Linear conditions module

Modelisation of linear relations involved in the optimization problem

pyrotor.linear_conditions.get_endpoints_bounds(endpoints, states)

Compute right-hand side for a linear condition associated with endpoints conditions and involved in the optimization problem.

Input:

• endpoints: dict

  Initial and final states that the optimized trajectory must satisfy ex: {‘Var 1’: {‘start’: 109, ‘end’: 98, ‘delta’: 10}, …}

• states: iterable

  State names

Outputs:

• left_endpoints: list

  List containing the lower conditions (at 0 and T) for each state

• right_endpoints: list

  List containing the upper conditions (at 0 and T) for each state

pyrotor.linear_conditions.get_endpoints_matrix(basis, basis_dimensions, endpoints)

Compute a matrix modelling the endpoints conditions involved in the optimization problem.

The upper-block of the matrix contains the starting conditions while the lower-blocks contains the ending conditions.

Inputs:

• basis: string

  Name of the functional basis

• basis_dimensions: dict

  Give the desired number of basis functions for each state

• endpoints: dict

  Initial and final states that the optimized trajectory must satisfy ex: {‘Var 1’: {‘start’: 109, ‘end’: 98, ‘delta’: 10}, …}

Output:

• phi: ndarray

  Matrix modelling the endpoints conditions

pyrotor.linear_conditions.get_implicit_bounds(null_space_sigma_phi, coefficients)

Project coefficients mean onto the intersection of null space of sigma and Im PhiT * Phi.

Provide right-hand side for a linear condition in the optimization problem.

Inputs:

null_space_sigma_phi: ndarray

Matrix whose columns are orthonormal vectors spanning the intersection between null space of sigma and phiT * phi

coefficients: list of ndarray

Each element of the list is an array containing all the coefficients associated with a trajectory

Ouput:

projected_mean_coefficients: ndarray

Vector given by the product between null_space_sigma_phi.T and coefficients mean

pyrotor.linear_conditions.get_implicit_matrix(sigma, phi)

Compute an orthonormal basis spanning the intersection between null space of sigma and phiT * phi. Return a matrix whose columns provide the basis and which is involved in implicit conditions in the optimization problem.

Inputs:

• sigma: ndarray

  Matrix interpreted as an estimated covariance matrix

• phi: ndarray

  Matrix modelling the endpoints conditions

Output:

• null_space_sigma_phi: ndarray

  Matrix whose columns are orthonormal vectors and spanning the intersection between null space of sigma and phiT * phi

pyrotor.linear_conditions.get_linear_conditions(basis, basis_dimensions, endpoints, coefficients, sigma)

Return scipy object containing the linear conditions for the optimization problem.

Inputs:

• basis: string

  Name of the functional basis

• basis_dimensions: dict

  Give the desired number of basis functions for each state

• endpoints: dict

  Initial and final states that the optimized trajectory must satisfy ex: {‘Var 1’: {‘start’: 109, ‘end’: 98, ‘delta’: 10}, …}

coefficients: list of ndarray

Each element of the list is an array containing all the coefficients associated with a trajectory

sigma: ndarray

Matrix interpreted as an estimated covariance matrix

Outputs:

• linear_conditions: LinearConstraint object

  Scipy object describing the linear conditions

• linear_conditions_matrix: ndarray

  Matrix modelling the linear conditions