bool ParameterSE2Offset::read(std::istream& is) {
Vector3 off;
for (int i=0; i<3; i++) {
is >> off[i];
std::cerr << off[i] << " " ;
}
std::cerr << std::endl;
setOffset(SE2(off));
return is.good() || is.eof();
}
bool EdgeSE2::read(std::istream& is)
{
Vector3 p;
is >> p[0] >> p[1] >> p[2];
setMeasurement(SE2(p));
_inverseMeasurement = measurement().inverse();
for (int i = 0; i < 3; ++i)
for (int j = i; j < 3; ++j) {
is >> information()(i, j);
if (i != j)
information()(j, i) = information()(i, j);
}
return true;
}
SE2 inverse() const {
return SE2(-(R.inverse()*t), R.inverse());
}
SE2 operator*(const SE2& other) const {
return SE2(t + R*other.t, R * other.R);
}
int main(int, char**)
{
// plan for hybrid car in SE(2) with discrete gears
ob::StateSpacePtr SE2(new ob::SE2StateSpace());
ob::StateSpacePtr velocity(new ob::RealVectorStateSpace(1));
// set the range for gears: [-1,3] inclusive
ob::StateSpacePtr gear(new ob::DiscreteStateSpace(-1,3));
ob::StateSpacePtr stateSpace = SE2 + velocity + gear;
// set the bounds for the R^2 part of SE(2)
ob::RealVectorBounds bounds(2);
bounds.setLow(-100);
bounds.setHigh(100);
SE2->as<ob::SE2StateSpace>()->setBounds(bounds);
// set the bounds for the velocity
ob::RealVectorBounds velocityBound(1);
velocityBound.setLow(0);
velocityBound.setHigh(60);
velocity->as<ob::RealVectorStateSpace>()->setBounds(velocityBound);
// create start and goal states
ob::ScopedState<> start(stateSpace);
ob::ScopedState<> goal(stateSpace);
// Both start and goal are states with high velocity with the car in third gear.
// However, to make the turn, the car cannot stay in third gear and will have to
// shift to first gear.
start[0] = start[1] = -90.; // position
start[2] = boost::math::constants::pi<double>()/2; // orientation
start[3] = 40.; // velocity
start->as<ob::CompoundState>()->as<ob::DiscreteStateSpace::StateType>(2)->value = 3; // gear
goal[0] = goal[1] = 90.; // position
goal[2] = 0.; // orientation
goal[3] = 40.; // velocity
goal->as<ob::CompoundState>()->as<ob::DiscreteStateSpace::StateType>(2)->value = 3; // gear
oc::ControlSpacePtr cmanifold(new oc::RealVectorControlSpace(stateSpace, 2));
// set the bounds for the control manifold
ob::RealVectorBounds cbounds(2);
// bounds for steering input
cbounds.setLow(0, -1.);
cbounds.setHigh(0, 1.);
// bounds for brake/gas input
cbounds.setLow(1, -20.);
cbounds.setHigh(1, 20.);
cmanifold->as<oc::RealVectorControlSpace>()->setBounds(cbounds);
oc::SimpleSetup setup(cmanifold);
setup.setStartAndGoalStates(start, goal, 5.);
setup.setStateValidityChecker(boost::bind(
&isStateValid, setup.getSpaceInformation().get(), _1));
setup.setStatePropagator(boost::bind(
&propagate, setup.getSpaceInformation().get(), _1, _2, _3, _4));
setup.getSpaceInformation()->setPropagationStepSize(.1);
setup.getSpaceInformation()->setMinMaxControlDuration(2, 3);
// try to solve the problem
if (setup.solve(30))
{
// print the (approximate) solution path: print states along the path
// and controls required to get from one state to the next
oc::PathControl& path(setup.getSolutionPath());
// print out full state on solution path
// (format: x, y, theta, v, u0, u1, dt)
for(unsigned int i=0; i<path.getStateCount(); ++i)
{
const ob::State* state = path.getState(i);
const ob::SE2StateSpace::StateType *se2 =
state->as<ob::CompoundState>()->as<ob::SE2StateSpace::StateType>(0);
const ob::RealVectorStateSpace::StateType *velocity =
state->as<ob::CompoundState>()->as<ob::RealVectorStateSpace::StateType>(1);
const ob::DiscreteStateSpace::StateType *gear =
state->as<ob::CompoundState>()->as<ob::DiscreteStateSpace::StateType>(2);
std::cout << se2->getX() << ' ' << se2->getY() << ' ' << se2->getYaw()
<< ' ' << velocity->values[0] << ' ' << gear->value << ' ';
if (i==0)
// null controls applied for zero seconds to get to start state
std::cout << "0 0 0";
else
{
// print controls and control duration needed to get from state i-1 to state i
const double* u =
path.getControl(i-1)->as<oc::RealVectorControlSpace::ControlType>()->values;
std::cout << u[0] << ' ' << u[1] << ' ' << path.getControlDuration(i-1);
}
std::cout << std::endl;
}
if (!setup.haveExactSolutionPath())
{
std::cout << "Solution is approximate. Distance to actual goal is " <<
setup.getProblemDefinition()->getSolutionDifference() << std::endl;
}
}
return 0;
}
