Causal Models of Mobile Service Robot Behavior

Michael Beetz and Henrik Grosskreutz University of Bonn,Dept. of ComputerScience IIl, Roemerstr. 164, D-53117Bonn, Germany, email: beetz, [email protected]

Abstract a priori unknownand varying. Theseflexible plans vi- olate assumptionsunderlying most action models used Temporalprojection, the process of predicting what for planning-- in particular the assumptionsabout the will happenwhen a robot executesits plan, is essen- irrelevance of the temporalstructure of actions and the tial for autonomousservice robots to successfullyplan exclusion of interferences betweenconcurrent actions. their missions. This paper describes a causal model of the behaviorexhibited by the mobilerobot RHINO Forestalling a wide range of behavior flaws typical whenrunning concurrent reactive plans for performing for service robots requires the planner to makeuse of office deliveryjobs. Themodel represents aspects of modelsthat represent continuous processes, exogenous robot behaviorthat cannotbe representedby mostac- events, interferences betweenconcurrent behavior, in- tion modelsused in AIplanning: it representsthe temporal structure of continuouscontrol processes, several complete information, and passive sensors. modesof their interferences, and variouskinds of un- This paper describes a certainty. This enhancedexpressiveness enables XFRM modelfor predicting the be- (McD92;BM94), a robot planningsystem, to predict, havior generated by a robot and thereforeforestall, variouskinds of behaviorflaws controller for office delivery includingmissed deadlines whilst exploitingincidental opportunities. Theproposed causal modelis experi- jobs. The controller is de- mentallyvalidated using the robot and its simulator. signed for robust and efficient executionof delivery plans on the autonomousmobile robot i} Introduction l:h-IINO (see Fig. 1), an Rwl Temporalprojection, the process of predicting what n21 robot. The causal model Fig. 1: RHINO will happenwhen a robot executes its plan, is essential represents various kinds of uncertainty, the temporal for autonomousservice robots to successfully plan their structure, and concurrentexecution of continuouscon- missions. For the projection of their plans robots must trol processes, and thereby enables the transforma- have causal modelsthat represent the effects of their tional planning system XF~M(McD92; BM97) to fore- actions. Most AI planning systems use fairly simple stall a variety of behavior flaws (BM94). modelsof their actions and restrict themselvesto work To predict possible execution scenarios quickly and on plans that are partially orderedsets of actions. to keep the representation of the scenarios concise Unfortunately, in autonomousrobot control we of- the causal modelsof continuous control processes are ten cannot consider plans as partially ordered sets of (partly) generated and revised during the temporal atomic actions without thwarting manyopportunities projection of the processes. This allows the projec- for improvingthe robots’ behavior through planning. tion algorithm to use causal models tailored for the The actions of robots have extents in both space and surrounding plan and its state of execution. These time and the informationavailable for planningis defi- context-specific causal modelspredict only those state cient. The actions’ extent and dependenceon time re- transitions caused by the continuous processes that quire planning systems to predict whenactions are ex- might affect the course of plan execution. ecuted, howlong they take, and howthey overlap with Weuse RHINO’Snavigation behavior as our princi- concurrent actions. Therestrictedness, unreliability, ple examplefor sensor-driven, concurrent control pro- and inaccuracy of sensors and effectors requires that cesses. Navigation behavior has several advantages planning systems computeflexible plans and are able overother kindsof controlprocesses: first., it’s difficult. to reason through contingencies whoselikelihoods are to imagine having a sophisticated planner for mobile Copyright© 1998 American A,~sociafion for Artificial Intelligence (www.am.org). All rights resexved. Beetz 163 From: AIPS 1998 Proceedings. Copyright © 1998, AAAI (www.aaai.org). All rights reserved. robot applications without having an adequate model construct WITH-POLICY. WITH-POLICY P B lneans "execute of navigation behavior; second, navigation is one of the primary activity B such that, the execution satisfies the best understood capabilities of mobile robots; and the policy P." Policies arc concurrent processes that third, navigation is a suitable means for experimentally run while the primary activity is active and interrupt validating the causal models of concurrent continuous the primary if necessary. processes. Events that require RHINOto