Class SolverFDDP

Defined in File fddp.hpp

Inheritance Relationships

Base Type

public SolverDDP

Derived Types

public crocoddyl::SolverBoxFDDP (Class SolverBoxFDDP)
public crocoddyl::SolverIntro (Class SolverIntro)

Class Documentation

class SolverFDDP : public SolverDDP

Feasibility-driven Differential Dynamic Programming (FDDP) solver.

The FDDP solver computes an optimal trajectory and control commands by iterates running backwardPass() and forwardPass(). The backward pass accepts infeasible guess as described in the SolverDDP::backwardPass(). Additionally, the forward pass handles infeasibility simulations that resembles the numerical behaviour of a multiple-shooting formulation, i.e.:

\[\begin{split}\begin{eqnarray} \mathbf{\hat{x}}_0 &=& \mathbf{\tilde{x}}_0 - (1 - \alpha)\mathbf{\bar{f}}_0,\\ \mathbf{\hat{u}}_k &=& \mathbf{u}_k + \alpha\mathbf{k}_k + \mathbf{K}_k(\mathbf{\hat{x}}_k-\mathbf{x}_k),\\ \mathbf{\hat{x}}_{k+1} &=& \mathbf{f}_k(\mathbf{\hat{x}}_k,\mathbf{\hat{u}}_k) - (1 - \alpha)\mathbf{\bar{f}}_{k+1}. \end{eqnarray}\end{split}\]

Note that the forward pass keeps the gaps \(\mathbf{\bar{f}}_s\) open according to the step length \(\alpha\) that has been accepted. This solver has shown empirically greater globalization strategy. Additionally, the expected improvement computation considers the gaps in the dynamics:

\[\begin{equation} \Delta J(\alpha) = \Delta_1\alpha + \frac{1}{2}\Delta_2\alpha^2, \end{equation}\]

with

\[\begin{split}\begin{eqnarray} \Delta_1 = \sum_{k=0}^{N-1} \mathbf{k}_k^\top\mathbf{Q}_{\mathbf{u}_k} +\mathbf{\bar{f}}_k^\top(V_{\mathbf{x}_k} - V_{\mathbf{xx}_k}\mathbf{x}_k),\nonumber\\ \Delta_2 = \sum_{k=0}^{N-1} \mathbf{k}_k^\top\mathbf{Q}_{\mathbf{uu}_k}\mathbf{k}_k + \mathbf{\bar{f}}_k^\top(2 V_{\mathbf{xx}_k}\mathbf{x}_k - V_{\mathbf{xx}_k}\mathbf{\bar{f}}_k). \end{eqnarray}\end{split}\]

For more details about the feasibility-driven differential dynamic programming algorithm see: