13 #ifndef _STRUCT_POLYNOMIAL 14 #define _STRUCT_POLYNOMIAL 31 template <
typename Time = double,
typename Numeric =
Time,
bool Safe =
false,
32 typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>,
34 std::vector<Point, Eigen::aligned_allocator<Point> > >
35 struct polynomial :
public curve_abc<Time, Numeric, Safe, Point> {
61 dim_(coefficients.rows()),
63 degree_(coefficients.cols() - 1),
78 dim_(coefficients.begin()->size()),
79 coefficients_(init_coeffs(coefficients.begin(), coefficients.end())),
93 template <
typename In>
97 dim_(zeroOrderCoefficient->size()),
116 throw std::invalid_argument(
"T_min must be strictly lower than T_max");
117 if (init.size() != end.size())
118 throw std::invalid_argument(
119 "init and end points must have the same dimensions.");
121 coeffs.push_back(init);
122 coeffs.push_back((end - init) / (max - min));
138 const Point& d_end,
const time_t
min,
const time_t
max)
141 throw std::invalid_argument(
"T_min must be strictly lower than T_max");
142 if (init.size() != end.size())
143 throw std::invalid_argument(
144 "init and end points must have the same dimensions.");
145 if (init.size() != d_init.size())
146 throw std::invalid_argument(
147 "init and d_init points must have the same dimensions.");
148 if (init.size() != d_end.size())
149 throw std::invalid_argument(
150 "init and d_end points must have the same dimensions.");
156 double T = max -
min;
157 Eigen::Matrix<double, 4, 4> m;
158 m << 1., 0, 0, 0, 1., T, T * T, T * T * T, 0, 1., 0, 0, 0, 1., 2. * T,
160 Eigen::Matrix<double, 4, 4> m_inv = m.inverse();
161 Eigen::Matrix<double, 4, 1> bc;
164 for (
size_t i = 0; i <
dim_;
189 const time_t
min,
const time_t
max)
192 throw std::invalid_argument(
"T_min must be strictly lower than T_max");
193 if (init.size() != end.size())
194 throw std::invalid_argument(
195 "init and end points must have the same dimensions.");
196 if (init.size() != d_init.size())
197 throw std::invalid_argument(
198 "init and d_init points must have the same dimensions.");
199 if (init.size() != d_end.size())
200 throw std::invalid_argument(
201 "init and d_end points must have the same dimensions.");
202 if (init.size() != dd_init.size())
203 throw std::invalid_argument(
204 "init and dd_init points must have the same dimensions.");
205 if (init.size() != dd_end.size())
206 throw std::invalid_argument(
207 "init and dd_end points must have the same dimensions.");
215 double T = max -
min;
216 Eigen::Matrix<double, 6, 6> m;
217 m << 1., 0, 0, 0, 0, 0, 1., T, T * T, pow(T, 3), pow(T, 4), pow(T, 5), 0,
218 1., 0, 0, 0, 0, 0, 1., 2. * T, 3. * T * T, 4. * pow(T, 3),
219 5. * pow(T, 4), 0, 0, 2, 0, 0, 0, 0, 0, 2, 6. * T, 12. * T * T,
221 Eigen::Matrix<double, 6, 6> m_inv = m.inverse();
222 Eigen::Matrix<double, 6, 1> bc;
225 for (
size_t i = 0; i <
dim_;
260 static polynomial_t
MinimumJerk(
const point_t& p_init,
const point_t& p_final,
261 const time_t t_min = 0.,
262 const time_t t_max = 1.) {
264 polynomial(coeff_t::Zero(p_init.size(), 6), t_min, t_max);
281 const point_t& p_final,
const time_t t_min = 0.,
282 const time_t t_max = 1.) {
284 throw std::invalid_argument(
285 "final time should be superior or equal to initial time.");
286 const size_t dim(p_init.size());
287 if (static_cast<size_t>(p_final.size()) !=
dim)
288 throw std::invalid_argument(
289 "Initial and final points must have the same dimension.");
290 const double T = t_max - t_min;
291 const double T2 = T * T;
292 const double T3 = T2 * T;
293 const double T4 = T3 * T;
294 const double T5 = T4 * T;
314 throw std::invalid_argument(
"Tmin should be inferior to Tmax");
317 throw std::runtime_error(
"Spline order and coefficients do not match");
330 check_if_not_empty();
331 if ((t < T_min_ || t >
T_max_) && Safe) {
332 throw std::invalid_argument(
333 "error in polynomial : time t to evaluate should be in range [Tmin, " 334 "Tmax] of the curve");
336 time_t
const dt(t -
T_min_);
338 for (
int i = (
int)(
degree_ - 1); i >= 0; i--) {
354 const polynomial_t& other,
355 const Numeric prec = Eigen::NumTraits<Numeric>::dummy_precision())
const {
356 return ndcurves::isApprox<num_t>(
T_min_, other.