perform actions such In this paper wc proceed as follows. The next se.c- as "passing a door" are handled through fluents, pro- tion describes the plans of the office delivery robot that grazn variables that signal changes of their values are to be projected. The rule language for specifying and thereby enable control threads to react to asyn- causal models of actions is sketched in the subsequent chronous events. For instance, the RPL statement section. The section on modeling RmNo’s behavior WHENEVERF B is an endless loop that executes B when- applies the rule language to model the base navigation ever the fluent. F gets the value "true." WA~T-FORF, plans and the events that occur in the environment. another control abstraction, blocks a thread of control Finally, we give some experimental resu[ts on the accu- until the lluent F becomestrue. rateness of the symbolic predictions of robot behavior. Whena delivery gets interrupted because the robot has detected that the door to A-120 is open, that op- Plans of an Office Delivery Robot portunity has a side effect: it movesthe robot into the We use structured r~:active plans (SRPs) to specify office A-120. The interrupted delivery plan has there- how the delivery robot is to respond to sensory input fore to be replanned before it can be continued. in order to accomplish its jobs. Theyarc written ill RPL This in mind, we implement the navigation routine (Reactive Plan Language) (Mc.Dgl), a LisP-like robot as a loop that generates and executes base navigation control language with conditionals, loops, local vari- plans until the robot has arrived at its destination. ables, processes, and subroutines. RPLprovides several Interrupts are handled ~’ terminating the current it- high-level concepts (interrupts, monitors) to synchro- eration of the loop and starting the next iteration in nize parallel actions, makeplans reactive, and so on. which a new navigation plan starting from RmNo’s new position is generated (BBFC98). Structured Reactive Delivery Plans To illustrate the advantages of high-level plans that Base Navigation Plans specify concurrent reactive behavior, we sketch a plan Base navigation plans are also specified as concurrent that specifies howR.I[mo (see Fig. 1) is to deliver mail reactive RPLplans. Figure 3 pictures such a navigation to the rooms A-120, A-113, A-121, and A-110. Ini- plan: that is automatically generated for a given desti- tially, the planner asked the robot to perform the de- nation by the SRP’s navigation planner. The plan con- liveries in the order A-120, A-113, A-121, and A-11{}. sists of two components. The first specifies a sequence However, because the room A-120 is closed the cor- of target points (the locations indexed by the numbers responding delivery cannot be completed. Therefore, 1 to 5 in Figure 3) to be reached by the robot. Tim the planning system revises the overall plan such that navigation between the target points is accomplished the robot is to accomplish the delivery for A- [20 as an by a standard path planner (TBB+98). opportunity. In other words, the robot will interrupt its current delivery to deliver the mail to A-120 (s~, Fig. 2) if the delivery can be completed.

WITH-POLICY WHENEVERPASSING A DOOR A-II0 ESTIMATE DOOR ANGLE WITH-POLICY SEQ_ WAIT-FOR OPEN?(A-120) DELIVER MAIL TO Dieter 1. GO-TO(A-113) 2. GO-TO(A-121) BEFORE10:30 A-121’-- 3. GO-TO(A-110)

Figure 2: Office delivery plan Constraints such as "whenever the robot passes a door it estimates the opening angle of the door using Fig. 3: Topological navigation plml its laser range finders" and opportunities such as "com- ’[’he second componentspecifics in detail when and plete the delivery to room A-120 as soon as you learn howthe robot is to adapt its travel modesas it follows the office is open," which are necessary for carrying out the navigation path (FBT97). In many indoor environ- the jobs opportunistically, are specified using the RPL ments it is advantageous to adapt the driving strategy

164 Robotics and Agents From: AIPS 1998 Proceedings. Copyright © 1998, AAAI (www.aaai.org). All rights reserved. to the surroundings: to drive carefully (and therefore An execution scenario represents how the execution slowly) within offices because offices are cluttered, to of a robot controller might go, that is, how the envi- switch off the sonars when driving through doorways ronment changes as the structured reactive controller (to avoid crosstalk between the sonars), and to drive gets executed. A timeline is a linear sequence of events quickly in the hallways. This part of the plan is de- and their results. Timelines represent the effects of picted by regions with different textures for the differ- plan execution in terms of time instants, occasions, ent travel modes "office," "hallway," and "doorway." and