Observational Uncertainty in Plan Recognition Among Interacting. Robots. Marcus J. Huber. Edmund H. Durfee

Transcription

1 Obervational Uncertainty in Plan Recognition Among Interacting Robot Marcu J. Huber Edmund H. Durfee Ditributed Intelligent Agent Group (DIAG) Articial Intelligence Laboratory The Univerity of Michigan Ann Arbor, Michigan May 16, 1994 Abtract Plan recognition i the proce of oberving another agent' behavior() and inferring what, and poibly why, the agent i acting a it i. Plan recognition become a very important mean of acquiring uch information about other agent in ituation and domain where explicit communication i either very cotly, dangerou, or impoible. Performing plan recognition in a phyical domain (i.e. the real world) force the world' ubiquitou uncertainty upon the oberving agent becaue of the neceity to ue real enor to make the obervation. We have developed a multiple reolution, hierarchical plan recognition ytem to coordinate the motion of two interacting mobile robot. Uncertainty arie in the ytem from dead reckoning that accumulate while the robot are moving, a well a by in the computer viion ytem that i ued to detect the other agent' behavior. Baed upon belief network, the plan recognition ytem gracefully degrade in performance a the level of uncertainty about obervation increae. 1 Introduction The eld of mobile robotic ha progreed to the point that there will oon be ignicant interaction among robot a they attempt to accomplih their aigned tak. If the robot expect to accomplih their goal in multiagent ituation, they mut coordinate their plan with the plan of the other interacting agent. While conict can be detected and reolved through the exchange and analyi of information concerning the plan and goal of the potentially conicting agent, explicit communication of thi information i not alway poible. The agent will then have to rely upon ome other mean by which to gather the neceary information regarding other agent' plan. Plan recognition i one uch paradigm. Plan recognition i the proce of oberving another agent' behavior() and inferring what, and poibly why, the other agent i acting a it i. Thi inferencing i performed uing ome form of model of the oberved agent' action, goal, and plan and the relationhip between them. An agent' action, then, provide poitive evidence toward it attempt to achieve certain goal and negative evidence toward other goal. By watching an agent' behavior over a period of time, thi et of alternative goal can be rened. Operation in phyical domain, however, introduce the iue of dealing with, and reaoning about, uncertainty. Thi uncertainty arie from the ening that i required in order to make obervation of another agent' behavior. In the remainder of thi paper, we dicu a plan recognition ytem deigned to operate in phyical domain, dealing with obervational uncertainty in a natural manner. Thi reearch wa ponored in part by the NSF under grant IRI , IRI , and IRI , and by DARPA under contract DAAE C-R012. 1

