Modular Design of Fuzzy Controller Integrating Deliberative and. Reactive Strategies. Technical Computer Science, Faculty of Technology,

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1 Modular Desin of Fuzzy Controller Interatin Deliberative and Reactive Strateies Jianwei Zhan, Frank Wille and Alois Knoll Technical Computer Science, Faculty of Technoloy, University of Bielefeld, Bielefeld, Germany Abstract This work presents the concept and realisation of the interation of deliberative and reactive strateies for controllin mobile robot systems. Prorammin at the task-level in a partially-known environment is divided into two consecutive steps: suboal plannin and suboal-uided plan execution. A modular fuzzy control scheme is proposed, which allows independent development and exible interation of dierent rule bases, each for fulllin a certain subtask. The desin process of the fuzzy controller is demonstrated with the examples of three rule bases. 1 Introduction This work aims at interatin sensin, plannin and control so that the couplin eects of these three components can be taken into account and then the performance of the whole system can be enhanced. Plannin methods which are totally separated from the sensin and control procedures normally assume that the robot motion environment is completely known. A survey of path plannin methods is iven in [2]. Pure eometric path plannin in known environments uses a deliberative stratey. The approaches followin this stratey normally have to solve problems of space division/representation, searchin and complexity analysis of plannin alorithms. By contrast, the reactive stratey reards path plannin as a local feedback control problem. The task of local motion control is to determine the motion parameters for drivin all the actuators by evaluatin the up-to-date sensor information as well as a predescribed path. If we compare the deliberative stratey with the reactive one, the followin conclusions can be drawn: While the advantae of the deliberative stratey mainly lies in the overview of the whole reachable space, the reactive stratey lends itself to takin into account dynamic aspects of the environment and applyin sensor data directly to determine the robot path. However, methods of the deliberative stratey must presuppose that a complete environment model is available. The main disadvantae of the reactive stratey is the so-called \dead-end" problem, because the robot does not possess the ability to read maps and thus behaves rather \shortsihtedly". Interation of deliberative and reactive strateies will contribute to the solution of robot motion control in a mixed environment with known and unknown objects. In most cases in the real world, the environment is partially-known. On the o-line modellin side, with the help of CAD data and by applyin a sensor fusion procedure, static information can be acquired, which represents xed objects like walls, tables, etc. On the on-line perception side, data from a sensory system provide the controller with dynamic feedback information for detectin slihtly moved objects and for avoidin unknown objects like clutters, pedestrians and other robots. Therefore it becomes an interestin problem how to desin a control scheme which can fully utilise on-line sensor feedback aswell as a priori knowlede. Beyond the classical control approaches, like potential eld [1], \intellient computin methods", like neural networks and fuzzy loic are increasinly applied in sensin, modellin and robot control. Our work employs the fuzzy control approach and the modular desin methodoloy. Actually, the principle of fuzzy control is intrinsically modular: a rule base is enerated by increasinly developin each sinle rule, which has linuistic interpretations and its own control function. The order of these rules does not make any dierence, both durin the controller desin and the rule evaluation. If we reard a rule base for fulllin a certain subtask as a separate module, it is easy

2 to understand that dierent rule bases can be developed independently and then interated for realisin a hih-level task like collision-free motion from a iven pair of start and oal position. Fuzzy control is becomin radually as a main approach of robot sensorbased control. Applications rane from the purely reactive fuzzy controller, e.. [5], to the mixture of \behaviours" like sinle-oal directness and reactive collision-avoidance, e.. [3] and [6]. This paper is oranised as follows: section 2 introduces suboals and the basic idea of the modular fuzzy control scheme. Then, plannin issues for mobile robot systems are discussed in section 3. Section 4 describes desin and implementation of the fuzzy controller and its interation in a control alorithm for suboal-uided motion. Section 5 ives some brief conclusions. 2 The Concept for Interation Our idea of interatin these two control strateies lies mainly in eneratin a set of critical points as suboals, then usin them for lobally uidin the robot motion and still leavin some freedom for the plan executor to react to uncertainties. 2.1 Introduction of Suboals For applications in a partially-known, dynamic environment, the plan executor does not need a detailed eometric path like aninterpolated spline curve provided by a planner since some of the path positions may have to be modied anyway due to the unknown static and dynamic obstacles. What is most useful for the on-line motion control is a set of suboals, e.. where the robot has to chane its direction relatively sharply in order to arrive the next suboal position. The main dierences between a suboal and a nal oal are as follows: Suboals should be much easier to reach than a nal oal The robot should usually move continuously throuh a suboal point while it should stop at a nal point A suboal can be exibly enerated, assined to the plan executor and abandoned if necessary Suboals need not be traversed exactly, while a nal oal is assumed to be xed and should be exactly reached. 