events. Time instants are points in time at which Whenever the robot crosses the boundaries between the world changes due to an action of the robot or regions the appropriate travel modeis set. an exogenous event. An occasion is a stretch of time over which a world state p holds and is specified by a Issues and Requirements proposition, which describes P, and the time interval Suppose RHINOhas received two pieces of evidence for which proposition is true. The plan projector works exactly like the plan inter- (1) "Dieter will be back at 10:25" and (2) "Tables are moved from room A-110 to A-117." In this sit- preter, except that, whenever the executed plan inter- uation the task of the temporal projection module is acts with the real world, correspondingly the projected the following: given the delivery plan in Fig. 2 predict plan interacts with the timeline. The places where this whether, in conjunction with the new evidence, the happens are the low-level plans, such as the base nav- plan is still appropriate. In particular, the projection igation plans: the projector guesses the results of exe- cuting these plans and asserts their effects in the form module should predict that the robot is likely to miss the deadline for the delivery to room A-121 (because of propositions on the timeline. it will take tile opportunity to complete the delivery The representational means for specifying causal models used in the remainder of the paper are sum- to A-120) and that the robot is likely to bumpinto table when entering room A-I10 (because it switches marized below (see (McD94)): ¯ Projection rules have the form (PROJECTC A E, O) off sonar sensors when entering doorways). and the following meaning: if routine C starts and Making these predictions requires that the robot A holds, then the events Es will occur and C will planning system uses models of return O upon completion. The outcome o is ei- ¯ continuous processesfor the base navigation plans ther of the form (FINtSH --VALUES--Iif the routine that predict whether and when endogenous events, is completed successfully or (FAIL--DESCRIP--)oth- such as adaptations of the driving strategy and pass- erwise. This statement specifies the signal that is ing a door will occur; sent by the behavior module when the behavior is ¯ exogenous events like the opening ofthe door to room completed. A-120 around 10:25 or the refurnishing of A-110; ¯ Effect rules (E->P A S r B} specify that whenever ¯ interferences betweenconcurrent behavior like the in- event E occurs and A holds, then with probability teruption of a delivery plan to make use of the open r create and clip states as specified. The effects of door to room A-120 to deliver the mail; the E->P rules have the form A, causing the occasion ¯ incomplete information including the duration of A to hold, (cuP A), causing A to cease to hold, and events, non-deterministic effects, and sensor models; (PERStSTt A), causing A to hold for t time units. ¯ passive sensors and obstacle avoidance such that the ¯ Exogenous event rules are specified as P->E rules. models predict readings from passive sensors only W->EA d El generate over any interval in which A is when they determine the course of action. true, generates random "Poisson-distributed" events with an average spacing of d time units. Probabilistic, Totally-Ordered McDermott (McD94) gives a formal semantics for the rule language introduced above, shows that a con- Temporal Projection sistent set of rules has a unique model, and proves the We use the representation of events and their effects ¯ algorithms for building and retrieving from the time- and the temporal projection algorithm developed by line to be correct. (BM97)show that the average per- McDermott and described in (McD92; McD94). The formance of robot plans can be improved based on a plan projection process takes the current world model, small number of randomly projected scenarios. a structured reactive plan, rules for generating exogenous events, and rules for probabilistically guessing Modeling RHINO’s Behavior missing pieces of the world model together with proba- After the description of the office delivery plans and the bilistic causal models of the basic control routines and introduction of projection, E->P, and P->E rules as a generates execution scenarios of the plan. means for representing action and change, we will now

