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2 10 Cooperative ormation Planning an Control of Multiple Mobile Robots R. M. Kuppan Chetty 1, M. Singaperumal 2 an T. Nagarajan 3 1 Monash University 2 Inian Institute of Technology Maras 3 Universiti Teknologi PETRONAS 1,3 Malaysia 2 Inia 1. Introuction Application of intelligent Wheele Mobile Robots (WMR) for material hanling in the manufacturing environment has been the topic of research in the past ecae. Even though researchers have succeee in applying mobile robots for material hanling purpose in the shop floor environment, transporting heavy objects in the assembly line is still a challenge. The ynamical characteristics of a manufacturing environment impose particular abilities a mobile robot shoul have if it is to operate on the shop floor efficiently, accurately an successfully. Consequently, a WMR nees to aapt itself to everlasting changes. Uner such conitions, the use of multiple WMR in close efine geometric spatial pattern/ formation can be a solution for such applications. One of the essential problems in guiing multiple mobile robots in such ynamically changing environments is to plan, navigate an coorinate the motion of robots, avoiing obstacles as well as each other while transporting the materials/objects towars the goal. urther it requires the robots to control their relative position an orientation between them on the fly. Hence the control of group of mobile robots performing such tasks requires coorination at ifferent levels starting from navigation to formation (Sugar et al., 2001). A variety of strategies an control approaches for formation control of group of coorinate robots, have been aopte in the literature such as Graph Theory (Desai, 2002), Vector Potential iel (Yamaguchi et al., 2001), Virtual Structure (Belta & Kumar, 2004), Leaer ollower (ierro et al., 2002) an Behaviour Base Approaches (Arkin, 1998; Golberg & Matarić, 2002). urther, a comprehensive review of robotic formation, control approaches an algorithms, applications an their avantages an isavantages have also been aresse (Chen & Wang, 2005). Among all the approaches mentione in the literature, behaviour base an leaer follower approach has been wiely aopte an well recognize by the researchers because of their simplicity an scalability. Even though robots are able to move in a close efine formation when controlle using the various methos reporte in the literature, the major limitation has been the ifficulty to achieve a stable formation between the robots in the group in ynamically changing, unknown environments fille with obstacles. Uner such circumstances, as the number of robots increases, the control methos such as the virtual structure, leaer follower an

3 204 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training graph theory fail ue to their centralization an requirement of higher communication banwith. urther it is ifficult to esign an moel the system in a traitional manner an necessitates the implementation of a istribute control strategy with wie communication capabilities between the group members to have knowlege about their states an actions of their teammates. Hence, the control of group of mobile robots performing such tasks requires coorination at ifferent levels starting from navigation to formation (Sugar et al., 2001). urther, in most of the stuies foun in the literature, the researchers have ealt the ormation planning an Navigation problems separately, in spite of consiering them as combine entity. However, as in the case of guiing the robot group in an unknown environment, in aition to formation planning, robots also nee other navigational capabilities to plan their paths to reach their particular goal by avoiing collision between themselves an obstacles in the environment of interest, which have not been aresse in the literature. Another important challenge for formation control is active obstacle avoiance on follower robots, which are not stuie in etail in the literature (Chaimowicz et al., 2004; Shi-cai et al., 2007). Therefore the more challenging an important problem is to combine the formation planning an active obstacle avoiance on the follower path, because the follower robot not only nees to perform obstacle avoiance but also has to control itself to remain in the esire formation in relation to the other robots in the group. In view of the limitations summarize above, three important issues relate to istribute formation planning an control of multiple mobile robots namely i) istribute layere formation control framework ii) ynamic role switching algorithm an iii) real-time implementations are aresse in this chapter. Towars acheiving these goals, a new istribute methoology for the multi robot formation platoons of unicycle robots is presente in this chapter. The presente methoology combines the formation planning an navigation base on the hierarchical architecture compose of layers, whose components are the funamental behaviours/motion states of the robots. Apart from combining formation planning an navigation, one of the most important problems an the major challenge is the avoiance of obstacles in the path of the robots esignate other than the leaer while guiing the robot group in an unknown environment. To aress this problem, a ynamic switching of roles, base on the exchange of leaership between the robots, is incorporate in the control methoology. This is an peculiar feature that istinguishes the presente methoology from the others that exist in the literature. In the first part of the chapter, the etaile escription an methoology regaring the layere approach evelope in this work, for solving the multi robot formation control problem is aresse. The control problem combines together formation planning, navigation an active obstacle avoiance, when operating in an unknown environment. In the subsequent parts, the etail about the metho of selection of the iniviual layers an behaviours of the presente approach is presente. Detaile escription about how the iniviual task achieving layers an behaviours are formulate is also provie. The theoretical formulation of formation behaviour base on the leaer reference moel an the evelopment of the tracking controller, which is use to minimize the tracking error asymptotically zero an makes the robot in the esire tight formation, is also aresse. In aition to that, the ynamic role switching methoology through the exchange of leaership between the robots an its behaviours, aopte by the robots other than leaer in the group, to actively avoi obstacles in their path is presente. inally the contributions on the evelopment of the presente formation control methoology an its avantages over the other methos foun in the literature are summarize an conclue.

4 Cooperative ormation Planning an Control of Multiple Mobile Robots Multi robot formation control The etaile escription an metho of the formation control approach is presente in this section. The main purpose of this approach is to achieve a formation control which guies a group of mobile robots in a close efine formation relative to each other, while navigating in an unknown unstructure environment. To perform this collective task, layere istribute control architecture whose components are the funamental behaviours/motion states of the robots, similar to (moifie form of) the pack an homogeneous controller (Harry Chia et al., 2005), is evelope an presente as shown in ig.1 (Kuppan Chetty et al., 2010, 2011). In this layere architecture, to achieve the esire objective of the formation planning an navigation in a istribute manner, the total functionality of the multi-robot system is ecompose into functional behaviours. The behaviours such as Navigation an ormation are obtaine, base on the motion states of the robots, utilizing the methoology of the behavior base reactive approach, as given in (Arkin, 1998; Xiaoming Hu et al., 2003; Golberg & Matarić, 2001). The funamental behaviours/motion states of the robots are erive base on the avantages of the behaviour base approach an the objective of the entire system. The states are arrange into two levels, a lower level navigation an a higher supervisor level formation, which works on iniviual goals concurrently an asynchronously. These two levels yiel the collective task upon integration. Both these layers an behaviours are relate using the priority base arbitration technique, where the entire sets of behaviours are swappe in an out of execution for achieving the goals such as navigation an formation. Therefore, the robots select a particular behaviour/motion state, base on the sensory information perceive by the robot sensors from environment uring the fly. ig. 1. Layere formation control architecture with task achieving behaviours classifie into supervisor level formation an lower level navigation

