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Drake
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Implementations of controllers that operate as Systems in a block diagram.
Algorithms that synthesize controllers are located in Feedback Control Design.
Classes | |
| class | InverseDynamicsController< T > |
| A state feedback controller that uses a PidController to generate desired accelerations, which are then converted into torques using InverseDynamics. More... | |
| class | InverseDynamicsController< T > |
| A state feedback controller that uses a PidController to generate desired accelerations, which are then converted into torques using InverseDynamics. More... | |
| class | LinearModelPredictiveController< T > |
| Implements a basic Model Predictive Controller that linearizes the system about an equilibrium condition and regulates to the same point by solving an optimal control problem over a finite time horizon. More... | |
| class | PidControlledSystem< T > |
| A system that encapsulates a PidController and a controlled System (a.k.a the "plant"). More... | |
| class | PidController< T > |
| Implements the PID controller. More... | |
Functions | |
| LinearQuadraticRegulatorResult | LinearQuadraticRegulator (const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::MatrixXd > &B, const Eigen::Ref< const Eigen::MatrixXd > &Q, const Eigen::Ref< const Eigen::MatrixXd > &R, const Eigen::Ref< const Eigen::MatrixXd > &N=Eigen::Matrix< double, 0, 0 >::Zero()) |
| Computes the optimal feedback controller, u=-Kx, and the optimal cost-to-go J = x'Sx for the problem: More... | |
| LinearQuadraticRegulatorResult | DiscreteTimeLinearQuadraticRegulator (const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::MatrixXd > &B, const Eigen::Ref< const Eigen::MatrixXd > &Q, const Eigen::Ref< const Eigen::MatrixXd > &R) |
| Computes the optimal feedback controller, u=-Kx, and the optimal cost-to-go J = x'Sx for the problem: More... | |
| std::unique_ptr< systems::LinearSystem< double > > | LinearQuadraticRegulator (const LinearSystem< double > &system, const Eigen::Ref< const Eigen::MatrixXd > &Q, const Eigen::Ref< const Eigen::MatrixXd > &R, const Eigen::Ref< const Eigen::MatrixXd > &N=Eigen::Matrix< double, 0, 0 >::Zero()) |
| Creates a system that implements the optimal time-invariant linear quadratic regulator (LQR). More... | |
| std::unique_ptr< systems::AffineSystem< double > > | LinearQuadraticRegulator (const System< double > &system, const Context< double > &context, const Eigen::Ref< const Eigen::MatrixXd > &Q, const Eigen::Ref< const Eigen::MatrixXd > &R, const Eigen::Ref< const Eigen::MatrixXd > &N=Eigen::Matrix< double, 0, 0 >::Zero(), int input_port_index=0) |
| Linearizes the System around the specified Context, computes the optimal time-invariant linear quadratic regulator (LQR), and returns a System which implements that regulator in the original System's coordinates. More... | |
| Eigen::MatrixXd | ControllabilityMatrix (const LinearSystem< double > &sys) |
| Returns the controllability matrix: R = [B, AB, ..., A^{n-1}B]. More... | |
| bool | IsControllable (const LinearSystem< double > &sys, optional< double > threshold) |
| Returns true iff the controllability matrix is full row rank. More... | |
| Eigen::MatrixXd ControllabilityMatrix | ( | const LinearSystem< double > & | sys | ) |
Returns the controllability matrix: R = [B, AB, ..., A^{n-1}B].
| LinearQuadraticRegulatorResult DiscreteTimeLinearQuadraticRegulator | ( | const Eigen::Ref< const Eigen::MatrixXd > & | A, |
| const Eigen::Ref< const Eigen::MatrixXd > & | B, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | Q, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | R | ||
| ) |
Computes the optimal feedback controller, u=-Kx, and the optimal cost-to-go J = x'Sx for the problem:
\[ x[n+1] = Ax[n] + Bu[n] \]
\[ \min_u \sum_0^\infty x'Qx + u'Ru \]
| A | The state-space dynamics matrix of size num_states x num_states. |
| B | The state-space input matrix of size num_states x num_inputs. |
| Q | A symmetric positive semi-definite cost matrix of size num_states x num_states. |
| R | A symmetric positive definite cost matrix of size num_inputs x num_inputs. |
| std::runtime_error | if R is not positive definite. |
| bool IsControllable | ( | const LinearSystem< double > & | sys, |
| optional< double > | threshold | ||
| ) |
Returns true iff the controllability matrix is full row rank.