Beetz 165 From: AIPS 1998 Proceedings. Copyright © 1998, AAAI (www.aaai.org). All rights reserved. apply these representations to describe the behavior lows: (1) analyze the computational state and extract caused by the execution of delivery plans, such as the the conditions eauscd by the process and waited for by one listed in Fig. 2. concurrent branches of the delivery plan; (2) estimate The delivery plans control a dynamic system when the conditions will become true and what the (cf. (DWgl)): the robot RHINOin its environment values of the system variables at that timc will be; and Fig. 4). The statc variables of the dynamic system (3) generatc a context-depcndent causal model that. that are relevant for the delivery plans are the vari- used for projecting the plan. ables x, v representing RHINO’Sposition, and the variables DOOR-ANaLE,representing the opening angle of the Projecting Continuous Behavior doors. The robot controller uses fluents to store the For efficiency reasons the process of projecting a con- robot’s measurementsof thcse state variables (RHINO- tinuous process p is divided into two phases. The X*, RHINO-Y*, DOOR-A120, etc.). The fluents arc steadily first phase estimates a schedule for endogenous events updated through "scnsing processes" such as the po- caused by p while considering possible effects of p sition tracking process (BBFC98) and a model-based on el.her processes but not the effccts of the other procedure for estimating the opening angles of doors. processes on p. This schedule is transformed into The actions generated by the controller are all changes a context-specific causal model tailored for the plan of the velocity and the heading of the robot. which is to be projected. The second phase projects the plan P using the model of endogenous events con- ._.____~ ~.(r-E,,~rr).acN)) I strttcted in the first phase. This phase takes into ac- SiloVa, nlbl~w. X y .dU~E count the interferences with concurrent events ~ud revises the causal model if situations arise in which the assumptions of the precomputed schedule m’e violated. The projection module uses a model of the dynanlir system that specifies for each continuous control pro- ress the state variables it changes and fiJr ea(’h st;tie variable the flw’nts that measure that state variable. For example, consider the base navigation plans that ste;v..lily changethe robot’s position (that is the vari- Fig. 4: Office delivery as a dynamicsystem ables x and v). The estimated position of the robot is Unfortunately, dynamic system models of plan exe- stored in t, he fluents RHINO-X*and RHINO-Y*: cution that describe all state transitions are too fine- CHA N GES(BASE-NAVIGATIO N-PLAN, X) CHANGES(BASE-NAVIGATIO N-PLAN, Y) grained to be useful for AI planning. On the other MEASURES(RHINO-X*, X) hand, we cannot simply make the model more coarse,- MEASURES(RHINO-Y*, Y) grained: as we have pointed out earlier, the dcliw,ry Extracting relevant conditions. When the projec- plans specify how the robot is to rcspond to changes tor starts projecting a base navigation plan it computes in the dynamic system, and therefore any states the the set of pending conditions that depend on RmNO-X* dynamic system traverses might potentially changc the and RHINO-Y*, which ore the fluents that measure the course of action drastically. state variables of the dynamic system and are changed Resolving the conflicting requirements of(l) predict- by the base navigation plan. These conditions are im- ing all relevant events and states and (2) both generat- plemented as fluent networks. ing projections quickly and representing them concisely constitutes a difficult problem in applying AI planning to autonomous robot control. Our approach to satisfy- ing these requirements is to construct part of the causal models of continuous processes in a context-dependent way based on an analysis of the computational state of plan execution at the start of the process. Fig. 5: Fluent network for being in roomA-120 We model the behavior generated by base navigation plans as a complexevent that. causes only qualita- Fluent networks are digital ¢’ircuits where the com- tivc changes of behavior (e.g. adaptations of the travel ponents of the circuit are fluents. Fig. 5 shows a fluent mode) and those changes of the robot’s position that network where the output fluent is true, if and only are relevant for the execution of the overall plan (e.g. if RmNOis in room A-120. The inputs of the circuit entering the hallway or passing a door). To realize this are the fiuents RmNO-X*and amNO-Y*and the circuit is model, the continuous processcs are projected as fol- updated whenever RHINO-X*and RmNO-Y’change.