2.2 Modular Fuzzy Control Scheme Conventionally, a preplanned trajectory is executed by a feedback position controller, which uses the sample of the trajectory as the desired value and the internal position sensor as the real value. With such acontroller the data from the external sensors for acquirin en route information cannot be interated into the controller. To solve this problem, we propose the followin control structure for realisin suboal-uided, sensor-based robot motions, Fi. 1. commandin of other robots, human users suboal plannin replannin suboal sequence suboal approachin fuzzy controller robot local collision avoidance command from others situation evaluation knowlede Base perception world model Fiure 1: Interation of suboal plannin and sensorbased plan execution based on fuzzy control Two main rule bases for drivin actuators are suboal approachin (SA) and local collision-avoidance (LCA). Rule base SA is responsible for the smooth tracin of suboal points. Rule base LCA should perform the subtask for avoidin unanticipated local collisions based on sensor data. In section 4, the ideas and desin procedures of rule bases SA and LCA will be presented in more detail. Parallel to the rule bases SA and LCA, further modules can be independently desined in the form of rule bases, each for a specied subtask, and be put into the knowlede base of the fuzzy controller. In multi-robot applications, the command of another robot, which arrives throuh a communication channel, can be viewed as an individual subtask and represented by a rule base. If human-robot interaction is desirable, the linuistic interference can be also dened, developed and then interated into the knowlede base. To resolve potential conicts between the output values, coordinatin the dierent rule bases becomes very important. Generally, criteria of such a coordination action are robot-specic, i.e. a robot controller can decide by itself the importance priority of each subtask and use it to modify the inuence on the outputs of these rule bases correspondinly.

3 situation-dependent, i.e. the importance priorities of these subtasks are not static and cannot be preassined they are dynamically determined by the situation evaluation. 3 Suboal Plannin Issues 3.1 Plannin with a Tanent-raph The suboal plannin problem is simplied to a 2- D case by representin the robot as a disc with radius r. Since the dynamic characteristics of the environment make the exact computation of suboals unnecessary, only a rather conservative approximation of the environment is employed. Obstacles are assumed to be described as polyons. They are enlared by a constant distance r. The robot is then shrunk to its reference point. In this procedure, edes and sharp vertices of these polyons are extended by r and the intersection points are computed as the new vertices of the enlared obstacles. After that, plannin suboals consists of ndin a sequence of straiht lines connectin the start and oal points with the shortest distance which do not intersect with the enlared obstacles. This problem can be solved best by searchin in a Tanent-raph (T-raph), a simplied V-raph, [4]. The number of arcs in a T-raph is considerably reduced by eliminatin non-convex edes and nontanential lines from the correspondin V-raph. An example of a T-raph is shown in Fi. 2. S Fiure 2: A T-Graph of enlared obstacles The A* alorithm is used to search for a lobal route in the T-raph since it can nd the shortest path if such a path exists. The nodes of the shortest path from a start position S to a oal position G are a sequence of vertices of the enlared obstacles. They are viewed as the suboals for uidin the lobal direction of the robot motion and can be represented as a sequence <Q 0 Q 1 ::: Q m >. G 3.2 A Mobile Robot System for Experiments This concept has been implemented for a real mobile ripper system Khepera, Fi. 3. Khepera is of circular shape with a diameter of 52mm. Additional modules can be mounted on the top of Khepera, e.. a ripper and a vision module. The environment is observed by eiht IR sensors (six on the front and two on the back). Khepera uses a Motorola MC68331 microcontroller, whose instruction set is compatible with the well known MC A RAM size of 128k is available for user prorams. Fiure 3: A mobile robot ripper system for experiments 3.3 Plannin Time Theoretically, the overall computation complexity of the pre-calculation for constructin a T-raph is on the order of O(n 2 lo n). In the case of the Khepera robot, by usin hihly optimised xed point arithmetics instead oatin point, Khepera, achieves nearly half the calculation speed of a SUN-workstation. The followin table shows the time for the calculation of V-raph, T-raph and suboals of three example environments: Polys/Edes 4/33 3/13 1/4 init T-raph 116 ms 21 ms 18 ms construct V-raph ms 591 ms 22 ms construct T-raph 289 ms 44 ms 5ms Suboal plan 538 ms 284 ms 30 ms 4 Desin of a Fuzzy Controller for Plan-Execution The modular fuzzy controller was developed with the TIL Shell of Toai Infra Loic. The local collision avoidance as well as the suboal approachin were realised by fuzzy if-then rules.

