Trajectory Phases

FreeFlyer's optimal control capabilities can be used to solve a variety of problems related to trajectory design, maneuver planning, and more. Optimization features are available in FreeFlyer's Mission tier.

The basic components of an optimization problem work flow are as follows, in order:

At the bottom of the page is a completed example demonstrating a continuous thrust orbit change maximizing delivered fuel which uses many of the properties and methods introduced on this page.

Creating and Initializing a TrajectoryPhase Object

A TrajectoryPhase object can be created either through the object browser or via FreeFlyer script, but must be edited through script. Once the TrajectoryPhase object has been created, users have the ability to edit properties and methods that pertain specifically to the collocation dynamical solver through the TrajectoryPhase.CollocationOptions property. The example below demonstrates creating a TrajectoryPhase object and configuring the ForceModel through the TrajectoryPhase.CollocationOptions property:

Configure the Control Model

The TrajectoryPhase object currently supports three control models: ballistic, simple thruster, and ideal solar sail to use for analysis through the TrajectoryPhase.ControlType property. All control models and their associated variables are formulated in the MJ2000 Earth Equator coordinate frame. The example below demonstrates configuring a TrajectoryPhase with a Simple Thruster control model:

For more information on control models and the properties associated with the supported control models, see the Control Models guide.

Generate Initial Guess

After the TrajectroyPhase has been initialized, the next step is to define the problem that must be solved. This involves setting up a Spacecraft object and adding nodes to the TrajectoryPhase object.

Set up Spacecraft

The first step is to configure a Spacecraft object which will be used to add nodes to the TrajectoryPhase object. This process includes defining the Spacecraft's Force Model and assigning an initial state to be used for propagation. Note, the Spacecraft object and initial guess for the TrajectoryPhase can also be set up using an Ephemeris object.

Adding Nodes

TrajectoryPhase.AddNode()

Nodes can be added using the TrajectoryPhase.AddNode() method through four different overloads as shown below:

1.TrajectoryPhase.AddNode(Spacecraft spacecraft): Add a node to the TrajectoryPhase object using the current state of the passed Spacecraft.

Note: If the Spacecraft's central body differs from the TrajectoryPhase's central body, a state conversion will take place automatically before the TrajectoryNode is added.

2.TrajectoryPhase.AddNode(TrajectoryNode trajectoryNode): Add a state to the TrajectoryPhase object using the passed TrajectoryNode.

3.TrajectoryPhase.AddNode(Spacecraft spacecraft, Array controlVariables): Add a state to the TrajectoryPhase object using the current state of the passed Spacecraft. The node control variables will also be assigned using the control Array argument.

Note: The number and order of elements in the controlVariables Array must equal the number and order of control variables in the selected ControlModel. Refer to the TrajectoryPhase.ControlModel property for more information on control variables.

4.TrajectoryPhase.AddNode(Array posvel, Variable mass, TimeSpan epoch, Array controlVariables): Adds a state to the TrajectoryPhase using the passed position, velocity, mass, epoch, and control variables.

TrajectoryPhase.AddNodes()

Nodes can be added using the TrajectoryPhase.AddNodes() method through three different overloads as shown below:

1.TrajectoryPhase.AddNodes(Ephemeris ephemeris): Uses the position, velocity, mass, and epoch data from the Ephemeris to create new TrajectoryNodes.

2.TrajectoryPhase.AddNode(TrajectoryPhase trajectoryPhase): Appends TrajectoryNodes from the passed TrajectoryPhase to the calling TrajectoryPhase.

3.TrajectoryPhase.AddNode(Spacecraft spacecraft, TimeSpan duration, Variable numberOfNodes, Variable resetSpacecraftState): Propagates the passed Spacecraft using its current Propagator for the passed duration and saves numberOfNodes equally spaced TrajectoryNodes during the propagation. If resetSpacecraftState = 1, then the Spacecraft's state will be restored to its original state once the process is complete.

Resampling Nodes

The TrajectoryPhase.ResampleNodes() method re-interpolates the TrajectoryPhase's nodes using new node spacing. Although you cannot change discretization while solving the problem, a common approach is to solve the problem using a relatively sparse discretization so it is easy for the optimizer to solve the problem, then resample to have a higher number of nodes. The script below demonstrates setting up a TrajectoryPhase object which is added to a ViewWindow for visualization. After setting up the TrajectoryPhase object, adding nodes to the TrajectoryPhase, and adding the TrajectoryPhase to the Optimizer, users can add any of the ResampleNodes() method calls to the bottom of the script to gain a better understanding of how nodes are resampled.