2 2 Related Work Note that there need to be no explicit communication between the involved agent. Obervation alone can be ucient for each of the agent to determine what (and perhap why) the other agent are acting the way that they are, and to then coordinate their activitie. While a great deal of reearch on coordinating multiple agent ha been done, particularly within Ditributed AI, much of thi work ha aumed (or require) explicit communication between agent [5, 7, 8]. In ome ituation, agent cannot communicate due to uch thing a noiy radio or broken equipment. Plan recognition may then be the only mean by which agent can coordinate with each other. Thi may alo be true in domain where communication, although poible, may be very cotly (e.g. ending meage conume a great deal of time) or dangerou (e.g. military agent operating behind enemy line). Becaue of thi, we ee plan recognition a being a very important mechanim by which agent can acquire the information that they need in order to coordinate their activitie with other agent. Plan recognition reearch to date, however, ha been primarily conducted in uch domain a tory undertanding [3, 4], intelligent interface [9, 14], and dicoure analyi [12, 13]. Thee domain lack an eential element of phyical domain, however, namely obervational uncertainty. In natural language-baed plan recognition ytem like tory undertanding and dicoure analyi, \obervation" are entence from ome textual databae; \obervation" in intelligent interface domain are command invoked by uch thing a the pre of a moue button. In that reearch, there i the aumption that the obervation are abolutely accurate; each word i correct and each command wa actually the command that wa invoked. 3 The Phyical World Performing plan recognition in a phyical domain (i.e. the real world) force the world' ubiquitou uncertainty upon the oberving agent; real enor mut be ued to make obervation. All real enor are inaccurate and uer to ome extent from noie in the environment and, therefore, each obervation ha ome level of uncertainty aociated with it. Becaue of thi, plan recognition ytem deigned for domain without obervational uncertainty are inadequate for the tak. We have developed a plan recognition ytem to invetigate the iue aociated with phyical domain. The domain that we have choen i that of interacting mobile robot. Uing a computer viion ytem, one of the two agent oberve the action of the other robot and, uing plan recognition to determine the goal detination of the other robot, plan it motion to rendezvou with the oberved robot. Uncertaintie are impoed upon the ytem from two eparate ource: dead reckoning that accumulate whenever the robot move; and etimation by the computer viion ytem that i ued to ene the other robot action. Our work to date ha dealt with agent moving and navigating through a at world. Repreenting the goal of the oberved robot require ome form of patial repreentation of the environment in which the robot operate, with particular ditinction given to pecial goal location (thoe deemed intereting for ome reaon). For operation in very mall area, or where the granularity of repreentation can be quite large, enumeration of poible location (e.g. at ome quantization level uch a centimeter interval) might be ueful. Larger area, or the need for a ner granularity of repreentation, require a dierent approach { ome form of abtraction { a the ytem can become bogged down by the heer number of poibilitie. We have developed a patial repreentation that employ a multiple reolution hierarchical cheme to make plan recognition feaible in our domain by reducing the computational demand upon the plan recognition ytem. 4 Spatial Repreentation The repreentation cheme that we have developed i imilar in ome repect to quad tree in that the \map" of the world in which the robot operate i ubdivided into quadrant. In thi cheme, quadrant are further broken down to higher reolution level in order to dierentiate the region in which the oberved robot i in from any of the region in which there are poible detination location. Thi heuritic i neceary o that the oberving agent can determine if the watched robot i actually \at" a detination, or merely cloe 2

3 Z Z Z Z ~Z = (1)(21)(221)(222)(2231)(2232) (2233)(2234)(224)(23)(24)(3)(4) Location Detination (1)(2)(3)(41)(42)(43)(44) (a) quadrant coding cheme Move (b) Figure 1: (a) Example of repreentation. The lled circle are poible detination location, the hollow quare i the oberved robot. (b) Belief network architecture. to one. Quadrant are not broken into higher reolution level if ome prepecied maximum reolution level ha been reached (a function of how accurate enor are, what make ene for the given environment, etc.) Two example of repreentation are hown in Figure 1(a). In the top repreentation in Figure 1(a), the highet reolution level ued wa very detailed cloe to the robot (the hollow quare) in order to ditinguih it location from the poible detination cloet to it (the lled{in circle immediately to it left). 1 In the bottom example, the repreentation did not have to go to uch a high level of detail ince the robot wa quite far from any of the poible detination. 5 Plan Recognition Architecture Our plan recognition ytem i baed upon belief network, a graph-oriented probabilitic repreentation of caual and dependency relationhip between concept (ee [2] for a gentle introduction). Belief network allow u to model action (obervable activitie of an agent), plan, and goal, and the relationhip between them. The belief network that we have tarted with i hown in Figure 1(b). Thi network i a model of a imple agent plan: an agent that ha a goal of moving to a particular location in the world will examine it current location and plan a equence of movement that will take it to it goal detination. In caual term, the belief network tate that the current location of the oberved robot and the detination that it wihe to attain determine the motion that the robot will take to get to it detination. Our model of motion i that the robot will try to move directly toward it goal, thereby moving in a traight line from it current location toward the detination. Each node in the belief network hown in Figure 1(b) contain the variou value that are poible for that particular concept. The Location node ha a poible tate all of the poible location region (of the current patial repreentation uch a that een in Figure 1(a)) that the oberved agent might have while it i trying to attain it goal detination. The Detination node contain all of thee poible region that contain one or more detination location (i.e. a ubet of the Location node). The Motion node i evidence for the agent having moved north, outh, eat, wet, or taying in the ame location, and i calculated baed upon the current and previou oberved location. The belief network i ued to perform plan recognition through the propagation of belief from evidence, in the form of obervation of the other robot' activitie, to the poible goal. By oberving the robot' 1 Had the repreentation not been o detailed, the oberving robot would have had to reaon that the other robot wa at a detination, an obervation ignicantly dierent than one in which it i \cloe" to a detination. 3

