void testIntegralAndDerivative() {
vector<Polynomial<CoefficientType>> polynomials;
int num_coefficients = 5;
int num_segments = 3;
typedef typename Polynomial<CoefficientType>::CoefficientsType CoefficientsType;
for (int i = 0; i < num_segments; ++i) {
CoefficientsType coefficients = CoefficientsType::Random(num_coefficients);
polynomials.push_back(Polynomial<CoefficientType>(coefficients));
}
// differentiate integral, get original back
PiecewisePolynomial<CoefficientType> piecewise(polynomials, generateSegmentTimes(num_segments));
PiecewisePolynomial<CoefficientType> piecewise_back = piecewise.integral().derivative();
if (!piecewise.isApprox(piecewise_back, 1e-10))
throw runtime_error("wrong");
// check value at start time
double value_at_t0 = uniform(generator);
PiecewisePolynomial<CoefficientType> integral = piecewise.integral(value_at_t0);
valuecheck(value_at_t0, integral.value(piecewise.getStartTime()), 1e-10);
// check continuity at knot points
for (int i = 0; i < piecewise.getNumberOfSegments() - 1; ++i) {
valuecheck(integral.getPolynomial(i).value(integral.getDuration(i)), integral.getPolynomial(i + 1).value(0.0));
}
}
PiecewisePolynomial<CoefficientType>
PiecewisePolynomial<CoefficientType>::integral(
const typename PiecewisePolynomial<CoefficientType>::CoefficientMatrixRef&
value_at_start_time) const {
PiecewisePolynomial ret = *this;
for (int segment_index = 0; segment_index < getNumberOfSegments();
segment_index++) {
PolynomialMatrix& matrix = ret.polynomials_[segment_index];
for (Eigen::Index row = 0; row < rows(); row++) {
for (Eigen::Index col = 0; col < cols(); col++) {
if (segment_index == 0) {
matrix(row, col) =
matrix(row, col).integral(value_at_start_time(row, col));
} else {
matrix(row, col) =
matrix(row, col).integral(
ret.segmentValueAtGlobalAbscissa(
segment_index - 1,
getStartTime(segment_index), row, col));
}
}
}
}
return ret;
}
ExponentialPlusPiecewisePolynomial<CoefficientType>::ExponentialPlusPiecewisePolynomial(const PiecewisePolynomial<CoefficientType>& piecewise_polynomial_part) :
PiecewiseFunction(piecewise_polynomial_part),
K(Matrix<CoefficientType, Dynamic, Dynamic>::Zero(piecewise_polynomial_part.rows(), 1)),
A(Matrix<CoefficientType, Dynamic, Dynamic>::Zero(1, 1)),
alpha(Matrix<CoefficientType, Dynamic, Dynamic>::Zero(1, piecewise_polynomial_part.getNumberOfSegments())),
piecewise_polynomial_part(piecewise_polynomial_part)
{
assert(piecewise_polynomial_part.cols() == 1);
}
bool PiecewisePolynomial<CoefficientType>::isApprox(
const PiecewisePolynomial<CoefficientType>& other, double tol) const {
if (rows() != other.rows() || cols() != other.cols()) return false;
if (!segmentTimesEqual(other, tol)) return false;
for (int segment_index = 0; segment_index < getNumberOfSegments();
segment_index++) {
const PolynomialMatrix& matrix = polynomials_[segment_index];
const PolynomialMatrix& other_matrix = other.polynomials_[segment_index];
for (Eigen::Index row = 0; row < rows(); row++) {
for (Eigen::Index col = 0; col < cols(); col++) {
if (!matrix(row, col).isApprox(other_matrix(row, col), tol))
return false;
}
}
}
return true;
}
double randomSpeedTest(int ntests) {
double ret = 0.0;
int num_segments = 3;
vector<double> segment_times = generateSegmentTimes(num_segments);
for (int i = 0; i < ntests; i++) {
double x0 = uniform(generator);
double xd0 = uniform(generator);
double xf = uniform(generator);
double xdf = uniform(generator);
