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Entry Abort Determination Using Non-Adaptive Neural Network for Mars Precision Landers

Sarah R. Graybeal* NASA Johnson Space Center, Houston, TX, 77058

Kara M. Kranzusch† Iowa State University, Ames, IA, 50012

The 2009 Mars Science Laboratory (MSL) is slated to attempt the first precision landing on Mars using a modified version of the Apollo Earth entry guidance program. The guidance routine, Entry Terminal Point Controller (ETPC), commands the deployment of a supersonic parachute after converging the range to the landing target. For very dispersed cases, i.e. trajectories that fall outside the range of normal mission design dispersions, ETPC may not converge the range to the target and safely command parachute deployment within Mach number and dynamic pressure constraints. A previous study showed that a full-lift up abort can save many of these failed trajectories while abandoning the precision landing objective. Though current MSL requirements do not call for an abort capability, an autonomous abort capability may be desired, for this mission or future Mars precision landers, to make the vehicle more robust. The application of artificial neural networks (NNs) as an abort determination technique was evaluated by personnel at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC).

I. Introduction he 2009 Mars Science Laboratory (MSL) is slated to attempt the first precision landing on Mars using a modified version of the Apollo Earth entry guidance program. The guidance routine, Entry Terminal Point Controller (ETPC), commands the deployment of a supersonic parachute after converging the range to the

landing target. For very dispersed cases, i.e. trajectories that fall outside the range of normal mission design dispersions, ETPC may not converge the range to the target and safely command parachute deployment within Mach number and dynamic pressure constraints. A previous study showed that a full-lift up abort can save many of these failed trajectories while abandoning the precision landing objective.4 Though current MSL requirements do not call for an abort capability, an autonomous abort capability may be desired, for this mission or future Mars precision landers, to make the vehicle more robust. The application of artificial neural networks (NNs) as an abort determination technique was evaluated by personnel at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC).

In order to implement an abort, a failed trajectory must be recognized in real time. Abort determination is dependent upon several trajectory parameters whose relationships to vehicle survival are not well understood, and yet the lander must be able to recognize unsafe situations. Artificial neural networks (NNs) provide a way to model these parameters and can provide MSL with the artificial intelligence necessary to independently declare an abort. Using the 2009 Mars Science Laboratory (MSL) mission as a case study, a non-adaptive NN was designed, trained, incorporated into ETPC and tested in a Monte Carlo simulation of MSL entry.

Detailed neural network theory, the full development history of the MSL NN, and initial testing with severe dust storm entry trajectory cases are discussed in Ref. 1 and are detailed only in passing here. That analysis demonstrated that NNs are capable of recognizing failed descent trajectories and can significantly increase the survivability of MSL for very dispersed cases. NN testing has been broadened to evaluate NN performance in Monte Carlo simulations of dispersed entry trajectories. This second, broader testing phase is discussed in this paper. * Aerospace Engineer, Descent Analysis Group, Flight Design and Dynamics Division, Lyndon B. Johnson Space Center, Mail Stop DM4, 2101 NASA Parkway, Houston, TX, 77058, AIAA member. † Undergraduate and NASA Johnson Space Center Cooperative Education Student, Department of Aerospace Engineering, AIAA Student Member.

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This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

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Model Outputs

Real Outputs

-

Error Feedback Used to Correct Model

Real or Simulated

World

Model

Real Inputs

A. Mars Entry Guidance The development of active onboard entry guidance is necessary for landing accuracy requirements of future

robotic and manned missions.2,3 Previous robotic Mars missions, including the Mars Pathfinder and the recent Mars Exploration Rovers, used a ballistic, uncontrolled entry with airbags to land within 100 km of the target. Future Mars missions will attempt to achieve a landing accuracy of five km or less. The Mars Science Laboratory (MSL) is used as a baseline vehicle and trajectory to evaluate artificial neural network (NN) performance as an abort determiner.