5 206 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training A reactive controller mae up of simple prepositional representation comprising of if then else moel with task specific sensing, reasoning an planning is use to formulate the behaviours at the navigational level. This controller provies the necessary navigational capabilities an eals with the ynamic control of robots while guiing them in the environment of interest. urther, to have the theoretical formalization an the convergence of the robots into the esire formation, a close-loop tracking controller at the supervisor level formation is realize using the kinematic moel of robots employe in the group in the leaer follower moel. This controller hanles the higher-level objective of multi robot formation. Hence, the propose approach conquers the eficiencies of the leaer follower approach an the behavior base approach, by wrapping up the former with the later, an has the avantages of both the approaches. Thus, the propose controllers have the capability to aress the combine problem of formation planning an navigation through obstacle avoiance. Referring to ig. 1 the rectangles in the architecture represent the robot sensors, with the sensor values being transmitte to the behaviors along the long ashe lines. The behaviors themselves are rawn as rectangles with roune corners arrange in three levels of hierarchical layers namely avoi obstacle layer, explore layer an supervisor layer. The otte lines represent the comman signals sent by the behaviors to the actuators an the inter behavior control signals. The arrowheas in the comman lines inicate the priority of the behaviors, which constitutes the pathway to the actuator. The subsumption style priority base arbitration scheme is represente by with the actuator comman coming from the upper level layer taking the preceence. The next section gives the etails of the layers, their corresponing behaviors, an the functionality of each behavior in the architecture. 3. Layers an behaviors This section briefs about the selection of layers an their corresponing task achieving behaviors an how these behaviors are formulate an coorinate to achieve the objective of formation maintenance an navigation tasks. 3.1 Selection of layers an behaviours In orer to have the istribute control nature, the collective task of formation planning an navigation, is ivie into three primitive tasks such as ormation, Navigation an Obstacle avoiance, base on the motion states of the robot. These primitive motion states are consiere as the basic funamental behaviors of the robot an are place in two separate hierarchical levels calle the control levels, terme as the supervisor level an the navigational level in the control architecture. The navigational level is the controller s low level. This is responsible for the robot esignate as the leaer to safely guie the team members towars the goal, without colliing with obstacles or with other team members in the environment of interest, using the behaviors/ motion states present in this level. The supervisor level is the controller s top level, which helps the robots esignate as followers to remain in the close efine formation with their leaer using the formation behavior present in this level. The selection of control levels by the robots are base on the priority number assigne to them. While consiering the specific problem of navigation, the leaer robot has to perform numerous motion states such as estimating the estination from current location, avoiing collisions with obstacles an other robots, an guiing the follower robots to move in the

6 Cooperative ormation Planning an Control of Multiple Mobile Robots 207 absence of obstacles to cover large areas. To o this the navigational behaviour is further ecompose into lower level behaviours such as Procee, Avoi obstacles, Safe-waner an Pit-sensing. All these behaviours are place in the avoi obstacle an explore layers in the navigational level as shown in ig. 1. urther, it is necessary to retain the robots in a close efine formation an to minimize the separation error between the robots. Hence, the formation behaviour is chosen to provie the necessary tracking control for the robots an place in the supervisor layer in the controller top level. In orer to retain the robot formation, it is necessary for the robots to have the postures, orientation an behaviour/state information of the other robots in the group. This helps the robots esignate as follower to position themselves relative to the leaer with the esire relative separation an orientation, while the leaer maneuvers inepenently. Therefore, the behaviour of message passing is use to provie the explicit communication between the robots using the wireless TCP/IP protocol an place in the supervisor level. Initially by efault, safe waner behaviour is activate in the controller s leaer level an others are suppresse. If one of the other behaviours becomes active, transition from the safe waner to the avoi obstacle occurs accoringly. If the robot is in the follower moe, it executes the formation behaviour which is responsible to keep the robot in a esire formation by minimizing the separation error to zero. Therefore, there are totally five behaviours which are erive base on the objective of the collective task an motion states of the robots, arrange in three layers an in two levels as shown in the ig 1. Even though the task of maintenance of formation has the highest priority in the approach, the obstacle avoiance priority also fins the higher orer of priority base on the role of the robots in the group. The formation behavior has the highest priority in the follower robot an the obstacle avoiance is consiere as the critical behavior, while in the leaer robot the obstacle avoiance has the higher priority an the Pit sensing behavior is consiere as the critical behavior. The next section presents the etails on how these layers an the behaviours on the control architecture are formulate. 3.2 Description of layers an behaviors The lower level navigational controller of layere formation control architecture consists of two layers such as explore an avoi obstacle layer, which are necessary to provie the navigation capability to the robots. The higher-level formation control consists of supervisor layer, necessary for high-level missions such as formation an communication. The etails of the behaviours in the above mentione layers are given below. a. Procee: This behaviour processes the positioning ata an provies approximate procee values for the safe wanering an the obstacle avoiance behaviours. This provies the robot current position an orientation information at every instant in the two-imensional workspace using ea reckoning principle an the kinematic configurations of the robots an makes the robot to hea towars the goal. Hence this behaviour is place uner avoi obstacle layer in the architecture. b. Avoi Obstacle: This behaviour makes the robot to avoi obstacles / objects without colliing an to manoeuvre within the workspace base on the information receive from its sensors as shown in ig 2 (a). When the robot sensors fins an obstacle/object within the workspace enclose by the semicircle, the avoi obstacle behaviour is activate an it manipulates the wheel velocities of the robot, as given by Eqn. 1 (a) an (b) necessary to avoi the obstacle.

7 208 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training (a) Safe wanering after 90 turn left after 25s Heaing after 90 turn right after 25s Turn Left Turn Right ig. 2. (a) Emergence of Obstacle Avoiance behaviour A top view look of robot an obstacle, (b) Safewaner Behavior (b) *( obs h v vavoi ) (1a) ( * sign( )) (1b) t where, v an correspon to the translational an rotational velocities in mm/s an ra/s respectively. v avoi is the avoi velocity in mm/s, obs is the istance of the obstacle with the robot, where the maximum istance is less than 5 m, is the esire threshol istance necessary to avoi the obstacle, h is the istance between the sensor assembly from the axis of rotation of the robot. t is the angle of turn in raians an is the angle of the obstacle with respect to the robot frame. This behaviour is place in the avoi obstacle layer, whose functionality is to prevent the collision of robot with obstacle or with other robots an to ensure the safety of the robot.