bool ClosedFormCalibration::calibrate(const MotionInformationVector& measurements, SE2& laserOffset, Eigen::Vector3d& odomParams)
{
std::vector<VelocityMeasurement, Eigen::aligned_allocator<VelocityMeasurement> > velMeasurements;
for (size_t i = 0; i < measurements.size(); ++i) {
const SE2& odomMotion = measurements[i].odomMotion;
const double& timeInterval = measurements[i].timeInterval;
MotionMeasurement mm(odomMotion.translation().x(), odomMotion.translation().y(), odomMotion.rotation().angle(), timeInterval);
VelocityMeasurement velMeas = OdomConvert::convertToVelocity(mm);
velMeasurements.push_back(velMeas);
}
double J_21, J_22;
{
Eigen::MatrixXd A(measurements.size(), 2);
Eigen::VectorXd x(measurements.size());
for (size_t i = 0; i < measurements.size(); ++i) {
const SE2& laserMotion = measurements[i].laserMotion;
const double& timeInterval = measurements[i].timeInterval;
const VelocityMeasurement& velMeas = velMeasurements[i];
A(i, 0) = velMeas.vl() * timeInterval;
A(i, 1) = velMeas.vr() * timeInterval;
x(i) = laserMotion.rotation().angle();
}
// (J_21, J_22) = (-r_l / b, r_r / b)
Eigen::Vector2d linearSolution = (A.transpose() * A).inverse() * A.transpose() * x;
//std::cout << linearSolution.transpose() << std::endl;
J_21 = linearSolution(0);
J_22 = linearSolution(1);
}
// construct M
Eigen::Matrix<double, 5, 5> M;
M.setZero();
for (size_t i = 0; i < measurements.size(); ++i) {
const SE2& laserMotion = measurements[i].laserMotion;
const double& timeInterval = measurements[i].timeInterval;
const VelocityMeasurement& velMeas = velMeasurements[i];
Eigen::Matrix<double, 2, 5> L;
double omega_o_k = J_21 * velMeas.vl() + J_22 * velMeas.vr();
double o_theta_k = omega_o_k * timeInterval;
double sx = 1.;
double sy = 0.;
if (fabs(o_theta_k) > std::numeric_limits<double>::epsilon()) {
sx = sin(o_theta_k) / o_theta_k;
sy = (1 - cos(o_theta_k)) / o_theta_k;
}
double c_x = 0.5 * timeInterval * (-J_21 * velMeas.vl() + J_22 * velMeas.vr()) * sx;
double c_y = 0.5 * timeInterval * (-J_21 * velMeas.vl() + J_22 * velMeas.vr()) * sy;
L(0, 0) = -c_x;
L(0, 1) = 1 - cos(o_theta_k);
L(0, 2) = sin(o_theta_k);
L(0, 3) = laserMotion.translation().x();
L(0, 4) = -laserMotion.translation().y();
L(1, 0) = -c_y;
L(1, 1) = - sin(o_theta_k);
L(1, 2) = 1 - cos(o_theta_k);
L(1, 3) = laserMotion.translation().y();
L(1, 4) = laserMotion.translation().x();
M.noalias() += L.transpose() * L;
}
//std::cout << M << std::endl;
// compute lagrange multiplier
// and solve the constrained least squares problem
double m11 = M(0,0);
double m13 = M(0,2);
double m14 = M(0,3);
double m15 = M(0,4);
double m22 = M(1,1);
double m34 = M(2,3);
double m35 = M(2,4);
double m44 = M(3,3);
double a = m11 * SQR(m22) - m22 * SQR(m13);
double b = 2*m11 * SQR(m22) * m44 - SQR(m22) * SQR(m14) - 2*m22 * SQR(m13) * m44 - 2*m11 * m22 * SQR(m34)
- 2*m11 * m22 * SQR(m35) - SQR(m22) * SQR(m15) + 2*m13 * m22 * m34 * m14 + SQR(m13) * SQR(m34)
+ 2*m13 * m22 * m35 * m15 + SQR(m13) * SQR(m35);
double c = - 2*m13 * CUBE(m35) * m15 - m22 * SQR(m13) * SQR(m44) + m11 * SQR(m22) * SQR(m44) + SQR(m13) * SQR(m35) * m44
+ 2*m13 * m22 * m34 * m14 * m44 + SQR(m13) * SQR(m34) * m44 - 2*m11 * m22 * SQR(m34) * m44 - 2 * m13 * CUBE(m34) * m14
- 2*m11 * m22 * SQR(m35) * m44 + 2*m11 * SQR(m35) * SQR(m34) + m22 * SQR(m14) * SQR(m35) - 2*m13 * SQR(m35) * m34 * m14
- 2*m13 * SQR(m34) * m35 * m15 + m11 * std::pow(m34, 4) + m22 * SQR(m15) * SQR(m34) + m22 * SQR(m35) * SQR(m15)
+ m11 * std::pow(m35, 4) - SQR(m22) * SQR(m14) * m44 + 2*m13 * m22 * m35 * m15 * m44 + m22 * SQR(m34) * SQR(m14)
- SQR(m22) * SQR(m15) * m44;
// solve the quadratic equation
double lambda1, lambda2;
if(a < std::numeric_limits<double>::epsilon()) {
if(b <= std::numeric_limits<double>::epsilon())
return false;
lambda1 = lambda2 = -c/b;
} else {
double delta = b*b - 4*a*c;
if (delta < 0)
return false;
lambda1 = 0.5 * (-b-sqrt(delta)) / a;
lambda2 = 0.5 * (-b+sqrt(delta)) / a;
}
Eigen::VectorXd x1 = solveLagrange(M, lambda1);
Eigen::VectorXd x2 = solveLagrange(M, lambda2);
double err1 = x1.dot(M * x1);
double err2 = x2.dot(M * x2);
const Eigen::VectorXd& calibrationResult = err1 < err2 ? x1 : x2;
odomParams(0) = - calibrationResult(0) * J_21;
odomParams(1) = calibrationResult(0) * J_22;
odomParams(2) = calibrationResult(0);
laserOffset = SE2(calibrationResult(1), calibrationResult(2), atan2(calibrationResult(4), calibrationResult(3)));
return true;
}