The entry guidance algorithm is a modified version of the Apollo Earth entry guidance algorithm, known as Entry Terminal Point Controller (ETPC). ETPC converges the predicted range to the target by controlling drag based on deviations in range, altitude rate and drag from an onboard reference trajectory.2 Because the MSL entry aeroshell generates lift with an offset center of mass, no direct angle of attack control is available. The magnitude of the vertical lift and drag vectors are controlled by commanding bank angles with reaction control systems thrusters. This allows the vehicle to fly higher or lower in the atmosphere to achieve the desired drag acceleration. ETPC guidance is terminated with the deployment of the supersonic parachute. Supersonic parachute deployment is currently limited to a Mach number between 1.13 and 2.2 (due to transonic and thermal concerns) and a dynamic pressure between 239 and 850 Pa (due to inflation and structural concerns).

The ETPC routine has been used for multiple MSL point designs for different landing sites, arrival dates, and entry vehicle configurations. NN performance has been investigated for three different point designs, and tested in a simulation for the most recent of those.

B. MSL Aborts For some dispersed cases beyond 3-sigma, ETPC may not converge the range to the landing target and safely

command deployment of the supersonic parachute within deployment constraints. A full-lift up abort implemented at a given drag acceleration/velocity profile has been shown to be an effective abort strategy.4 As a result, the vehicle is saved but it overflies the landing target, landing beyond the desired range.

In order to implement an abort within ETPC, a reliable abort determiner must be found which can predict if MSL is on a failed trajectory. Many analytical methods of abort determination have been judged impractical due to altitude error within MSL navigation and the number of parameters that would have to be included in the decision.

As a result, abort determination with artificial neural networks using inputs available onboard the spacecraft was investigated.

C. Artificial Neural Networks The power of artificial neural networks lies in their ability to make predictions based on input parameters whose

relationships are not fully understood, allowing processes and systems to be modeled when conventional, analytical methods fail. An NN is a form of artificial intelligence based on simple curve fits. “Intelligent” systems learn with the iterative process shown in Figure 1. Real inputs are processed in a mathematical model to produce model outputs. The same real inputs are processed in a real world simulation to produce real outputs which are the target for the model. The real and model outputs are compared to produce error feedback, which is used to correct the model.

This cycle is repeated for every set of inputs and targets in the training data set. Each cycle of the entire training set is called an “epoch.” The forward process (shown with solid arrows in Figure 1) is termed “feedforward” and error correction process (shown with dotted arrows) is called “backpropagation.”

Figure 1. Learning process of intelligent systems.

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Output Layer

Input1

Input m

Output 1

Output n

Hidden Layer

Input Layer

When no model is available, as is the case for determining the necessity of an MSL abort, linear combinations of an activation function provide a generic method of curve fitting. One of the most common activation functions used in neural net research is the binary sigmoid function shown in Equation 1 where the constant sigma, σ , is usually 0.5 to 1.

xe

xf σ−+=

1

1)( (1)

The artificial neuron or “node,” shown in Figure 2, is the basic information-processing unit of the neural net. Input signals from other artificial neurons are multiplied by a weight factor, which results in amplification or attenuation. A bias is added to the summation of all inputs received by the node and this collective signal becomes the input for an activation function. The output of the activation function is the output of the node.5 Connecting several nodes together in layers creates the neural network. The most common NN architecture is a three-layer network as shown in Figure 3. This example has m inputs, n outputs, and any number of hidden layer nodes.

The feedforward and backpropagation processes occur for every set of input parameters. The process is repeated until the network performance reaches an acceptable level as measured by parameters such as error, gradient, or number of epochs. Sets of inputs not included in the training set can be fed through a trained network using only the feedforward process. The prediction of outputs for these inputs not included in a training set is called “generalization” and measures how well the NN reacts to data it has not previously seen, or, how well the NN has been trained thus far.

II. Methodology

A. Entry Abort Determination with NNs The NN is designed to use trajectory parameters from navigation to predict if the entry trajectory would require

an abort. The NN is not adaptive, meaning it would not train in real time or autonomously modify itself. Instead, the designed NN would be trained and verified on the ground using Monte Carlo simulations and the resulting weight and bias vectors would be stored onboard. Updated weights and biases could be uplinked to the spacecraft as necessary while in transit to Mars, however, it is important to remember that the NN would not change without manual input from the ground.