8 Cooperative ormation Planning an Control of Multiple Mobile Robots 209 c. Pit sensing: Existence of pit in the environment is a very critical issue, which has to be avoie by robots manoeuvring the environment of interest. This behaviour makes the robot to avoi pits by controlling the motion of the robot in the backwar irection to a preetermine istance, base on the sensor information. Hence this critical behaviour is place with the highest priority in the explore layer.. Safe wanering: This behaviour guies the robot through the workspace/environment with piece wise constant velocity by turning left or right at regular intervals with preetermine angles as shown in ig. 2(b). This makes the robot to waner through the environment thoroughly an to look for goals if specifie. Hence this behaviour is place uner the explore layer in the architecture. e. Message passing: Message passing behaviour provies the necessary interaction between the robots allowing them to exchange their motion states, position, orientation an velocity information, using the explicit socket communication capability through wireless links (Hu et al., 1998; Crowley & Reignier, 1993). A 5-10 Hz upation rate is provie making the inter-robot communication feasible. This helps other robots in the group to know the current task or behaviour of their teammates. This in turn helps the iniviual robot in the group to make suitable ecisions. Hence this behaviour is assigne with highest priority an is place on top of all the layers. f. ormation: When the followers know the trajectory or plan of the leaer, this behaviour manipulates the necessary wheel velocities of the follower to maintain its position relative to the leaer with esire separation an orientation through the tracking controller. This behaviour is place in the supervisor level, since our main objective is to maintain the esire formation between the leaer an the follower with the robots manoeuvring the workspace/environment. Mathematical moelling of this behavioural function is given in etail in the next section. 4. Mathematical moeling of formation behavior ormation behavior is mae up of mathematical formulation of tracking controller base on the kinematics of the wheele mobile robot. This section etails the formulation of such moel to keep the multiple mobile robots in a efine geometric spatial pattern. In formation control problem of multiple wheele mobile robots, the objective of the robots is to remain in the close efine geometrical pattern with their teammates. There are several approaches iscusse in the literature for formation control. One of the prominent approaches is the leaer follower approach where one or more robots acts as the leaer an other robots esignate as followers follow them. Therefore, the major critical task is to erive a control methoology for the followers to maintain their esire linear an angular separation with their leaer to remain in the efine formation topology. This section etails about the methoology aopte in eriving a control strategy for the formation behavior, which plays a major role for the robots. To erive a suitable control methoology the following assumptions are mae. 4.1 Research assumptions - Robots employe in the group are ientical in their kinematic moel, an have same set of sensors, actuators an control strategies. - Tire ifferences, moel uncertainties, oometry errors by slie an ski are ignore. - Cartesian coorinate representation as mentione in (Xiaohai Li et al., 2004) is utilize to evelop the control algorithm.

9 210 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training - Robots employe are assume as perfect velocity controlle robot without consiering the ynamics. Hence, the kinematic moel is use for evelopment of multi robot leaer follower formation framework. - Robots are aware of each other through explicit inter robot communication with onboar sensing, computation an communication capability. - The relative information between the robots is utilize rather than the global information systems. - Leaer Reference moel is use, in which other robots maintain the esire position to the leaer. 4.2 Leaer reference multi robot system Let us consier a simple system consisting of two robots in a leaer-follower framework an assume that the pose vectors of both the robots are given in the global reference frame of the cartesian coorinate representation as given by Eqn. 3. ig. 3 shows the kinematic moel of non-holonomic ifferential rive wheele mobile robots arrange in such a configuration. Here R L represents the leaer robot, R represents the follower robot an R r represent the esire position to be reache by the follower robot to remain in close formation with the leaer by keeping the leaer as its reference. In the formation control of pair or robots as shown in figure 3, there are two critical parameters l an that etermine the geometric shape of the two-vehicle sub system as given by the following representation i i i i S L l (2) Where, i = 1, 2, 3 n enotes the robots ientification number an S i enotes the shape of the formation. y L L x y R L l l = L y y R r R x x L, x ig. 3. Kinematic moel of the robots in Leaer ollower ormation

10 Cooperative ormation Planning an Control of Multiple Mobile Robots 211 Let l an l be the relative an esire linear separation an an be the relative an the esire angular separation between the robots respectively. To achieve the esire formation the control has to make l l an an to bring the separation an orientation errors asymptotically to zero. In this case, the control problem reuces to a trajectory tracking control problem rather than the regulation problem of the follower, where it plans its path to efficiently position itself relative to its leaer by observing the leaer s information. Hence, a tracking controller is to be esigne for the follower robots to remain in the close formation. Therefore, the objective of the tracking controller is to fin the velocities of the follower robots. 4.3 Tracking controller In formation control, the objective of the tracking controller is to fin the values of the translational an rotational wheel velocities v an of the follower robots in such a way that the formation/separation errors (linear an angular) ecay asymptotically to zero, an position the follower in the esire geometric pattern with its leaer. In orer to formulate the tracking control algorithm to fin out the wheel velocities of the follower, let the position of the leaer an the follower robot in a unit time as in ig. 3; be given by X L, Y L an X, Y respectively in the fixe groun coorinate system. Let X r an Y r be the position of the reference robot, which is the esire position to be reache by the follower to remain in a formation with the esire linear an angular separation with the leaer. The orientation of leaer an follower robots is given by L an respectively, an the orientation of the reference robot r is same as the orientation of the leaer, which is the basic requirement for the formation platoons Generalize tracking controller in global frame The motion for a non-holonomic ifferential rive wheele mobile robot is governe by Eqn. 3, x cos 0 v v y sin 0 J 0 1 Where, J is the Jacobian matrix which efines the kinematics of the WMR. Here, the robot pose vectors are assume in the global (inertial) reference frame of the cartesian coorinate representation. Base on the above kinematic moel, the velocity equations of the leaer robot in the groun frame is given by (3) x cos L L L y v sin L L L L v Similarly, for the robot esignate as follower, the velocity equations are x L cos y v sin v (4) (5)

11 212 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training In orer to minimize the separation errors, the follower robot ajusts its position relative to its leaer by estimating the leaer s current posture an velocity information. However, as in the real case, the estimation of information in the global coorinates in the real time requires complex estimation methos. There exists a reference position, which is obtaine base on the esire linear an angular separation relative with the leaer, since the reference position cannot be estimate irectly in the real worl. This reference position is use as the esire position for the follower robot to be reache to remain in the formation an to minimize the separation error. Therefore the pose vector of the reference/esire position to be reache by the follower from its position relative with the leaer is given by x cos sin r v L L l y v sin l cos r L L r L L ig. 4 shows the block iagram of the tracking controller assuming that the robots are in the global coorinate frames. (6) Information about Leaer Robot Leaer Posture (X L,Y L, L ) Separation values (l, ) Leaer Velocity (V L, L ) Desire Posture (X r,y r, r ) (X e, Y e, e ) Tracking Controller (V, ) Actuator Control Robot Motion ig. 4. Block Diagram of the Tracking Controller Robot Posture (X,Y, ) The next step is to fin the tracking error vector between the reference an actual position for the follower robot. This is given by the Eqn. 7. x ( ) e x r x y e ( y r y ) e ( r ) (7)