double x1 = uniform(generator);
double x2 = uniform(generator);
PiecewisePolynomial<double> result = twoWaypointCubicSpline(segment_times, x0, xd0, xf, xdf, x1, x2);
ret += result.value(0.0);
}
return ret;
}
void mexFunction(int nlhs, mxArray *plhs[],int nrhs, const mxArray *prhs[]) {
string usage = "[coefs, objval] = nWaypointCubicSplinemex(ts, xs, xd0, xdf)";
if (nrhs != 4)
mexErrMsgIdAndTxt("Drake:nWaypointCubicSplinemex:WrongNumberOfInputs", usage.c_str());
if (nlhs > 2)
mexErrMsgIdAndTxt("Drake:nWaypointCubicSplinemex:WrongNumberOfOutputs", usage.c_str());
const std::vector<double> segment_times = matlabToStdVector<double>(prhs[0]);
MatrixXd xs = matlabToEigen<Dynamic, Dynamic>(prhs[1]);
auto xd0 = matlabToEigen<Dynamic, 1>(prhs[2]);
auto xdf = matlabToEigen<Dynamic, 1>(prhs[3]);
mwSize ndof = static_cast<mwSize>(xs.rows());
mwSize num_segments = static_cast<mwSize>(xs.cols())-1;
mwSize num_knots = num_segments - 1;
mwSize num_coeffs_per_segment = 4;
mwSize dims[] = {ndof, num_segments, num_coeffs_per_segment};
plhs[0] = mxCreateNumericArray(3, dims, mxDOUBLE_CLASS, mxREAL);
double objective_value = 0.0;
for (mwSize dof = 0; dof < ndof; dof++) {
VectorXd xi = xs.block(dof, 1, 1, num_knots).transpose();
PiecewisePolynomial<double> spline = nWaypointCubicSpline(segment_times, xs(dof, 0), xd0[dof], xs(dof, num_segments), xdf[dof], xi);
PiecewisePolynomial<double> acceleration_squared = spline.derivative(2);
acceleration_squared *= acceleration_squared;
PiecewisePolynomial<double> acceleration_squared_integral = acceleration_squared.integral();
objective_value += acceleration_squared_integral.scalarValue(spline.getEndTime()) - acceleration_squared_integral.scalarValue(spline.getStartTime());
for (mwSize segment_index = 0; segment_index < spline.getNumberOfSegments(); segment_index++) {
for (mwSize coefficient_index = 0; coefficient_index < num_coeffs_per_segment; coefficient_index++) {
mwSize sub[] = {dof, segment_index, num_coeffs_per_segment - coefficient_index - 1}; // Matlab's reverse coefficient indexing...
*(mxGetPr(plhs[0]) + sub2ind(3, dims, sub)) = spline.getPolynomial(static_cast<int>(segment_index)).getCoefficients()[coefficient_index];
}
}
}
if (nlhs > 1) {
plhs[1] = mxCreateDoubleScalar(objective_value);
}
}
void evaluateXYZExpmapCubicSpline(double t, const PiecewisePolynomial<double> &spline, Isometry3d &body_pose_des, Vector6d &xyzdot_angular_vel, Vector6d &xyzddot_angular_accel) {
Vector6d xyzexp = spline.value(t);
auto derivative = spline.derivative();
Vector6d xyzexpdot = derivative.value(t);
Vector6d xyzexpddot = derivative.derivative().value(t);
xyzdot_angular_vel.head<3>() = xyzexpdot.head<3>();
xyzddot_angular_accel.head<3>() = xyzexpddot.head<3>();
Vector3d expmap = xyzexp.tail<3>();
auto quat_grad = expmap2quat(expmap,2);
Vector4d quat = quat_grad.value();
body_pose_des.linear() = quat2rotmat(quat);
body_pose_des.translation() = xyzexp.head<3>();
Vector4d quat_dot = quat_grad.gradient().value() * xyzexpdot.tail<3>();
quat_grad.gradient().gradient().value().resize(12,3);
Matrix<double,12,3> dE = quat_grad.gradient().gradient().value();
Vector3d expdot = xyzexpdot.tail<3>();
Matrix<double,4,3> Edot = matGradMult(dE,expdot);
Vector4d quat_ddot = quat_grad.gradient().value()*xyzexpddot.tail<3>() + Edot*expdot;
Matrix<double,3,4> M;
Matrix<double,12,4> dM;
quatdot2angularvelMatrix(quat,M,&dM);
xyzdot_angular_vel.tail<3>() = M*quat_dot;
