AUTONOMOUS HAZARD AVOIDANCE FOR PLANETARY LANDERS

AUTONOMOUS HAZARD AVOIDANCE FOR PLANETARY LANDERS Y. Devouassoux, M. Drieux, S. Reynaud, G. Gelly, E. Ferreira, A. Muller Astrium Space Transportation – 66, Route de Verneuil 78130 Les Mureaux – France

Abstract: Robotic exploration of planets in rugged landscape requires autonomous planning and decision making during the critical phases of final descent and landing. The lander maps the terrain during descent and selects a suitable landing site based on the terrain characteristics and a set of predefined criteria. A trajectory planning algorithm then computes a trajectory to reach the selected target. Hazard avoidance components – hazard mapping, site selection and trajectory planning – are described and improvements on previous work are presented. Copyright  2007 by Astrium Space Transportation. Keywords: Interplanetary spacecraft, Autonomous vehicle, Obstacle avoidance, Trajectory planning, Guidance systems, Decision making.

1. INTRODUCTION The solar system exploration by robotic probes has yielded highly valuable scientific data and greatly improved the knowledge of our immediate space environment. Since 1966 successful landings were performed on the moon, Venus and Mars. The surface analysis of planets is a precious complement to in-orbit observation and is essential to prepare future human exploration of Mars. Two kinds of landing scenarios were used in the past. In the recent Pathfinder and MER missions semi-hard landings were performed, where after a braking phase by parachutes, airbags were inflated around the lander that was then released and bounced onto the surface until it came to rest. In the soft landing scenario played in the earlier missions, the lander had propulsive capabilities and achieved a touchdown with quasi zero velocity. In both cases the landing area had to be safe – gentle slopes, small boulders, no cliffs or ridges – in order not to tear the airbags or have the lander tip over at landing. Areas of scientific interest are however often characterised by erosion or heavily cratered: rocks, cliffs and rifts are part of the landscape. Landing in such areas therefore excludes the semi-hard landing scenario. Since moreover communication delays with Earth and the lander high dynamics do not allow real-time monitoring of the descent, autonomous hazard avoidance capability is foreseen for future lander missions. The descent module should be able to do what Apollo astronauts did, i.e. detect hazards on the ground, select a safe landing site that can be different from the nominal one and perform the necessary trajectory update to reach the target. Astrium Space Transportation has been working on the subject of lander autonomy since the early 1990s in the frame of the European Space Agency (ESA) Integrated Vision and Navigation (IVN) project for the exploration of the moon (Jean-Marius, et al., 1999).

Following developments aimed at adapting the different schemes to planets with an atmosphere such as Mars. The hazard avoidance function, which is at the heart of the autonomous landing capability, is usually divided into three sub-functions (Fig. 1): - hazard mapping, that estimates the terrain hazards based on an imaging sensor outputs, - site selection, that decides a suitable landing site based on the hazard information and trajectory and mission constraints, - guidance and trajectory planning, that computes a trajectory update when a new target is selected and then steers the vehicle to the landing site.

Fig. 1. Hazard avoidance architecture It is fed by the navigation state and images from the terrain. The two main imaging sensors envisaged for future exploration missions are the CCD camera and the Lidar. This paper presents the latest studies performed at Astrium Space Transportation on hazard avoidance. Sections 2 deals with hazard mapping, section 3 site selection and section 4 with guidance and trajectory planning.

2. HAZARD MAPPING The hazard mapping function provides estimations of hazards in the form of maps for the selection of a safe landing site. Usually, three types of hazard information can be extracted from the terrain images: shadow, the surface roughness – that depends on the size of boulders – and slope. The algorithms employed depend on the on-board imaging sensor.

in practice, particularly on planets with an atmosphere. Other techniques that do not rely on these hypotheses such as stereo by motion depth map reconstruction (Xiong, et al., 2005) or B-splines interpolation using 3D points tracked by the navigation function are therefore being investigated (Fig. 4). Real-time implementation should be achievable using efficient hardware design.

2.1 Hazard mapping with a passive camera The CCD camera is a mature technology for hazard mapping purposes; vision based algorithms can provide all three types of hazard maps. Shadow maps. With a passive camera, hazard information is not available in dark or saturated zones, which must therefore be avoided. Simple thresholding methods can be used to discriminate such areas as shown on Fig. 2 (most risky areas are in white).