12 Cooperative ormation Planning an Control of Multiple Mobile Robots 213 By substituting Eqn. 5 an Eqn. 6 in the above Eqn. 7, the tracking error becomes x x x ( v cos v cos l sin( )) (8) e r L L y y y ( v sin v sin l cos( )) (9) e L L (10) e L The above equations are nonlinear. In orer to erive a controller, the non linear nature of the above equations are linearize by Input-Output linearization technique an by choosing xe K1xe, ye K2ye an e K3 e The control equation becomes V V K L(cosL sin L) 1Xe K2Ye l cos l sin (11) (cos sin ) K ( (12) 3 L ) L Tracking controller with mapping of coorinate frames As in the first case, the state of the robot is escribe in relation to the global coorinate system. But in the real case of the robots, their coorinate system is ifferent from the global coorinate system. In this case, X-axis represents the forwar motion of the robot. Hence, to escribe the robot motion in terms of component motion, it is necessary to map the motion along the axes of the global reference frame to motion along the axes of the robot local reference frame as shown in ig. 3. The following orthogonal rotational transformation matrix is use to accomplish the mapping. cos sin 0 R( ) sin cos 0 (13) urther in the case of the Multi Robot Systems (MRS), ifferent robots in the group as members must be able to compare measurements an coorinate their actions with in a common frame of reference. Hence, it is necessary to match the coorinate frame of robots esignate as the followers relative to the leaer coorinate frames, using the relationship between the inertial an relative coorinate representation of the robots. When the leaer is subjecte to only rotation by an angle, it is reflecte in the reference robot (esire position to be reache by the follower) as a combination of translation an rotation, following a circular path with linear separation as the raius. Hence, the velocity equations of the reference robot in the groun frame is given by X cos sin( r v L L l L ) L Y v sin l cos( r L L L ) L r L L (14)

13 214 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training Similarly, the velocity equations of the follower robot is given by X v cos hsin Y v sin hcos The next step in eriving the tracking controller is to obtain the error ynamics of the system in the robot frame by choosing the error coorinates x e in the irection of v an y e perpenicular to this irection as epicte in ig Therefore, to obtain the error in the common local reference/ robot frame, where the coorinate system of the follower is relate with leaers system, the orthogonal rotation matrix given above takes the form as x e cos sin 0 ( X X ) r y e sin cos 0. ( Y r Y ) e ( r ) cos sin 0 where, R( ) sin cos 0is the orthogonal rotation matrix ig. 5 shows the block iagram of tracking controller in which the tracking error is represente in the new coorinate system of robot frame. (15) (16) Information about Leaer Leaer Posture Separation values Leaer Velocity (V L, L ) Desire Posture Coorinate Transformati (X e, Y e, e ) (V, ) Tracking Controller Actuator Control Robot Motion Robot Posture (X,Y, ) ig. 5. Block iagram of tracking controller in the robot frame

14 Cooperative ormation Planning an Control of Multiple Mobile Robots 215 By substituting Eqn. 14 an Eqn. 15 in the above Eqn. 16, the tracking error in the new coorinate system is obtaine as, x ( ) cos sin e X r X ( r ) 0 e ( ). X X x R y e ( Y ) sin cos ( ) 0 y r Y Yr Y e (17) e L L L L e x v v cos( ) l sin( ) y (18) e L L L L e y v sin( ) l cos( ) x b (19) The next step is to fin a control law for the velocity input an to position the follower in the esire position w.r.t the leaer an to minimize the tracking error to zero. An obvious complexity of the above equations of the error ynamics is that the presence of the terms yean xe inirectly relating the output x an y with the inputs v an through the state variable. Thus, in turn makes the system moel to be nonlinear in nature. In orer to fin the control law for the velocity inputs of the tracking controller, the Eqn. 18 an 19 are linearize using suitable linearization technique. Here the iea is to algebraically transform the nonlinear system ynamics in to a fully or partly one, so that the linear control theory can be applie. Hence, eeback linearization technique fins the best solution to linearize the above nonlinear system moel especially for tracking controllers (Khalil, 1996; Shankar Shastry, 1999) where the approach involves coming up with a transformation of the nonlinear system into an equivalent linear system through a change of variables an a suitable control input. The ifficulty of the tracking controller esign is ecrease by fining a simple an irect relation between the system output y an the control input u = [v ] T by applying x e ye kx 1 e y k y x e 2 e e (20) an hence, after the feeback linearization the control law for v an is obtaine as where, cose l sin( ) e k1 0 v vl xe sine l cos( e) k 2 L 0 y e h h h xe XL l cos( L) X cos YL l sin( L) Y sin ye XL l cos( L) X sin YL l sin( L) Y sin stans for the position error between the esire position i.e. position of the reference robot, an the position of the follower robot in the new coorinate system an k 1 an k 2 are controller gains that are constant positive integers greater than zero, which guarantee the system stability. (21) (22) (23)

15 216 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training 4.4 Obstacle avoiance on follower One of the most important problems an the major challenge is the avoiance of obstacles in the path of the robots esignate other than the leaer while guiing the robots group in an unknown environment. To avoi this problem, a ynamic role switching methoology base on the exchange of leaership between the robots is incorporate in the evelope formation control methoology. The principle behin the switching strategy is that the robot esignate as the leaer in the real time takes the responsibility of guiing the group through the environment by executing the navigational part of the controller an the robot esignate as the follower follows the leaer by executing the formation controller. The ollower only leas the group uring short time perios in the fly when it has to avoi the obstacle present on its path. Therefore, at any moment uring the coorination motion, the robot performing the leaing role can become a follower, an any follower can take over the leaership of the team an makes the robot controller to exchange their control moes from navigation to formation an formation to navigation, base on their previous roles an sensory information through explicit inter-robot communication. As the follower perceives the obstacle on its path base on the sensory information receive from its sensors, it sens a request packet to the leaer to release the leaership. When the current leaer receives the request of releasing the leaership, it immeiately releases the leaership to the follower, through an explicit inter-robot socket communication mechanism. Once the follower attains the leaership, it switches its role from follower to leaer. Hence, the follower switches from the controllers formation moe to the navigational moe an starts navigating the environment as a temporary leaer. In the other sie leaer robot switches its control to the formation moe an plans its path to track the temporary leaer in the efine spatial pattern until the obstacle has been avoie. Uner such conitions, the esire linear separation of the follower remains the same an the angular separation changes base on the geometric relationship between the robots as given by Eqn. 24 an shown in ig. 6. ; ; (24) ig. 7 shows three robots R 1, R 2 an R 3 in a wege shape formation topology, with R 1 esignate as leaer an R 2 an R 3 esignate as followers. When any one of the follower robots R 2 an R 3 perceives the obstacle on its path, the analogous robot attains the leaership temporarily. Let us consier that the follower robot R 2 perceives the obstacle in it paths. Uner such conitions, the Robot R 2 attains the leaership, the esire formation parameter between R 1 an R 2 is obtaine as given by the Eqn. 25, an the other robot R 3 tracks the robot R 1 as its reference, without changing the formation parameters between them, which in turn tracks the temporary leaer R2 using the simple geometrical relationship between the robots. Similarly, when robot R 3 attains the leaership temporarily, esire formation parameter between R 3 an R 1 is obtaine as given by the Eqn. 26, an the other robot R 2 tracks the robot R 1 as its reference. This methoology reuces the computational an inter-robot communication complexity, an helps to minimize the transitory errors between the robots, ue to the abrupt change in the formation parameters an the switching of leaership between the robots.