166 Robotics and Agents From: AIPS 1998 Proceedings. Copyright © 1998, AAAI (www.aaai.org). All rights reserved. Structured reactive plans are set up such that the The occasion (NEXT-NAV-EVENT?ID) triggers the next fluent networks that compute conditions for which the endogenousevent (BEGIN (FOLLOW-PATHTHERE (?X,?Y)) plan is waiting can be automatically determined using ?ID)). The remaining two conditions determine the pa- (PROLOG-Iike)relational queries: rameters of the FOLLOW-PATHevent: the next scheduled (SETOF?FL-NET (AND (FLUENT?FL) (STATUS?FL PENDING) event and RHINO’sposition. (CHANGESBASE-NAV-PLAN ?STATE-VAR) (P->E (AND (NEXT-NAY-EVENT?ID) (MEASURES?STATE-VAR-FL ?STATE-TAR) (PREDICTED-EVENTS?ID (DEPENDS-ON?FL ?STATE-VAR-FL) ((?DT (?X,?Y) ?EVS)!?REMAINING-EVS)) (FLUENT-NETWORK?FL ?FL-NET)) (RHINO-LOCTHERE)) ?PENDING-FL-NETS) 0.0 (BEGIN(FOLLOW-PATH ?HERE (?X,?Y) ?DT ?ID))) This query determines ?PENDING-FL-NETS,the set of flu- Theeffect rule of the (BEGIN(FOLLOW-PATH ...)) event ent networks ?FL-NETsuch that ?FL-NETis a network with specifies amongother things that the next endogenous output fluent ?FL. ?FL causes a plan thread to pend and eventwill occur after ?DT time units (PERSIST ?DT (SLEEP- depends itself on a fluent measuring a state variable ING?lO)). ?STATE-VARchanged by the base navigation plan. (E->P (RHINO-LOC?COORDS) Endogenous event schedules. For each class of con- (BEGIN (FOLLOW-PATH?FROM ?TO ?DT ?ID)) 1.0 (AND (RUNNING(FOLLOW-PATH ?FROM ?TO ?DT ?ID)) tinuous processes we have to provide an endogenous (CLIP (RHINO-LOC?COORDS)) event scheduler that takes the initial conditions of the (CLIP (NEXT-NAV-EVENT?ID)) process, the parameter(Tat(on of the process, and the (PERSIST?DT (SLEEPING ?ID)))) fluent networks that might be triggered by the process If a running follow path event has finished sleeping and computes the endogenous event schedule. The en- the(END (FOLLOW-PATH ...)) eventoccurs. dogenous event scheduler for the base navigation plans (P->E (AND(NOT (SLEEPING?lO)) (RUNNING(FOLLOW-PATH ?FROM ?TO ?TIME ?ID))) is described in the next section. Given the kind of pro- o.o (END (FOLLOW-PATH?FROM ?TO ?TIME ?ID))) cess (e.g., base navigation plan), the process parame- Our model of base navigation plan presented so far ters (e.g., the destination of the robot), and the pend- suffices as long as nothing important happens while ing fluent networks, the scheduler returns the sequence carrying out the plan. However, suppose that an ex- of predicted endogenousevents, which are triples of the ogenous event that causes an object to slip out of the form(At, (ST1..... sv~). {,vl ..... ev,}). At is the delay robot’s hand is projected at time instant t while the tween the ith and the i+lth event in the schedule, (sv;. robot is in motion. To predict the new location of the .... ST,) the values of the state variables, and {=vl..... =,,} object the projector predicts the location l of the robot the events that are to take place. at the time t and asserts it in the timeline. If a state for which the plan is waiting, becomestrue Qualitative changes in the behavior of the robot at a time instance t, then at t a PASSIVE-SENSOR-UPDATEcaused by adaptations of the travel modeare described event is triggered. PASSIVE-SENSOR-UPDATEis an event through E->P-rules. The following E->P-rule describes model that takes a set of fluents as its parameters, theeffects of theevent (NAY-EVENT (SET-TRAVEL-MODE 7N)): retrieves the values of the state variables measured by (E->P (TRAVEL-MODE?M) these fluents, applies the sensor model to these values, (NAV-EVENT(SET-TRAVEL-MODE DOORWAY)) 1.0 (AND (CLIP (TRAVEL-MODE?M)) and then sets the fluents accordingly. (CLIP (OBSTACLE-AVOIDANCE-WITHSONAR)) A causal model of base navigation plans. Pro- (TRAVEL-MODEDOORWAY))) jecting the initiation of the execution of a navigation The rule specifies that if at a time instant at which plan causes two events: the start event and a hypo- an event (NAY-EVENT(SET-TRAVEL-MODE ?N)) occurs thetical completion event after infinite numberof time state (TRAVEL-MODE?M)holds for some?M, then the states units. This is shownin the following projection rule. (TRAVEL-MODE?M) and (OBSTACLE-AVOIDANCE-WITHSONAR) (PROJECT(BASE-NAV-PLAN ?DEST-DESCR ?ID ?FLUENT) will (with a probability of x.0) not persist after the event (TRUE) (0 (BEGIN (BASE-NAY-PLAN?DEST-DESCR ?ID ?FLUENT)) has occurred, i.e., they are clipped by the event. The oo (END (BASE-NAY-PLAN?DEST-DESCR ?ID ?FLUENT))) event also causes the state (TRAVEL-MODE DOORWAY) to (FINISH)) hold until it is adapted the next time. The effect rule of the start event of the base navigation plan computes the endogenous event schedule and Endogenous Event Scheduler asserts the schedule the occurrence of the next endoge- We have just shown how events are projected from nous navigation event as an occasion to the timeline. a given endogenous event schedule, but we have not (E->P (ENDOGENOUS-EVENT-SCHEDULE shownhow the schedule is constructed. Thus, this sec- BASE-NAY-PLAN?DEST-DESCR ?SCHEDULE) (BEGIN (BASE-NAV-PLAN?DEST-DESCR ?ID ?FLUENT)) tion describes the implementation of the endogenous 1.0 (AND (PREDICTED-EVENTS?ID ?SCHEDULE) event scheduler for base navigation plans. The sched- (RUNNING(RHINO-GOTO ?DESCR ?ID)) (NEXT-NAV-EVENT?ID))) uler predicts the effects of the base navigation plan