Fig. 2. Camera image and shadow map

Fig. 4. Stereo (left) and B-Spline 3D reconstruction (right) methods

2.2 Hazard mapping with LIDAR Lidar based hazard avoidance algorithms have the advantage to estimate slope and terrain roughness directly from the range maps provided by the sensor. Classical least squares method or robust plane fitting (Johnson, et al., 2001) can be used. Fig. 5 shows the slope estimation on the central portion of the Martian image Fig. 2. It is much more accurate than the shape from shading estimation, as can be seen by comparison with Fig 3 (yellow box). More generally, slope and roughness estimations should be better than with camera images. Here again most treatments can be efficiently hardware implemented.

Texture maps. Terrain irregularities such as rocks, crater rims, and rifts, can be detected using classical methods based on the variance, correlation or correlation derivative computation (Câmara, et al., 2005). More involved algorithms such as multi resolution analysis using Gaussian pyramids are preferred since they allow data analysis at different scales and thus a better detection of various size obstacles as shown on Fig. 3. Slope maps. Slope is the most challenging feature to assess using camera images. Different techniques can be applied. Shape from shading (SFS) methods relate the pixel grey level to the local slope. The simplest algorithm gives the minimum and maximum slopes that can be expected (Jean-Marius, et al., 1999). The minimum slope value is a good approximation of the real value, particularly for gentle slopes (Fig. 3).

Fig. 5. Slopes obtained from a LIDAR map of the terrain on the left. Shadows detection is not straightforward. It may be possible to detect dark areas knowing the relief and sun position but the required computing power should be overwhelming for real-time applications.

2.3 Conclusion

Fig. 3. Texture (left) and min slope from SFS (right) The more sophisticated Carlotto line integration method (Carlotto, 1998) computes a Digital Elevation Model (DEM) to extract slope information. Shape from shading algorithms are however based on stringent hypotheses that are frequently violated

Vision-based hazard mapping techniques are attractive because a camera is a lightweight and low power sensor that can be easily integrated on board a spacecraft. Images are however sensitive to dust and real difficulties arise for the estimation of slope. Lidar is more robust to environmental conditions and Lidar based slope estimation is reliable, but progress needs to be made with respect to the sensor weight and power consumption. For these reasons both solutions are still being investigated. Field tests are planned by ESA in 2008 and 2009 for the consolidation of performances.

3. SITE SELECTION The site selection function has to provide a “suitable” landing site to the trajectory planning. Suitability is defined by a set of mission and vehicle constraints that the chosen target site should respect. One set of constraints is related to the safety of the lander: the slope at the landing site must not exceed some threshold so that the vehicle does not tip over at landing and the size of rocks should be less than some value that depends on the lander architecture (size of the legs, etc). Both slope and rock sizes (via roughness maps) are provided by hazard mapping. IVN experience showed that it is moreover desirable that those site characteristics remain stable over time: it raises confidence in the hazard mapping estimation and limits the number of target changes during the descent. Another set of constraints is linked to the environment. Shadowed areas are usually avoided so that batteries can be reloaded after landing, the site should be visible from Earth for telecommunications, direct sun visibility may be required, etc. Finally guidance and propulsion constraints apply. The target site must be reachable in terms of dynamics achievable by the lander, there must be enough fuel left to go there and the site must remain in the field of view of the imaging sensor along the trajectory so that its characteristics can be continuously evaluated by hazard mapping. Proximity of candidate landing sites to the current target is favoured, since it increases the likelihood that the candidate sites will be compliant with the guidance constraints. Table 1 shows the criteria retained for the site selection algorithm. Criteria values are numerical, Boolean or linguistic. Table 1 Decision criteria for the landing site selection Criterion Desirable value Slope < 10° Rock size < 50cm Shadow Little Reachability True Fuel cost Small Proximity to current target Close Site visibility along descent True The selection of a site is then clearly a multiple attributes or multiple criteria decision making problem (MADM or MCDM). Alternatives (landing sites) are ranked according to the degree of fulfilment of the different criteria. An exhaustive review of previously studied MADM schemes is presented in (Ribeiro, 1996). The degrees of satisfaction of candidate sites with respect to the different criteria are computed and aggregated to yield a global score for each site. The scores are used to rank the different sites. These steps are detailed in the following paragraphs.

3.1 Degree of satisfaction The innovative solutions developed for IVN (JeanMarius, et al., 1999) are still used. Only a brief explanation is provided in the next paragraphs. Slope, boulders and shadows. Slope, roughness and shadow maps are merged using evidence theory to obtain risk maps. The risk depends on the map values and the confidence in the estimation of those values. It is 0 if the area is completely safe and 1 is the maximum risk. Let Rn the risk at time n. The degree of satisfaction of the criteria “the site is safe” is then µS= (1-Rn). Next, a list of safe sites uniformly distributed in the image is made from the risk map and the next 3 criteria are computed for each site. Reachability & site visibility along descent. The computation of this degree of satisfaction µR is based on the retained guidance algorithm (cf. section 4). Fuel consumption. The guidance model also provides an estimation fuel_c of the fuel cost to reach a given site. The degree of satisfaction µF is then computed by Eq. 1 

 fuel _ c − a    b − a   

µ F = 1 − max 0, min 1, 

(1)

where a=(1-m0).fuel_left, b=(1-m1).fuel_left, m0 and m1 are security margins. Proximity to current target. The degree of satisfaction increases with the proximity of the site to the current target. It is computed by Eq. 2. −

µD =

(d − d0 ) dyn d0

f (d max ) − f (d ) 1− e , f (d ) = (d −d 0 ) f (d max ) − f (0 ) − dyn 1 + e d0

(2)

d is the distance between the site and the current target, dmax is the maximum retargeting distance, d0 is the distance for which µD is 0.5 and dyn adjusts the transition of the law between 0 and 1.

3.2 Aggregation of criteria In the end, there remain 4 criteria for the site selection: site safety, reachability, fuel economy and proximity to current target. The choice of a particular decision method depends on its adequacy to the problem, the number of its parameters, the ease of implementation and the nature of the input data. Here all 4 criteria have crisp values (as opposed to fuzzy). There exist quantities of methods allowing making a decision in that context and several have been studied to refine or adapt the one used in IVN. They can be classified into two categories: the non comparative methods that compute a score based on the current

alternative’s criteria only and the comparative methods that compute an alternative’s score taking into account the criteria of the other alternatives. Let S={Si}i=1..n the set of alternatives (candidate sites) and {µj}j=1..m the set of criteria. wi’s are weights that are used in the ranking. Their sum is equal to 1. Simple Additive Weighting method (SAW). It is a simple and intuitive method where the score is a weighted average of criteria. It can be classified into the numerical “OR” methods. The score of an alternative Si is: m

d (S i ) =

∑w µ j

j

(S i )

(3)

TOPSIS method. TOPSIS stands for Technique for Order Preference by Similarity to Ideal Solution (Olson, 2004). Criteria are first normalized by Eq. 7. µ j (S k ) µn j (S k ) = (7) n

∑µ

j

(S i )2

i =1

Then similarities to the positive and negative ideals are computed (Eq. 8). The positive ideal is the hypothetical alternative that for every criterion would have the highest value among all alternatives. Similarly, the negative ideal has the lowest criteria values.

j =1 m

This method is very simple to implement. Its main drawback for the site selection is that it does not penalize sites where a criterion is not fulfilled: an unreachable site could have a rating higher than a reachable one provided that its score in the other criteria are sufficient. Weighted Product Model (WPM). Also called Weighted Product Method or Multiplicative Exponent Weighting, this method is also quite simple to implement. The decision is made by making the product of criteria. It can be classified into the numerical “AND” methods. m

d (S i ) =

∑ [µ

j

(S i )]w

j

(4)

j =1

Here the “AND” logic implies that all criteria must be satisfied. This is the strategy that was used in IVN with all weights being equal. The drawback of such a method is that an unimportant or less important criterion that is badly fulfilled can eliminate a solution. Bellman and Zadeh’s method. This method uses a rather intuitive set reasoning. The decision is made using the max or min operator depending on the logic retained (OR or AND).

