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velocity-profile.cpp
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velocity-profile.cpp
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#include "velocity-profile.hpp"
#include "constants.h"
#include <limits>
#include "arclength-param.hpp"
#include "splines.hpp"
using namespace std;
namespace VelocityProfiling {
// isolated constraints
// k: curvature ( = w/v), 1/cm
// vsat: max vl (or vr) in cm/s
// vwmax: max centripetal acceleration, cm/s^2
// return: vmax, cm/s
double vmax_isolated(double k, double vsat, double vwmax ) {
double res;
// saturation considering curvature
// remember, v is always positive, sign of k decides sign of w
if (k > 0) {
res = vsat/(1+Constants::d*k/2);
} else {
res = vsat/(1-Constants::d*k/2);
}
// centripetal acceleration constraint:
res = min(res, sqrt(vwmax/fabs(k)));
// add obstacle constraints later on if needed
return res;
}
typedef pair<double, double> Interval;
// acceleration constraints
// translational acceleration constraint
// atmax: max translational acceleration, +ve, cm/s^2
// dels: distance between this and old point, cm
Interval trans_acc_limits(double vwold, double vwmax, double vold, double atmax, double dels) {
double vmin, vmax;
// use curvature to find maximum allowed acceleration
// using the relation:
// (dv/dt)^2/(atmax)^2+(vwold)^2/(vwmax)^2 < 1
// hence dv/dt < sqrt(1-(vwold/vwmax)^2)*atmax
// and at = sqrt(1-(vwold/vwmax)^2)*atmax
// make sure units are all correct!
if (fabs(vwold/vwmax) > 1) {
vwold = vwmax;
}
assert(fabs(vwold/vwmax) <= 1.);
double at = sqrt(1-(vwold/vwmax)*(vwold/vwmax))*atmax;
// qDebug() << "in trans acc, vwold and vwmax = " << vwold << vwmax << ", at = " << at;
if (vold*vold > 2*atmax*dels)
vmin = sqrt(vold*vold - 2*at*dels);
else
vmin = 0;
vmax = sqrt(vold*vold + 2*at*dels);
// // qDebug() << "vold = " << vold << ", (min,max)= " << vmin << vmax;
return Interval(vmin, vmax);
}
// rotational acceleration constraint
// awmax: maximum rotational acceleration, 1/s^2
vector<Interval> rot_acc_limits(double vold, double kold, double k, double dels,
double awmax) {
vector<Interval> ans;
double v1, v2, v1_star, v2_star, v1_cap, v2_cap;
if (k > 1e-5) {
double term = (k+kold)*(k+kold)*vold*vold-8*k*awmax*dels;
if (term < 0) {
{
double term = sqrt((k+kold)*(k+kold)*vold*vold+8*k*awmax*dels);
v1 = 1/(2*k)*((kold-k)*vold+term);
v2 = 1/(2*k)*((kold-k)*vold-term);
}
Interval i(v2, v1);
ans.push_back(i);
return ans;
} else {
{
double term = sqrt((k+kold)*(k+kold)*vold*vold+8*k*awmax*dels);
v1 = 1/(2*k)*((kold-k)*vold+term);
v2 = 1/(2*k)*((kold-k)*vold-term);
}
{
double term = sqrt((k+kold)*(k+kold)*vold*vold-8*k*awmax*dels);
v1_star = 1/(2*k)*((kold-k)*vold+term);
v2_star = 1/(2*k)*((kold-k)*vold-term);
}
Interval i1(v2, v2_star);
Interval i2(v1_star, v1);
ans.push_back(i1);
ans.push_back(i2);
return ans;
}
} else if (k < -1e-5) {
double term = (k+kold)*(k+kold)*vold*vold+8*k*awmax*dels;
if (term < 0) {
{
double term = sqrt((k+kold)*(k+kold)*vold*vold-8*k*awmax*dels);
v1_star = 1/(2*k)*((kold-k)*vold+term);
v2_star = 1/(2*k)*((kold-k)*vold-term);
}
Interval i(v1_star, v2_star);
ans.push_back(i);