16 Cooperative ormation Planning an Control of Multiple Mobile Robots 217 (a) ig. 6. Role of angular separation while role switching when (a) R1 as leaer an R2 as follower, (b) R2 as leaer an R1 as follower (b) ig. 7. Role of angular an linear separation while role switching when more than two robots in the group ; 12 ; When obstacle is on R 2 (25) ; 12 12

17 218 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training ; 13 ; When obstacle is on R 3 (26) ; Another important problem in the three-robot formation is, when the follower robots R 2 an R 3 perceive the obstacle in their path at the same time. In these circumstances, Robot R 1 retains the leaership by itself an commans the follower robots to change the type of formation to inline formation from their initial formation. Therefore, the require change in the esire formation parameters is obtaine base on the simple geometric relationship between the robots, an are given by Eqn. 27 an 28. or Robot R 2 an for Robot R ; 12 an l l12 (27) ; 12 ; ; an ; 13 l13; 13 l l l (28) This kin of change in formation topology is preferre to avoi the ealock situation in the release of leaership, when more than one robot requests the leaership simultaneously. After avoiing the obstacle, temporary leaer releases the leaership back to the previous leaer, starts executing the formation behaviour, an plans its path accoring to the leaer. Hence, the ynamic switching roles/behaviours in the control architecture allow the robots to trae their roles between them an to actively avoi obstacles on the robots esignate as follower s path while maintaining the esire formation. 5. Simulation stuies 5.1 Simulation escription The main objective of the simulation stuies is to evaluate the ifferent aspects of the control architecture, i.e. to measure the emergence of all possible reactive behaviours/asm of the layere approach. The response of the active behaviour yiel the motor control output to the robot actuator, which etermines the motion of the robot. Simulation stuies are carrie out in a phase manner. Before going into the stuy of multi Robot formation systems, simulation stuies to measure the response of the reactive task achieving behaviours of the navigational controller are carrie out. The relationship between the formation parameters such as the Instantaneous Centre of Raius/Curvature (ICR/ICC), linear separation (l ) an the angular separation ( ), an their effects on the tracking controller are investigate. Then the error ynamics of the tracking controller which are responsible for positioning the follower robots in the esire separation an orientation with the leaer is teste for various formation topologies. In this simulation stuy, the leaer robot is mae to move in a preefine trajectory such as straight line, arc, S-shape an eight shape trajectories, with the generalize parameters obtaine from the simulation stuies. ormation strategies such as in-line, parallel an wege shape

18 Cooperative ormation Planning an Control of Multiple Mobile Robots 219 have been simulate for both two an three robots in the group. inally, the ynamic switching of roles for active obstacle avoiance in the follower is incorporate along with the formation planning an navigation. Matlab SIMULINK/ Stateflow environment as the simulation tool to evaluate the ifferent aspects of the propose formation control architecture, since it is an interactive graphical esign an evelopment tool that works with Simulink to moel an simulate complex systems moele as finite state machines, also calle reactive event riven systems (Stormont & Chen, 2005; Dougherty et al., 2004). In this simulation moel, simulation is carrie out for 160 units in the time frame with two robots R1 an R2 performing the Leaer ollower formation. Leaer is mae to navigate the environment using the lower level navigational behaviour, with a piecewise constant wheel velocity of 100 mm/s an the Instantaneous Centre of Rotation (ICR) of 5732mm. ollower is mae to track the leaer with the esire separation an orientation using the supervisor level formation behaviour. Wheel velocities, wheel irection of rotation an the position an orientation information of the robots are taken as the behavioural outputs an are logge into the ata loggers. Simulation parameters an the threshol values for the behavioural activation are provie in the simulation environment taking the kinematics of the robots into account. The wheel velocities obtaine as behavioural outputs are constraine an boune by the conitions v < v max < 300 mm/s an < max < 50 /s 5.2 Simulation results Relationship between the formation parameters an ICR / ICC ig. 8 shows the simulation results that are obtaine to aress the generalize relationship between the formation parameters such as the linear separation (l ), angular separation ( ) an the Instantaneous center of curvature ICC/ICR. The critical value of the ICC/ICR neee for the robots to remain in the close efine formation is obtaine for various values of linear separation (l ) starting from 500mm to 3000 mm, in several formation topologies starting from parallel line to inline formation, using the eqn. 21. The various values of angular separation ( ) represent the type of formation topology employe between the leaer an follower robots as shown in ig. 9. The esire angular separation values of 90 an 270 represents the parallel line, 180 represents the inline an the values between 91 an 179 & 181 an 269 represents the collateral line spatial pattern between the robots. It is observe from ig. 8, that for a particular type of formation topology either for a parallel, inline or collateral spatial pattern, as the value of the linear separation increases the value of the ICC/ICR also increases making it to be irectly proportional in nature. It is also observe that the maximum ICR/ICC is at the collateral formation topology with the esire angular separation of (( ) = 157 an 202, in which the follower robots are place in the II an IV quarant of the cartesian coorinates w.r.t the robot frame as shown in ig. 9. or the further investigations, the line representing the collateral formation of = 157 an 202 is taken as the reference base on the consieration of the length an the iameter of the real robots, which are 420mm an 345mm respectively, use in the experimental setup. With this information, in orer to have the close efine stable formation between the robots in all formation topologies, the value of the linear separation an ICC/ICR of 1000mm an 2.3m is chosen as generalize values, by consiering the wheel base of the robot.

19 220 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training ig. 8. Relationship between ormation Parameters ig. 9. Robot formation topologies ormation control combine with ynamic switching of roles rom the several simulation stuies carrie out, the results obtaine from the state base simulation stuies, in which the ynamic switching control strategy is incorporate along with formation planning an navigation between the robots is presente. The input parameters for simulation stuies are given in Table 1 ig. 10 shows the trajectory of robots R 1 an R 2, where the leaer robot navigates the environment by switching between safe wanering, avoi obstacle, an pit sensing behaviours marke as S, O an P respectively. The ynamic switching of roles an exchange of leaership between the robots are inicate by the otte circles in the figures. At these places R 2 encounters obstacles/pit. Hence robot R 1 acts as the follower an ajusts its wheel velocities to track its temporary leaer R 2 maintaining the linear an angular separations as require. ig. 11 shows the orientation profile of both the robots, where it is observe that both robots remain in the same orientation throughout the workspace. This

20 Cooperative ormation Planning an Control of Multiple Mobile Robots 221 Parameter ormation topology Desire Linear separation (l ) Value Parallel 1000 mm Desire Angular separation ( ) R 1 acts as leaer R 2 acts as leaer ICR/ICC 2.3 m Translational an Rotational velocity 100 mm/s; 2.5 /s Initial Positions of the Robots Robot R 1 Robot R 2 Simulation time (0,0)mm (-1000, -2000)mm 1600 s Table 1. Simulation Parameters ig. 10. Trajectory of two robots in parallel line formation. type of formation is best suite for the application of platoon of vehicles in search an surveillance an inustrial transport systems. ig. 12 (a) an (b) provies the iniviual behavioural/state output of the robots R 1 an R 2 for the given set of sensory information, in which logical 1 represents the behaviours that are active at that time instant to have control over the robot actuator. ig. 13 shows the relative linear an angular separation between the robots being trae to meet the esire one, where = 270 an 90 shows the esire angular separation of the robots when R 1 an R 2 acts as the leaer respectively. The ynamic motions of the follower robots to remain in the tight spatial pattern with its leaer were