min()) &&
357 ndcurves::isApprox<num_t>(
T_max_, other.
max()) &&
363 const curve_abc_t* other,
364 const Numeric prec = Eigen::NumTraits<Numeric>::dummy_precision())
const {
365 const polynomial_t* other_cast =
dynamic_cast<const polynomial_t*
>(other);
377 return !(*
this == other);
385 virtual point_t
derivate(
const time_t t,
const std::size_t order)
const {
386 check_if_not_empty();
387 if ((t < T_min_ || t >
T_max_) && Safe) {
388 throw std::invalid_argument(
389 "error in polynomial : time t to evaluate derivative should be in " 390 "range [Tmin, Tmax] of the curve");
392 time_t
const dt(t -
T_min_);
394 point_t currentPoint_ = point_t::Zero(
dim_);
395 for (
int i = (
int)(order); i < (int)(
degree_ + 1); ++i, cdt *= dt) {
396 currentPoint_ += cdt *
coefficients_.col(i) * fact(i, order);
398 return currentPoint_;
402 check_if_not_empty();
430 num_t fact(
const std::size_t n,
const std::size_t order)
const {
432 for (std::size_t i = 0; i < std::size_t(order); ++i) {
433 res *= (
num_t)(n - i);
438 coeff_t deriv_coeff(coeff_t
coeff)
const {
439 if (coeff.cols() == 1)
440 return coeff_t::Zero(coeff.rows(), 1);
441 coeff_t coeff_derivated(coeff.rows(), coeff.cols() - 1);
442 for (std::size_t i = 0; i < std::size_t(coeff_derivated.cols()); i++) {
443 coeff_derivated.col(i) = coeff.col(i + 1) * (
num_t)(i + 1);
445 return coeff_derivated;
448 void check_if_not_empty()
const {
450 throw std::runtime_error(
451 "Error in polynomial : there is no coefficients set / did you use " 452 "empty constructor ?");
461 std::size_t
virtual dim()
const {
return dim_; };
474 assert_operator_compatible(p1);
489 assert_operator_compatible(p1);
531 polynomial_t
cross(
const polynomial_t& pOther)
const {
532 assert_operator_compatible(pOther);
534 throw std::invalid_argument(
535 "Can't perform cross product on polynomials with dimensions != 3 ");
537 coeff_t nCoeffs = Eigen::MatrixXd::Zero(3, new_degree + 1);
538 Eigen::Vector3d currentVec;
539 Eigen::Vector3d currentVecCrossed;
542 for (
long j = 0; j < pOther.
coeff().cols(); ++j) {
543 currentVecCrossed = pOther.
coeff().col(j);
544 nCoeffs.col(i + j) += currentVec.cross(currentVecCrossed);
548 long final_degree = new_degree;
549 while (nCoeffs.col(final_degree).norm() <= ndcurves::MARGIN &&
566 throw std::invalid_argument(
567 "Can't perform cross product on polynomials with dimensions != 3 ");
569 Eigen::Vector3d currentVec;
570 Eigen::Vector3d pointVec = point;
573 nCoeffs.col(i) = currentVec.cross(pointVec);
576 long final_degree =
degree();
577 while (nCoeffs.col(final_degree).norm() <= ndcurves::MARGIN &&
592 void assert_operator_compatible(
const polynomial_t& other)
const {
593 if ((fabs(
min() - other.
min()) > ndcurves::MARGIN) ||
594 (fabs(
max() - other.
max()) > ndcurves::MARGIN) ||
596 throw std::invalid_argument(
597 "Can't perform base operation (+ - ) on two polynomials with " 598 "different time ranges or different dimensions");
602 template <
typename In>
603 coeff_t init_coeffs(In zeroOrderCoefficient, In highestOrderCoefficient) {
605 std::distance(zeroOrderCoefficient, highestOrderCoefficient);
606 coeff_t res =
coeff_t(dim_, size);
608 for (In cit = zeroOrderCoefficient; cit != highestOrderCoefficient;
619 template <
class Archive>
620 void serialize(Archive& ar,
const unsigned int version) {
624 ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(curve_abc_t);
625 ar& boost::serialization::make_nvp(
"dim", dim_);
626 ar& boost::serialization::make_nvp(
"coefficients", coefficients_);
627 ar& boost::serialization::make_nvp(
"dim", dim_);
628 ar& boost::serialization::make_nvp(
"degree", degree_);
629 ar& boost::serialization::make_nvp(
"T_min", T_min_);
630 ar& boost::serialization::make_nvp(
"T_max", T_max_);
635 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
642 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
650 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
658 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
666 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
674 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
680 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
687 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
694 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
701 template <
typename T,
typename N,
bool S,
typename P,
typename TP>
715 #endif //_STRUCT_POLYNOMIAL #define SINGLE_ARG(...)
Definition: archive.hpp:23
Definition: bernstein.h:20
polynomial< Time, Numeric, Safe, Point, T_Point > polynomial_t
Definition: polynomial.h:43
polynomial_t & operator*=(const double d)
Definition: polynomial.h:518
virtual num_t min() const
Get the minimum time for which the curve is defined.
Definition: polynomial.h:464
polynomial_t & operator+=(const polynomial_t::point_t &point)
Definition: polynomial.h:503
time_t T_max_
Definition: polynomial.h:588
coeff_t coefficients_
Definition: polynomial.h:586
std::size_t degree_
Definition: polynomial.h:587
polynomial(const coeff_t &coefficients, const time_t min, const time_t max)
Constructor.
Definition: polynomial.h:59
static void MinimumJerk(polynomial_t &out, const point_t &p_init, const point_t &p_final, const time_t t_min=0., const time_t t_max=1.)
MinimumJerk Build a polynomial curve connecting p_init to p_final minimizing the time integral of the...
Definition: polynomial.h:280
interface for a Curve of arbitrary dimension.
virtual point_t operator()(const time_t t) const
Evaluation of the cubic spline at time t using horner's scheme.
Definition: polynomial.h:329
polynomial(const polynomial &other)
Definition: polynomial.h:241
polynomial_t cross(const polynomial_t &pOther) const
Compute the cross product of the current polynomial by another polynomial. The cross product p1Xp2 of...
Definition: polynomial.h:531
friend class boost::serialization::access
Definition: polynomial.h:617
virtual bool operator==(const polynomial_t &other) const
Definition: polynomial.h:372
bezier_curve< T, N, S, P > operator/(const bezier_curve< T, N, S, P > &p1, const double k)
Definition: bezier_curve.h:805
polynomial(const Point &init, const Point &end, const time_t min, const time_t max)
Constructor from boundary condition with C0 : create a polynomial that connect exactly init and end (...
Definition: polynomial.h:112
bezier_curve< T, N, S, P > operator+(const bezier_curve< T, N, S, P > &p1, const bezier_curve< T, N, S, P > &p2)
Definition: bezier_curve.h:748
point_t coeffAtDegree(const std::size_t degree) const
Definition: polynomial.h:421
curve_abc_t::curve_ptr_t curve_ptr_t
Definition: polynomial.h:44
Numeric num_t
Definition: polynomial.h:39
T_Point t_point_t
Definition: polynomial.h:37
boost::shared_ptr< curve_t > curve_ptr_t
Definition: curve_abc.h:46
curve_abc< Time, Numeric, Safe, Point > curve_abc_t
Definition: polynomial.h:40
virtual bool operator!=(const polynomial_t &other) const
Definition: polynomial.h:376
std::vector< Point, Eigen::aligned_allocator< Point > > T_Point
Definition: effector_spline.h:29
Represents a polynomial of an arbitrary order defined on the interval . It follows the equation : ...