xyzddot_angular_accel.tail<3>() = M*quat_ddot + matGradMult(dM,quat_dot)*quat_dot;
}
void encodePiecewisePolynomial(const PiecewisePolynomial<double>& piecewise_polynomial, drake::lcmt_piecewise_polynomial& msg)
{
msg.num_segments = piecewise_polynomial.getNumberOfSegments();
msg.num_breaks = piecewise_polynomial.getNumberOfSegments() + 1;
msg.breaks = piecewise_polynomial.getSegmentTimes();
msg.polynomial_matrices.resize(piecewise_polynomial.getNumberOfSegments());
for (int i = 0; i < piecewise_polynomial.getNumberOfSegments(); ++i) {
encodePolynomialMatrix<Eigen::Dynamic,Eigen::Dynamic>(piecewise_polynomial.getPolynomialMatrix(i), msg.polynomial_matrices[i]);
}
}
void evaluateXYZExpmapCubicSpline(double t,
const PiecewisePolynomial<double> &spline,
Isometry3d &body_pose_des,
Vector6d &xyzdot_angular_vel,
Vector6d &xyzddot_angular_accel) {
Vector6d xyzexp = spline.value(t);
auto derivative = spline.derivative();
Vector6d xyzexpdot = derivative.value(t);
Vector6d xyzexpddot = derivative.derivative().value(t);
// translational part
body_pose_des.translation() = xyzexp.head<3>();
xyzdot_angular_vel.head<3>() = xyzexpdot.head<3>();
xyzddot_angular_accel.head<3>() = xyzexpddot.head<3>();
// rotational part
auto expmap = xyzexp.tail<3>();
auto expmap_dot = xyzexpdot.tail<3>();
auto expmap_ddot = xyzexpddot.tail<3>();
// construct autodiff version of expmap
// autodiff derivatives represent first and second derivative w.r.t. time
// TODO(tkoolen): should use 1 instead of dynamic, but causes issues
// with eigen on MSVC 32 bit; should be fixed in 3.3
typedef AutoDiffScalar<Matrix<double, Dynamic, 1>> ADScalar;
// TODO(tkoolen): should use 1 instead of dynamic, but causes issues
// with eigen on MSVC 32 bit; should be fixed in 3.3
typedef AutoDiffScalar<Matrix<ADScalar, Dynamic, 1>> ADScalarSecondDeriv;
Matrix<ADScalarSecondDeriv, 3, 1> expmap_autodiff;
for (int i = 0; i < expmap_autodiff.size(); i++) {
expmap_autodiff(i).value() = expmap(i);
expmap_autodiff(i).derivatives().resize(1);
expmap_autodiff(i).derivatives()(0) = expmap_dot(i);
expmap_autodiff(i).derivatives()(0).derivatives().resize(1);
expmap_autodiff(i).derivatives()(0).derivatives()(0) = expmap_ddot(i);
}
auto quat_autodiff = expmap2quat(expmap_autodiff);
Vector4d quat = autoDiffToValueMatrix(autoDiffToValueMatrix(quat_autodiff));
body_pose_des.linear() = quat2rotmat(quat);
// angular velocity and acceleration are computed from quaternion derivative
// meaning of derivative vectors remains the same: first and second
// derivatives w.r.t. time
decltype(quat_autodiff) quat_dot_autodiff;
for (int i = 0; i < quat_dot_autodiff.size(); i++) {
quat_dot_autodiff(i).value() = quat_autodiff(i).derivatives()(0).value();
quat_dot_autodiff(i).derivatives().resize(1);
quat_dot_autodiff(i).derivatives()(0).value() =
quat_autodiff(i).derivatives()(0).derivatives()(0);
quat_dot_autodiff(i).derivatives()(0).derivatives().resize(1);
quat_dot_autodiff(i).derivatives()(0).derivatives()(0) =
std::numeric_limits<double>::quiet_NaN(); // we're not interested in
// second deriv of angular
// velocity
}
auto omega_autodiff =
(quatdot2angularvelMatrix(quat_autodiff) * quat_dot_autodiff).eval();
auto omega = xyzdot_angular_vel.tail<3>();
auto omega_dot = xyzddot_angular_accel.tail<3>();
for (int i = 0; i < omega_autodiff.size(); i++) {
omega(i) = omega_autodiff(i).value().value();
omega_dot(i) = omega_autodiff(i).derivatives()(0).value();
}
}
