sleipnir.optimization.OCP Class Reference

Inheritance diagram for sleipnir.optimization.OCP:

Public Member Functions
None	__init__ (self, int num_states, int num_inputs, datetime.timedelta|float dt, int num_steps, Callable[[VariableMatrix, VariableMatrix], VariableMatrix] dynamics, DynamicsType dynamics_type=DynamicsType.EXPLICIT_ODE, TimestepMethod timestep_method=TimestepMethod.FIXED, TranscriptionMethod transcription_method=TranscriptionMethod.DIRECT_TRANSCRIPTION)
None	constrain_initial_state (self, float initial_state)
None	constrain_initial_state (self, int initial_state)
None	constrain_initial_state (self, Variable initial_state)
None	constrain_initial_state (self, Annotated[NDArray[numpy.float64], dict(shape=(None, None))] initial_state)
None	constrain_initial_state (self, VariableMatrix initial_state)
None	constrain_final_state (self, float final_state)
None	constrain_final_state (self, int final_state)
None	constrain_final_state (self, Variable final_state)
None	constrain_final_state (self, Annotated[NDArray[numpy.float64], dict(shape=(None, None))] final_state)
None	constrain_final_state (self, VariableMatrix final_state)
None	for_each_step (self, Callable[[VariableMatrix, VariableMatrix], None] callback)
None	set_lower_input_bound (self, float lower_bound)
None	set_lower_input_bound (self, int lower_bound)
None	set_lower_input_bound (self, Variable lower_bound)
None	set_lower_input_bound (self, Annotated[NDArray[numpy.float64], dict(shape=(None, None))] lower_bound)
None	set_lower_input_bound (self, VariableMatrix lower_bound)
None	set_upper_input_bound (self, float upper_bound)
None	set_upper_input_bound (self, int upper_bound)
None	set_upper_input_bound (self, Variable upper_bound)
None	set_upper_input_bound (self, Annotated[NDArray[numpy.float64], dict(shape=(None, None))] upper_bound)
None	set_upper_input_bound (self, VariableMatrix upper_bound)
None	set_min_timestep (self, datetime.timedelta|float min_timestep)
None	set_max_timestep (self, datetime.timedelta|float max_timestep)
VariableMatrix	X (self)
VariableMatrix	U (self)
VariableMatrix	dt (self)
VariableMatrix	initial_state (self)
VariableMatrix	final_state (self)
Public Member Functions inherited from sleipnir.optimization.Problem
Variable	decision_variable (self)
VariableMatrix	decision_variable (self, int rows, int cols=1)
VariableMatrix	symmetric_decision_variable (self, int rows)
None	minimize (self, Variable cost)
None	minimize (self, VariableMatrix cost)
None	minimize (self, float cost)
None	maximize (self, Variable objective)
None	maximize (self, VariableMatrix objective)
None	maximize (self, float objective)
None	subject_to (self, EqualityConstraints constraint)
None	subject_to (self, InequalityConstraints constraint)
ExpressionType	cost_function_type (self)
ExpressionType	equality_constraint_type (self)
ExpressionType	inequality_constraint_type (self)
ExitStatus	solve (self, **kwargs)
None	add_callback (self, Callable[[IterationInfo], bool] callback)
None	clear_callbacks (self)

Detailed Description

This class allows the user to pose and solve a constrained optimal
control problem (OCP) in a variety of ways.

The system is transcripted by one of three methods (direct
transcription, direct collocation, or single-shooting) and additional
constraints can be added.

In direct transcription, each state is a decision variable constrained
to the integrated dynamics of the previous state. In direct
collocation, the trajectory is modeled as a series of cubic
polynomials where the centerpoint slope is constrained. In single-
shooting, states depend explicitly as a function of all previous
states and all previous inputs.

Explicit ODEs are integrated using RK4.

For explicit ODEs, the function must be in the form dx/dt = f(t, x,
u). For discrete state transition functions, the function must be in
the form xₖ₊₁ = f(t, xₖ, uₖ).

Direct collocation requires an explicit ODE. Direct transcription and
single-shooting can use either an ODE or state transition function.

https://underactuated.mit.edu/trajopt.html goes into more detail on
each transcription method.

Template parameter ``Scalar``:
    Scalar type.

Constructor & Destructor Documentation

__init__()

None sleipnir.optimization.OCP.__init__	(		self,
		int	num_states,
		int	num_inputs,
		datetime.timedelta | float	dt,
		int	num_steps,
		Callable[[VariableMatrix, VariableMatrix], VariableMatrix]	dynamics,
		DynamicsType	dynamics_type = DynamicsType.EXPLICIT_ODE,
		TimestepMethod	timestep_method = TimestepMethod.FIXED,
		TranscriptionMethod	transcription_method = TranscriptionMethod.DIRECT_TRANSCRIPTION
	)

Build an optimization problem using a system evolution function
(explicit ODE or discrete state transition function).

Parameter ``num_states``:
    The number of system states.

Parameter ``num_inputs``:
    The number of system inputs.

Parameter ``dt``:
    The timestep for fixed-step integration.

Parameter ``num_steps``:
    The number of control points.

Parameter ``dynamics``:
    Function representing an explicit or implicit ODE, or a discrete
    state transition function. - Explicit: dx/dt = f(x, u, *) -
    Implicit: f([x dx/dt]', u, *) = 0 - State transition: xₖ₊₁ = f(xₖ,
    uₖ)

Parameter ``dynamics_type``:
    The type of system evolution function.

Parameter ``timestep_method``:
    The timestep method.

Parameter ``transcription_method``:
    The transcription method.

Reimplemented from sleipnir.optimization.Problem.

