5 ] = vel( _t[ 5 ] );
_v[ 6 ] = vel( _t[ 6 ] );
_plannedProfile = true;
}
double DoubleS::scaleToDuration( double newDuration )
{
if ( newDuration <= ( _t[ 7 ] - _t[ 0 ] ) )
{
std::cerr << ( "New duration must be longer!\n" );
return _t[ 7 ] - _t[ 0 ];
}
double t0 = _t[ 0 ];
double p0 = _x[ 0 ];
double pf = _x[ 7 ];
double v0 = _v[ 0 ];
double vf = _v[ 7 ];
double j_limit = _j[ 1 ];
double Ta = _t[ 3 ] - _t[ 0 ];
double Tv = _t[ 4 ] - _t[ 3 ];
double Td = _t[ 7 ] - _t[ 4 ];
double T = _t[ 7 ] - _t[ 0 ];
Ta = Ta * newDuration / T;
Tv = Tv * newDuration / T;
Td = Td * newDuration / T;
// decrease the cursing velocity
double vmax = -( p0 - pf + ( Ta * v0 ) / 2 + ( Td * vf ) / 2 ) / ( Ta / 2 + Td / 2 + Tv );
double amax_a = _a[ 1 ];
// decrease jmax_a jmin_a jmax_d jmin_d and re-plan time interval
double Ta_acc, Ta_dec, jmax_a, jmax_d, amin_d;
if ( ( vmax - v0 ) * j_limit < amax_a * amax_a )
{
Ta_acc = 0.5 * Ta;
jmax_a = ( vmax - v0 ) / ( Ta_acc * Ta_acc );
}
else
{
Ta_acc = Ta - ( vmax - v0 ) / amax_a;
jmax_a = amax_a / Ta_acc;
}
if ( ( vmax - vf ) * j_limit < amax_a * amax_a )
{
Ta_dec = 0.5 * Td;
jmax_d = -( vmax - vf ) / ( Ta_dec * Ta_dec );
}
else
{
Ta_dec = Td - ( vmax - vf ) / amax_a;
jmax_d = -amax_a / Ta_dec;
}
amax_a = jmax_a * Ta_acc;
amin_d = jmax_d * Ta_dec;
vmax = v0 + ( Ta - Ta_acc ) * amax_a;
double tempTv = ( pf - p0 ) / vmax - Ta / 2.0 * ( 1.0 + v0 / vmax ) - Td / 2.0 * ( 1.0 + vf / vmax );
if ( tempTv < 0 || fabs( tempTv - Tv ) > 1e-4 )
{
std::cerr << ( "Re-plan to scale duration failed!\n" );
return getDuration( );
}
T = Ta + Tv + Td;
_j[ 1 ] = jmax_a;
_j[ 3 ] = -jmax_a;
_j[ 5 ] = jmax_d;
_j[ 7 ] = -jmax_d;
double Td_acc = Ta_acc;
double Tv_acc = Ta - 2.0 * Ta_acc;
double Td_dec = Ta_dec;
double Tv_dec = Td - 2.0 * Ta_dec;
_t[ 0 ] = t0;
_t[ 1 ] = _t[ 0 ] + Ta_acc;
_t[ 2 ] = _t[ 1 ] + Tv_acc;
_t[ 3 ] = _t[ 2 ] + Td_acc;
_t[ 4 ] = _t[ 3 ] + Tv;
_t[ 5 ] = _t[ 4 ] + Ta_dec;
_t[ 6 ] = _t[ 5 ] + Tv_dec;
_t[ 7 ] = _t[ 6 ] + Td_dec;
_a[ 1 ] = amax_a;
_a[ 2 ] = amax_a;
_a[ 5 ] = amin_d;
_a[ 6 ] = amin_d;