4 (X1R2,Y1R2) Robot 2 motion (X2R2,Y2R2) viion Obervation 1 viion R1 dead reckoning Obervation 2 (X2R1,Y2R1) R1 dead reckoning Robot 1 motion (X1R1,Y1R1) Figure 2: Uncertainty bound a the oberving and oberved robot move. location, and by calculating the motion exhibited by the other robot ince the lat obervation, we can then propagate thi evidence through the belief network to update the belief of where it i going. 6 Obervational Uncertainty In Figure 2 we illutrate the uncertaintie that arie in our ytem. Robot 1, the oberving robot, tart at poition (X1R1; Y 1R1), while the oberved robot, Robot 2, tart at (X1R2; Y 1R2). In the gure, we how what Robot 1 calculate a the uncertainty of each robot' poition at both their initial poition and after both robot have moved to their econd poition. In the gure, Robot 1 tart with no uncertainty in it poition, perhap having jut been homed to thi poition. Obervation of the other robot, however, introduce uncertainty into Robot 1' etimate of where Robot 2 tart. 2 Thi i a function of the ditance between the two agent; the farther apart the two robot, the greater the poible in the localization. Furthermore, after each robot move to it repective econd poition, dead reckoning alo become a factor. The dead reckoning accumulated by Robot 1 i hown by the increaed uncertainty bound urrounding Robot 1' econd poition. Viual localization of Robot 2 again introduce. The two are additive, o that Robot 1' uncertainty in the poition of Robot 2 i potentially even greater from it new poition. Thi poitional uncertainty will continue to increae unle Robot 1 manage to more accurately determine it own poition or the agent move uciently cloe together to oet the larger dead reckoning. 3 The impact of the obervational uncertainty on the performance of the ytem i dramatic. Experiment in which no method for dealing with the uncertainty wa ued how that the ytem can be entirely baed, and broken, by the poitional that arie from the dead reckoning and computer viion ytem [11]. The ytem, being committed to auming obervation are correct and exact, occaionally micalculate the location, and therefore the motion. Thi reult in an oberved motion of north intead of outh (for intance), contradicting previou, correct obervation, and violating the motion model of the belief network. 2 The computer viion ytem that i ued to make obervation return an etimate of the location of other agent in the current eld of view, and thi etimate i known to be incorrect due to quantization, noie, poor lighting, etc. 3 Note that the dead reckoning accumulated by Robot 2 doe not aect Robot 1' uncertainty in Robot 2' poition. If Robot 2 wa alo doing plan recognition, it own dead reckoning would be that which contribute to it uncertainty about Robot 1' location. 4

5 (x2,y2) poitional (x1,y1) (1)(2)(3)(41) (a) poitional (b) Figure 3: (a) Uncertainty in the location of the oberved agent caued by the accumulation of dead reckoning and computer viion mean that the agent could be in any of the region indicated. (b) Motion between two uncertain location. To deal with the uncertaintie aociated with thi domain, we needed to relax the aumption that obervation were accurate and correct and, intead, allow a probabilitic mix of poible obervation value. By imple modeling of the dead reckoning and computer viion a bound, we can then calculate the poible motion and location value. The two are additive, and are proportional (with dierent contant) to the ditance travelled by the oberving robot (in the cae of dead reckoning) and the viual ditance between the two robot (in the cae of the computer viion ytem). Roughly, dead reckoning accumulate at approximately 1 meter for every 30 meter of travel, and the computer viion ytem i in approximately 20 millimeter for every meter of viual ditance for CARMEL, our robot (ee Section 7). The eect of thi upon modeling where the oberved agent i at any time can be een in gure 3(a). Intead of making an obervation that the current location of the oberved agent i at a ingle region in the hierarchical repreentation, we now have to allow for the poibility that it can be in any of region that the uncertainty bound overlap, weighted by the amount of overlap. The motion between two location with uncertainty i depicted in Figure 3(b). The calculation of the oberved agent' motion to incorporate the uncertainty i a function of the amount of overlap of the bound and the magnitude of the motion in the cardinal direction. For example, given the motion of the other agent a that depicted in Figure 3(b), the agent could have moved north or outh, and eat, but not wet. We have implemented a imple approximation of the motion uncertainty for our experiment, weighting each direction by the ditance of travel along that direction, relative to the level of uncertainty. Long motion relative to the uncertainty bound, then, help in reducing the ambiguity of the motion. A the accumulation of dead reckoning grow, however, the ambiguity of the motion increae, and the obervation become more uncertain. 7 CARMEL: The Implemented Sytem We have implemented our ytem on CARMEL, a Cybermotion K2A mobile robot ued previouly in reearch on obtacle avoidance [1] and autonomou robotic [6]. CARMEL erve a the oberver, performing plan recognition baed on obervation of other agent in it environment with which it may interact. CARMEL perform thee obervation uing a computer viion ytem that detect and calculate the poition of object marked with a pecial bar code [10]. The \agent"' that CARMEL ha oberved include another robot (a TRC Labmate) and variou people. A mentioned earlier, CARMEL' purpoe i to determine where the other agent i moving and then rendezvou at that location. In our implementation, the oberving robot periodically look for the other robot, detect it new location, and calculate the motion that brought the robot to that new poition. Thi data i given to the belief network a evidence and propagated through it, reulting in new poterior probabilitie for each of the detination region in the Detination node of the network. Probabilitie for individual detination (a more than one detination location may be contained in a ingle region) are then determined, either by aociating 5

