lambertSolver#
Executive Summary#
This module solves Lambert’s problem using either the algorithm by R.H. Gooding (longer, extensive report available here ) or the algorithm by D. Izzo. Given two position vectors \(\mathbf{r}_{1}\) and \(\mathbf{r}_{2}\) as well as a requested time-of-flight \(t\), the solution to Lambert’s problem provides the corresponding velocity vectors v1 and v2 of the transfer orbit. The information about the type of algorithm (Gooding or Izzo), the position vectors, the time-of-flight as well as the number of complete revolutions around the central body, is provided by the lambertProblemMsgPayload input message. The velocity vectors are computed in the same frame as the input position vectors.
The algorithms by Gooding and Izzo provide solutions for elliptic, parabolic and hyperbolic transfer orbits. In the zero-revolution case, exactly one solution exists. In the multi-revolution case (meaning that the transfer orbit completes at least one complete revolution about the central body), either two or zero solutions exist, depending on whether the requested transfer time is greater or less than the minimum time-of-flight for the given number of revolutions. The LambertSolutionMsgPayload output message includes two solutions. If a solution does not exist, the corresponding velocity vectors in the message are equal to the zero vector, and the “validity” flag is equal to zero. Otherwise, the “validity” flag is set to 1.
Message Connection Descriptions#
The following table lists all the module input and output messages. The module msg connection is set by the user from python. The msg type contains a link to the message structure definition, while the description provides information on what this message is used for.
Msg Variable Name |
Msg Type |
Description |
|---|---|---|
lambertProblemInMsg |
lambertProblemMsgPayload |
lambert problem setup input message |
lambertSolutionOutMsg |
LambertSolutionMsgPayload |
lambert problem solution output message |
lambertPerformanceOutMsg |
LambertPerformanceMsgPayload |
lambert problem performance message (additional information about the solution process) |
Module Assumptions and Limitations#
The algorithms only compute solutions for a positive time-of-flight, and for positive transfer angles (meaning that the true anomaly of \(\mathbf{r}_{2}\) is greater than the true anomaly of \(\mathbf{r}_{1}\).
An edge case exists for a transfer angle of 0 or 180 degrees, as the two position vectors do not define a plane, so an infinite number of solutions exist. The module checks if the angle between the two position vectors is smaller than the threshold “alignmentThreshold”. In this case, the computed velocity vectors are set equal to the zero vector and the validity flag of the solution is set to zero.
While the module also works for parabolic transfer orbits, the solutions for orbits that are very close to - but not exactly - parabolic, may not be as accurate.
User Guide#
The module is first initialized as follows:
lambertModule = lambertSolver.LambertSolver()
lambertModule.modelTag = "lambertSolver"
lambertModule.alignmentThreshold = 1.0 # module defaults this value to 1.0 degrees if not specified
unitTestSim.AddModelToTask(unitTaskName, lambertModule)
The lambert problem input message is either created as a standalone message in python
lambertProblemInMsgData = messaging.LambertProblemMsgPayload()
lambertProblemInMsgData.solverMethod = messaging.IZZO
lambertProblemInMsgData.r1vec = np.array([10000. * 1000, 0. ,0.])
lambertProblemInMsgData.r2vec = np.array([0., 8000. * 1000,0.])
lambertProblemInMsgData.transferTime = 10000.
lambertProblemInMsgData.mu = 3.986004418e14
lambertProblemInMsgData.numRevolutions = 0
lambertProblemInMsg = messaging.LambertProblemMsg().write(lambertProblemInMsgData)
or obtained from another FSW module. The lambert problem input message is then connected.
lambertModule.lambertProblemInMsg.subscribeTo(lambertProblemInMsg)
Class LambertSolver#
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class LambertSolver : public SysModel#
This module solves Lambert’s problem using either the Gooding or the Izzo algorithm.
Public Functions
-
LambertSolver()#
This is the constructor for the module class. It sets default variable values and initializes the various parts of the model
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~LambertSolver()#
Module Destructor
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void reset(uint64_t currentSimNanos) override#
This method is used to reset the module and checks that required input messages are connected.
- Parameters:
currentSimNanos – current simulation time in nano-seconds
- Returns:
void
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void updateState(uint64_t currentSimNanos) override#
This is the main method that gets called every time the module is updated. It computes the solution of Lambert’s problem.
- Parameters:
currentSimNanos – current simulation time in nano-seconds
- Returns:
void
Public Members
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ReadFunctor<LambertProblemMsgPayload> lambertProblemInMsg#
lambert problem input message
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Message<LambertSolutionMsgPayload> lambertSolutionOutMsg#
lambert solution output message
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Message<LambertPerformanceMsgPayload> lambertPerformanceOutMsg#
lambert performance output message
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BSKLogger bskLogger#
— BSK Logging
[deg] minimum angle between position vectors such that they are not considered too aligned.
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LambertSolver()#