(

)

d (S i ) = max min w j µ j (S i ) j

j

C + (S i ) =

n   w j  µn j ( S i ) − max µn j ( S k )  k =1   j =1

∑

(

m

C − (S i ) =

∑w



j =1

 min µn j ( S k )  k =1  n

j  µn j ( S i ) −



(

Yager’s method. It is identical to the Bellman-Zadeh method except that the weights are used as exponents

j

([

] )

The next two methods are comparative.

(8)

2

An alternative close to the positive ideal and far from the negative one is then selected.

d (S i ) =

C − (Si )

(9)

C + (S i ) + C − (S i )

Promethee method. Promethee stands for Preference ranking organization method of enrichment evaluation (Geldermann, et al., 2000). Here the decision is based on the comparison between the criteria. The degree of superiority of one alternative with respect to another for a specific criterion is defined by a function dd of the difference between the criteria (Eq. 10).

(

dd k ( S i , S j ) = dd µ k ( S i ) − µ k ( S j )

)

(10)

Possible dd functions are provided Fig. 6. The threshold a characterizes how great the difference must be for the superiority to be maximum.

Fig. 6. Possible functions for the computation of the superiority degree The preference index of one alternative with respect to another is then given by a weighted average of the superiority degrees (Eq. 11). m

π (S i , S j ) =

∑w

k

× dd k ( S i , S j )

k =1

j

)

2

(5)

If the “max” operator is used, the decision is made on the best criterion only. If on the contrary the operator “min” is used the decision is made on all criteria, since the least fulfilled criterion is considered. That logic is an alternative to the IVN concept.

d (S i ) = max min µ j (S i ) w j

)

(6)

The decision is finally made using Eq.12.

(11)

n

∑ d (S i ) =

j =1

n

π (S i , S j ) −

∑ π (S

j , Si )

j =1

(12)

n −1

Conjunctive and Disjunctive methods. These methods do not provide a score for the alternatives, but work by elimination. The outputs are subsets of the set of alternatives. Rejection and acceptance thresholds are defined for each criterion (Eq. 13).

{ A = {a

R = r1 , r2 , ... , r j , ... , rm 1

}

, a 2 , ... , a j , ... , a m

}

(13)

Then for the conjunctive method, alternative Si is rejected if there exists a k such that µk(Si)≤ rk. The disjunctive method retains an alternative Si if there exists a k such that µk(Si) ≥ak. These methods could be advantageously used to eliminate alternatives before applying another decision process. For example unreachable sites shall not be considered in the decision process.

3.3 Ranking The aggregation of the different criteria leading to a crisp number, the ranking is straightforward: sites are ranked from best to worst score. The methods described in 3.2 are illustrated on a theoretical example. Consider 8 candidate sites whose degrees of satisfaction for each criterion are given Table 2. A commonly used weight selection process is to qualify the importance of a criterion by a linguistic variable corresponding to an integer weight according to the rule “very high” = 5, “high” = 4, “average” = 3, “low” = 2, “very low” = 1. Normalization is made afterwards. In the site selection case, safety and reachability are very high (the selection of an unsafe or unreachable landing site could lead to mission loss) whereas fuel economy and proximity are considered to have an average importance (low values for these criteria would just lead to higher fuel consumption). Table 2 Criteria for the selection of a landing site Criterion\Site 1 2 3 4 5 6 7 8 Safety 0.6 0.1 0.3 0.6 0.2 0.3 0.8 0.1 Fuel economy 0.0 0.5 0.4 0.9 1.0 0.7 0.1 0.8 Proximity 0.1 0.0 0.1 0.7 0.6 0.4 0.2 0.9 Reachability 0.6 0.0 1.0 1.0 1.0 0.6 0.6 0.2 An adequate decision process, from our expertise in the field, should reject sites 1 and 2 because they are too costly in terms of fuel or unreachable. Site 4 should be ranked first, and site 7 preferred to site 8. The ranking results Table 3 are obtained for the min operator in the Yager and Bellman & Zadeh methods and the dd1 function in Promethee. As wanted, site 4 is ranked first by all methods. Non comparative methods using multiplicative weights

