void TimeOptimizeTest2DCircleBezier()
{
CartesianCSpace space(2);
SphereConstraint sphereConstraint;
SmoothConstrainedInterpolator interp(&space,&sphereConstraint);
interp.ftol = 1e-8;
interp.xtol = 1e-2;
interp.maxNewtonIters = 100;
vector<Vector> pts;
pts.resize(5);
pts[0].resize(2);
pts[1].resize(2);
pts[2].resize(2);
pts[3].resize(2);
pts[4].resize(2);
pts[0](0)=1; pts[0](1)=0;
pts[1](0)=0; pts[1](1)=1;
pts[2](0)=-1; pts[2](1)=0;
pts[3](0)=0; pts[3](1)=-1;
pts[4](0)=1; pts[4](1)=0;
Timer timer;
TimeScaledBezierCurve curve;
MultiSmoothInterpolate(interp,pts,curve.path);
for(size_t i=0;i<curve.path.segments.size();i++)
Assert(curve.path.segments[i].space == &space);
printf("Num segments: %d\n",curve.path.segments.size());
Vector vmin(2,-1.0),vmax(2,1.0);
Vector amin(2,-1.0),amax(2,1.0);
bool res=curve.OptimizeTimeScaling(vmin,vmax,amin,amax);
if(!res) {
printf("Error optimizing path\n");
return;
}
printf("End time: %g\n",curve.EndTime());
printf("Solution time: %g s\n",timer.ElapsedTime());
Assert(curve.timeScaling.times.size()==curve.timeScaling.params.size());
#if PRINT_TIME_SCALING
cout<<"t,s,ds,x,y,dx,dy:"<<endl;
for(size_t i=0;i<curve.timeScaling.times.size();i++) {
Vector x,v;
curve.Eval(curve.timeScaling.times[i],x);
curve.Deriv(curve.timeScaling.times[i],v);
cout<<curve.timeScaling.times[i]<<","<<curve.timeScaling.params[i]<<","<<curve.timeScaling.ds[i]<<","<<x[0]<<","<<x[1]<<","<<v[0]<<","<<v[1]<<endl;
}
#endif
}
bool CheckBounds(Robot& robot,const TimeScaledBezierCurve& traj,const vector<Real>& times)
{
Vector v,a,maxv,maxa;
Vector oldv,diffa,maxdiffa;
bool res=true;
for(size_t i=0;i<times.size();i++) {
//double-checking velocity and acceleration bounds
traj.Deriv(times[i],v);
traj.Accel(times[i],a);
if(i==0) { maxv=v; maxa=a; }
else {
for(int j=0;j<v.n;j++) {
maxv[j] = Max(maxv[j],Abs(v[j]));
maxa[j] = Max(maxa[j],Abs(a[j]));
}
}
for(int j=0;j<v.n;j++) {
if(Abs(v[j]) > robot.velMax[j]+1e-3) {
printf("Exceeded vel max %s=%g at time %g\n",robot.LinkName(j).c_str(),v(j),times[i]);
res = false;
}
if(Abs(a[j]) > robot.accMax[j]+1e-3) {
printf("Exceeded accel max %s=%g at time %g\n",robot.LinkName(j).c_str(),a(j),times[i]);
res = false;
}
}
if(!oldv.empty()) {
diffa = (v-oldv)/(times[i]-times[i-1]);
for(int j=0;j<v.n;j++) {
if(Abs(diffa[j]) > robot.accMax[j]+1e-3) {
printf("Diff accel max %s=%g at time %g\n",robot.LinkName(j).c_str(),diffa(j),times[i]);
res = false;
}
}
}
oldv = v;
}
cout<<"Max vel "<<maxv<<endl;
cout<<"Max accel "<<maxa<<endl;
cout<<"End vel "<<v<<endl;
cout<<"End accel "<<a<<endl;
return res;
}
bool GenerateAndTimeOptimizeMultiPath(Robot& robot,MultiPath& multipath,Real xtol,Real dt)
{
Timer timer;
vector<GeneralizedCubicBezierSpline > paths;
if(!InterpolateConstrainedMultiPath(robot,multipath,paths,xtol))
return false;
printf("Generated interpolating path in time %gs\n",timer.ElapsedTime());
RobotCSpace cspace(robot);
RobotGeodesicManifold manifold(robot);
for(size_t i=0;i<multipath.sections.size();i++) {
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].space = &cspace;
paths[i].segments[j].manifold = &manifold;
}
for(int iters=0;iters<gNumTimescaleBisectIters;iters++)
paths[i].Bisect();
}
#if SAVE_INTERPOLATING_CURVES
int index=0;
printf("Saving sections, element %d to section_x_bezier.csv\n",index);
for(size_t i=0;i<paths.size();i++) {
{
stringstream ss;
ss<<"section_"<<i<<"_bezier.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"duration,x0,x1,x2,x3"<<endl;
for(size_t j=0;j<paths[i].segments.size();j++) {
out<<paths[i].durations[j]<<","<<paths[i].segments[j].x0[index]<<","<<paths[i].segments[j].x1[index]<<","<<paths[i].segments[j].x2[index]<<","<<paths[i].segments[j].x3[index]<<endl;
