Class SolverAbstract

Defined in File solver-base.hpp

Inheritance Relationships

Derived Types

public crocoddyl::SolverIpopt (Class SolverIpopt)
public crocoddyl::SolverKKT (Class SolverKKT)

Class Documentation

class SolverAbstract

Abstract class for optimal control solvers.

A solver resolves an optimal control solver of the form

\[\begin{split}\begin{eqnarray*} \begin{Bmatrix} \mathbf{x}^*_0,\cdots,\mathbf{x}^*_{T} \\ \mathbf{u}^*_0,\cdots,\mathbf{u}^*_{T-1} \end{Bmatrix} = \arg\min_{\mathbf{x}_s,\mathbf{u}_s} && l_T (\mathbf{x}_T) + \sum_{k=0}^{T-1} l_k(\mathbf{x}_t,\mathbf{u}_t) \\ \operatorname{subject}\,\operatorname{to} && \mathbf{x}_0 = \mathbf{\tilde{x}}_0\\ && \mathbf{x}_{k+1} = \mathbf{f}_k(\mathbf{x}_k,\mathbf{u}_k)\\ && \mathbf{x}_k\in\mathcal{X}, \mathbf{u}_k\in\mathcal{U} \end{eqnarray*}\end{split}\]

where \(l_T(\mathbf{x}_T)\), \(l_k(\mathbf{x}_t,\mathbf{u}_t)\) are the terminal and running cost functions, respectively, \(\mathbf{f}_k(\mathbf{x}_k,\mathbf{u}_k)\) describes evolution of the system, and state and control admissible sets are defined by \(\mathbf{x}_k\in\mathcal{X}\), \(\mathbf{u}_k\in\mathcal{U}\). An action model, defined in the shooting problem, describes each node \(k\). Inside the action model, we specialize the cost functions, the system evolution and the admissible sets.

The main routines are computeDirection() and tryStep(). The former finds a search direction and typically computes the derivatives of each action model. The latter rollout the dynamics and cost (i.e., the action) to try the search direction found by computeDirection. Both functions used the current guess defined by setCandidate(). Finally, solve() function is used to define when the search direction and length are computed in each iterate. It also describes the globalization strategy (i.e., regularization) of the numerical optimization.