Definition: fwd.h:42
bezier_curve< T, N, S, P > operator*(const bezier_curve< T, N, S, P > &p1, const double k)
Definition: bezier_curve.h:812
double Time
Definition: effector_spline.h:27
Eigen::Ref< coeff_t > coeff_t_ref
Definition: polynomial.h:42
polynomial(const T_Point &coefficients, const time_t min, const time_t max)
Constructor.
Definition: polynomial.h:76
polynomial_t & operator/=(const double d)
Definition: polynomial.h:513
virtual std::size_t degree() const
Get the degree of the curve.
Definition: polynomial.h:470
virtual num_t max() const
Get the maximum time for which the curve is defined.
Definition: polynomial.h:467
virtual std::size_t dim() const
Get dimension of curve.
Definition: polynomial.h:461
#define DEFINE_CLASS_TEMPLATE_VERSION(Template, Type)
Definition: archive.hpp:27
Time time_t
Definition: polynomial.h:38
polynomial_t cross(const polynomial_t::point_t &point) const
Compute the cross product of the current polynomial p by a point point. The cross product pXpoint of ...
Definition: polynomial.h:564
void serialize(Archive &ar, const unsigned int version)
Definition: polynomial.h:620
bool isApprox(const polynomial_t &other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const
isApprox check if other and *this are approximately equals. Only two curves of the same class can be ...
Definition: polynomial.h:353
Eigen::Matrix< Numeric, Eigen::Dynamic, 1 > Point
Definition: effector_spline.h:28
polynomial()
Empty constructor. Curve obtained this way can not perform other class functions. ...
Definition: polynomial.h:51
Point point_t
Definition: polynomial.h:36
polynomial(const Point &init, const Point &d_init, const Point &end, const Point &d_end, const time_t min, const time_t max)
Constructor from boundary condition with C1 : create a polynomial that connect exactly init and end a...
Definition: polynomial.h:137
double Numeric
Definition: effector_spline.h:26
polynomial_t & operator+=(const polynomial_t &p1)
Definition: polynomial.h:473
Eigen::MatrixXd coeff() const
Definition: polynomial.h:419
polynomial_t * compute_derivate_ptr(const std::size_t order) const
Compute the derived curve at order N.
Definition: polynomial.h:415
polynomial_t & operator-=(const polynomial_t::point_t &point)
Definition: polynomial.h:508
time_t T_min_
Definition: polynomial.h:588
polynomial(const Point &init, const Point &d_init, const Point &dd_init, const Point &end, const Point &d_end, const Point &dd_end, const time_t min, const time_t max)
Constructor from boundary condition with C2 : create a polynomial that connect exactly init and end a...
Definition: polynomial.h:187
virtual bool isApprox(const curve_abc_t *other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const
Definition: polynomial.h:362
bezier_curve< T, N, S, P > operator-(const bezier_curve< T, N, S, P > &p1)
Definition: bezier_curve.h:755
std::size_t dim_
Definition: polynomial.h:585
polynomial_t compute_derivate(const std::size_t order) const
Definition: polynomial.h:401
static polynomial_t MinimumJerk(const point_t &p_init, const point_t &p_final, const time_t t_min=0., const time_t t_max=1.)
MinimumJerk Build a polynomial curve connecting p_init to p_final minimizing the time integral of the...
Definition: polynomial.h:260
virtual ~polynomial()
Destructor.
Definition: polynomial.h:239
virtual point_t derivate(const time_t t, const std::size_t order) const
Evaluation of the derivative of order N of spline at time t.
Definition: polynomial.h:385
Eigen::MatrixXd coeff_t
Definition: polynomial.h:41
polynomial(In zeroOrderCoefficient, In out, const time_t min, const time_t max)
Constructor.
Definition: polynomial.h:94
polynomial_t & operator-=(const polynomial_t &p1)
Definition: polynomial.h:488