The goal of the Mars precision lander NN is to correctly classify trajectories as an abort or non-abort case. The difference between network output and the target is insignificant as long as the trajectory is correctly classified. The selected NN training target is a 1 for a non-abort trajectory and a 0.1 for an abort case. Accordingly, the network usually outputs a number between 0.1 and 1. Outputs below a defined abort boundary (AB) are considered abort

Figure 2. Architecture of an Artificial Neuron (Node)

Figure 3. Three Layer NN Architecture. 6

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Gate 4

Gate 3

Gate 1

Gate 2 Region

Drag profile limits for all cases

cases and outputs above or equal to the AB are interpreted as non-abort cases. For the cases considered here, failure is defined as supersonic parachute deployment below 6 km altitude.

B. NN Inputs Ideally, the NN would use parameters from all points along the entry trajectory to make an abort determination.

The number of input parameters, however, correlates to the number of weights that must be stored in memory aboard the spacecraft. In order to keep the amount of memory necessary for NN implementation at a minimum, the descent trajectory is described by four “snapshots” called gates shown in Figure 4.

Gate 1 is recorded at Entry Interface (EI), which occurs when the navigation altitude is 3,522.2 km from the

center of Mars. Gate 2 is recorded at maximum sensed filtered drag acceleration. Gate 3 is the equilibrium glide boundary (EGB) intercept which occurs in the middle of the optimum abort survivability region and corresponds to a bank angle of 81.4°. Gate 4 is the equilibrium glide boundary intercept which occurs two seconds before the end of the optimum survivability region; two seconds is a conservative estimate of the time required to recognize and implement an abort. This boundary corresponds to a bank angle of 75.5°.

The EGB defined in Equation 2 quantifies the minimum acceleration needed to be in equilibrium glide, the state in which vertical lift acceleration and centrifugal acceleration balance the gravitational acceleration and the flight path angle is constant. Once the vehicle has passed the EGB, the flight path angle will always be decreasing for bank angles at or above the minimum bank angle.

mincos

2

21

φ⋅

−

=D

Lsatv

vsg

EGBD (2)

Input gates 2, 3 and 4 are each based on drag because of this parameter’s significance to both ETPC guidance and the NN. In addition, drag is monotonic in the optimum abort survivability region,4 which gives a more predictable trend and allows a consistent gate to be selected. Altitude rate is significant to the NN but has an oscillatory pattern which makes gate selection difficult. Navigated altitude is also a significant parameter but the large error associated with this variable makes it unreliable for use in gate definition.

Input parameters in a training set are preprocessed to prevent one parameter from dominating the network due to a larger magnitude. The most effective method of preprocessing found for this problem is based on minimums and

Figure 4. MSL NN input gates and the optimum abort survivability region.

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maximums, where the values of a parameter in a training set are scaled to the value in a nominal reference trajectory and then scaled a second time such that the largest value is 1 and the smallest is –1.

During training, the NN searches for weight and bias values that minimize output error. Figure 5 shows the sum of the absolute value of the weights from the input to hidden layer for each input parameter for the last point design training set developed. Greater sums imply the parameter is more significant to the overall performance neural network.

The significance of so many parameters illustrates the difficulty in finding an abort determiner with traditional

analytical techniques. Another advantage of NNs, as compared to traditional curve fits, is the ability to find the relative significance of one parameter to another based on the weights selected during the training process. The significance of each input parameter to network output also reveals whether any parameters can be removed from the network without significant effects. By removing insignificant parameters from the network, the number of weights which must be stored aboard the spacecraft is reduced.