21 222 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training observe from the translational an rotational velocity profiles plots obtaine uring simulation as shown in ig. 14. A positive spike in the follower s wheel is ue to the transitory error that persiste in the controller when a suen reversal of the wheel velocity are involve in the non-holonomic robot systems, when pit sensing behaviour is execute to overcome a pit in both the robots. ig. 11. Orientation profiles of robots in parallel line formation (a) (b) ig. 12. Iniviual Behavior/state output of (a) Robot R 1 an (b) Robot R 2

22 Cooperative ormation Planning an Control of Multiple Mobile Robots 223 ig. 13. ormation errors with role switching. ig. 14. Velocity profiles of robots with role switching The ynamic switching of roles an exchange of leaership between the robots are marke by a otte circle in the above figures, which can also be observe from the encircle portions of the ig. 14, where robot R 1 acts as the follower an ajusts its wheel velocities to track its temporary leaer R 2 by keeping the linear separation of 1000mm an angular separation as given by Eqn. 25; to avoi the obstacle foun in the path of R 2. Similarly, the formation errors in both linear an angular separation for several formation topologies are tabulate in Table 2. rom the simulation stuies, it is seen that the tracking error between the robots is aroun 1.8% an 0.44% in the linear an angular separation respectively, even though the roles an behaviours of the robots are interchange ynamically

23 224 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training Input Parameters for Leaer Robot R 1 : % Error K 1 =0.55, K2 =-0.55; ICC/ICR of 2.3m ormation l e l - l - l Topology (mm) (eg) (eg) (mm) (eg) Parallel Parallel Wege Wege Wege Wege Wege Wege Mean Value of error Table 2. ormation errors in simulation Switching of formation topology ig 15 (a) an (b) shows the results for the simulation stuies carrie out to measure the error ynamics an formation convergence of the controller when the formation between the robots are switche from one topology to another. This stuy has been carrie out to investigate the application of switching of formation topologies between the robots to avoi the ealock situation that occurs when more than two follower robots requests for leaership. In this case the follower robots are mae to change their initial formation into an inline formation with the leaer, to avoi the ealock situation encountere while taking up the leaership. Two ifferent configurations are simulate which can be use to solve the ealock when two or more than two robots are use in the formation framework. In the first configuration, the formation topology between the robots is varie by changing the angular separation at a efine rate w.r.t time an the linear separation between the robots is kept constant. This is use when only two robots are in the group. When more than two robots are involve in the formation framework, the linear separation between the robots are also varie at a efine rate along with the angular separation, inorer to avoi the positioning of the robots to overlap each other. ig. 15 (a) shows the results of the simulation stuy, where the leaer is mae to move in a straight line trajectory an the follower is mae to switch from parallel line to inline formation by varying its angular separation at a continuous rate. In this simulation stuy, initial positions of the leaer an follower robots are taken as (0,0) an (-200, -1000) an the esire linear separation between the robots is set as 800 mm. The change in the formation topology is initiate as a continuous change in the angular separation at various rates to fin the optimum value that can be use in the experimental stuies. It is also clearly observe that the esign of the tracking controller makes the follower robot to switches its formation topology from parallel line to inline spatial pattern with the leaer. ig. 15 (b) shows the linear separation errors between the robots for various rate of change of the angular separation values that etermines the change in formation topology. It can be clearly observe from the above results that the continuous rate of change of angular separation at a value of 3 /s, makes the robot to graually change its formation topology to inline topology with minimum error even though it takes more time when compare with other values. urther, it takes aroun 39s to settle in the esire linear separation with the leaer

24 Cooperative ormation Planning an Control of Multiple Mobile Robots 225 which inclues 30 s taken by the controller to change its angular separation at a rate of 3 /s until it changes from 270 to 180. (a) (b) ig. 15. Switching of ormation topology with variations in angular separation (a) trajectory of robots switching from Parallel line (b) Separation plot of robots 6. Real time implementations an experimental investigations 6.1 Experimental environment Experiments are carrie out with two commercially available Pioneer P3DX Robot research platforms, name as PEIL R 1 an R 2 as shown in ig. 16. These have ientical sensor, actuator an kinematic configurations. A Bi-irectional multiple Client-Server architecture incorporating the Pioneer platforms is evelope as an experimental architecture. Robot R1 is esignate as server/leaer an Robot R2 as client/follower performing the combine task of navigation an formation.

25 226 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training ig. 16. Experimental Robot Research Platforms The iniviual task achieving behaviours are programme as parallel motion functions, an they are integrate as the functional classes/library files in the application interfaces of the mobile robots. An explicit wireless socket communication mechanism is evelope by using the Net packet functional library classes of the mobile robots, to provie the necessary inter-robot communication an to initiate the exchange of leaership between the robots. A trapezoial acceleration function with the acceleration an eceleration value of 50% is use as the velocity function. During startup, the robots are consiere to be in the origin position of 0, 0, 0 in X, Y an. The initial velocities of the robots are consiere to be zero. urther, the Leaer robot is mae to initiate its motion, only if the connection between the follower robots is establishe by the wireless socket communication protocol. Hence, when two robots are employe in the formation framework, leaer robot is powere first an then the followers are starte up. Several experiments have been carrie out to measure the performance of the propose formation control approach for formation convergence an as a supplement to the investigation of the same in the simulation stuies reporte in the previous section. irst experiment is carrie out to investigate the performance of the tracking controller an the formation errors when applie to multiple WMRs moving as a whole in a tightly couple coorination in all formation topologies. In this experiment, the robot R 1 esignate as leaer is mae to move in the environment in preefine trajectories such as arc, S-shape an eight shape trajectories, with the generalize parameters obtaine from the simulation stuies. These trajectories are preferre, since they provie both translational an rotational profiles to the robot an the translational an rotational changes can be consiere as step changes in the input to the controller as consiere in the simulation stuies. Secon experiment is carrie out to measure the performance of the propose formation control architecture combine with lower level navigation an supervisor level formation. In this experiment, the initial an esire separation values are taken as 1414 mm, 262 an 1000 mm, 270 respectively an both the robots are employe with the layere control architecture. The leaer is mae to navigate an environment of 12m by 10m rectangular workspace fille with rectangular obstacles of size 200 x 180 mm an 550 x 400 mm. Leaer velocities are fixe at 160 mm/s an 4/s, obstacle istance of 800 mm an safe waner time of 6 s, an the follower is mae to follow the leaer with the esire separation an orientation as mentione earlier.