}
out.close();
}
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_vel.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"v(0),v(0.5),v(1)"<<endl;
Vector temp;
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].Deriv(0,temp);
temp /= paths[i].durations[j];
out<<temp[index];
paths[i].segments[j].Deriv(0.5,temp);
temp /= paths[i].durations[j];
out<<","<<temp[index];
paths[i].segments[j].Deriv(1,temp);
temp /= paths[i].durations[j];
out<<","<<temp[index];
out<<endl;
}
out.close();
}
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_acc.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"a(0),a(1)"<<endl;
Vector temp;
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].Accel(0,temp);
temp /= Sqr(paths[i].durations[j]);
out<<temp[index];
paths[i].segments[j].Accel(1,temp);
temp /= Sqr(paths[i].durations[j]);
out<<","<<temp[index];
out<<endl;
}
out.close();
}
}
#endif //SAVE_INTERPOLATING_CURVES
#if SAVE_LORES_INTERPOLATING_CURVES
paths.clear();
if(!InterpolateConstrainedMultiPath(robot,multipath,paths,xtol*2.0))
return false;
for(size_t i=0;i<multipath.sections.size();i++) {
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].space = &cspace;
paths[i].segments[j].manifold = &manifold;
}
}
for(size_t i=0;i<paths.size();i++) {
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_x2.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"duration,x0,x1,x2,x3"<<endl;
for(size_t j=0;j<paths[i].segments.size();j++) {
out<<paths[i].durations[j]<<","<<paths[i].segments[j].x0[index]<<","<<paths[i].segments[j].x1[index]<<","<<paths[i].segments[j].x2[index]<<","<<paths[i].segments[j].x3[index]<<endl;
}
out.close();
}
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_vel_x2.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"v(0),v(0.5),v(1)"<<endl;
Vector temp;
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].Deriv(0,temp);
temp /= paths[i].durations[j];
out<<temp[index];
paths[i].segments[j].Deriv(0.5,temp);
temp /= paths[i].durations[j];
out<<","<<temp[index];
paths[i].segments[j].Deriv(1,temp);
temp /= paths[i].durations[j];
out<<","<<temp[index];
out<<endl;
}
out.close();
}
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_acc_x2.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"a(0),a(1)"<<endl;
Vector temp;
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].Accel(0,temp);
temp /= Sqr(paths[i].durations[j]);
out<<temp[index];
paths[i].segments[j].Accel(1,temp);
temp /= Sqr(paths[i].durations[j]);
out<<","<<temp[index];
out<<endl;
}
out.close();
}
}
paths.clear();
if(!InterpolateConstrainedMultiPath(robot,multipath,paths,xtol*4.0))
return false;
for(size_t i=0;i<multipath.sections.size();i++) {
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].space = &cspace;
paths[i].segments[j].manifold = &manifold;
}
}
for(size_t i=0;i<paths.size();i++) {
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_x4.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"duration,x0,x1,x2,x3"<<endl;
for(size_t j=0;j<paths[i].segments.size();j++) {
out<<paths[i].durations[j]<<","<<paths[i].segments[j].x0[index]<<","<<paths[i].segments[j].x1[index]<<","<<paths[i].segments[j].x2[index]<<","<<paths[i].segments[j].x3[index]<<endl;
}
out.close();
}
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_vel_x4.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"v(0),v(0.5),v(1)"<<endl;
Vector temp;
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].Deriv(0,temp);
temp /= paths[i].durations[j];
out<<temp[index];
paths[i].segments[j].Deriv(0.5,temp);
temp /= paths[i].durations[j];
out<<","<<temp[index];
paths[i].segments[j].Deriv(1,temp);
