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  • SEARCH ALGORITHMS FOR SPACE TUG RENDEZVOUS:SIMULATION AND EXPERIMENT

    Gergana A. BounovaTimothee de MierryOlivier L. de Weck

    Department of Aeronautics and AstronauticsMassachusetts Institute of Technology

    Cambridge, MA 02139

    AbstractThe goal of this study is to evaluate the efficiencyof three possible two-dimensional search strategies in thecontext of autonomous rendezvous in space. As part of abroader undergoingSpace Tugproject, a number of model-ing challenges were addressed to validate the experimentalresults. A crucial problem was to reduce the complex spaceproblem involving at least four degrees of freedom to a simpletwo-dimensional model and to run two-dimensional searchesfor an inert target using LEGO robots. The data collected,as well as results from simulations, showed strong trends inthe relationship between time and energy expended duringthe search. The project provided a starting point for the ren-dezvous control system to be implemented in aSpace Tugve-hicle by showing which of the three strategies - random, semi-autonomous and autonomous - is most efficient in the two-dimensional case. It was found that the semi-autonomous al-gorithm is the most energetically efficient approach, but themost time-consuming. This finding disproved our initial be-lief that the semi-autonomous strategy is the most efficient interms for both time and energy. Instead, the conclusion is thatan autonomous algorithm is more suitable for space applica-tions. The results also suggest that, depending on knowledgeof the search space and the mission requirements, a hybridapproach might be more efficient. With knowledge of orbitaldynamics, the meaning of these results can be extended to thespace problem.

    TABLE OF CONTENTS

    1 INTRODUCTION

    2 PREVIOUS WORK

    3 EXPERIMENTAL APPROACH

    4 DATA ANALYSIS

    5 SUMMARY AND CONCLUSIONS

    6 ACKNOWLEDGEMENTS

    REFERENCES

    0-7803-8155-6/04$17.00/c2004 IEEEIEEEAC paper # 1281

    1. INTRODUCTION

    Background and Motivation

    During the past decade there has been an increasing need toservice vehicles in space. Satellites and entire missions havebeen lost due to misalignments, wrong placements in orbitand software errors. These problems have triggered effortsto design a new type of vehicle called theSpace Tug, alsoknown as the Orbital Express. TheSpace Tugis a satellitethat carries out rendezvous and docking with a target satel-lite. Its functions are to capture targets, change their positionand orbital elements by a preset amount and release them atdestination safely. TheSpace Tughas to be capable of orbitaldebris removal, satellite rescue missions and tactical opera-tions. The control system of the tug is a major aspect of this

    Figure 1. The Space Tugmoving a satellite; GEO orbitalretirement or LEO orbital reconfiguration

    project. The search for the target satellite is a complex pro-cedure. Although approximate coordinates for its locationwould be provided, the tug would still have to search a finitespace to find it, since current tracking does not give precisionbelow a magnitude of the order of one hundred meters. As aresult, theSpace Tughas to have intelligent identification andsensing strategies implemented in its control system in orderto approach the target.

    A major technology risk in theSpace Tugproject is the targetidentification and docking. Showing that such a process isfeasible would reduce this risk and would provide a possiblesolution to the problem. In addition, given that the controlsystem of theSpace Tughas thus far been modeled as a blackbox, the results of this research project could give clues as towhat the architecture of the entire vehicle should be. Further-

  • more, successful search and rendezvous strategies could beused in other aeronautical applications, such as autonomousand formation flight.

    Search strategies and algorithms for robots have been studiedextensively in the past years. As a result, the design part ofthis project was influenced by previous work done on searchalgorithms, notably by the MIT Department of Electrical En-gineering and Computer Science. The basic strategies wereenhanced to fit the purpose of theSpace Tug. Time and en-ergy consumption, as well as the successful implementationof three searching strategies, are the focus of this research en-deavor. The search strategies tested are: (1) random sensor-less search, (2) semi-autonomous with a human in the loopsearch and (3) fully autonomous search with sensors. Thosewere chosen to be general enough (representative of familyof algorithms), yet tailored to our purposes. At the onset, itwas expected that the semi-autonomous with a human in theloop search will be the relatively most efficient approach.