26 Cooperative ormation Planning an Control of Multiple Mobile Robots 227 Experimental stuy on ynamic switching of roles is carrie out as the thir experiment, to test the performance of the approach on combine formation an navigation capability of multi-robot systems, to have active obstacle avoiance in the follower path. Experiment is conucte in a similar environment as use in the secon experiment with the robots moving in a parallel line formation. The initial an esire separation values are taken as 1019 mm, 258 an 800mm, 270 between the robots. In this experiment, both the robots are employe with the same control configuration, having the capability to perform both navigation an formation an they are allowe to trae their roles between themselves using the leaership exchange metho. These experiments have been carrie out in a workspace of 12 m by 10 m with three obstacles of size 200 x 180 mm, 200 x 180 mm an 550 x 400 mm as shown in ig. 17. ig. 17. Arrangement of robots an obstacles in the 2D workspace inally, experiments on switching of formation topology between the robots are carrie out to measure the capability of the propose approach to avoi from the ealock situation when three robots are use in the formation stuy. The iea is to measure the aaptability of the propose approach an convergence of the tracking controller, when the robots esignate as followers encounter obstacle on their path simultaneously. In this case the follower robots are mae to change their initial formation into an inline formation with the leaer, to avoi the ealock situation encountere while taking up the leaership. This experiment is conucte with two robots instea of three robots ue to the limite availability of research platforms, an the robots esignate as leaer is mae to navigate a straight line in the workspace an the follower is mae to switch from the parallel line to the in-line formation to measure the formation convergence. In this experiment, the initial an esire separation between the robots are taken as 0, 0 an mm, 264 an 800 mm, 180 respectively an are given by the following relationship. The change in formation is initiate with constant linear separation an varying the angular separation at the rate of

27 228 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training 3/s. The results of all the above experiments are reporte an iscusse in etail in the following sub section. 6.2 Experimental results ig. 18 to ig. 21 shows the results of the experiments illustrating the goo performance of the control algorithm (Kuppan Chetty et al., 2010). or the first experiment, ig. 18 (a) shows the trajectory of the robots in the parallel line formation, where the leaer robot navigates the environment by switching between safe wanering, avoi obstacle behaviours marke as S, O respectively whenever it perceives the obstacle information from the environment. Moreover the performance of the formation controller is also observe from figure 18, where follower tracks the behaviour of the leaer form its initial linear an angular separation an remains in the esire formation relative to the leaer throughout the workspace. It also shows that, the formation controller minimizes the separation error to zero, keeping the robots in the tight couple formation in the environment fille with obstacles. ig. 18 (b) shows the orientation plot of the above experiments, where it can be observe that the tracking controller makes the follower to remain in the same orientation with the leaer throughout the fly, making the system suitable for transporting objects from one location to the goal in the ynamic inustrial environments. ig. 19 an 20 shows the experimental results on ynamic switching of roles, carrie out to test the obstacle avoiance in the follower path. ig. 19(a) shows the trajectory of leaer an follower robots performing the combine task of navigation, formation an obstacle avoiance where 'O' represents the obstacles in the path of the robots an the otte rectangles represents the switching of roles an leaership between the robots to reach the esire goal. ig. 19 (b) shows the behavioural / state output of the robots R 1 an R 2 involve in the experiments. Initially, robot R 1 is esignate as the leaer an leas R 2 which follows the motion of the leaer in the parallel line formation with the esire separation of 800 mm an 270. At t = 8.4 an 26s, follower fins the obstacle on its path, request for exchange of leaership with the leaer, acquires the leaership an performs obstacle avoiance on its path. After avoiing the obstacle, robot R 2 relinquishes the leaership back to the leaer at t=14 an 30s. This can be clearly observe from ig. 19 (b), where the role switching behaviour takes preceence which intern activates obstacle avoiance behaviour present in the control architecture of robot R 2. This clearly inicates that at any moment uring the coorinate motion, the follower robot, which experiences obstacle on its path, can take over the leaership from the leaer an the robot performing the lea role can become a follower by switching their leaership between themselves. ig. 20 shows the variation in the linear an angular separation errors, where the robot R 2 performs obstacle avoiance on its path by switching its roles with R 1 an preserves the formation by ajusting its angular separation as given by Eqn. 25. It is also observe; that the formation controller takes 9s to settle in the esire formation with the leaer an the formation errors is estimate to be less than 1.4% an 0.5% in both linear an angular separation between the robots. igs. 21 (a) an (b) show a comparison between the simulation an experimental results inicating the behaviour of the tracking controller to position the follower robots even after switching of formation topology from parallel line to inline spatial pattern. The angular separation ( ) is change at a rate of 3 /s, which is the critical parameter to initiate the formation change.

28 Cooperative ormation Planning an Control of Multiple Mobile Robots 229 (a) (b) ig. 18. Performance of ormation Controller combine with Navigation an ormation behaviors (a) Trajectory of robots in parallel line formation (b) Orientation profile between the robots

29 230 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training (a) (b) ig. 19. (a) Trajectory of robots performing obstacle avoiance on both leaer an follower robots in a parallel line formation (b) Behavioral/State outputs of the Robots

30 Cooperative ormation Planning an Control of Multiple Mobile Robots 231 ig. 20. ormation plot of in Parallel line formation along with switching of roles

31 232 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training Input Parameters for Leaer Robot R 1 : K 1 =0.55, K 2 =-0.55; ICC/ICR of 2.3m % Error ormation Topology l (mm) (eg) e (eg) l - l (mm) - (eg) l Parallel Parallel Parallel Parallel Collateral Collateral Collateral Mean value of Error Table 3. ormation errors (experimental analysis)

32 Cooperative ormation Planning an Control of Multiple Mobile Robots 233 (a) ig. 21. (a) Trajectory of robots switching from parallel to straight line formation (b) ormation plot of robots switching from parallel to straight line. (b)

33 234 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training It is observe from the results, that the tracking controller takes less than 12 s to settle in the esire linear separation of 800mm between the robots from their initial position an it takes another 40s to switch the formation topology between the robots which inclues the 30s time taken for the rate of change of esire angular separation. This metho of changing the formation topology is one of the remey to avoi the ealock cause when one or more robots in the group request for leaership simultaneously, to avoi the obstacle on their path an the group leaer is free to move in the environment. 7. Conclusion A combine layere formation control approach to conquer the eficiencies of the leaer follower approach an the behavior base approach, by wrapping up the former with the later is evelope. The evelope approach has the avantages of both the approaches, which have the capability to aress the combine problem of formation planning an navigation through obstacle avoiance. In orer to have the istribute control nature collective task of formation planning an navigation is ivie into three major (primitive) tasks such as ormation, Navigation an Obstacle avoiance base on the motion states of the robot. These primitive motion states are consiere as the basic funamental behaviors of the robot accoring to the reactive behavior base approach an are place in three separate layers, which yiels the collective task upon integration. urther, to have the theoretical formalization an the convergence of the robots into the esire formation, an the close loop tracking controller base on the leaer follower moel an the kinematics of the unicycle mobile robots is formulate to keep the robots in the team in a close efine spatial pattern, where the separation errors are,minimize asymptotically to zero. A unique feature of the evelope formation control approach is the incorporation of ynamic role switching methoology through the exchange of leaership between the robots an their behaviours, to actively avoi the obstacle in the path of the robots esignate other than the leaer in the group. The results show the capability to avoi the obstacle in the follower s path. This clearly inicates the capability of the approach to make the robots to remain in a close efine stable formation between them even though the roles are switche ynamically uring the fly. Uner these circumstances, the tracking controller takes less than 12s to make the follower to remain in the formation with the leaer an the formation errors are less than 2.81% an 0.82% in both linear an angular separation between the robots respectively. As a whole the formation error for the projecte formation control approach combine with formation planning, navigation an obstacle avoiance capability between the robots, the formation errors are estimate at less than ±3% an ±0.81% in linear an angular separation between the robots; when compare to ±5.5% an ±3.6% reporte in the literature (ierro et. al., 2002 an LIU Shi-Cai et. al., 2007). In future, we plan to test the capability of the evelope control methoology by conucting the experiments carrying a real object in the real ynamic inustrial environment fille with obstacles. The switching control strategy between the behaviours an robots arises many interesting questions such as ealocks between the robots when they exchange the leaership. There are many cases to be solve to answer this ealock phenomenon. We also plan to exten into the issues to overcome the ealock situation in the multi robot systems through simulation an experimentation stuies.