Beetz 167 From: AIPS 1998 Proceedings. Copyright © 1998, AAAI (www.aaai.org). All rights reserved. on the state variables × and Y. The endogenous event tersections with the regions (see Figure 6). The result scheduler assumes the robot follows a straight path of the schcduling step is a sequence of triples of the between the locations z to s. As we have pointed out form(ate, (x,, Y,), ~.ev~..... ev.}). earlier, there are two kinds of events that need to be predicted: the ones causing qualitativc physical change and the ones causing the trigger conditions that the plan is waiting for. 1 The qualitative events caused by the base navigation plan pictured in Fig. 2 ate the ones that occur whenthe robot arrives at the locations z, 2, 3.4, and 5 in which the robot either changes its travel modeor arrives at. its destination. For each of these thne instants the occurrence of a SET-TRAVEL-MODE-eventis predicted. The scheduler for trigger events works in two phases: Fig. 7: Modified endogenousevent schedule (1) it transforms the fluent network into a condition R.escheduling endogenous events. One problem that it is able to predict and (2) it applies all algo- that our temporMprojector has to deal with is that a rithm for computing when these events occur. The WAIT-FORstep might be executed while a base naviga- conditions that are caused by the base navigation plan tion plan is projected. For example, when the robot can be represented as regions in the environment such enters thc hallway, the policy that looks for the open- that the condition is true if and only if the robot is ing angles of doors when passing them is triggered. within this region. The elementary conditions arc nu- Therefore, the causal model that was computed by the meric constraints on RHINO’sposition or the distance endogenous event scheduler is no longer sufficient. It of l~mNOto a given target point. The scheduler as- fails to predict the "passing a door" events. sumes that RHINO-X*and RHINO-Y*are the only fluents These problems arc handled by modifying the en- iu these networks that change their value during the dogenous event schedule: whenever the robot starts execution of the plan. More complex networks can be waiting for a condition that is a function of the robot’s constructed as conjunctions and disjunctions of the el- position, it interrupts the projection of the base navi- ementary conditions. gation plan, .adapts the causal model of the base navigation plan, and continues with the projection. In the case of entering thc hallway, a new endogenous event schedule is computed that contains endogenous events I for passing doorways. This updated schedule of endogenous events is pictured in Fig. 7.

Projecting Exogenous Events One type of exogenous event is an event for which we have additional information about their time of occurrence, such as thc event that Dieter will bc back from Fig. 6: Initially predicted endogenousevcnts lunch around z2:25. These kinds of events are repre- The endogenous event scheduler approximates the sented by an E->P rule together with a t->P rule. The regions by rectangular areas in order to apply faster t->O rule specifies that the (START)event causes the computation methods. Consequently, circles, that is state (BEFORE-DIETERS-DOOR-OPENS)to hold mad persist regions specified by a maximal distance to a giwm for ?TIMEtime units. The event (mETERS-DOOR-OPENS) point, are approximated as the surrounding squares. triggercd as soon as (BEFORE-THE-DOOR-OPENS)no longer Thus, the step performed by the endogenous event holds. scheduler is to transform the given fluent network into (E->P (AND (ABOUT?TIME za:2s) (DIFFERENCE?TIME *NOW~ ?WAIT-FOR)) a union or intersection of rectangles. (START) In the next step the endogenous event schedulcr 1.0 (PERSIST ?WAIT-FOR(BEFORE-THE-DOOR-OPENS))) (P->E (NOT (BEFORE-THE-DOOR-OPENS)) overlays the straightline path through the intermedi- 0.0 (DIETERS-DOOR-IS-OPENED)) ate goal points of the topological navigation path (see Fig. 2) with the regions computedin the previous step. Passive Sensors and Obstacle Avoidance It then computes ~ schedule for the endogenous events Collision avoidance is not modeled except in situations by following the navigation path and collecting the in- in which the robot is told about objects that are moved