coef.push_back(3.0); coef.push_back(1.0); coef.push_back(0.0); coef.push_back(0.0); coefs.push_back(coef); coef.clear(); coef.push_back(0.0); coef.push_back(0.0); coef.push_back(0.0); coef.push_back(3.0); coefs.push_back(coef); coef.clear(); intervals.push_back(Interval(0.0, 1.0)); intervals.push_back(Interval(1.0, 2.0)); intervals.push_back(Interval(2.0, 3.0)); PiecewisePolynomial poly(4, intervals, coefs); RadialDistributionFunction* RDFp; CHECK(RadialDistributionFunction::RadialDistributionFunction()) RDFp = new RadialDistributionFunction(); TEST_NOT_EQUAL(RDFp, 0) RESULT CHECK(RadialDistributionFunction::~RadialDistributionFunction()) delete RDFp; RESULT CHECK(RadialDistributionFunction::RadialDistributionFunction(const RadialDistributionFunction& rdf))
int main(int argc, char **argv) {
int num_segments = 3;
vector<double> segment_times = generateSegmentTimes(num_segments);
double x0 = uniform(generator);
double xd0 = uniform(generator);
double xf = uniform(generator);
double xdf = uniform(generator);
double x1 = uniform(generator);
double x2 = uniform(generator);
PiecewisePolynomial<double> result = twoWaypointCubicSpline(segment_times, x0, xd0, xf, xdf, x1, x2);
for (int i = 0; i < num_segments; i++) {
valuecheck(segment_times[i], result.getStartTime(i));
}
valuecheck(segment_times[num_segments], result.getEndTime(num_segments - 1));
// check value constraints
double tol = 1e-10;
PiecewisePolynomial<double> derivative = result.derivative();
PiecewisePolynomial<double> second_derivative = derivative.derivative();
valuecheck(result.value(result.getStartTime(0)), x0, tol);
valuecheck(derivative.value(result.getStartTime(0)), xd0, tol);
valuecheck(result.value(result.getEndTime(num_segments - 1)), xf, tol);
valuecheck(derivative.value(result.getEndTime(num_segments - 1)), xdf, tol);
valuecheck(result.value(result.getStartTime(1)), x1, tol);
valuecheck(result.value(result.getStartTime(2)), x2, tol);
// check continuity constraints
double eps = 1e-10;
int num_knots = num_segments - 1;
for (int i = 0; i < num_knots; i++) {
double t_knot = result.getEndTime(i);
valuecheck(result.value(t_knot - eps), result.value(t_knot + eps), 1e-8);
valuecheck(derivative.value(t_knot - eps), derivative.value(t_knot + eps), 1e-8);
valuecheck(second_derivative.value(t_knot - eps), second_derivative.value(t_knot + eps), 1e-8);
}
#if !defined(WIN32) && !defined(WIN64)
int ntests = 1000;
cout << "time: " << measure<chrono::microseconds>::execution(randomSpeedTest, ntests) / (double) ntests << " microseconds." << endl;
#endif
cout << "test passed" << endl;
return 0;
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
string usage =
"[coefs, ts, objective_value] = "
"nWaypointCubicSplineFreeKnotTimesmex.cpp(t0, tf, xs, xd0, xdf)";
if (nrhs != 5)
mexErrMsgIdAndTxt(
"Drake:nWaypointCubicSplineFreeKnotTimesmex.cpp:WrongNumberOfInputs",
usage.c_str());
if (nlhs < 2 || nlhs > 3)
mexErrMsgIdAndTxt(
"Drake:nWaypointCubicSplineFreeKnotTimesmex.cpp:WrongNumberOfOutputs",
usage.c_str());
double t0 = mxGetPrSafe(prhs[0])[0];
double tf = mxGetPrSafe(prhs[1])[0];
MatrixXd xs = matlabToEigen<Dynamic, Dynamic>(prhs[2]);
auto xd0 = matlabToEigen<Dynamic, 1>(prhs[3]);
auto xdf = matlabToEigen<Dynamic, 1>(prhs[4]);
mwSize ndof = static_cast<mwSize>(xs.rows());
mwSize num_segments = static_cast<mwSize>(xs.cols()) - 1;
mwSize num_knots = num_segments - 1;
if (num_knots >= 3)
mexWarnMsgTxt(