Training sets were created for each MSL point design tested; the data contained in this paper is specific to the most recent point design investigated. The training set was created from more than 118,000 trajectories which explored the entry performance of several atmosphere and vehicle inputs dispersed parametrically to create worst-on-worst cases (this resulted in a higher failure rate than seen in Monte Carlo simulations). The resulting training sets for NN training included trajectories from at least 9,000 MSL trajectory simulations. Each set also includes two subsets of trajectories containing the maximum and minimum of each parameter and the five largest and smallest vector sum of the scaled parameters. Because they are a type of curve fit, NNs are better at interpolation than extrapolation. The inclusion of these subsets helps bound the training data set and ensures that the network interpolates more than extrapolates. The training set also alternates abort trajectories with non-abort trajectories. If too many trajectories of one classification are seen consecutively, network weights become biased and fail to recognize the other type.

C. NN Training and Design Neural network design is a process of trial and error since each NN problem behaves differently with the same

set of design parameters. Network design is also time consuming because each training session may require several hours of computational time and thousands of epochs. Network design parameters, such as the number of hidden nodes, the learning rate and momentum constant in backpropagation, and the constant, σ, in the binary sigmoid activation function were tested individually to find the best parameter combination. Network performance was also evaluated using different numbers of trajectories in the training set, and different input parameters. Table 1 shows the current configuration of the NN designed for the MSL case study.

Figure 5. Summation of absolute value of weights from the input to hidden layer for each input.

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Intercept Min Combined Error

Parameter Value Number of Hidden Nodes (z) 7 Momentum (m) 0.9 Learning Rate (α) 0.05 Binary sigmoid constant (σ) 0.5

III. Results

D. Loss of Vehicle Reduction with NNs Once a network is trained, generalization can be quickly performed with the feedforward process. Because the

MSL NN separates trajectories into two classifications, there are two types of errors possible—a trajectory can require an abort and the network fails to recognize it, or the network can call for an abort when it is not required. The first error is more serious since it will result in loss of vehicle (LOV). The second error results in failure of the precision landing objective, but the vehicle survives.

The distinction between which output value is an abort and a non-abort is crucial to network performance. The location of this abort boundary affects the type of error that dominates the network. Figure 6 shows the number of training cases incorrectly classified for each failure type for the entire range of ABs. Output above the abort boundary will not abort, while output below the boundary will abort; as the abort boundary moves towards a value of 1, more cases will abort. It also shows that the two types of error are not equivalent at the abort boundary that results in the minimum total error. The minimum combined error for these cases, 2.4%, occurs at an abort boundary of 0.17.

The NN significantly reduces the chance of LOV for the MSL at the cost of the precision landing goal. It is

assumed that all cases which require an abort will result in the loss of the vehicle if an abort is not made and that all aborts will cause MSL to miss the target. In addition, Monte Carlo simulations have shown that 0.5% of trajectories will miss the target under normal circumstances, and 15.4% of aborts, even if correctly called, will be unable to save the vehicle.4 With these assumptions, LOV will occur in 4.91% of the cases in the 118,000+ trajectory training set, and the target will be missed 0.5% of the time without the neural network.

Table 1. Parameters of the MSL NN

Figure 6. Effect of AB location on network error for worst-on-worst data with 4.9% abort cases.

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Using an abort boundary of 0.17 (the location of the minimum combined abort prediction error), the NN makes the correct abort call in 97.58% of trajectories. This is illustrated in Figure 7.

Table 2, which is derived from Figure 6, shows how the reduction of probability of LOV is dependent upon the abort boundary. With an AB of 0.17, the chance of LOV is reduced from 4.91% to 1.62%. By moving the AB to 0.99 (an extreme case where the network almost always predicts an abort, the chance of losing the vehicle can be reduced to 0.78% but 40% of cases fail to meet mission objectives. Failure of mission objectives is defined as losing

the vehicle and/or missing the target site. If NN abort determination is implemented in the MSL mission, it would be left to mission management to decide what level of target miss is acceptable in order to lower the risk of LOV.