4 4.1 Approach of Suboals For briefness, we introduce the followin rule base SA for tracin the path to the next suboal. It is required to pre-calculate the two input variables shortest distance to path and anle of diverence: d: The shortest distance between the robot and the path sement connectin the previous suboal and the next one (in the followin called path for short). a: The anular diverence between orientation of the path and the robot. SA enerates the followin output variables: Speed: The speed of the robot. Steer: The steerin anle, based on the current direction of movement. A typical fuzzy rule of this module looks like this: IF (d IS n) AND (a IS z) THEN Speed IS hih AND Steer IS p If the robot is located slihtly to the left of the path, but its orientation is almost on the path, then it will steer slihtly to the riht by applyin a hih speed. The 49 rules of suboal approachin can be found in Appendix A. The implementation of this rule base for Khepera takes a computation time of 3 ms. 4.2 Local Collision Avoidance Typically, for local collision avoidance we need to determine the value and chane of ve proximity sensors, e.. infrared or ultrasonic sensors (left, half-left, front, half-riht and riht). The LCA rule base tries to avoid collisions with unknown or dynamic obstacles. By observin the current values and the chane of the ve proximity sensors LCA calculates the speed and steerin anle, which is needed to avoid obstacles. The input variables are: SL85, SL45, SLR0, SR45, SR85: Current value of the proximity sensors (left, half-left, front, halfriht, riht). dsl85, dsl45, dslr0, dsr45, dsr85: They represent the dierence between the current and last sensor value. LCA enerates the same Speed and Steer output variables as SA. A rule set is listed in Appendix B. 4.3 Situation Evaluation Situation evaluation enerates two parameters: the importance priority K, the replannin selector Replan. K: Importance priority for the LCA rule base. Each specic situation has its importance priority assined. Replan: Decides if a situation, which requires the path plannin procedure to be invoked once aain, is reached. That will be indicated by a hih value in Replan. A typical fuzzy rule of this module looks like this: IF (SL85 IS hih) AND (SL45 IS vl) AND (SLR0 IS vl) AND (SR45 IS vl) AND (SR85 IS vl) THEN K IS hih AND Replan IS low If the leftmost proximity sensor detects an obstacle, which is near and the other sensors detect no obstacle at all, then mainly perform obstacle avoidance. No replannin of the path is required. The implementation of this rule base for Khepera takes a computation time of between 8 and 14 ms. 4.4 Coordinatin LCA and SA The coordination of the rule bases LCA and SA is based on the importance priority K, see also [3]. By denotin the Speed and Steer parameters of both rule bases as Speed SA, Steer SA for suboal approach and Speed LCA and Steer LCA for local collision avoidance, the eective Speed and Steer becomes: Speed = Speed LCA K + Speed SA (1 ; K) Steer = Steer LCA K + Steer SA (1 ; K): If more than two rule bases function toether, such a principle can be further applied. In eneral, for n rule bases to coordinate, n importance priorities, e.. K 1 K2 ::: K n should be set. By classifyin dierent situations, the dynamic decision for these parameters can be formulated with fuzzy rules and then interated in the situation evaluation. 4.5 An Alorithm for Motion Control alon Suboals In order to interate sensor-based maneuver as well as suboal approachin in the motion control process,