temp /= paths[i].durations[j];
out<<","<<temp[index];
out<<endl;
}
out.close();
}
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_acc_x4.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"a(0),a(1)"<<endl;
Vector temp;
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].Accel(0,temp);
temp /= Sqr(paths[i].durations[j]);
out<<temp[index];
paths[i].segments[j].Accel(1,temp);
temp /= Sqr(paths[i].durations[j]);
out<<","<<temp[index];
out<<endl;
}
out.close();
}
}
paths.clear();
if(!InterpolateConstrainedMultiPath(robot,multipath,paths,xtol*8.0))
return false;
for(size_t i=0;i<multipath.sections.size();i++) {
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].space = &cspace;
paths[i].segments[j].manifold = &manifold;
}
}
for(size_t i=0;i<paths.size();i++) {
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_x8.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"duration,x0,x1,x2,x3"<<endl;
for(size_t j=0;j<paths[i].segments.size();j++) {
out<<paths[i].durations[j]<<","<<paths[i].segments[j].x0[index]<<","<<paths[i].segments[j].x1[index]<<","<<paths[i].segments[j].x2[index]<<","<<paths[i].segments[j].x3[index]<<endl;
}
out.close();
}
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_vel_x8.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"v(0),v(0.5),v(1)"<<endl;
Vector temp;
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].Deriv(0,temp);
temp /= paths[i].durations[j];
out<<temp[index];
paths[i].segments[j].Deriv(0.5,temp);
temp /= paths[i].durations[j];
out<<","<<temp[index];
paths[i].segments[j].Deriv(1,temp);
temp /= paths[i].durations[j];
out<<","<<temp[index];
out<<endl;
}
out.close();
}
{
stringstream ss;
ss<<"section_"<<i<<"_bezier_acc_x8.csv";
ofstream out(ss.str().c_str(),ios::out);
out<<"a(0),a(1)"<<endl;
Vector temp;
for(size_t j=0;j<paths[i].segments.size();j++) {
paths[i].segments[j].Accel(0,temp);
temp /= Sqr(paths[i].durations[j]);
out<<temp[index];
paths[i].segments[j].Accel(1,temp);
temp /= Sqr(paths[i].durations[j]);
out<<","<<temp[index];
out<<endl;
}
out.close();
}
}
#endif //SAVE_LORES_INTERPOLATING_CURVES
//concatenate sections into a single curve
TimeScaledBezierCurve traj;
vector<int> edgeToSection,sectionEdges(1,0);
for(size_t i=0;i<multipath.sections.size();i++) {
traj.path.Concat(paths[i]);
for(size_t j=0;j<paths[i].segments.size();j++)
edgeToSection.push_back((int)i);
sectionEdges.push_back(sectionEdges.back()+(int)paths[i].segments.size());
}
timer.Reset();
bool res=traj.OptimizeTimeScaling(robot.velMin,robot.velMax,-1.0*robot.accMax,robot.accMax);
if(!res) {
printf("Failed to optimize time scaling\n");
return false;
}
else {
printf("Optimized into a path with duration %g, (took %gs)\n",traj.EndTime(),timer.ElapsedTime());
}
double T = traj.EndTime();
int numdivs = (int)Ceil(T/dt);
printf("Discretizing at time resolution %g\n",T/numdivs);
numdivs++;
Vector x,v;
int sCur = -1;
for(int i=0;i<numdivs;i++) {
Real t=T*Real(i)/Real(numdivs-1);
int trajEdge = traj.timeScaling.TimeToSegment(t);
if(trajEdge == (int)edgeToSection.size()) trajEdge--; //end of path
Assert(trajEdge < (int)edgeToSection.size());
int s=edgeToSection[trajEdge];
if(s < sCur) {
fprintf(stderr,"Strange: edge index is going backward? %d -> %d\n",sCur,s);
fprintf(stderr," time %g, division %d, traj segment %d\n",t,i,trajEdge);
}
Assert(s - sCur >=0);
while(sCur < s) {
//close off the current section and add a new one
Real switchTime=traj.timeScaling.times[sectionEdges[sCur+1]];
Assert(switchTime <= t);
traj.Eval(switchTime,x);
traj.Deriv(switchTime,v);
if(sCur >= 0) {
multipath.sections[sCur].times.push_back(switchTime);
multipath.sections[sCur].milestones.push_back(x);