"More knots than two is likely to be super slow in a grid search!\n");
if (num_knots <= 0)
mexErrMsgIdAndTxt(
"Drake:nWaypointCubicSplineFreeKnotTimesmex.cpp:"
"NotEnoughKnotsToJustifyThisFunction",
usage.c_str());
mwSize num_coeffs_per_segment = 4;
mwSize dims[] = {ndof, num_segments, num_coeffs_per_segment};
plhs[0] = mxCreateNumericArray(3, dims, mxDOUBLE_CLASS, mxREAL);
std::vector<double> segment_times;
segment_times.resize(static_cast<size_t>(num_segments) + 1);
segment_times[0] = t0;
segment_times[static_cast<size_t>(num_segments)] = tf;
std::vector<double> best_segment_times = segment_times;
double t_step = (tf - t0) / GRID_STEPS;
double min_objective_value = numeric_limits<double>::infinity();
// assemble the knot point locations for input to nWaypointCubicSpline
MatrixXd xi = xs.block(0, 1, ndof, num_knots);
if (GRID_STEPS <= num_knots) {
// If we have have too few grid steps, then by pigeonhole it's
// impossible to give each a unique time in our grid search.
mexErrMsgIdAndTxt(
"Drake:nWaypointCubicSplineFreeKnotTimesmex.cpp:"
"TooManyKnotsForNumGridSteps",
usage.c_str());
}
std::vector<int> t_indices;
t_indices.reserve(num_knots);
for (mwSize i = 0; i < num_knots; i++) {
t_indices.push_back(i + 1); // assume knot point won't be the same time as
// the initial state, or previous knot point
}
while (t_indices[0] < (GRID_STEPS - static_cast<int>(num_knots) + 1)) {
for (mwSize i = 0; i < num_knots; i++)
segment_times[i + 1] = t0 + t_indices[i] * t_step;
bool valid_solution = true;
double objective_value = 0.0;
for (mwSize dof = 0; dof < ndof && valid_solution; dof++) {
try {
PiecewisePolynomial<double> spline = nWaypointCubicSpline(
segment_times, xs(dof, 0), xd0[dof], xs(dof, num_segments),
xdf[dof], xi.row(dof).transpose());
PiecewisePolynomial<double> acceleration_squared = spline.derivative(2);
acceleration_squared *= acceleration_squared;
PiecewisePolynomial<double> acceleration_squared_integral =
acceleration_squared.integral();
objective_value +=
acceleration_squared_integral.scalarValue(spline.getEndTime()) -
acceleration_squared_integral.scalarValue(spline.getStartTime());
} catch (ConstraintMatrixSingularError &) {
valid_solution = false;
}
}
if (valid_solution && objective_value < min_objective_value) {
best_segment_times = segment_times;
min_objective_value = objective_value;
}
// Advance grid search counter or terminate, counting from
// the latest t_index, and on overflow carrying to the
// next lowest t_index and resetting to the new value of that
// next lowest t_index. (since times must always be in order!)
t_indices[num_knots - 1]++;
// carry, except for the lowest place, which we
// use to detect doneness.
for (size_t i = num_knots - 1; i > 0; i--) {
if ((i == num_knots - 1 && t_indices[i] >= GRID_STEPS) ||
(i < num_knots - 1 && t_indices[i] >= t_indices[i + 1])) {
t_indices[i - 1]++;
t_indices[i] = t_indices[i - 1] + 1;
}
}
}
for (mwSize dof = 0; dof < ndof; dof++) {
PiecewisePolynomial<double> spline = nWaypointCubicSpline(
best_segment_times, xs(dof, 0), xd0[dof], xs(dof, num_segments),
xdf[dof], xi.row(dof).transpose());
for (mwSize segment_index = 0;
segment_index < static_cast<mwSize>(spline.getNumberOfSegments());
segment_index++) {
for (mwSize coefficient_index = 0;
coefficient_index < num_coeffs_per_segment; coefficient_index++) {
mwSize sub[] = {dof, segment_index,
num_coeffs_per_segment - coefficient_index -
1}; // Matlab's reverse coefficient indexing...