    Hypothesis

    The use of a semi-autonomous search system with a humanin the loop is the algorithm that is the most effective for ren-dezvous and docking strategies in terms of time and energyconsumption.

    2. PREVIOUS WORK

    We looked at several references devoted to Mars rovers dueto the similar autonomy and energy requirements and con-straints of their missions.

    Literature Review

    Morrison and Nguyen [1] describe the software used to con-trol the motion of the rover on Mars. The constraints, in termsof communication and energy, on the control system of theMars rover are similar to what the tug will face in space. Dueto electrical and processing power limitations, the control sys-tem of the rover is unable to communicate and move at thesame time. In addition, due the transmit delay from Mars toEarth and back, the control system of the rover uses waypointnavigation and autonomous collision avoidance algorithms.In the absence of any obstacles, the rover proceeds directlyforward to the waypoint, including stops for proximity scan-ning - for hazard detection. During proximity scanning pro-cesses, the rover uses its on-board optical sensors to generatean approximate map of the terrain map in front of the vehicle.Based on height differences in the map, the navigation systemanalyzes the possible locations of obstacles.An alternate working mode of the control system is the rockfinding option, which uses the terrain map to detect a rock.The navigation system corrects the rover heading, centering itbetween the rock edges. This feature together with an adaptedversion of the collision-avoidance rover control system can beused as a basis for the tug control architecture.

    Search algorithms are thoroughly explored in computer sci-

    ence. Gelenbes paper [2] provides an example of the com-puter science point of view. The author models the au-tonomous process in which an agent, a robot or a softwarealgorithm searching for information in a computer database,searches the space around its current location for desired in-formation. The search area is divided in a set of locations(x, y), defined in Cartesian coordinates. Associated with eachlocation is a probability q(x, y) representing the likelihoodof finding the information wanted at this location. Assumingthe environment is static, the space can thus be described asa probability space. The agent, which in the context of thisproject is the tug, always moves in the direction where theprobability q(x, y) is the greatest. Once the agent moves tothe new location - from (x0, y0) to (xnew, ynew) -, the prob-ability q(xnew, ynew) of finding information at the new pointis updated depending on what was found.

    The algorithm thus continuously updates the probabilityspace, until the agent finds the right information - the targetfor the tug. The mathematical tools used in the greedy algo-rithm were applied to the tugs autonomous search strategy,since the underlying probabilistic decision-making processesare similar (e.g. the agent goes to the location with the great-est probability in the space). The modeling process used byGelenbe in his experiment is also useful in developing themodel of the search space for the tug. In addition, the agentis also able to build a map of the environment revealing theexact location of the information with greater precision. Ge-lenbes paper only discusses this simple strategy and does notconsider sensor range effects on the search efficiency.

    Another important aspect of rendezvous is target identifica-tion. Hillenbrand and Hirzinger [3] discuss object recognitionas a two-part process. First, a sequence of hypotheses aboutthe object - its location, geometric shape, and movements - isgenerated, using exterior sensors. The second part of the pro-cess evaluates these hypotheses based on the object model.This paper describes a new technique for object recognitionin a specific scene in a probabilistic framework. It also intro-duces a new statistical criterion - the truncated object proba-bility - to produce optimal hypotheses about the object to beevaluated for its match to the data collected by sensors. Theauthor further develops a mathematical model to fit the searchsequence in the experiment. The object recognition techniquedeveloped by Hillenbrand and Hirzinger is beyond the scopeof the Space Tugproject. However, some of their conceptsare useful for the autonomous search strategy model.

    Another Mars Pathfinder mission deals with crater and rockhazard modeling for Mars landing [4]. Measures for safelanding on the rough and hazardous terrain of Mars are de-scribed. The investigation examines simple models of cratersize-frequency distribution, rock size-frequency distributionand scaling relationships to determine the hazard probabil-ities and choose landing terrains. The approach to hazardmodeling and navigation generated a useful idea. A search ofsatellite sizes and geometries was performed in order to scale

  • the search space for the experimental setup [7]. For example,a 100-meter radius in space with a 2-meter long target trans-lates to a 5-meter experimental radius wit