Minimalism + Distribution = Supermodularity

Minimalism Distribution Sup ermo dularity Bruce Donald Jim Jennings Department of Computer Science Department of Computer Science Cornell University Tulane University Ithaca NY New Orleans LA Daniela Rus Department of Computer Science Dartmouth College Hanover NH April mechanicallybased rob ot algorithm for pushing and Abstract grasping eg Mas While quite general in prin We have designed and implemented multiagent ciple these oline algorithms are usually designed for strategies for manipulation tasks by distributing rob otics devices such as gripp ers or ngers attached to mechanical lybased sequential algorithms across sev a traditional rob ot arm To extend these results for eral autonomous spatial lyseparated agents such as distributed manipulation dened in this pap er in Sec mobile robots Our experience using mobile robots for tion there are several challenges Autonomous the manipulation of large objects couches boxes le mobile rob ots mob ots have a suite of sensing and cabinets etc leads us to recommend a minimalist control mo dalities that dier across rob ot architec architecture for multiagent programming In particu tures Mob ots are often b etter suited to online lar our methodology has led us to derive asynchronous approaches and hence the algorithms must b e adapted distributed strategies that require no direct communi to rely less extensively on geometrical and dynamical cation between agents and very sparse geometric and mo dels A host of diculties arises when a task dynamic models of the objects our robots manipulate must b e p erformed by a distributed team instead of We argue for a design principle cal led sup ermo du a single agentand hence the algorithms must com larity which is orthogonal both to the notion of modu p ensate by changing their communication sensing larity in cognitive AI and also to horizontal decompo or knowledge requirementsDon DJR DJRa sition the nonmodularity advocated in the subsump RDJ tionconnectionist literature We have rep orted on several sets of manipulation Final ly we discuss a simple mobotScheme in strategies which we call protocols and also on the frastructure to implement supermodular architectures + metho dology which generated them Don BBD In the past few years we have programmed many su RDJ Jen Our most interesting proto cols are permodular manipulation protocols and tested them ex asynchronous and do not require communication b e tensively on our team of mobile robots We describe tween the agents In this pap er we address the ar why we think the supermodular infrastructure results chitecture and the programming environment we used in robust simple readable manipulation strategies to develop our proto cols We also discuss how the that can be recycled and reused class of distributed manipulation algorithms we have Intro duction develop ed leads naturally to certain architectural con straints In rob otics most manipulation algorithms are de signed to execute in a single pro cess on a single com This pap er is organized as follows We b egin with puter that takes input from all the sensors and con a discussion on minimalism and sup ermo dularity We trols all the eectors To develop distributed ma continue by describing three dierent minimalist ma nipulation strategies we b egan with a sequential but nipulation proto cols we have implemented and ana lyzed in the information invariants framework and we sp ond to the data paths through which the informa highlight their sup ermo dular structure Then we de tion passes Circuits can b e transformed by changing scrib e the infrastructure we used for developing our the edge or vertex structure of their graphs Dier strategies Finally we discuss how sup ermo dularity ent immersions of the graphs corresp ond to dierent and minimalism aect distributed rob ot architectures spatial allo cations of resources An imp ortant class of transformations consists of p ermutations A circuit Minimalism p ermutation is a vertex p ermutation followed by an Minimalism pursues the following agenda For a edge p ermutation of its graph given rob otics task nd the minimal conguration of Roughly sp eaking a subroutine is modular if it can resources required to solve the task Thus minimal b e reused without changing the interface We say a ism attempts to reduce the resource signature for a circuit is supermodular if it can b e relo cated to a dier task in the same way that say Stealth technology de ent physical lo cation and still function correctly even creases the radar signature of an aircraft Minimalism in the absence of circuits that formerly surrounded it is interesting b ecause doing task A without resource B and in the presence of new circuits at this new lo proves that B is somehow inessential to the informa cation In this pap er we will describ e sup ermo dular tion structure of the task We will discuss our exp eri circuits according to the following hierarchy of circuit mental demonstrations and show how their implemen transformations A circuit is replicated when it is du tation relates to our theoretical pro ofs of minimalist plicated at the same or at a dierent lo cation A cir systems In particular we will describ e our Mobot cuit is distributed when it is split up and the parts are Scheme systema distributed multithreaded high recombined to form dierent circuits A supermodular level rob ot programming environment permutation consists of moving circuits around while In rob otics minimalism has b ecome increasingly resp ecting sup ermo dular b oundaries inuential Marc Raib ert showed that walking and The chief debate b etween cognitive AI and archi running machines could b e built without static sta tecturally constrained approaches such as subsump bility Erdmann and Mason showed how to do dex tionism and connectionism is as follows cognitive AI trous manipulation without sensing Tad McGeer advo cates that skills should b e mo dular Connection built a bip ed kneed walker without sensors com ismsubsumption enforces a particular architecture puters or actuators Ro d Bro oks has develop ed on ab ove all else and this architecture may violate mo d line algorithms that rely less extensively on planning ularity We maintain that this socalled dichotomy and worldmo dels Canny and Goldb erg have demon opp oses the wrong categories the issue is not mo du strated rob ot systems of minimal complexity We have larity vs nonmo dularitythis faux dichotomy arises taken a minimalist approach to distributed manipula from only considering singleagent systems in which all tion dened in this pap er in Section and also to resources are physically colo catedin this case sup er our choice of a software architecture for writing our mo dularity reduces or more accurately masquerades rob ot programs We claim that the resulting proto as simple naked mo dularity cols consume a nearminimum amount of resources On the other hand in distributed systems re The accompanying software development debugging sources are of course not physically colo cated and executiontime system are concomitantly parsi In order to achieve the following goals monious and lean simplicity Sup ermo dularity ease of reuse This pap er intro duces the concept of sup ermo du larity and in particular it brings to the foreground p erformance guarantees the sup ermo dularity of our manipulation strategies In programming it is natural to talk ab out units of fault tolerance organization called subroutines In mobile rob otics we cho ose the design constraint of sup ermo dularity particularly for distributed strategieswe have devel We will show how sup ermo dularity achieves this goal op ed analysis and synthesis to ols for units of orga Since this design constraint denes an architecture nization called circuits Don Intuitively a circuit our architecture could also b e called sup ermo dular is a sensoricomputational unit consisting of sensors ity and actuators connected by data paths We mo del our circuits as graphs Vertices corresp ond to dier As an example of a sup ermo dular circuit illustrat ent sensoricomputational comp onents Edges corre ing these p oints we discuss in detail two circuits called align and pushtrack see Section has a predictable functionality for example it p er align is a virtual orientation sensor which by ac forms to within sp ecied accuracy as in the case of the tively exerting compliant control changes the rob ots align circuit discussed in Section In addition heading to lie at a particular desired angular relation ii ensures that the circuit has the same functional to a manipulated ob ject pushtrack is a virtual ef ity when moved to a dierent lo cation The goal here fector that given a velo city control executes a guarded is to show that under any p ermutation that resp ects move while in contact to apply a force along a desired codesignation constraints Don the sup ermo du lineofpushing to a manipulated ob ject We will de lar circuits retain at least lo cally their p erformance scrib e a sup ermo dular proto col called AsyncOnline guarantees Finally iii ensures that the p erformance that uses pushtrack for multirob ot reorienting of guarantees of a sup ermo dular circuit are preserved in large ob jects the presence of other circuits or agents that might a Sup ermo dularity is a continuum A circuit X is said priori interfere with its basic functionality to b e more supermodular than circuit Y if the region We have already derived p erformance guarantees CX of the conguration space C in which X func for sequential and single agent circuits An example tions correctly

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