return ans;
} else {
{
double term = sqrt((k+kold)*(k+kold)*vold*vold+8*k*awmax*dels);
v1 = 1/(2*k)*((kold-k)*vold+term);
v2 = 1/(2*k)*((kold-k)*vold-term);
}
{
double term = sqrt((k+kold)*(k+kold)*vold*vold-8*k*awmax*dels);
v1_star = 1/(2*k)*((kold-k)*vold+term);
v2_star = 1/(2*k)*((kold-k)*vold-term);
}
Interval i1(v1_star, v1);
Interval i2(v2, v2_star);
ans.push_back(i1);
ans.push_back(i2);
return ans;
}
} else {
// k ~ 0
if (kold > -1e-5 && kold < 1e-5) {
// kold ~ 0
Interval i(-numeric_limits<double>::infinity(),
numeric_limits<double>::infinity());
ans.push_back(i);
return ans;
} else {
{
v1_cap = -2*dels*awmax/(kold*vold)-vold;
v2_cap = 2*dels*awmax/(kold*vold)-vold;
}
if (kold > 1e-5) {
Interval i(v1_cap, v2_cap);
ans.push_back(i);
return ans;
} else {
Interval i(v2_cap, v1_cap);
ans.push_back(i);
return ans;
}
}
}
}
vector<ProfileDatapoint> generateVelocityProfile(Spline &p, int numPoints, double vls, double vrs, double vle, double vre)
{
// all calculations are done AFTER converting strategy coordinates to cm!
assert(numPoints >= 2);
double full = Integration::integrate(p, 0, 1);
double vs = (vls+vrs)/2.;
double ve = (vle+vre)/2.;
//qDebug() << "Starting ending vel:"<< vs << " " << ve << endl;
//assert(vs >= 0 && ve >= 0);
vector<ProfileDatapoint> v(numPoints, ProfileDatapoint());
double dels = full/(numPoints-1);
Integration::refreshMatrix();
Integration::computeInverseBezierMatrices(p);
Integration::computeSplineApprox(p);
//Integration::computeBezierMatrices(p);
for (int i = 0; i < v.size(); i++) {
double s = full/(numPoints-1)*(double)i;
double u = Integration::getArcLengthParam(p, s, full);
double k = p.k(u);
// double r = 1/k;
//NOTE: hardcoding vsat here!!
v[i].v = min(vmax_isolated(k, Constants::vsat), Constants::vsat);//100
v[i].u = u;
v[i].s = s;
}
// forward consistency
v[0].v = vs;
for (int i = 1; i < numPoints; i++) {
double vwold = v[i-1].v*v[i-1].v*p.k(v[i-1].u);
double vw = Constants::vwIntercept + Constants::vwSlope/p.k(((i-1)*1.0)/numPoints);
if( vw < Constants::vwmax)
vw = vwmax;
// vw = Constants::vwmax;
// qDebug() << "forward " << p.k(((i-1)*1.0)/numPoints) << " " << vw << endl;
v[i].v = min(v[i].v, trans_acc_limits(vwold, vw, v[i-1].v, Constants::atmax, dels).second);
}
// backward consistency
v[numPoints-1].v = ve;
for (int i = numPoints-2; i >= 0; i--) {
double vwold = v[i+1].v*v[i+1].v*p.k(v[i+1].u);
double vw = Constants::vwIntercept + Constants::vwSlope/p.k(((i-1)*1.0)/numPoints);
if( vw < Constants::vwmax)
vw = vwmax;
// vw = Constants::vwmax;
// qDebug() << "backward " << vw << endl;
v[i].v = min(v[i].v, trans_acc_limits(vwold, vw, v[i+1].v, Constants::atmax, dels).second);
}
// set time to reach for each datapoint
v[0].t = 0;
for (int i = 1; i < numPoints; i++) {
v[i].t = v[i-1].t + 2*dels/(v[i].v+v[i-1].v);
}
// qDebug() << "profile:" ;
for (int i = 0; i< numPoints; i++) {
// qDebug() << v[i].u << v[i].t << v[i].s << v[i].v;
}
return v;
}
ProfileDatapoint::ProfileDatapoint(): u(0), v(0), s(0), t(0)
{
}
ProfileDatapoint::ProfileDatapoint(double u, double v, double s, double t): u(u), v(v), s(s), t(t)
{
}
bool ProfileDatapoint::operator<(const ProfileDatapoint &dp) const
{
return t < dp.t;
}
}