Nodes can be resampled using the TrajectoryPhase.ResampleNodes() method through three different overloads as shown below:

1.TrajectoryPhase.ResampleNodes(Variable numberOfPoints): Re-interpolates the TrajectoryPhase's nodes using a uniform spacing of node points in time.

2.TrajectoryPhase.ResampleNodes(Array numberOfPointsArray, Array barriers): Re-interpolates the TrajectoryPhase's nodes using independent uniform distributions of TrajectoryNodes in time within user-defined barriers.

Note: The numberOfPoints Array must have one less element than the barriers Array argument. Additionally, the barriers Array argument must begin with 0 and end with 1.

3.TrajectoryPhase.ResampleNodes(Variable numberOfPoints, String shape, Variable weight):

Example: Adding Nodes to a TrajectoryPhase

The script example below demonstrates configuring a Spacecraft with a semi-major axis of 10,000 km and propagating it for one period adding one node to the TrajectoryPhase object at each step. Once all the nodes have been added to the TrajectoryPhase, the TrajectoryPhase.ResampleNodes() method is called to re-interpolate the TrajectoryPhase's nodes creating 50 uniform spaced node points.

// Initialize TrajectoryPhase object

TrajectoryPhase phase;

phase.CollocationOptions.ForceModel.Sun = 0;

phase.CollocationOptions.ForceModel.Moon = 0;

phase.CollocationOptions.ForceModel.PlanetFieldType[2] = 0;

phase.CollocationOptions.ForceModel.Drag = 0;

// Configure the TrajectoryPhase to have a 'Simple Thruster' control model and set thruster parameters

phase.ControlModel.ControlType = 1;

phase.ControlModel.SimpleThrusterOptions.Thrust = 100;

phase.ControlModel.SimpleThrusterOptions.Isp = 200;

// Configure the Spacecraft and its ForceModel

Spacecraft sc;

Alias scFM = (sc.Propagator AsType Integrator).ForceModel;

scFM.Sun = 0;

scFM.Moon = 0;

scFM.PlanetFieldType[2] = 0;

scFM.Drag = 0;

sc.MassTotal = 1000;

sc.A = 10000;

sc.E = 0.0001;

sc.I = 10;

sc.TA = 0;

// Create TimeSpan object for propagation loop

TimeSpan stepTo = sc.Epoch + (sc.Period).ToTimeSpan("min");

// Propagate the Spacecraft for 1 period, adding a node at each Step

WhileStepping sc to (sc.Epoch == stepTo);

phase.AddNode(sc);

End;

// Report the number of nodes in the TrajectoryPhase before re-sampling nodes

Report phase.Nodes.Count;

// Re-interpolate the TrajectoryPhase's nodes to create 50 uniform spaced node points

phase.ResampleNodes(50);

// Report the number of nodes in the TrajectoryPhase after re-sampling nodes

Report phase.Nodes.Count;

Set Bounds

To further constrain the problem, users can set bounds on variables associated with the TrajectoryPhase through a number of useful methods. These variables can be locked at the "first" or "last" node of the TrajectoryPhase or along the entire "path" of the TrajectoryPhase with a passed range and/or index.

1.SetPositionBounds(): Set bounds for the Cartesian position variables associated with the passed range and index.

2.SetVelocityBounds(): Set bounds for the Cartesian velocity variables associated with the passed range and index.

3.SetMassBounds(): Set bounds for the TrajectoryPhase mass associated with the passed range.

4.SetEpochBounds(): Set bounds for the TrajectoryPhase epoch associated with the passed range.

6.SetControlVariableBounds(): Set bounds for the TrajectoryPhase's control variables associated with the passed range and indices.

Lock Variables

The TrajectoryPhase object allows users to 'Lock' variables through a number of useful methods. These variables can be locked at either the "first" or "last" node in the TrajectoryPhase and/or can be passed user-defined values for either endpoint.

1.LockPosition(): Lock Cartesian position variables associated with the passed endpoint to their current values or to user defined passed values.

2.LockVelocity(): Lock Cartesian velocity variables associated with the passed endpoint to their current values or to user defined passed values.