*(mxGetPr(plhs[0]) + sub2ind(3, dims, sub)) =
spline.getPolynomial(static_cast<int>(segment_index))
.GetCoefficients()[coefficient_index];
}
}
}
plhs[1] = stdVectorToMatlab(best_segment_times);
if (nlhs > 2) plhs[2] = mxCreateDoubleScalar(min_objective_value);
}
ExponentialPlusPiecewisePolynomial<double> s1Trajectory(const TVLQRData &sys, const PiecewisePolynomial<double> &zmp_trajectory,const Ref<const MatrixXd> &S) {
size_t n = static_cast<size_t>(zmp_trajectory.getNumberOfSegments());
int d = zmp_trajectory.getSegmentPolynomialDegree(0);
int k = d + 1;
for (size_t i = 1; i < n; i++) {
assert(zmp_trajectory.getSegmentPolynomialDegree(i) == d);
}
VectorXd dt(n);
std::vector<double> breaks = zmp_trajectory.getSegmentTimes();
for (size_t i = 0; i < n; i++) {
dt(i) = breaks[i + 1] - breaks[i];
}
MatrixXd zmp_tf = zmp_trajectory.value(zmp_trajectory.getEndTime());
PiecewisePolynomial<double> zbar_pp = zmp_trajectory - zmp_tf;
Matrix2d R1i = sys.R1.inverse();
MatrixXd NB = sys.N.transpose() + sys.B.transpose() * S; //2 x 4
Matrix4d A2 = NB.transpose() * R1i * sys.B.transpose() - sys.A.transpose();
MatrixXd B2 = 2 * (sys.C.transpose() - NB.transpose() * R1i * sys.D) * sys.Qy; //4 x 2
Matrix4d A2i = A2.inverse();
MatrixXd alpha = MatrixXd::Zero(4, n);
vector<MatrixXd> beta;
VectorXd s1dt;
for (size_t i = 0; i < n ; i++) {
beta.push_back(MatrixXd::Zero(4, k));
}
for (int j = static_cast<int>(n) - 1; j >= 0; j--) {
auto poly_mat = zbar_pp.getPolynomialMatrix(j);
size_t nq = poly_mat.rows();
MatrixXd poly_coeffs = MatrixXd::Zero(nq, k);
for (size_t x = 0; x < nq; x++) {
poly_coeffs.row(x) = poly_mat(x).getCoefficients().transpose();
}
beta[j].col(k - 1) = -A2i * B2 * poly_coeffs.col(k - 1);
for (int i = k - 2; i >= 0; i--) {
beta[j].col(i) = A2i * ((i+1) * beta[j].col(i + 1) - B2 * poly_coeffs.col(i));
}
if (j == n - 1) {
s1dt = VectorXd::Zero(4);
} else {
s1dt = alpha.col(j+1) + beta[j + 1].col(0);
}
VectorXd dtpow(k);
for (size_t p = 0; p < k; p++) {
dtpow(p) = pow(dt(j), static_cast<int>(p));
}
alpha.col(j) = (A2*dt(j)).eval().exp().inverse() * (s1dt - beta[j]*dtpow);
}
vector<PiecewisePolynomial<double>::PolynomialMatrix> polynomial_matrices;
for (int segment = 0; segment < n ; segment++) {
PiecewisePolynomial<double>::PolynomialMatrix polynomial_matrix(4, 1);
for(int row = 0; row < 4; row++) {
polynomial_matrix(row) = Polynomial<double>(beta[segment].row(row));
}
polynomial_matrices.push_back(polynomial_matrix);
}
PiecewisePolynomial<double> pp_part = PiecewisePolynomial<double>(polynomial_matrices, breaks);
auto s1traj = ExponentialPlusPiecewisePolynomial<double>(Matrix4d::Identity(), A2, alpha, pp_part);
return s1traj;
}
void mexFunction(int nlhs, mxArray *plhs[],int nrhs, const mxArray *prhs[]) {
string usage = "[coefs, ts, objective_value] = twoWaypointCubicSplineFreeKnotTimesmex.cpp(t0, tf, xs, xd0, xdf)";
if (nrhs != 5)