Member Function Documentation

constrain_final_state() [1/5]

None sleipnir.optimization.OCP.constrain_final_state	(		self,
		Annotated[NDArray[numpy.float64], dict(shape=(None, None))]	final_state
	)

constrain_final_state() [2/5]

None sleipnir.optimization.OCP.constrain_final_state	(		self,
		float	final_state
	)

Utility function to constrain the final state.

Parameter ``final_state``:
    the final state to constrain to.

constrain_final_state() [3/5]

None sleipnir.optimization.OCP.constrain_final_state	(		self,
		int	final_state
	)

constrain_final_state() [4/5]

None sleipnir.optimization.OCP.constrain_final_state	(		self,
		Variable	final_state
	)

constrain_final_state() [5/5]

None sleipnir.optimization.OCP.constrain_final_state	(		self,
		VariableMatrix	final_state
	)

constrain_initial_state() [1/5]

None sleipnir.optimization.OCP.constrain_initial_state	(		self,
		Annotated[NDArray[numpy.float64], dict(shape=(None, None))]	initial_state
	)

constrain_initial_state() [2/5]

None sleipnir.optimization.OCP.constrain_initial_state	(		self,
		float	initial_state
	)

Utility function to constrain the initial state.

Parameter ``initial_state``:
    the initial state to constrain to.

constrain_initial_state() [3/5]

None sleipnir.optimization.OCP.constrain_initial_state	(		self,
		int	initial_state
	)

constrain_initial_state() [4/5]

None sleipnir.optimization.OCP.constrain_initial_state	(		self,
		Variable	initial_state
	)

constrain_initial_state() [5/5]

None sleipnir.optimization.OCP.constrain_initial_state	(		self,
		VariableMatrix	initial_state
	)

dt()

VariableMatrix sleipnir.optimization.OCP.dt

(

self

)

Get the timestep variables. After the problem is solved, this will
contain the timesteps corresponding to the optimized trajectory.

Shaped 1x(num_steps+1), although the last timestep is unused in the
trajectory.

Returns:
    The timestep variable matrix.

final_state()

VariableMatrix sleipnir.optimization.OCP.final_state

(

self

)

Convenience function to get the final state in the trajectory.

Returns:
    The final state of the trajectory.

for_each_step()

None sleipnir.optimization.OCP.for_each_step	(		self,
		Callable[[VariableMatrix, VariableMatrix], None]	callback
	)

Set the constraint evaluation function. This function is called
`num_steps+1` times, with the corresponding state and input
VariableMatrices.

Parameter ``callback``:
    The callback f(x, u) where x is the state and u is the input
    vector.

initial_state()

VariableMatrix sleipnir.optimization.OCP.initial_state

(

self

)

Convenience function to get the initial state in the trajectory.

Returns:
    The initial state of the trajectory.

set_lower_input_bound() [1/5]

None sleipnir.optimization.OCP.set_lower_input_bound	(		self,
		Annotated[NDArray[numpy.float64], dict(shape=(None, None))]	lower_bound
	)

set_lower_input_bound() [2/5]

None sleipnir.optimization.OCP.set_lower_input_bound	(		self,
		float	lower_bound
	)

Convenience function to set a lower bound on the input.

Parameter ``lower_bound``:
    The lower bound that inputs must always be above. Must be shaped
    (num_inputs)x1.

set_lower_input_bound() [3/5]

None sleipnir.optimization.OCP.set_lower_input_bound	(		self,
		int	lower_bound
	)

set_lower_input_bound() [4/5]

None sleipnir.optimization.OCP.set_lower_input_bound	(		self,
		Variable	lower_bound
	)

set_lower_input_bound() [5/5]

None sleipnir.optimization.OCP.set_lower_input_bound	(		self,
		VariableMatrix	lower_bound
	)

set_max_timestep()

None sleipnir.optimization.OCP.set_max_timestep	(		self,
		datetime.timedelta | float	max_timestep
	)

Convenience function to set an upper bound on the timestep.

Parameter ``max_timestep``:
    The maximum timestep.

set_min_timestep()

None sleipnir.optimization.OCP.set_min_timestep	(		self,
		datetime.timedelta | float	min_timestep
	)

Convenience function to set a lower bound on the timestep.

Parameter ``min_timestep``:
    The minimum timestep.

set_upper_input_bound() [1/5]

None sleipnir.optimization.OCP.set_upper_input_bound	(		self,
		Annotated[NDArray[numpy.float64], dict(shape=(None, None))]	upper_bound
	)

set_upper_input_bound() [2/5]

None sleipnir.optimization.OCP.set_upper_input_bound	(		self,
		float	upper_bound
	)

Convenience function to set an upper bound on the input.

Parameter ``upper_bound``:
    The upper bound that inputs must always be below. Must be shaped
    (num_inputs)x1.

set_upper_input_bound() [3/5]

None sleipnir.optimization.OCP.set_upper_input_bound	(		self,
		int	upper_bound
	)

set_upper_input_bound() [4/5]

None sleipnir.optimization.OCP.set_upper_input_bound	(		self,
		Variable	upper_bound
	)

set_upper_input_bound() [5/5]

None sleipnir.optimization.OCP.set_upper_input_bound	(		self,
		VariableMatrix	upper_bound
	)

U()

VariableMatrix sleipnir.optimization.OCP.U

(

self

)

Get the input variables. After the problem is solved, this will
contain the inputs corresponding to the optimized trajectory.

Shaped (num_inputs)x(num_steps+1), although the last input step is
unused in the trajectory.

Returns:
    The input variable matrix.

X()

VariableMatrix sleipnir.optimization.OCP.X

(

self

)

Get the state variables. After the problem is solved, this will
contain the optimized trajectory.

Shaped (num_states)x(num_steps+1).

Returns:
    The state variable matrix.

---

The documentation for this class was generated from the following file:

• python/src/sleipnir/optimization/__init__.py