3.LockPositionVelocity(): Lock Cartesian position and velocity variables associated with the passed endpoint to their current values or to user defined passed values.

4.LockMass(): Lock the TrajectoryPhase mass variable associated with the passed endpoint to their current values or to user defined passed values.

5.LockEpoch(): Lock the TrajectoryPhase epoch variable associated with the passed endpoint to their current values or to user defined passed values.

6.Lock(): Locks all TrajectoryPhase position, velocity, mass, and epoch variables associated with the passed endpoint argument to their current values.

7.LockByIndices(): Locks only the TrajectoryPhase variables associated with the passed endpoint and indices.

Note: Any indices after 7 represent potential control variables. Certain control variable indices may or may not exist depending on which ControlModel is selected.

8.LockTimeOfFlight(): Locks the time of flight of the TrajectoryPhase to the current value or to a user defined passed value.

9.LockControlVariables(): Locks the TrajectoryPhase control variables associated with the passed endpoint and index to its current or user defined passed values.

Example: Initial Configuration for an Earth to Mars Low-Thrust transfer

The script example below demonstrates configuring a Spacecraft performing a low thrust transfer from Earth to Mars. Two TrajectoryPhases are configured, one for the Earth outbound leg and one for the Mars inbound leg of the trajectory. Both TrajectoryPhases are configured with a 'Simple Thruster' control model. The Earth outbound leg of the trajectory (phaseEarth) is loaded with node points by forward propagating to the epoch at the "midpoint" of the initial guess trajectory, then the ResampleNodes() method is called to create 25 uniform nodes along the path. The Mars inbound leg of the trajectory (phaseMars) is loaded with node points by backwards propagating from the end epoch to the epoch at the "midpoint" of the initial guess trajectory, then the Reverse() method is called to put the node points in order before resampling to create 25 uniform nodes along the path. The LockMass() method is called to lock the mass at the end point of the trajectory to 1287 kg, and the SetVelocityBounds() method is called to constrain both TrajectoryPhases Cartesian velocity between -100 and 100 km/s. The FirstNode.Mass property is used to minimize mass at the start of the trajectory, which is the equivalent of minimizing fuel usage.

// Initialize Earth Outbound Trajectory Segment

TrajectoryPhase phaseEarth;

phaseEarth.SetCentralBody(Sun);

Alias phaseEarthFM = phaseEarth.CollocationOptions.ForceModel;

phaseEarthFM.Earth = 0;

phaseEarthFM.Moon = 0;

phaseEarthFM.Drag = 0;

// Configure the TrajectoryPhase to have a 'Simple Thruster' control model and set thruster parameters

phaseEarth.ControlModel.SimpleThrusterOptions.Thrust = 0.7;

phaseEarth.ControlModel.SimpleThrusterOptions.Isp = 3800;

phaseEarth.ControlModel.ControlType = 1;

// Initialize Mars Inbound Trajectory Segment

TrajectoryPhase phaseMars;

phaseMars.SetCentralBody(Sun);

Alias phaseMarsFM = phaseMars.CollocationOptions.ForceModel;

phaseMarsFM.Earth = 0;

phaseMarsFM.Moon = 0;

phaseMarsFM.Drag = 0;

// Configure the TrajectoryPhase to have a 'Simple Thruster' control model and assign thruster parameters

phaseMars.ControlModel.SimpleThrusterOptions.Thrust = phaseEarth.ControlModel.SimpleThrusterOptions.Thrust;

phaseMars.ControlModel.SimpleThrusterOptions.Isp = phaseEarth.ControlModel.SimpleThrusterOptions.Isp;

phaseMars.ControlModel.ControlType = phaseEarth.ControlModel.ControlType;

// Configure the Spacecraft and its ForceModel

Spacecraft sc;

sc.SetCentralBody(Sun);

Alias scFM = (sc.Propagator AsType Integrator).ForceModel;

scFM.Earth = 0;

scFM.Moon = 0;

scFM.Drag = 0;

sc.MassTotal = 1500;

// Initial Guesses for launch epoch, time of flight, and epoch at the midpoint

TimeSpan launch_initialGuess = TimeSpan.FromDays(54700);

TimeSpan tof_initialGuess = TimeSpan.FromDays(300);

TimeSpan midpoint_initialGuess = launch_initialGuess + tof_initialGuess.Scaled(0.5);

sc.Epoch = launch_initialGuess;

sc.SetCartesianState(Earth.GetPosVelAtEpoch(sc.Epoch));

