#include <BipedalLocomotion/Math/Spline.h>
template<typename T>
BipedalLocomotion::Math::Spline class

Spline implement a basic spline.

Template parameters
T type of the spline. T must be an Eigen type (i.e. Eigen::Vector3d).

Base classes

template<class Output>
class BipedalLocomotion::System::Source<TrajectoryPoint<T>>
Source is a template specialization of Advanceable and represents a block that does not contains input.

Derived classes

template<typename T>
class CubicSpline
Cubic spline implements a 3-rd order polynomial spline in $\mathbb{R}^n$ .
template<typename T>
class LinearSpline
LinearSpline implements a 1-st order polynomial spline in $\mathbb{R}^n$ .
template<typename T>
class QuinticSpline
Quintic spline implements a 5-th order polynomial spline in $\mathbb{R}^n$ .
template<typename T>
class ZeroOrderSpline
ZeroOrderSpline implements a 0 order polynomial spline in $\mathbb{R}^n$ .

Public types

struct DerivativeBoundaryConditions
BoundaryConditions is a struct that contains the boundary conditions of the spline.

Constructors, destructors, conversion operators

~Spline() defaulted virtual
Destructor.

Public functions

auto setAdvanceTimeStep(const std::chrono::nanoseconds& dt) -> bool
Set the time step of the advance interface.
auto setKnots(const std::vector<T>& position, const std::vector<std::chrono::nanoseconds>& time) -> bool
Set the knots of the spline.
auto setInitialConditions(const DerivativeBoundaryConditions& initialConditions) -> bool
Set the initial condition of the spline.
auto setFinalConditions(const DerivativeBoundaryConditions& finalConditions) -> bool
Set the final condition of the spline.
auto setInitialConditions(Eigen::Ref<const T> initialVelocity, Eigen::Ref<const T> initialAcceleration) -> bool
Set the initial condition of the spline.
auto setFinalConditions(Eigen::Ref<const T> finalVelocity, Eigen::Ref<const T> finalAcceleration) -> bool
Set the final condition of the spline.
auto evaluatePoint(const std::chrono::nanoseconds& t, Eigen::Ref<T> position, Eigen::Ref<T> velocity, Eigen::Ref<T> acceleration) -> bool
Evaluate the spline at a given point.
auto evaluatePoint(const std::chrono::nanoseconds& t, Eigen::Ref<T> position) -> bool
Evaluate the spline at a given point.
auto evaluatePoint(const std::chrono::nanoseconds& t, Eigen::Ref<T> position, Eigen::Ref<T> velocity) -> bool
Evaluate the spline at a given point.
auto evaluateOrderedPoints(const std::vector<std::chrono::nanoseconds>& t, std::vector<T>& position, std::vector<T>& velocity, std::vector<T>& acceleration) -> bool
Evaluate the spline at given set of points.
auto evaluatePoint(const std::chrono::nanoseconds& t, TrajectoryPoint<T>& state) -> bool
Evaluate the spline at a given point.
auto isOutputValid() const -> bool final
Check if the output is valid.
auto getOutput() const -> const TrajectoryPoint<T>& final
Get the output of the system.
auto advance() -> bool final
Advance the system.

Protected types

struct Polynomial
Polynomial is a struct that contains the information of a polynomial.

Protected functions

auto computePhasesDuration() -> bool
Compute the duration of each phase (sub-trajectory).
void computeIntermediateQuantities() pure virtual
Compute the intermediate quantities of the spline.
void updatePolynomialCoefficients(Polynomial& polynomial) pure virtual
Set the coefficients of the polynomial.

Protected variables

std::vector<TrajectoryPoint<T>> m_knots
Knots of the spline.
std::vector<Polynomial> m_polynomials
Polynomials of the spline.

Function documentation

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::setAdvanceTimeStep(const std::chrono::nanoseconds& dt)

Set the time step of the advance interface.

Parameters
dt the time step of the advance block.
Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::setKnots(const std::vector<T>& position, const std::vector<std::chrono::nanoseconds>& time)

Set the knots of the spline.

Parameters
position position of the knots in $\mathbb{R}^n$ .
time vector containing the time instant of the knots.
Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::setInitialConditions(const DerivativeBoundaryConditions& initialConditions)

Set the initial condition of the spline.

Parameters
initialConditions initial conditions of the spline.
Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::setFinalConditions(const DerivativeBoundaryConditions& finalConditions)

Set the final condition of the spline.

Parameters
finalConditions final conditions of the spline.
Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::setInitialConditions(Eigen::Ref<const T> initialVelocity, Eigen::Ref<const T> initialAcceleration)

Set the initial condition of the spline.

Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::setFinalConditions(Eigen::Ref<const T> finalVelocity, Eigen::Ref<const T> finalAcceleration)

Set the final condition of the spline.

Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::evaluatePoint(const std::chrono::nanoseconds& t, Eigen::Ref<T> position, Eigen::Ref<T> velocity, Eigen::Ref<T> acceleration)

Evaluate the spline at a given point.

Parameters
t instant time
position position at time t
velocity velocity at time t
acceleration acceleration at time t
Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::evaluatePoint(const std::chrono::nanoseconds& t, Eigen::Ref<T> position)

Evaluate the spline at a given point.

Parameters
t instant time
position position at time t
Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::evaluatePoint(const std::chrono::nanoseconds& t, Eigen::Ref<T> position, Eigen::Ref<T> velocity)

Evaluate the spline at a given point.

Parameters
t instant time
position position at time t
velocity velocity at time t
Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::evaluateOrderedPoints(const std::vector<std::chrono::nanoseconds>& t, std::vector<T>& position, std::vector<T>& velocity, std::vector<T>& acceleration)

Evaluate the spline at given set of points.

Parameters
t ordered vector containing the time instant
position position at time t
velocity velocity at time t
acceleration acceleration at time t
Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::evaluatePoint(const std::chrono::nanoseconds& t, TrajectoryPoint<T>& state)

Evaluate the spline at a given point.

Parameters
t instant time
state of the system
Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::isOutputValid() const final

Check if the output is valid.

Returns True if the output is valid, false otherwise.

template<typename T>
const TrajectoryPoint<T>& BipedalLocomotion::Math::Spline<T>::getOutput() const final

Get the output of the system.

Returns The output of the system.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::advance() final

Advance the system.

Returns True in case of success, false otherwise.

template<typename T>
bool BipedalLocomotion::Math::Spline<T>::computePhasesDuration() protected

Compute the duration of each phase (sub-trajectory).

Returns True in case of success, false otherwise.

template<typename T>
void BipedalLocomotion::Math::Spline<T>::computeIntermediateQuantities() pure virtual protected

Compute the intermediate quantities of the spline.

Returns True in case of success, false otherwise.

template<typename T>
void BipedalLocomotion::Math::Spline<T>::updatePolynomialCoefficients(Polynomial& polynomial) pure virtual protected

Set the coefficients of the polynomial.

Parameters
polynomial polynomial to be updated.
Returns True in case of success, false otherwise.