State-space model for contact phase. More...
#include <LinearMpcZ.h>
Public Member Functions | |
| ModelContactPhase (double mass) | |
| Constructor. More... | |
 Public Member Functions inherited from CCC::StateSpaceModel< StateDim, InputDim, OutputDim > | |
| EIGEN_MAKE_ALIGNED_OPERATOR_NEW | StateSpaceModel (int state_dim=StateDim, int input_dim=InputDim, int output_dim=OutputDim) |
| Constructor. More... | |
| virtual | ~StateSpaceModel ()=default |
| Destructor. More... | |
| int | stateDim () const |
| Gets the state dimension. More... | |
| int | inputDim () const |
| Gets the input dimension. More... | |
| int | outputDim () const |
| Gets the output dimension. More... | |
| StateDimVector | stateEq (const StateDimVector &x, const InputDimVector &u) const |
| Calculate the continuous state equation. More... | |
| StateDimVector | stateEqDisc (const StateDimVector &x, const InputDimVector &u) const |
| Calculate the discrete state equation. More... | |
| OutputDimVector | observEq (const StateDimVector &x) const |
| Calculate the observation equation. More... | |
| OutputDimVector | observEq (const StateDimVector &x, const InputDimVector &u) const |
| Calculate the observation equation. More... | |
| void | calcDiscMatrix (double dt) |
| Calculate the discrete system matrices \(\boldsymbol{A}_d, \boldsymbol{B}_d, \boldsymbol{e}_d\). More... | |
Additional Inherited Members | |
| Public Types inherited from CCC::StateSpaceModel< StateDim, InputDim, OutputDim > | |
| using | StateDimVector = Eigen::Matrix< double, StateDim, 1 > |
| Type of state vector. More... | |
| using | InputDimVector = Eigen::Matrix< double, InputDim, 1 > |
| Type of input vector. More... | |
| using | OutputDimVector = Eigen::Matrix< double, OutputDim, 1 > |
| Type of output vector. More... | |
| Public Attributes inherited from CCC::StateSpaceModel< StateDim, InputDim, OutputDim > | |
| const int | state_dim_ = 0 |
| State dimension. More... | |
| const int | input_dim_ = 0 |
| Input dimension. More... | |
| const int | output_dim_ = 0 |
| Output dimension. More... | |
| Eigen::Matrix< double, StateDim, StateDim > | A_ |
| Matrix \(\boldsymbol{A}\) of continuous state equation. More... | |
| Eigen::Matrix< double, StateDim, InputDim > | B_ |
| Matrix \(\boldsymbol{B}\) of continuous state equation. More... | |
| Eigen::Matrix< double, OutputDim, StateDim > | C_ |
| Matrix \(\boldsymbol{C}\) of observation equation. More... | |
| Eigen::Matrix< double, OutputDim, InputDim > | D_ |
| Matrix \(\boldsymbol{D}\) of observation equation. More... | |
| StateDimVector | E_ |
| Offset vector \(\boldsymbol{e}\) of continuous state equation. More... | |
| OutputDimVector | F_ |
| Offset vector \(\boldsymbol{f}\) of observation equation. More... | |
| double | dt_ = 0 |
| Discretization timestep [sec] (zero if discrete coefficients are not initialized) More... | |
| Eigen::Matrix< double, StateDim, StateDim > | Ad_ |
| Matrix \(\boldsymbol{A}_d\) of discrete state equation. More... | |
| Eigen::Matrix< double, StateDim, InputDim > | Bd_ |
| Matrix \(\boldsymbol{B}_d\) of discrete state equation. More... | |
| StateDimVector | Ed_ |
| Offset vector \(\boldsymbol{e}_d\) of discrete state equation. More... | |
Detailed Description
State-space model for contact phase.
Dynamics is expressed by the following equation.
\begin{align*} P_z &= m \dot{c}_z \\ \dot{P}_z &= f_z - m g \end{align*}
\(c_z\), \(P_z\), and \(f_z\) are CoM height, vertical linear momentum, and vertical contact force, respectively.
This can be represented as a linear time-invariant system as follows.
\begin{align*} \boldsymbol{\dot{x}} &= \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \boldsymbol{x} + \begin{bmatrix} 0 \\ 1 \end{bmatrix} u + \begin{bmatrix} 0 \\ - m g \end{bmatrix} \\ y &= \begin{bmatrix} \dfrac{1}{m} & 0 \end{bmatrix} \boldsymbol{x} \end{align*}
State, control input, and output are expressed as follows.
\begin{align*} \boldsymbol{x} = \begin{bmatrix} m c_z \\ P_z \end{bmatrix}, u = f_z, y = c_z \end{align*}
Definition at line 75 of file LinearMpcZ.h.
Constructor & Destructor Documentation
◆ ModelContactPhase()
| CCC::LinearMpcZ::ModelContactPhase::ModelContactPhase | ( | double | mass | ) |
Constructor.
- Parameters
-
mass robot mass [kg]
The documentation for this class was generated from the following file:
- /home/runner/work/CentroidalControlCollection/CentroidalControlCollection/catkin_ws/src/CentroidalControlCollection/include/CCC/LinearMpcZ.h