mexErrMsgIdAndTxt("Drake:twoWaypointCubicSplineFreeKnotTimesmex.cpp:WrongNumberOfInputs", usage.c_str());
if (nlhs < 2 || nlhs > 3)
mexErrMsgIdAndTxt("Drake:twoWaypointCubicSplineFreeKnotTimesmex.cpp:WrongNumberOfOutputs", usage.c_str());
double t0 = mxGetPrSafe(prhs[0])[0];
double tf = mxGetPrSafe(prhs[1])[0];
MatrixXd xs = matlabToEigen<Dynamic, Dynamic>(prhs[2]);
auto xd0 = matlabToEigen<Dynamic, 1>(prhs[3]);
auto xdf = matlabToEigen<Dynamic, 1>(prhs[4]);
mwSize ndof = static_cast<mwSize>(xs.rows());
mwSize num_segments = 3;
mwSize num_coeffs_per_segment = 4;
mwSize dims[] = {ndof, num_segments, num_coeffs_per_segment};
plhs[0] = mxCreateNumericArray(num_segments, dims, mxDOUBLE_CLASS, mxREAL);
std::vector<double> segment_times;
segment_times.resize(static_cast<size_t>(num_segments) + 1);
segment_times[0] = t0;
segment_times[static_cast<size_t>(num_segments)] = tf;
std::vector<double> best_segment_times = segment_times;
double t_step = (tf - t0) / GRID_STEPS;
double min_objective_value = numeric_limits<double>::infinity();
for (int t1_index = 0; t1_index < GRID_STEPS; t1_index++) {
segment_times[1] = t0 + t1_index * t_step;
for (int t2_index = t1_index; t2_index < GRID_STEPS; t2_index++) {
segment_times[2] = t0 + t2_index * t_step;
bool valid_solution = true;
double objective_value = 0.0;
for (int dof = 0; dof < ndof && valid_solution; dof++) {
try {
PiecewisePolynomial<double> spline = twoWaypointCubicSpline(segment_times, xs(dof, 0), xd0[dof], xs(dof, 3), xdf[dof], xs(dof, 1), xs(dof, 2));
PiecewisePolynomial<double> acceleration_squared = spline.derivative(2);
acceleration_squared *= acceleration_squared;
PiecewisePolynomial<double> acceleration_squared_integral = acceleration_squared.integral();
objective_value += acceleration_squared_integral.value(spline.getEndTime()) - acceleration_squared_integral.value(spline.getStartTime());
}
catch (ConstraintMatrixSingularError&) {
valid_solution = false;
}
}
if (valid_solution && objective_value < min_objective_value) {
best_segment_times[1] = segment_times[1];
best_segment_times[2] = segment_times[2];
min_objective_value = objective_value;
}
}
}
for (mwSize dof = 0; dof < ndof; dof++) {
PiecewisePolynomial<double> spline = twoWaypointCubicSpline(best_segment_times, xs(dof, 0), xd0[dof], xs(dof, 3), xdf[dof], xs(dof, 1), xs(dof, 2));
for (mwSize segment_index = 0; segment_index < spline.getNumberOfSegments(); segment_index++) {
for (mwSize coefficient_index = 0; coefficient_index < num_coeffs_per_segment; coefficient_index++) {
mwSize sub[] = {dof, segment_index, num_coeffs_per_segment - coefficient_index - 1}; // Matlab's reverse coefficient indexing...
*(mxGetPr(plhs[0]) + sub2ind(3, dims, sub)) = spline.getPolynomial(segment_index).getCoefficients()[coefficient_index];
}
}
}
plhs[1] = stdVectorToMatlab(best_segment_times);
if (nlhs > 2)
plhs[2] = mxCreateDoubleScalar(min_objective_value);
}