168 Robotics and Agents From: AIPS 1998 Proceedings. Copyright © 1998, AAAI (www.aaai.org). All rights reserved. around. In this case the endogenous event scheduler itative aspects of the robot’s behavior: whether or not adds a region corresponding to the object. If the region the robot bumps into the table and whether or not it blocks the way to the destination --- that is the robot misses the deadline. cannot movearound the region -- then a POSSIBLE-BUMP- We have also validated our causal models by com- EVENTi$ generated.The effect rule for a possible bump paring the symbolically projected behavior generated event specifies that, if the robot has activated sen- by the delivery plans, with the behavior they generate sors that can detect the object, the base navigation in the robot sinmlator and crosschecked the behavior plan fails with a failure description "path blocked." of the simulated with the real robot ill a shorter series Otherwise a bump event is generated. For example. of experiments. The predictions for the time needed to since sonar sensors are the only sensors placed at table perform a single navigation task (taking about 1 to height, the collision avoidance module can avoid a col- minutes) are often off by 10 to 20%. These inaccura- lision with a table only if the sonar sensors are activc. cies are mainly due to the high variances in navigation Thus, to predict a bump, the projector has to deter- behavior. Because the grain size for time in everyday mine how long the sonar sensors have been switched activity (deadlines, when people leave and come back. off before the possible bumpevent occurs. etc.) is in the range of minutes the accuracy of our predictions is more than sufficient. Experimental Results We have validated our causal model of base naviga- Related Work tion plans and their role in office delivery plans with Due to space limitations we cannot give a detailed ac- respect to computational resources, qualitative predic- count of all aspects of related work. Related work com- tion results, and quantitative results in a series of ex- prises research on reasoning about action and change, periments. A typical experiment is described below. probabilistic planning, numerical simulation, and qual- Projecting the plan listed in Fig. 2 takes on aver- itative reasoning. age 5 seconds (without optimizations). The projection (AF94) gives an excellent and detailed a discussion generates a timeline that is about 330 events long and of important issues in the representation of temporally about 1200 stack frames. Many of these events are complex and concurrent of actions and events with- generated through rescheduling the endogenous events out considering probabilistic information. (HMG95) (21 times}. If the robot were to be solely concerned presents a frameworkfor representing probabilistic in- with navigation, the projection process would be too formation, and exogenous and endogenous events for slow. An office delivery robot, however, spends much medical prediction problems. They consider smaller of its time interacting with people, picking up and de- problems and do not have to generate context-specific livering mail and therefore the planner has more than causal models. adequate time for debugging its delivery plan. Planning algorithms, such as SNLP(MR91), have been extended in various ways to handle more ex- pressive action models and different kinds of uncertainty (about the initial state and the occurrence and ’ outcome of events) (e.g. (KHW95; DHW94)). planning algorithms compute bounds for the prob- abilities of plan outcomes and are computationally very expensive. They also abstract away from the rich temporal structure of events by assuming discrete atomic actions and ignore various kinds of uncertainty. Partially observable Markov decision pro- Fig. 8: Projected navigation behavior and behavior cesses (POMDPs}focus on choosing optimal actions Figure 8 snows. generated me prealctea in thesimulator enaogenous events (de- under uncertainty (KCK96). So far approximation noted by the numbered circles) and the behavior gen- algorithms for POMDPsare computationally too ex- erated by the navigation plan in the robot simula- pensive to be applied to state spaces as large as ours tor. The qualitative predictions of behavior relevant (PR95). for plan debugging are perfect. In Fig. 8 the projector Workin qualitative reasoning has researched issues predicts correctly that the robot will exploit the oppor- in the quantization of continuous proccsses and fo- tunity to go to location 5 while going from location 1 cussed among other things on quantizations that are to 9. For the two scenarios that we have discussed ear- relevazlt to the kind of reasoning performed. (Hen73) lier, the projector perfectly predicts the relevant qual- points out the limitations of discrete event represen-

