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]);
}
}
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);
}
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 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);
}