5 an alorithm Motion Control was developed. The task of this alorithm is to uide the robot from a start position alon a iven suboal sequence to the oal position with the help of the rule bases of the fuzzy controller. At the position of the next suboal, a nishline is dened to be orthoonal to the path sement. When the nish-line is crossed, the alorithm switches to the next path sement. The whole alorithm is presented as follows: expected, the test in a completely unknown environment with the rule base LCA shows that collisions with obstacles can be avoided, but the robot can possibly move into a dead-end. In a partially-known environment, SA and LCA are coordinated by the rule base situation evaluation, realise the lobal suboaluided collision-free motion. Alorithm Motion Control(in SGL, in head0) Inputs: SGL - a list of suboals <Q0 Q1 ::: Q m > head0 - start headin of robot f /* Initialisin (set motor pid, etc.) */ i:=0 /* suboal index */ POS := Q0 /* start position of robot */ HDG := head0 /* start headin of robot */ while i<m do f PSG := Q i /* previous suboal */ NSG := Q i+1 /* next suboal */ i := i+1 /* calculate direction of current path sement and the nish line at NSG */ precalculations while (nish line was not crossed) do f S := read sensor data /* calculate new position and headin by evaluatin incremental sensor dierences */ HDG := calc new hd(pos,s) POS := calc new pos(pos,s) /* anular diverence between robot and path sement headin */ a:=calcanle(hdg, subse hd) /* shortest distance */ d := calc distance(pos, PSG, subse hd) /* evaluate rule bases */ eval rule base SE(S,K,REPLAN) eval rule base SA(a,d,STEER SA,SPEED SA) eval rule base LCA(S,STEER LCA,SPEED LCA) /* weihtin */ STEER =K*STEER LCA + (1-K) * STEER SA SPEED = K * SPEED LCA + (1-K) * SPEED SA if REPLAN then f replan new suboal list(pos,sgl) call Motion Control(SGL, HDG) compute motor velocities(steer,speed) output to actuators Experiments have demonstrated the nice modular features of this concept, Fi. 4. The rule base SA alone works well for realisin its suboal approachin subtask in a completely known environment. As 5 Conclusions Fiure 4: A test environment A fuzzy controller is used for executin suboaluided motions. Fuzzy rule bases, like local collisionavoidance, can work toether with the rule base for passin throuh suboals, each of which with only limited amount of control rules. In this way, durin motion between suboals, the robot does not move alon a statically planned trajectory, but under the control of a suboal-uided, sensor-based controller. On-line sensor data can be evaluated to detect local collisions and the motion control is adapted to the dynamic environment. The modular desin features enable a sinicant reduction of developin time, which is achieved by simple desin of a sinle rule base, fast prototypin and ecient debuin. Further fuzzy rule bases, such as for dealin with the commands from other robots or a human user, can be separately developed by usin heuristics or trainin. Due to the parallel characteristics of fuzzy control, these rules can be processed in real time durin each control cycle. In our opinion, fuzzy control is a promisin approach for realisin ef- cient and robust robot motions. References [1] J. Barraquand, B. Lanlois, and J.-C. Latombe. Numerical potential eld techniques for robot path plannin. IEEE Transactions on System, Man and Cybernetics, 22(2):224{241, 1992.