No NN AB = 0.16 AB = 0.17 AB = 0.99 LOV 4.91% 1.78% 1.62% 0.78% Target Missed + 0.50% 4.91% 5.16% 39.21% Failure of Mission Objectives 5.41% 6.69% 6.78% 39.99%

Using a reasonable choice of abort boundary, the NN significantly reduces the chance of LOV while slightly

increasing the failure of mission objectives since a commanded abort results in MSL overflying the landing target. Vehicle survivability is essential to the scientific mission of MSL and is therefore more important than successfully making a precision landing.

E. Implementation of the NN into ETPC Implementing the feedforward process into ETPC requires a mere 15 lines of Fortran code and 8 uploadable

variables. Four of these variables are arrays of network weights and biases; the current design of the NN, with 32 inputs and 7 hidden nodes, requires 239 weight and bias values. Implementation of the NN does not alter the guidance algorithms in any manner except to override the commanded bank angle if an abort is commanded. If modified with NN, the ETPC would record real-time trajectory parameters as the four input gate conditions are met during MSL descent. Once the NN input array is filled and input parameters from all four gates are available, ETPC would call the NN function and each value in the input matrix would be compared to a reference and scaled to between -1 and 1 based on trajectory maximums and minimums stored onboard the vehicle. The input would then be

Figure 7. NN Abort Prediction for 118,098 Worst-on-Worst Training Trajecotories, AB = 0.17

Table 2. Effect of NN on MSL mission objectives, 118,098 parameterized cases, 4.9% need abort

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Min Combined Error from Monte Carlo set Min Combined Error from Training Set

fed through the trained network using the weights and biases stored onboard. The output is then interpreted with a predetermined AB and the commanded bank angle is altered if necessary.

F. NN Testing via Trajectory Simulation The NN designed for the MSL case study has been tested using a POST simulation developed at NASA Langley

Research Center. Each Monte Carlo set contains 2,000 trajectories and four different sets of Monte Carlo variations were tested. For the nominal set of Monte Carlo simulations, no trajectories require an abort. Incorporation of the NN has no effect on these cases; no false aborts are called and each trajectory reaches the same supersonic parachute deployment target as it would without NN logic.

The second Monte Carlo set changed the atmospheric dust tau from a uniform distribution between 0.1 and 0.9 (the nominal case) to a constant value of 2.7 and increased navigation attitude error from ±0.2 deg (nominal case) to ±0.5 deg. Each of these values is consistent with the values used in creating the worst-on-worst training set. Results for this Monte Carlo set are presented in Figure 8, Figure 9, and Table 3.

Figure 8. Effect of AB location on network error for Monte Carlo data with 0.6% abort cases

Figure 9. NN Abort Prediction for Monte Carlo Simulation within Training Set Bounds, AB = 0.17

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Min Combined Error from Monte Carlo set Min Combined Error from Training Set

No NN AB = 0.1 AB = 0.17 AB = 0.99 LOV 0.60% 0.55% 0.55% 0.51% Target Missed + 0.50% 1.78% 2.00% 8.49% Failure of Mission Objectives 1.10% 2.33% 2.55% 9.00%

The third Monte Carlo kept the atmospheric dust tau value constant at 2.7 and navigation attitude error at ±0.5

deg but also changed the entry vehicle supersonic drag coefficient multiplier from a uniform distribution between -0.1 and 0.1 to a constant value of -0.1. This in effect increases the ballistic coefficient of the vehicle and leads to many more failure cases. Results for this Monte Carlo set are presented in Figure 10, Figure 11, and Table 4.

Table 3. Effect of NN on MSL mission objectives, 2,000 Monte Carlo cases, 0.6% need abort

Figure 10. Effect of AB location on network error for Monte Carlo data with 43.3% abort cases.