multipath.sections[sCur].velocities.push_back(v);
}
multipath.sections[sCur+1].milestones.resize(0);
multipath.sections[sCur+1].velocities.resize(0);
multipath.sections[sCur+1].times.resize(0);
multipath.sections[sCur+1].milestones.push_back(x);
multipath.sections[sCur+1].velocities.push_back(v);
multipath.sections[sCur+1].times.push_back(switchTime);
sCur++;
}
if(t == multipath.sections[s].times.back()) continue;
traj.Eval(t,x);
traj.Deriv(t,v);
multipath.sections[s].times.push_back(t);
multipath.sections[s].milestones.push_back(x);
multipath.sections[s].velocities.push_back(v);
}
#if DO_TEST_TRIANGULAR
timer.Reset();
TimeScaledBezierCurve trajTri;
Real Ttrap = 0;
printf("%d paths?\n",paths.size());
for(size_t i=0;i<paths.size();i++)
Ttrap += OptimalTriangularTimeScaling(paths[i],robot.velMin,robot.velMax,-1.0*robot.accMax,robot.accMax,trajTri);
printf("Optimal trapezoidal time scaling duration %g, calculated in %gs\n",Ttrap,timer.ElapsedTime());
printf("Saving plot to opt_tri_multipath.csv\n");
trajTri.Plot("opt_tri_multipath.csv",robot.velMin,robot.velMax,-1.0*robot.accMax,robot.accMax);
#endif // DO_TEST_TRAPEZOIDAL
#if DO_CHECK_BOUNDS
CheckBounds(robot,traj,dt);
#endif // DO_CHECK_BOUNDS
#if DO_SAVE_PLOT
printf("Saving plot to opt_multipath.csv\n");
traj.Plot("opt_multipath.csv",robot.velMin,robot.velMax,-1.0*robot.accMax,robot.accMax);
#endif //DO_SAVE_PLOT
#if DO_SAVE_LIMITS
SaveLimits(robot,traj,dt,"opt_multipath_limits.csv");
#endif // DO_SAVE_LIMITS
{
multipath.settings.set("resolution",xtol);
multipath.settings.set("program","GenerateAndTimeOptimizeMultiPath");
}
return true;
}
void SaveLimits(Robot& robot,const TimeScaledBezierCurve& traj,Real dt,const char* fn)
{
Real T=traj.EndTime();
int numdivs = (int)Ceil(T/dt);
printf("Saving time-scaled values to %s\n",fn);
ofstream out(fn,ios::out);
out<<"t";
for(size_t i=0;i<robot.links.size();i++)
out<<",q["<<robot.linkNames[i]<<"]";
for(size_t i=0;i<robot.links.size();i++)
out<<",v["<<robot.linkNames[i]<<"]";
for(size_t i=0;i<robot.links.size();i++)
out<<",a["<<robot.linkNames[i]<<"]";
out<<",activeVLimit,activeAlimit,vsaturation,asaturation";
out<<endl;
Vector q,v,a,maxv,maxa;
for(int i=0;i<=numdivs;i++) {
//double-checking velocity and acceleration bounds
Real t = Real(i)/Real(numdivs)*T;
traj.Eval(t,q);
traj.Deriv(t,v);
traj.Accel(t,a);
out<<t;
for(int j=0;j<q.n;j++)
out<<","<<q(j);
for(int j=0;j<v.n;j++)
out<<","<<v(j);
for(int j=0;j<a.n;j++)
out<<","<<a(j);
Real maxVSat=0,maxASat=0;
int maxVSatInd=0,maxASatInd=0;
for(int j=0;j<v.n;j++)
if(Abs(v(j))/robot.velMax(j) > maxVSat) {
maxVSat = Abs(v(j))/robot.velMax(j);
maxVSatInd = j;
}
for(int j=0;j<a.n;j++)
if(Abs(a(j))/robot.accMax(j) > maxASat) {
maxASat = Abs(a(j))/robot.accMax(j);
maxASatInd = j;
}
out<<","<<robot.linkNames[maxVSatInd];
out<<","<<robot.linkNames[maxASatInd];
out<<","<<maxVSat<<","<<maxASat<<endl;
}
out<<endl;
for(size_t i=0;i<traj.timeScaling.times.size();i++) {
//double-checking velocity and acceleration bounds
Real t = traj.timeScaling.times[i];
traj.Eval(t,q);
traj.Deriv(t,v);
traj.Accel(t,a);
out<<t;
for(int j=0;j<q.n;j++)
out<<","<<q(j);
for(int j=0;j<v.n;j++)
out<<","<<v(j);
for(int j=0;j<a.n;j++)
out<<","<<a(j);
Real maxSat=0;
int maxSatInd=0;
bool maxSatA=false;
for(int j=0;j<v.n;j++)
if(Abs(v(j))/robot.velMax(j) > maxSat) {
maxSat = Abs(v(j))/robot.velMax(j);
maxSatInd = j;
}
for(int j=0;j<a.n;j++)
if(Abs(a(j))/robot.accMax(j) > maxSat) {
maxSat = Abs(a(j))/robot.accMax(j);
maxSatInd = j;
maxSatA=true;
}
if(maxSatA)
out<<",a["<<robot.linkNames[maxSatInd]<<"]";
else
out<<",v["<<robot.linkNames[maxSatInd]<<"]";
out<<","<<maxSat<<endl;
}
}