6 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h 9 h 10 h Figure 4: Experiment environment with location of interet indicated. the probability aociated with a region to a lone detination within that region, or by equally dividing the probability of a region among all of the detination within it. The detination that ha the highet probability i taken to be the mot likely goal of the oberved agent. CARMEL then calculate a path to that location in order to rendezvou with the agent. CARMEL only travel a hort ditance toward the detination, however. By periodically topping along the way, CARMEL can make new obervation and continually update it belief about the oberved agent' intention. Early, incorrect guee about the goal location can then be corrected by further obervation. The plan recognition ytem even work in ituation where the agent \feint" toward a particular detination for a while and then head for another goal. The ytem, having ettled on a particular detination, become temporarily confued by the change of direction until enough upporting evidence for the new goal i accumulated. 8 Experiment A erie of experiment wa conducted to invetigate the repone of the plan recognition ytem to varying degree of uncertainty in obervation. Becaue of the diculty with repeatability uing the real robot that we have in our lab, thee experiment were conducted in imulation. The experiment conited of two mobile robot in a two{dimenional grid world. In thi world were ditributed point of interet to the agent, place in the world that they would like to viit. Thi \world" i hown in Figure 4. One robot imply moved from it initial poition to a deignated location of interet. The other robot oberved the action (motion) of the other robot and tried to infer it \goal", the location that the other robot wa moving to a it nal detination. The watching robot wa given the tak of rendezvouing with the other robot, o that it would move toward the location of interet with the highet probability. In the cae of a tie between location, the watching agent would move toward the candidate location cloet to the center of the environment. The experiment that were performed conited of tarting the agent at predetermined initial location and letting them continue to act until the robot had uccefully rendezvoued. Each initial conguration wa repeated for varying amount of obervational uncertainty, and meaure of the probability ditribution for the variou location aved. Alo recorded wa the total amount of accumulated by the oberving agent with regard to it dead reckoning and viual ening. The reult of one experiment i hown in Figure 5. Here, the belief of the nal detination of the oberved robot i graphed relative to the time tep of the imulation. Each line in the graph repreent a dierent level of uncertainty, a indicated in the legend. The number for Viion and Motion indicate the number of grid unit viewed or moved for one unit of uncertainty attributed to the viion or dead reckoning, repectively. The graph how that, when the oberving robot had very little uncertainty in it obervation, it would rt believe that a dierent location wa the intended nal detination of the watched robot (a 6