Beetz 169 From: AIPS 1998 Proceedings. Copyright © 1998, AAAI (www.aaai.org). All rights reserved. tationsand introducesa very limitednotion of con- M. Beetz and l). McDermott. Fast probabilistic plan de- tinuous process as a representationof change. He bugging. In Recent Adrmnces in AI Planning. Proceedings doesnot considerthe influenceof multipleprocesses on of the 19.97 European Conference on Planning, pages 77- statevariables. (Hay85) represents events ms histories, 90. Springer Publishers, 1997. spatiallybounded, but temporallyextended, pieces in D. Draper, S. Hanks, and D. Vqeld. Probabilistic planning time space,and proposesthat historieswhich do not with information gathcring and contingent execution. In K. Hammond,editor, Proc. 2nd. Int. Conf. on ..l I Plan- intersectdo not interact.In Forbus’Qualitative pro- ning Systems. Morgan Kaufmann, 1994. cessTheory (For84) a techniquecalled limit analysis T. Deml and M. Wellmann. Phrasing and (’ontroL Mof appliedto predictqualitative state transitions caused gas KaufmmmPublishers. San Mateo, CA. 199t. by continuousevents. Also, work on simulationofl.en D. Fox, W. Burgard, azld S. Thrun. The dynamic win- ¯ addressesthe adequacyof causalmodels for a given dow approach to collision avoidance. IEEE Robotics U rangeof predictionqueries, an issuethat is neglected Automation Magazine, 4(1):23-33, March 1997. in most modelsused for AI planning. K. Fo,’bus. Qualit.ative process theory. Artificiol httclli- gcnec. 2,1:85 1.68, 1984. Conclusion P. llayes. The second naive physics manifesto. In .I. It. To improve tl,e perfomance of robot tu:tion planners we Hobbs and I{.. C. Moore, editors, f;.’mai Thcorics of tht must equip tl,em with better and nmre realistic models (.:ommonscnsc World, pages 1-.36. Ablex, Xorwood, N J, 1985. of the robots’ behavior and the physics of the world. This paper has described a causal model of the behav- (;. Ilendrix. Modelingsimultaneous actions ~mtl conl.intl- otis processes. Artificial Intelligence. ,1: 145-180, 1973. ior exhil)ited by the mobile robot R.IIINO when running concurrent reactive plans for performing office deliv- S. Hanks. D. Madigan, and J. Gavrin. Prol}al~ilistic tent- poral reasoning with endogenous chmtge. In l’roceedings ery jobs. The model represents the temporal structure of the 11 th Conferc’nt’e on Uncertainty iv Artifieml Intel- of continuous control processes, several nmdes of their ligence, 1995. interferences, and various kinds of uncertainty. The Leslie Pack Kaelbling, Anthony R. Cassandra, mid rnodel is used in FeeD (BM97), a plan revision tech- James A. Kurien. Acting under uncertainty: Discrete nique that can. with high probability, forestall proba- bayesian models for mobile-robot navigation. In Proceed- ble situation-specific execution failures based on ran- ings of the IEEE/RSJ International Confi’,vncc on Intel- domly projecting a small number of execution scenar- ligent Robots and 5"ystems, /996. ios. N. Kushmerick, S. ltanks, and D. Weld. An algorithm for We believe that the use of detailed models of au- probabilistic planning. Artificial h~telligencr, 76:239 286. tonomous robot behavior together with plan revision 1995. techniques such as FPPD will enable us to implement I). McDermott. A reax:tive plan Imagnage. llesrarch Re- port YAI,EU/DC..S/RR-864, Y~de University. 1991. control systems for service robots that. perform on average better than they possibly could without planning D. McDermott. Transformational plamfing o1" reactive and that avoid categories of behavior flaws that can- behavior. Research Report; YALEU/DCS/RR-941, Yale (Inive~,’sity, 1992. not. be avoided by nmst other planning systems (see (BM94)). I). McDermott. An algorithm for probabilistic, totally-ordered temporal projection. Research Report Our future work on developiug causal models of YAI,EU/I)CS/RR-1014,Y,’de University, 199,1. robot behavior will focus on optimization, learning David McAllester and David Rosenblitt. Systematic non- causal models, and modeling other interesting pro- lincm" planning. In Proceedings of the Ninth Natiomd(:on- cesses such as map building, searching for objects, vi- ference on Artificial Intelligence (AAAI-9I), vohtme 2, sion routines, and manipulation actions. pages 634-639, Anaheim, California, USA, July 1991. AAAI Press/MIT Press. References R. PInT and S. Russell. Approximating optimal policies J. Allen and (3. I’erguson. Actions and events in inter- for partially observable stochastic doInains. In Proc. of val temporal logic. Technical Report 521, University of the Fourteenth International Joint (:onfl’rencc on ..lrtifl- Rodmster, Computer Science I)epartment, 1994. ciai bllelligenee, 1995. M. Beetz, W. Burgard, D. leox, and A. Cremers. Inte- S. Thrun, A. Biicken, W. Burgard, l). Fox, grating active localization into high-level control systems. T. FrShlinghaus, D. Hennig, T. Hofmann, M. Krell, Robotics and Autonomous Systems, 1998. and T. Schimdt. Map learning and high-speed navigation in RHINO. In D. Kortenkamp, R.P. Bona,sso, and M. Beetz and D. McDermott. Improving robot plans dur- R. Murphy, cditors: A l-based Mobile Robots: Case studies ing their execution. In Kris Hammond, editor, Second of successful robot systems. MIT Press, Cambridge, MA, International Conference on A I Planning Systems, pages 1998. to appear. 3-12, Morgan Kaufmann, 1994.

170 Robotics and Agents