6 [2] Y. K. Huan and N. Ahuja. Gross motion plannin - a survey. ACM Computer Surveys, 24(3):219{ 291, September B Appendix B - Rule Base LCA (Local Collision Avoidance) and SE (Situation Evaluation) [3] S. Ishikawa. A method of autonomous mobile robot naviation by usin fuzzy control. Advanced Robotics, 9(1):29{52, [4] Y.-H. Liu and S. Arimoto. Proposal of tanent raph and extended tanent raph for path plannin of mobile robots. Proceedins of the IEEE International Conference on Robotics and Automation, [5] F. G. Pin and Y. Watanabe. Drivin a car usin reexive fuzzy behavior. IEEE International Conference on Fuzzy Systems, paes 1425{1430, [6] E. H. Ruspini. Fuzzy loic-based plannin and reactive control of autonomous mobile robots. In IEEE International Conference onfuzzy Systems, paes 1071{1076, A Appendix A - Rule Base SA (Suboal Approachin) Rules for tracin the path and approach the next suboal, with a = anle between the orientation of the robot and the planned path sement and d = shortest distance between path and robot. Rules for the output variable Steer a nb nm n z p pm pb nb pb pb pm pm p z n nm pb pb pm pm p z n n pb pb pm p z n nb d z pb pm p z n nm nb p pb p z n nm nb nb pm p z n nm nm nb nb pb p z n nm nm nb nb Rules for the output variable Speed a nb nm n z p pm pb nb low low low hih hih vh hih nm low low low hih hih hih hih n low low hih hih vh hih low d z low low hih vh hih low low p low hih vh hih hih low low pm hih hih hih hih low low low pb hih vh hih hih low low low Input LCA output SE output SL85 SL45 SLR0 SR45 SR85 Sp. St. K Repl. Dead end situation. Requires replannin. vh vh - vh vh vl z vh hih hih vh vh vh vh vl z vh hih vh hih vh vh vh vl z vh hih vh vh vh hih vh vl z vh hih vh vh vh vh hih vl z vh hih hih hih vh vh vh vl z vh hih vh hih hih vh vh vl z vh hih vh vh hih hih vh vl z vh hih vh vh vh hih hih vl z vh hih Collision avoidance in free space - Obstacle from riht vl vl vl vl low hih n low low vl vl vl low low low nm low low vl vl low low low low nb hih low vl low low low low low nb hih low vl vl vl vl hih low nm hih low vl vl vl low hih vl nb hih low vl vl low low hih vl nb vh low vl vl vl hih hih vl nb vh low vl vl hih hih hih vl nb vh low vl vl vl vl vh vl nb vh low vl vl vl low vh vl nb vh low vl vl vl hih vh vl nb vh low vl vl low hih vh vl nb vh low vl low hih hih vh vl nb vh low vl vl vl vh vh vl nb vh low vl vl low vh vh vl nb vh low vl vl vh vh vh vl nb vh low vl low vh vh vh vl nb vh low low hih vh vh vh vl nb vh low Collision avoidance in free space - Obstacle from left low vl vl vl vl hih p low low low low vl vl vl low pm low low low low low vl vl low pb hih low low low low low vl low pb hih low hih vl vl vl vl low pm hih low hih low vl vl vl vl pb hih low hih low low vl vl vl pb vh low hih hih vl vl vl vl pb vh low hih hih hih vl vl vl pb vh low vh vl vl vl vl vl pb vh low vh low vl vl vl vl pb vh low vh hih vl vl vl vl pb vh low vh hih low vl vl vl pb vh low vh hih hih low vl vl pb vh low vh vh vl vl vl vl pb vh low vh vh low vl vl vl pb vh low vh vh vh vl vl vl pb vh low vh vh vh low vl vl pb vh low vh vh vh hih low vl pb vh low Avoidin direct collision with obstacle ahead vl vl low vl vl low z hih low vl vl hih vl vl vl z vh low vl vl vh vl vl vl pb vh low vl low hih low vl low z vh low vl hih hih hih vl vl z vh low vl hih vh hih vl vl pb vh low vl vh vh vh vl vl pb vh low Avoidin direct collision with obstacle from half-left/riht vl low hih vl vl low pm vh low vl low vh vl vl vl pb vh low vl low low vl vl low pm hih low vl hih vh vl vl vl pb vh low vl vh hih vl vl vl pb vh low vl vh vh vl vl vl pb vh low low hih hih low vl vl pb vh low hih vh hih vl vl vl pb vh low hih vh vh low vl vl pb vh low hih vh vh hih vl vl pb vh low hih vh vh hih low vl pb vh low vl vl hih low vl low nm vh low vl vl vh low vl vl nb vh low vl vl low low vl low nm hih low vl vl vh hih vl vl nb vh low vl vl hih vh vl vl nb vh low vl vl vh vh vl vl nb vh low vl low hih hih low vl nb vh low vl vl hih vh hih vl nb vh low vl low vh vh hih vl nb vh low vl hih vh vh hih vl nb vh low low hih vh vh hih vl nb vh low No obstacle in vicinity vl vl vl vl vl vh z vl low