7 (x2,y2) poitional (x1,y1) poitional Figure 5: Belief in the nal detination of the watched agent a the imulation progreed for varying level of uncertainty in the obervation made by the overwatching agent. indicated by the very low value). However, at a point where the watched robot got very cloe to it nal location, the oberving robot would quickly change it mind to the correct location, and would eventually rendezvou. 4 With large amount of obervational uncertainty, however, the oberving agent wa neither miled o everely, nor a quick to change it belief toward the mot likely nal detination of the other robot. Conequently, the oberving robot took much longer to nally rendezvou, and never did achieve the ame high level of condence a in experiment with lower level of uncertainty. However, the ytem demontrated a graceful degradation in performance. Thi i a very important characteritic for agent operating in uncertain and dynamic environment. Our experience with CARMEL ha hown that dead reckoning and other ening i an important and peritent iue that mut be dealt with, or, a in our earliet experiment, the inability to deal with the and aociated uncertainty will come back to haunt you. 9 Concluion We have developed and implemented a plan recognition ytem that deal naturally with the uncertainty aociated with operation in phyical domain. Thi ytem permit the eective coordination of multiple, interacting robot. Our hierarchical patial repreentation make inferencing feaible in thi domain by reducing the computational complexity of the inferencing ytem. The ue of belief network, a the bai of the plan recognition ytem, facilitate both modeling of the obervational uncertaintie probabilitically, a well a providing the mechanim by which the other agent' goal are inferred. Experiment have hown the performance of the ytem to degrade gracefully under increaing uncertainty in it obervation. 10 Future Work There are everal extenion to the current ytem that we plan on invetigating in the near future. Thee include: being able to handle more realitic navigation environment, which contain obtruction, dierent type of terrain, etc.; plan recognition of group; plan recognition for antagonitic agent; dynamically changing goal model; and unknown plan/goal. 4 The time at which the robot uccefully rendezvoued in an experiment i indicated by the nal graph point for that particular plot. 7

8 11 Acknowledgement We would like to thank Michael Wellman for many dicuion on reaoning under uncertainty and belief network. Reference [1] Johann Borentein and Yoram Koren. Hitogramic in-motion mapping for mobile robot obtacle avoidance. IEEE J. Robotic and Automation, 7(4), [2] Eugene Charniak. Bayeian network without tear. AI Magazine, 12(4):50{63, Winter [3] Eugene Charniak and Robert Goldman. Plan Recognition in Storie and in Life, volume Uncertainty in Articial Intelligence (5). Elevier Science Publiher, [4] Eugene Charniak and Robert Goldman. A probabilitic model of plan recognition. In Proceeding Ninth National Conference on Articial Intelligence, page 160{165, Anaheim, CA, July American Aociation for Articial Intelligence. [5] Philip R. Cohen and C. Raymond Perrault. Element of a plan-baed theory of peech act. Cognitive Science, 3(3):177{212, [6] Clare Congdon, Marcu Huber, David Kortenkamp, Kurt Konolige, Karen Myer, Aleandro Saotti, and Enrique Rupini. CARMEL v. akey: A comparion of two winner. AI Magazine, 14(1):49{57, Spring [7] Edmund H. Durfee, Victor R. Leer, and Daniel D. Corkill. Coherent cooperation among communicating problem olver. IEEE Tranaction on Computer, C-36(11):1275{1291, November (Alo publihed in Reading in Ditributed Articial Intelligence, Alan H. Bond and Le Gaer, editor, page 268{284, Morgan Kaufmann, 1988.). [8] Edmund H. Durfee and Thoma A. Montgomery. A hierarchical protocol for coordinating multiagent behavior. In Proceeding of the National Conference on Articial Intelligence, page 86{93, July [9] Bradley A. Goodman and Diane J. Litman. Plan recognition for intelligent interface. In Proceeding of the Sixth Conference on Articial Intelligence Application, page 297{303, [10] Marcu Huber, Clint Bidlack, David Kortenkamp, Kevin Mangi, Doug Baker, Annie Wu, and Terry Weymouth. Computer viion for CARMEL. In Mobile Robot VII, Boton, MA, November SPIE. [11] Marcu J. Huber and Edmund H. Durfee. Plan recognition for real-world autonomou agent: Work in progre. In Working Note: Application of Articial Intelligence to Real-World Autonomou Mobile Robot, AAAI Fall Sympoium, page 68{75, Boton, MA, October American Aociation for Articial Intelligence. [12] Kurt Konolige and Martha E. Pollack. Acribing plan to agent. In Proceeding of the Eleventh International Joint Conference on Articial Intelligence, page 924{930, Detroit, Michigan, Augut [13] K. Lochbaum, B. Groz, and C. Sidner. Model of plan to upport communication: An initial report. In Proceeding Eighth National Conference on Articial Intelligence, Boton, MA, AAAI. [14] Bhavani Rakutti and Ingrid Zuckerman. Handling uncertainty during plan recognition in tak-oriented conultation ytem. In Proceeding of the Seventh Conference on Uncertainty in Articial Intelligence, page 308{315, Lo Angele, CA, July