// While stepping to the epoch at the midpoint add a node for each step of the Spacecraft

WhileStepping sc to (sc.Epoch == midpoint_initialGuess);

phaseEarth.AddNode(sc);

End;

// Re-interpolate the TrajectoryPhase's nodes to create 25 uniform spaced node points

phaseEarth.ResampleNodes(25);

// Reset the Spacecraft's epoch to the end point (Mars)

sc.Epoch = launch_initialGuess + tof_initialGuess;

sc.SetCartesianState(Mars.GetPosVelAtEpoch(sc.Epoch));

// While stepping backwards to the epoch at the midpoint add a node for each step of the Spacecraft

WhileStepping sc to (sc.Epoch == midpoint_initialGuess);

phaseMars.AddNode(sc);

End;

// Reverse the order of the TrajectoryPhase's nodes so all nodes are in order

phaseMars.Reverse();

// Re-interpolate the TrajectoryPhase's nodes to create 25 uniform spaced node points

phaseMars.ResampleNodes(25);

// Lock the epoch at the first node

phaseEarth.LockEpoch("first");

// Lock the mass at the last node point to be 1287 kg

phaseMars.LockMass("last", 1287);

// Set velocity bounds along the entire trajectory path between -100/100 km/s for both TrajectoryPhases

phaseEarth.SetVelocityBounds("path", -100, 100);

phaseMars.SetVelocityBounds("path", -100, 100);

Add Trajectory Phases to the Optimizer

After all TrajectoryPhases have been configured, the next step is to add the TrajectoryPhase object to the optimization problem by using the Optimizer.AddTrajectoryPhase() method. When the Optimizer.LoadEngine() method is called, all variables and constraints associated with the added TrajectoryPhases will automatically be added to the optimization problem. Continuing the example above, Initial Configuration for an Earth to Mars Low-Thrust transfer, the script example below demonstrates adding multiple TrajectoryPhase objects to the Optimizer. For more information on configuring and using the Optimizer object, see the Using the Optimizer guide.

Define Phase Links and Add General Constraints

Constraints are used in an optimization process to define conditions which must be met in order for a solution produced by the Optimizer object to be considered feasible. Similar to state variables, constraints can be added to the process via the Optimizer.AddConstraint() or Optimizer.AddConstraintBlock() methods, which require the user to set a label to be used to identify the constraint within the process. For more information on configuring constraints, see the Configuring Constraints section of the Using the Optimizer Guide.

When solving an optimization problem that includes multiple TrajectoryPhase objects that are intended to be continuous (e.g., Initial Configuration for an Earth to Mars Low-Thrust transfer), users have the ability to link the phases across the position, velocity, mass, and epoch variables through the Optimizer.AddPhaseLink() method. Continuing the example above, the script below demonstrates linking the last node of the phaseEarth TrajectoryPhase to the first node of the phaseMars TrajectoryPhase using two different method overloads. Both methods add constraint(s) to the optimization problem to ensure that the phases are continuous. This script example also demonstrates adding generalized constraints to the optimization problem.

Solve and Query Results

Once defined, the problem must be loaded into a third-party optimization library. FreeFlyer includes built-in support for Ipopt and NLopt. FreeFlyer also supports SNOPT, but the user must have an SNOPT license and provide the path to the SNOPT shared library file (.dll on Windows, .so on Linux). For more information on each third-party tool, see Optimization Engines.

Load the Optimization Engine

The optimization engine is loaded by calling the LoadEngine() method on the Optimizer object. If called with no arguments, Ipopt will be loaded by default.

If using SNOPT, the user must provide the path to their shared library file. The user can specify the shared library file for Ipopt or NLopt as well, if they wish to use their own version of the library instead of the one built in to FreeFlyer.

Each optimization engine has additional settings specific to each library. The process for accessing these tuning parameters is described on the Optimization Engines page.

Create the Evaluation Loop and Retrieve the Best Solution

The process of creating an evaluation loop and retrieving the best solution is summarized below but can be found in more detail on the Using the Optimizer guide. The basic steps of creating the evaluation loop and retrieving the best solution are as follows, in order:

1.Loop Condition: The optimization process happens within a While loop; the Optimizer object will continue to iterate until the condition in the loop evaluates to false. Two methods on the Optimizer object can be used as the loop condition, depending on the desired behavior: HasNotConverged() or IsRunning().

