Template Class SolverBoxFDDPTpl

To compute the feedforward \(\mathbf{k}_k\) and feedback \(\mathbf{K}_k\) terms, we use a Cholesky decomposition to solve \(\mathbf{Q}_{\mathbf{uu}_k}^{-1}\) term:

\[\begin{split}\begin{eqnarray}\mathbf{k}_k &=& \mathbf{Q}_{\mathbf{uu}_k}^{-1}\mathbf{Q}_{\mathbf{u}},\\ \mathbf{K}_k &=& \mathbf{Q}_{\mathbf{uu}_k}^{-1}\mathbf{Q}_{\mathbf{ux}}. \end{eqnarray}\end{split}\]

Note that if the Cholesky decomposition fails, then we re-start the backward pass and increase the state and control regularization values.

virtual void forwardPass(const Scalar steplength)

template<typename NewScalar> SolverBoxFDDPTpl<NewScalar> cast() const

Cast the Box-FDDP solver to a different scalar type.

It is useful for operations requiring different precision or scalar types.

Template Parameters:: NewScalar – The new scalar type to cast to.
Returns:: SolverBoxFDDPTpl<NewScalar> An Box-FDDP solver with the new scalar type.

const std::vector<MatrixXs> &get_Quu_inv() const

Public Members

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar Scalar

Protected Functions

void allocateData()

virtual void resizeRunningData() override: Resize data associated with the running models of the shooting problem.

Protected Attributes

BoxQP qp_

std::vector<MatrixXs> Quu_inv_

std::vector<VectorXs> du_lb_

std::vector<VectorXs> du_ub_

VectorXs xnext_: Next state \(\mathbf{x}^{'}\).

std::vector<VectorXs> dx_: State error during the roll-out/forward-pass (size T).

DynamicsSolverType dyn_solver_: Type of dynamics solver.

std::vector<MatrixXsRowMajor> K_: Feedback gains \(\mathbf{K}\).

std::vector<VectorXs> k_: Feed-forward terms \(\mathbf{l}\).

std::vector<VectorXs> Qu_: Gradient of the Hamiltonian \(\mathbf{Q_u}\).

std::vector<MatrixXs> Quu_: Hessian of the Hamiltonian \(\mathbf{Q_{uu}}\).

std::vector<MatrixXs> Qxu_: Hessian of the Hamiltonian \(\mathbf{Q_{xu}}\).

Scalar reg_decfactor_: Regularization factor used to decrease the damping value

Scalar reg_incfactor_: Regularization factor used to increase the damping value

Scalar rho_: Parameter used in the merit function to predict the expected reduction

EqualitySolverType term_solver_: Type of terminal solver.

Scalar th_acceptminstep_: Threshold used for accepting step along with a minimum length

Scalar th_acceptnegstep_: Threshold used for accepting step along ascent direction

Scalar th_grad_: Tolerance of the expected gradient used for testing the step

Scalar th_minfeas_: Threshold for switching to feasibility.

Scalar th_minimprove_: Minimum improvement threshold used in the regularization scheme

Scalar th_noimprovement_: Threshold used to accept steps that cannot be be improved due to numerical errors

Scalar th_stepdec_: Step-length threshold used to decrease regularization.

Scalar th_stepinc_: Step-length threshold used to increase regularization.

Scalar upsilon_decfactor_: Estimated penalty parameter factor used to decrease its value

std::vector<VectorXs> Vx_: Gradient of the Value function \(\mathbf{V_x}\).

std::vector<MatrixXs> Vxx_: Hessian of the Value function \(\mathbf{V_{xx}}\).

bool zero_upsilon_: True if we wish to set estimated penalty parameter (upsilon) to zero when solve is called.