(SAW and Bellman) rank sites 7 and 8 in the “wrong” order, whereas methods with exponent weights (WPM and Yager) do not. This clearly illustrates the remark made at the end of the paragraph about WPM. Exponent weights are here preferable because they reflect more accurately our preference that bad fulfilment of secondary criteria is not so important (small values at small powers get close to 1 whereas small values multiplied by small weights get smaller). Comparative methods (Topsis and Promethee) do not classify site 1 in the last two because it has good safety and reachability scores. For the same reason, they rank site 7 higher than the other methods. Associated with a conjunctive method to eliminate sites like sites 1 and 2 they would in the present case provide a ranking close to a human decision maker. Table 3 Rank of each site according to the decision method. Method\ Site n° 1 2 3 4 5 6 7 SAW 7 8 4 1 2 3 6 WPM 8 8 5 1 2 3 4 Bellman 8 8 6 1 3 2 6 Yager 8 8 4 1 5 2 4 Topsis 5 8 4 1 3 6 2 Promethee 6 8 4 1 2 5 3

8 5 6 4 6 7 7

Further studies will be made to address other aspects of the decision process and in particular to take into account the variations of the different criteria along time. If necessary, more complex architectures such as multi-agent systems and expert systems could be considered for the implementation of this site selection process.

4. TRAJECTORY PLANNING AND GUIDANCE During the first part of the descent, the trajectory planning algorithm computes an acceleration profile such that the target chosen by the site selection algorithm is reached at the end of the landing manoeuvre while minimizing the propellant consumption and taking into account possible path constraints (e.g. control of the final vertical velocity, or keeping of the target into the imaging sensor’s field of view). The trajectory planning schemes should be robust to re-targeting commands given by the site selection algorithm. During the second and last part of the flight, the guidance main purpose is to avoid erratic movements and/or non-vertical attitude as the landing approaches. Fig. 6 shows the role of trajectory planning and guidance on a typical descent scenario. Trajectory planning is also used by site selection to evaluate the fuel consumption and reachability of candidate sites. For soft-landing missions, there exists a wide range of possible ways to solve the guidance problem. The relative simplicity of the dynamic equations of a lander (atmospheric effects are negligible at low velocity) allows an explicit resolution of the guidance two-point boundary problem. Then, most of the explicit guidance algorithms studied and

developed by Astrium Space Transportation along the years could be applied to such missions.

Fig. 6. Guidance and trajectory planning for a soft landing scenario. The most known (and widely used) approach for performing a landing is the Gravity Turn scheme, which is based on a quite simple concept. It however leads to a very poor position accuracy at landing and consequently does not allow retargeting. Alternatives can be simple explicit optimization methods such as the Apollo E guidance, the Bilinear Tangent law, the Chandler scheme, etc. These explicit schemes aim at autonomously reaching the target by self-building a steering law adjusted on board according to the current flight conditions. They can also be used for trajectory planning in case a retargeting is commanded during the descent. More sophisticated methods can be considered, such as the Optimal Command steering law, a predictor corrector, collocation methods or even more exotic methods such as Neural Networks trained to solve this specific trajectory problem. The main added value in this case is the potential gain in performance (propellant saving) and robustness towards perturbations and landing target change. The behaviour of these guidance algorithms has already been or is being studied by Astrium Space Transportation. They were used in the Integrated Vision and Navigation, Mars Sample Return and ExoMars projects in closed loop simulations to help sizing the vehicle and evaluate the performances of the whole GNC chain. Examples are illustrated on Fig. 7.

Fig. 7. Behaviour of five different guidance schemes on a soft landing mission

5. CONCLUSION Autonomous hazard avoidance capability is mandatory for landing in rugged landscape. Three main algorithms support that capability: hazard mapping, which measures safety-related terrain characteristics, site selection, which chooses a suitable landing site based on the hazard mapping outputs and guidance and mission constraints, and trajectory planning and guidance, which computes a new trajectory when the target changes and safely steers the vehicle to the chosen site. Early work on that subject was performed in the frame of the Integrated Vision and Navigation contract. Recent developments performed by Astrium Space Transportation promise to bring considerable improvements on the existing schemes. Hazard mapping is now available for planets with and without atmosphere with both camera and Lidar as imaging sensors, and a whole range of guidance algorithms are available, including sophisticated techniques such as neural networks. A fine analysis of the decision process in the site selection module leaves room for further enhancement. Those new algorithms are incorporated into a closed loop planetary landing simulator for incoming exhaustive trade-off and performance analyses.

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