2.Restore Saved Objects: The first step within the evaluation loop is to restore any objects that have been saved to the process and need to be returned to their initial state for each iteration.

3.Update and Retrieve State Variables: At the beginning of each iteration of the evaluation loop, the state variables must be updated using the Optimizer.UpdateStateVariables() method. This method advances all the state variables in the process to the Optimizer object's next guess.

4.Perform Analysis: Once the latest state variable values have been retrieved from the Optimizer object, any analysis that is necessary to calculate the constraints or objective function should be performed. This could include Spacecraft propagation, contact analysis, performing maneuvers, and more.

5.Update Constraints: Once any necessary analysis has been performed, the resulting constraints must be calculated and fed back into the Optimizer object using the Optimizer.SetConstraintValue() method.

6.Provide Known Derivatives: If desired, the user can provide the optimization engine with any known derivatives of the problem constraints or objective function by populating the Jacobian Matrix and Gradient Array properties of the Optimizer object on every nominal case iteration within the evaluation loop. This is an optional input that can improve performance; see Specifying Known Derivatives for more information.

7.Minimize or Maximize the Objective Function: The objective function defines the quantity which needs to be minimized or maximized by the Optimizer object in order to produce an optimal solution. The objective function is passed in as an argument to the Optimizer.Minimize() or Optimizer.Maximize() method, and the Optimizer object works to vary the state variable values in order to find the best solution to the objective function that meets the problem's defined constraints.

8.Solve Constraints: An alternative to minimizing or maximizing an objective function is the Optimizer.SolveConstraints() method, which finds a feasible solution to satisfy the problem constraints without needing to specify an objective function. This approach will allow the Optimizer object to converge on a solution that is feasible, but not necessarily optimal.

9.Generate Output: Data reports and graphical output can be generated within the evaluation loop of an optimization process as well as after converging on a solution and/or exiting the loop. Views, Plots, and Reporting mechanisms all behave the same way within an optimization loop as they do in any other context; FreeFlyer's suite of Optimization Sample Mission Plans contain numerous examples of output generation within an optimization process. There are various convenient properties and methods on the Optimizer object that enable the user to easily retrieve information about the optimization process both during and after iteration. Reports about the optimization process within an evaluation loop should always be generated after the call to Optimizer.Minimize(), Optimizer.Maximize(), or Optimizer.SolveConstraints() to ensure that the most up-to-date values are being reported.

Visualization

The TrajectoryPhase object allows users to visualize nodes and paths in 3D views. The TrajectoryPhase.DrawNode property determines whether a tick mark will be drawn at the current node. The size of the drawn node can be increased or decreased using the TrajectoryPhase.NodeTickWidth property. The shape of the drawn node can be set using the TrajectoryPhase.NodeTickType property. Nodes can be colored in three different ways using the TrajectoryPhase.NodeColorMode property:

2.Collocation Defect Error - color coded according to the collocation defect error (gradient of red/orange/yellow/green). Red indicates collocation defect error, and green indicates collocation defect integrity.

3.Dynamical Error - color coded according to the dynamical error (gradient of red/orange/yellow/green). Red indicates collocation defect error, and green indicates collocation defect integrity.

The TrajectoryPhase.DrawPath property determines whether a line will be drawn between the previous node and the current node when updating the view. Paths can be colored in three different ways similar to coloring nodes using the TrajectoryPhase.PathColorMode property:

2. Collocation Defect Error - color coded according to the collocation defect error (gradient of red/orange/yellow/green). Red indicates collocation defect error, and green indicates collocation defect integrity.

3. Dynamical Error - color coded according to the dynamical error (gradient of red/orange/yellow/green). Red indicates collocation defect error, and green indicates collocation defect integrity.

To gain more insight into the optimization process, users have the ability to draw control vectors for a TrajectoryPhase using the TrajectoryPhase.DrawControlVector property. The TrajectoryPhase.DrawControlVector determines whether a control vector will be drawn at the current node. Note, when using a ballistic control model the control vector does not exist in which case this property has no effect. Control vectors can be colored in three different ways similar to coloring nodes using the TrajectoryPhase.ControlVectorColorMode property:

2. Collocation Defect Error - color coded according to the collocation defect error (gradient of red/orange/yellow/green). Red indicates collocation defect error, and green indicates collocation defect integrity.