Figure 11. NN Abort Prediction for Monte Carlo with -0.1 Drag Coefficient Multiplier, AB = 0.17

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No NN AB = 0.1 AB = 0.17 AB = 0.99 LOV 43.35% 42.65% 42.61% 40.03% Target Missed + 0.50% 1.86% 2.00% 9.50% Failure of Mission Objectives 43.85% 44.51% 44.61% 49.53%

Both the second and third Monte Carlo sets show inherent issues not with the NN itself (which was pleasantly

silent in the nominal Monte Carlo when no trajectory required an abort) but with the sensitivity of the NN to the selection of the training set. Because the Monte Carlo simulation randomly disperses inputs, it rarely produces the type of worst-on-worst trajectories contained in the training set. In the second set of 2,000 cases, only 12 required an abort. With this already low chance of needing an abort, implementing the NN in ETPC guidance has little effect on the LOV and 11 of the 12 bad trajectories were not recognized. In the third set, where the drag coefficient has been lowered to force more failure cases, the NN still fails to correctly classify many trajectories that require an abort, regardless of where the abort boundary is drawn. An improved training set should improve this performance.

While the NN abort determination method was successfully implemented in ETPC code and its operation validated in a simulation, there is still ample room for improvement in its abort prediction performance.

IV. Future Work The most immediate area for refinement and possible improvement of NN performance is the generation of a

better set of training data. While the current training set of worst-on-worst trajectories ensures that the NN is trained for expected trajectory extremes, NN performance may improve if the NN is trained with a more well-rounded set of trajectories that retains the extreme cases but also includes a greater selection of cases within the nominal Monte Carlo boundaries.

A second possibility for future refinement is the input gate selection process. Different trajectory gates may improve the performance of the neural network. The timing of these gates may also have significant impact on performance; the final gate should be located as late in the trajectory as possible while still allowing time to implement an abort.

V. Conclusions The ability to make safe precision landings on Mars is vital to future exploration of the planet. ETPC is a

reliable, proven algorithm for range convergence, but in order to meet current supersonic parachute constraints, chute deployment may occur too late to allow a safe descent and landing in very dispersed cases. The ability to recognize these situations and command an abort can increase lander survivability and overall mission success.

The NN developed for MSL correctly determines whether an abort is needed for most cases in a large set of parametric worst-on-worst trajectories. This result for these cases, in which the vehicle is almost always in a very dispersed situation, are promising because the NN positively impacts mission success by significantly lowering the risk of LOV. However, the NN is not currently able to match this level of performance when tested in Monte Carlo simulations because the NN fails to recognize whether a trajectory will need an abort. While the NN rarely calls a false abort, it also rarely calls an abort when one is truly needed. This result calls into question the suitability of the worst-on-worst training data set. NN performance in a Monte Carlo simulation will almost certainly improve with revisions to the training set.

If successfully called, commanding a full-lift up abort abandons the precision landing goal and results in missing the landing target. Landing successfully downrange, however, is preferable to crashing at the target.

References

1Kranzusch, Kara M., “Abort Determination with Artificial Neural Networks for the 2009 Mars Science Laboratory,” Undergraduate Thesis, Dept. of Aerospace Engineering, Iowa State University, Ames, IA, 2005.

2Carman, Gilbert L., Ives, Dallas G., and Geller, David K., “Apollo-Derived Mars Precision Lander Guidance,” AIAA Atmospheric Flight Mechanics Conference, AIAA, Reston, VA, 1998.

3Carman, Gilbert L, and Mendeck, Gavin F., “Guidance Design for Mars Smart Landers Using the Entry Terminal Point Controller,” AIAA Atmospheric Flight Mechanics Conference, AIAA, Reston, VA, 2002.

4Ozimek, Martin. T., “Mars Science Laboratory Abort Entry Study and Abort Guidance Development,” Undergraduate Thesis, Dept. of Aerospace Engineering, Pennsylvania State University at University Park, University Park, PA, 2003.

Table 4. Effect of NN on MSL mission objectives, 2,000 Monte Carlo runs, 43.3% need abort.

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5Mrozinski, Richard B., “X-38 Integrated Navigation and Control Design with Neural Network Gain Scheduling,” Master’s Thesis, The University of Texas At Austin, Austin, TX, 1998.

6Fausett, Laurene V., Fundamentals of Neural Networks: Architectures, Algorithms, and Applications, Prentice Hall, Inc., Upper Saddle River, NJ, 1994.