BSpline

Functions

void interpolate(InputDataSet Input, int Num, int P, OutputDataSet *Output): This function takes the Input structure, performs the BSpline interpolation and outputs the result into Output structure

void approximate(InputDataSet Input, int Num, int Q, int P, OutputDataSet *Output): This function takes the Input structure, performs the BSpline LS approximation and outputs the result into Output structure

void basisFunction(double t, Eigen::VectorXd U, int I, int P, double *NN, double *NN1, double *NN2): This function calculates the basis functions NN of order P, and derivatives NN1, NN2, for a given time t and knot vector U

class InputDataSet

#include <BSpline.h>

The InputDataSet class contains the information about the points that must be interpolated. It is used as a data structure to intialize the inputs that are passed to the interpolating function.

Public Functions

InputDataSet(): This constructor initializes an Input structure for BSpline interpolation

InputDataSet(Eigen::VectorXd X1, Eigen::VectorXd X2, Eigen::VectorXd X3): The constructor requires 3 N-dimensional vectors containing the coordinates of the waypoints

~InputDataSet(): Generic destructor

void setXDot_0(Eigen::Vector3d XDot_0): Set the first derivative of the starting point (optional)

void setXDot_N(Eigen::Vector3d XDot_N): Set the first derivative of the last point (optional)

void setXDDot_0(Eigen::Vector3d XDDot_0): Set the second derivative of the starting point (optional)

void setXDDot_N(Eigen::Vector3d XDDot_N): Set the second derivative of the last point (optional)

void setT(Eigen::VectorXd T): Set the time tags for each waypoint (optional). Cannot be imposed together with avg velocity norm below

void setW(Eigen::VectorXd W): Set the weights for each waypoint. Weights are used in the LS approximation

void setAvgXDot(double AvgXDot): Set the average velocity norm (optional). Cannot be imposed together with time tag vector above

Public Members

double AvgXDot: desired average velocity norm

Eigen::VectorXd T: time tags: specifies at what time each waypoint is hit

Eigen::VectorXd W: weight vector for the LS approximation

Eigen::VectorXd X1: coordinate #1 of the waypoints

Eigen::VectorXd X2: coordinate #2 of the waypoints

Eigen::VectorXd X3: coordinate #3 of the waypoints

Eigen::Vector3d XDot_0: 3D vector containing the first derivative at starting point

Eigen::Vector3d XDot_N: 3D vector containing the first derivative at final point

Eigen::Vector3d XDDot_0: 3D vector containing the second derivative at starting point

Eigen::Vector3d XDDot_N: 3D vector containing the second derivative at final point

bool T_flag: indicates that time tags have been specified; if true, AvgXDot_flag is false

bool AvgXDot_flag: indicates that avg velocity norm has been specified; if true, T_flag is false

bool W_flag: indicates that weight vector has been specified

bool XDot_0_flag: indicates that first derivative at starting point has been specified

bool XDot_N_flag: indicates that first derivative at final point has been specified

bool XDDot_0_flag: indicates that second derivative at starting point has been specified

bool XDDot_N_flag: indicates that second derivative at final point has been specified

class OutputDataSet

#include <BSpline.h>

The OutputDataSet class is used as a data structure to contain the interpolated function and its first- and second-order derivatives, together with the time-tag vector T.

Public Functions

OutputDataSet(): This constructor initializes an Output structure for BSpline interpolation

~OutputDataSet(): Generic destructor

void getData(double t, double x[3], double xDot[3], double xDDot[3]): This method returns x, xDot and xDDot at the desired input time T

double getStates(double t, int derivative, int index)

This method returns single coordinates of x, xDot and xDDot at the desired input time T.

It is designed to be accessible from Python

Public Members

Eigen::VectorXd T: time tags for each point of the interpolated trajectory

Eigen::VectorXd X1: coordinate #1 of the interpolated trajectory

Eigen::VectorXd X2: coordinate #2 of the interpolated trajectory

Eigen::VectorXd X3: coordinate #3 of the interpolated trajectory

Eigen::VectorXd XD1: first derivative of coordinate #1 of the interpolated trajectory

Eigen::VectorXd XD2: first derivative of coordinate #2 of the interpolated trajectory

Eigen::VectorXd XD3: first derivative of coordinate #3 of the interpolated trajectory

Eigen::VectorXd XDD1: second derivative of coordinate #1 of the interpolated trajectory

Eigen::VectorXd XDD2: second derivative of coordinate #2 of the interpolated trajectory

Eigen::VectorXd XDD3: second derivative of coordinate #3 of the interpolated trajectory

int P: polynomial degree of the BSpline

Eigen::VectorXd U: knot vector of the BSpline

Eigen::VectorXd C1: coordinate #1 of the control points

Eigen::VectorXd C2: coordinate #2 of the control points

Eigen::VectorXd C3: coordinate #3 of the control points