3. Dynamical Error - color coded according to the dynamical error (gradient of red/orange/yellow/green). Red indicates collocation defect error, and green indicates collocation defect integrity.

The TrajectoryPhase.ControlVectorMaximumLength property determines the maximum length in kilometers of the control vectors in the mission view. When the control model is producing less than the maximum possible thrust, the actual length of the visualized control vector will be scaled down proportionately to the ratio of actual thrust to maximum possible thrust. Users can set this property to zero to have FreeFlyer scale the control vectors so that the maximum control vector length is about 1/8th the scale of the TrajectoryPhase itself in a central body-centric inertial frame.

Complete Example

The Continuous Thrust Orbit Change example that has been constructed throughout this page is presented in its entirety below, with descriptions to indicate each section of the workflow.

//==============================================

// Procedure for visualizations

//==============================================

Define Procedure visualize(Optimizer opt, ViewWindow vw, Variable clearTails);

Variable phase;

Variable node;

Array colors = ColorTools.GetPaletteColors("Light");

If (clearTails);

vw.ResetTails();

End;

vw.BeginBatchUpdate();

// Loop through each TrajectoryPhase loaded into the Optimizer

For phase = 0 to opt.TrajectoryPhases.Count - 1;

opt.TrajectoryPhases[phase].PathConstantColor = colors[phase];

// Loop through each node in the TrajectoryPhase and display the current node

For node = 0 to opt.TrajectoryPhases[phase].NumberOfNodes-1;

opt.TrajectoryPhases[phase].NodeIndexToView = node;

Update vw;

End;

vw.InsertLineBreak();

End;

vw.EndBatchUpdate();

EndProcedure;

ViewWindow vw;

//==============================================

// Set up TrajectoryPhase objects

//==============================================

TrajectoryPhase phase;

Alias phaseFM = phase.CollocationOptions.ForceModel;

phaseFM.Sun = 0;

phaseFM.Moon = 0;

phaseFM.PlanetFieldType[2] = 0;

phaseFM.Drag = 0;

phase.ControlModel.ControlType = 1;

phase.ControlModel.SimpleThrusterOptions.Thrust = 100;

phase.ControlModel.SimpleThrusterOptions.Isp = 200;

phase.DrawNode = 1;

vw.AddObject(phase);

//========================================================

// Generate initial guess

//========================================================

Spacecraft sc;

Alias scFM = (sc.Propagator AsType Integrator).ForceModel;

scFM.Sun = 0;

scFM.Moon = 0;

scFM.PlanetFieldType[2] = 0;

scFM.Drag = 0;

sc.MassTotal = 1000;

sc.A = 10000;

sc.E = 0.0001;

sc.I = 10;

sc.TA = 0;

TimeSpan stepTo = sc.Epoch + (sc.Period).ToTimeSpan("min");

WhileStepping sc to (sc.Epoch == stepTo);

phase.AddNode(sc, {0.1, 0.1, 0.1});

Update vw;

End;

phase.ResampleNodes(42);

//========================================================

// Set up TrajectoryPhase variable bounds/constraints

//========================================================

phase.SetPositionBounds("path", -15000, 15000);

phase.SetVelocityBounds("path", -10, 10);

phase.SetMassBounds("path", 0, 1e20);

phase.Lock("first");

//========================================================

// Set up Optimizer and generic constraints/variables

//========================================================

Optimizer opt;

opt.AddTrajectoryPhase(phase);

Variable new_radius = 11000;

Variable v_circ = sqrt(Earth.Mu / new_radius);

opt.AddConstraint("r", new_radius, new_radius, new_radius);

opt.AddConstraint("v", v_circ, v_circ, 1);

opt.AddConstraint("RdotV", 0, 0);

opt.AddConstraint("i", 13, 13, 1);

opt.MaximumNominalEvaluationCount = 400;

opt.ValidateUserDerivatives = 0;

opt.FiniteDifferenceMethod = 2;

IpoptOptions ipopt;

//========================================================

// Solve

//========================================================

opt.LoadEngine(ipopt);

