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| | ActionModelAbstractTpl (boost::shared_ptr< StateAbstract > state, const std::size_t nu, const std::size_t nr=0) |
| | Initialize the action model. More...
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| virtual void | calc (const boost::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) |
| | Compute the total cost value for nodes that depends only on the state. More...
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| virtual void | calc (const boost::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u)=0 |
| | Compute the next state and cost value. More...
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| virtual void | calcDiff (const boost::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) |
| | Compute the derivatives of the cost functions with respect to the state only. More...
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| virtual void | calcDiff (const boost::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u)=0 |
| | Compute the derivatives of the dynamics and cost functions. More...
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virtual bool | checkData (const boost::shared_ptr< ActionDataAbstract > &data) |
| | Checks that a specific data belongs to this model.
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| virtual boost::shared_ptr< ActionDataAbstract > | createData () |
| | Create the action data. More...
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bool | get_has_control_limits () const |
| | Indicates if there are defined control limits.
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std::size_t | get_nr () const |
| | Return the dimension of the cost-residual vector.
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std::size_t | get_nu () const |
| | Return the dimension of the control input.
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const boost::shared_ptr< StateAbstract > & | get_state () const |
| | Return the state.
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const VectorXs & | get_u_lb () const |
| | Return the control lower bound.
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const VectorXs & | get_u_ub () const |
| | Return the control upper bound.
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| virtual void | print (std::ostream &os) const |
| | Print relevant information of the action model. More...
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| virtual void | quasiStatic (const boost::shared_ptr< ActionDataAbstract > &data, Eigen::Ref< VectorXs > u, const Eigen::Ref< const VectorXs > &x, const std::size_t maxiter=100, const Scalar tol=Scalar(1e-9)) |
| | Computes the quasic static commands. More...
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| VectorXs | quasiStatic_x (const boost::shared_ptr< ActionDataAbstract > &data, const VectorXs &x, const std::size_t maxiter=100, const Scalar tol=Scalar(1e-9)) |
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void | set_u_lb (const VectorXs &u_lb) |
| | Modify the control lower bounds.
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void | set_u_ub (const VectorXs &u_ub) |
| | Modify the control upper bounds.
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template<typename _Scalar>
class crocoddyl::ActionModelAbstractTpl< _Scalar >
Abstract class for action model.
An action model combines dynamics and cost models. Each node, in our optimal control problem, is described through an action model. Every time that we want describe a problem, we need to provide ways of computing the dynamics, cost functions and their derivatives. All these is described inside the action model.
Concretely speaking, the action model describes a time-discrete action model with a first-order ODE along a cost function, i.e.
\[ \begin{aligned} &\delta\mathbf{x}^+ = \mathbf{f_{x}}\delta\mathbf{x}+\mathbf{f_{u}}\delta\mathbf{u}, &\textrm{(dynamics)}\\ &l(\delta\mathbf{x},\delta\mathbf{u}) = \begin{bmatrix}1 \\ \delta\mathbf{x} \\ \delta\mathbf{u}\end{bmatrix}^T \begin{bmatrix}0 & \mathbf{l_x}^T & \mathbf{l_u}^T \\ \mathbf{l_x} & \mathbf{l_{xx}} & \mathbf{l_{ux}}^T \\ \mathbf{l_u} & \mathbf{l_{ux}} & \mathbf{l_{uu}}\end{bmatrix} \begin{bmatrix}1 \\ \delta\mathbf{x} \\ \delta\mathbf{u}\end{bmatrix}, &\textrm{(cost)} \end{aligned} \]
where the state \(\mathbf{x}\in\mathcal{X}\) lies in the state manifold described with a nx-tuple, its rate \(\delta\mathbf{x}\in T_{\mathbf{x}}\mathcal{X}\) is a tangent vector to this manifold with ndx dimension, and \(\mathbf{u}\in\mathbb{R}^{nu}\) is the input commands. Note that the we could describe a linear or linearized action system, where the cost has a quadratic form.
The main computations are carrying out in calc and calcDiff. calc computes the next state and cost and calcDiff computes the derivatives of the dynamics and cost function. Concretely speaking, calcDiff builds a linear-quadratic approximation of an action model, where the dynamics and cost functions have linear and quadratic forms, respectively. \(\mathbf{f_x}\in\mathbb{R}^{nv\times ndx}\), \(\mathbf{f_u}\in\mathbb{R}^{nv\times nu}\) are the Jacobians of the dynamics; \(\mathbf{l_x}\in\mathbb{R}^{ndx}\), \(\mathbf{l_u}\in\mathbb{R}^{nu}\), \(\mathbf{l_{xx}}\in\mathbb{R}^{ndx\times ndx}\), \(\mathbf{l_{xu}}\in\mathbb{R}^{ndx\times nu}\), \(\mathbf{l_{uu}}\in\mathbb{R}^{nu\times nu}\) are the Jacobians and Hessians of the cost function, respectively. Additionally, it is important remark that calcDiff() computes the derivates using the latest stored values by calc(). Thus, we need to run first calc().
- See also
calc(), calcDiff(), createData()
Definition at line 59 of file action-base.hpp.
1.8.17