| LinearQuadraticRegulatorResult LinearQuadraticRegulator | ( | const Eigen::Ref< const Eigen::MatrixXd > & | A, |
| const Eigen::Ref< const Eigen::MatrixXd > & | B, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | Q, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | R, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | N = Eigen::Matrix< double, 0, 0 >::Zero() |
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| ) |
Computes the optimal feedback controller, u=-Kx, and the optimal cost-to-go J = x'Sx for the problem:
\[ \dot{x} = Ax + Bu \]
\[ \min_u \int_0^\infty x'Qx + u'Ru + 2x'Nu dt \]
| A | The state-space dynamics matrix of size num_states x num_states. |
| B | The state-space input matrix of size num_states x num_inputs. |
| Q | A symmetric positive semi-definite cost matrix of size num_states x num_states. |
| R | A symmetric positive definite cost matrix of size num_inputs x num_inputs. |
| N | A cost matrix of size num_states x num_inputs. If the matrix is zero-sized, N will be treated as a num_states x num_inputs zero matrix. |
| std::runtime_error | if R is not positive definite. |
| std::unique_ptr< LinearSystem< double > > LinearQuadraticRegulator | ( | const LinearSystem< double > & | system, |
| const Eigen::Ref< const Eigen::MatrixXd > & | Q, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | R, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | N = Eigen::Matrix< double, 0, 0 >::Zero() |
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| ) |
Creates a system that implements the optimal time-invariant linear quadratic regulator (LQR).
If system is a continuous-time system, then solves the continuous-time LQR problem:
\[ \min_u \int_0^\infty x^T(t)Qx(t) + u^T(t)Ru(t) dt. \]
If system is a discrete-time system, then solves the discrete-time LQR problem:
\[ \min_u \sum_0^\infty x^T[n]Qx[n] + u^T[n]Ru[n]. \]
| system | The System to be controlled. |
| Q | A symmetric positive semi-definite cost matrix of size num_states x num_states. |
| R | A symmetric positive definite cost matrix of size num_inputs x num_inputs. |
| N | A cost matrix of size num_states x num_inputs. |
| std::runtime_error | if R is not positive definite. |
| std::unique_ptr< AffineSystem< double > > LinearQuadraticRegulator | ( | const System< double > & | system, |
| const Context< double > & | context, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | Q, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | R, | ||
| const Eigen::Ref< const Eigen::MatrixXd > & | N = Eigen::Matrix< double, 0, 0 >::Zero(), |
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| int | input_port_index = 0 |
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| ) |
Linearizes the System around the specified Context, computes the optimal time-invariant linear quadratic regulator (LQR), and returns a System which implements that regulator in the original System's coordinates.
If system is a continuous-time system, then solves the continuous-time LQR problem:
\[ \min_u \int_0^\infty (x-x_0)^TQ(x-x_0) + (u-u_0)^TR(u-u_0) dt. \]
If system is a discrete-time system, then solves the discrete-time LQR problem:
\[ \min_u \sum_0^\infty (x-x_0)^TQ(x-x_0) + (u-u_0)^TR(u-u_0), \]
where \( x_0 \) is the nominal state and \( u_0 \) is the nominal input. The system is considered discrete if it has a single discrete state vector and a single unique periodic update event declared.
| system | The System to be controlled. |
| context | Defines the desired state and control input to regulate the system to. Note that this state/input must be an equilibrium point of the system. See drake::systems::Linearize for more details. |
| Q | A symmetric positive semi-definite cost matrix of size num_states x num_states. |
| R | A symmetric positive definite cost matrix of size num_inputs x num_inputs. |
| N | A cost matrix of size num_states x num_inputs. If the matrix is zero-sized, N will be treated as a num_states x num_inputs zero matrix. |
| int_port_index | The index of the input port to linearize around. |
| std::runtime_error | if R is not positive definite. |