While (opt.IsRunning());

opt.UpdateStateVariables();

opt.TrajectoryPhases[0].LastNode.SetSpacecraftState(sc);

opt.SetConstraintValue("r", sc.Radius);

opt.SetConstraintValue("v", sc.VMag);

opt.SetConstraintValue("RdotV", sc.Position.Normalized().DotProduct(sc.Velocity.Normalized()));

opt.SetConstraintValue("i", sc.I);

opt.Maximize(opt.TrajectoryPhases[0].LastNode.Mass * 1e1); // optimize fuel expended

// Evaluating a nominal case

If (opt.OptimizationPhase == 1);

Call visualize(opt, vw, 1);

End;

// Reset to use exact hessian

opt.Reset();

ipopt.UseExactHessian = 1;

opt.LoadEngine(ipopt);

// Resolve using the exact hessian

While (opt.IsRunning());

opt.UpdateStateVariables();

opt.TrajectoryPhases[0].LastNode.SetSpacecraftState(sc);

opt.SetConstraintValue("r", sc.Radius);

opt.SetConstraintValue("v", sc.VMag);

opt.SetConstraintValue("RdotV", sc.Position.Normalized().DotProduct(sc.Velocity.Normalized()));

opt.SetConstraintValue("i", sc.I);

opt.Maximize(opt.TrajectoryPhases[0].LastNode.Mass * 1e1); // optimize fuel expended

// Evaluating a nominal case

If (opt.OptimizationPhase == 1);

Call visualize(opt, vw, 1);

End;

//========================================================

// Show results

//========================================================

opt.Reset();

phase.ApplyBestSolution();

// Query the Mass at the last node and the total time of flight

Report phase.LastNode.Mass, phase.TimeOfFlight.ToHours();

// Update the ViewWindow to show the best solution

Call visualize(opt, vw, 1);

// Loop through each node in the TrajectoryPhase and plot the mass

Variable i;

For i = 0 to phase.NumberOfNodes - 1;

Plot i, phase.Nodes[i].Mass;

End;

// Add the Spacecraft to the ViewWindow

vw.AddObject(sc);

vw.SetTailLength(sc.ObjectId, 1e5);

sc.Propagator.StepSize = TimeSpan.FromSeconds(10);

vw.InsertLineBreak();

// Set the Spacecraft's state to the first node in the TrajectoryPhase

phase.FirstNode.SetSpacecraftState(sc);

sc.Color = ColorTools.Red;

vw.Update();

// Step the Spacecraft for a single period and update the ViewWindow

WhileStepping sc to (sc.ElapsedTime.ToMinutes() == sc.Period);

vw.Update();

End;

vw.InsertLineBreak();

// Set the Spacecraft's state to the last node in the TrajectoryPhase

phase.LastNode.SetSpacecraftState(sc);

sc.Color = ColorTools.Lime;

vw.Update();

// Step the Spacecraft for a single period and update the ViewWindow

WhileStepping sc to (sc.ElapsedTime.ToMinutes() == sc.Period);

vw.Update();

End;

Output

This page contains all of the basic components needed to configure a TrajectorySegment object for use within an optimization problem. For more information on the collocation algorithm or control models please see the respective page in the Optimal Control Guide.

Trajectory Phases

Creating and Initializing a TrajectoryPhase Object

Configure the Control Model

Generate Initial Guess

Set up Spacecraft

Adding Nodes

TrajectoryPhase.AddNode()

Nodes can be added using the TrajectoryPhase.AddNode() method through four different overloads as shown below:

TrajectoryPhase.AddNodes()

Nodes can be added using the TrajectoryPhase.AddNodes() method through three different overloads as shown below:

Resampling Nodes

Nodes can be resampled using the TrajectoryPhase.ResampleNodes() method through three different overloads as shown below:

Example: Adding Nodes to a TrajectoryPhase

Set Bounds

Lock Variables

The TrajectoryPhase object allows users to 'Lock' variables through a number of useful methods. These variables can be locked at either the "first" or "last" node in the TrajectoryPhase and/or can be passed user-defined values for either endpoint.

Example: Initial Configuration for an Earth to Mars Low-Thrust transfer

Add Trajectory Phases to the Optimizer

Define Phase Links and Add General Constraints

Solve and Query Results

Load the Optimization Engine

Create the Evaluation Loop and Retrieve the Best Solution

The process of creating an evaluation loop and retrieving the best solution is summarized below but can be found in more detail on the Using the Optimizer guide. The basic steps of creating the evaluation loop and retrieving the best solution are as follows, in order:

Visualization

Complete Example

Output

See Also