34 Cooperative ormation Planning an Control of Multiple Mobile Robots Acknowlegement We woul like to acknowlege Dr. Eng. Tetsunari Inamura, of Interactive Intelligent Systems Laboratory, National Institute of Informatics, Tokyo, Japan, for offering visiting researcher position an proviing the necessary laboratory research facilities to perform preliminary experimental investigations at Chiba Annexe. We woul also like to acknowlege National Institute of Informatics for the financial assistance provie uring the course of stay in Japan. This work has been supporte by an conucte at Precision Engineering an Instrumentation Laboratory, Department of Mechanical Engineering, Inian Institute of Technology Maras (IIT Maras), Chennai, INDIA. 9. References Arkin, R. (1998). Behaviour-Base Robotics. Chap 3 & 4, The MIT Press, Cambrige, Massachusetts, USA. Belta, C. & Kumar, V. (2002). Trajectory esign of formations of robots by kinetic energy shaping, Proc. of. The IEEE International Conference on Robotics an Automation, Washington, pp Chaimowicz,L., Vijay kumar, R. & Mario.M. Campos (2004). A mechanism for Dynamic coorination of Multiple Robots. Int. J. Autonomous Robots, 17, pp Chen, Y.Q. & Wang, Z. (2005). ormation control: A Review an Consieration. In Proceeings of the IEEE/RSJ international Conference on Intelligent Robots an Systems, Alberta, Canaa, August, pp Crowley, J. & Reignier, P. (1993). Asynchronous Control of Rotation an Translation for a Robot Vehicle. International Journal of Robotics an Autonomous Systems, 10, pp Desai, J.P. (2002). A graph theoretic approach for moeling mobile robot team formations. Journal of Robotic Systems, 19(11), pp Dougherty, R., Ochoa, V., Ranies, Z. & Kitts, C. (2004). A Behavioral Control approach to formation keeping through an obstacle fiel. In Proceeings of the IEEE Aerospace conference, Big Sky MT, March, 1, pp ierro, R., Das, A., Spletzer, J., Exposito, J., Kumar, V., Ostrowski, J.P., Taylor, C.J., Hur, Y., Alur, R., Lee, I., Gruic, G. & Southall, B. (2002). A framework an architecture for multiple-robot coorination. International Journal of Robotics Research, 21(10-11), pp Golberg, D. & Matarić, M.J., (2002). Design an Evaluation of Robust Behavior-Base controller for istribute multi robot collection tasks, , In T. Balch an L. E. Parker, Robot Teams: rom Diversity to Polymorphism, A.K. Peters, Natick, M.A, USA. Harry Chia, Hung Hsu, & Alan Liu (2005). Multiagent-Base Multi team ormation Control for Mobile Robots. Int. Journal of Intelligent an Robotic Systems, 42 (1), pp Hu, H., Kelly, I., Keating, D. & Vinagre, D. (1998). Coorination of Multiple Mobile robots via Communication. Proceeings of SPIE'98 Mobile Robots XIII Conference, Boston, USA, pp Khalil, H. (1996). Nonlinear Systems, Prentice - Hall International, UK.

35 236 Mobile Robots Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training Kuppan Chetty, RM., Singaperumal, M. an Nagarajan, T. (2010). Behavior Base Planning an Control of Leaer ollower ormations in Wheele Mobile Robots. International Journal of Avance Mechatronics Systems, 2(4), pp Kuppan Chetty, RM., Singaperumal, M. & Nagarajan, T. (2011). Distribute ormation planning an Navigation ramework for Wheele Mobile Robots. Journal of Applie Sciences, 11 (9), pp LIU Shi-Cai, TAN Da-Long & LIU Guang-Jun (2007). ormation Control of Mobile Robots with Active Obstacle Avoiance. International Journal of Acta Automatica Sinica, 33(5), pp Shankar Shastry., (1999). Nonlinear systems: analysis, stability, an control, Springer Verilag. Stormont, D.P. & Chen, Y.Q. (2005). Using mobile robots for controls an Mechatronic eucation. International Journal of Engineering Eucation, 21(3), pp Sugar, T., Desai, J.P., Kumar, V. & Ostrowski, J.P. (2001). Coorination of multiple mobile manipulators. Proceeings of the IEEE International conference on Robotics an Automation, 3(1), pp Xiaohai Li, Jizhong Xiao & Jinong Tan (2004). Moeling an Controller esign for multiple mobile robots formation control. Proceeings of the IEEE International conference on Robotics an Biometrics, Shenyang, China, Aug, pp Xiaoming Hu, Alarcon, D.. & Gustavi, T. (2003). Sensor Base Navigation Coorination for Mobile Robots. Proceeings of the IEEE International Conference on Decision & Control, Yamaguchi, H., Arai, T. & Beni, G. (2001). A istribute control scheme for multiple mobile robotic vehicles to make group formations, Int. Journal of Robotics an Autonomous systems, 36 (4), pp

36 Mobile Robots - Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training Eite by Dr. Janusz Bȩkowski ISBN Har cover, 390 pages Publisher InTech Publishe online 02, December, 2011 Publishe in print eition December, 2011 The objective of this book is to cover avances of mobile robotics an relate technologies applie for multi robot systems' esign an evelopment. Design of control system is a complex issue, requiring the application of information technologies to link the robots into a single network. Human robot interface becomes a emaning task, especially when we try to use sophisticate methos for brain signal processing. Generate electrophysiological signals can be use to comman ifferent evices, such as cars, wheelchair or even vieo games. A number of evelopments in navigation an path planning, incluing parallel programming, can be observe. Cooperative path planning, formation control of multi robotic agents, communication an istance measurement between agents are shown. Training of the mobile robot operators is very ifficult task also because of several factors relate to ifferent task execution. The presente improvement is relate to environment moel generation base on autonomous mobile robot observations. How to reference In orer to correctly reference this scholarly work, feel free to copy an paste the following: R. M. Kuppan Chetty, M. Singaperumal an T. Nagarajan (2011). Cooperative ormation Planning an Control of Multiple Mobile Robots, Mobile Robots - Control Architectures, Bio-Interfacing, Navigation, Multi Robot Motion Planning an Operator Training, Dr. Janusz Bȩkowski (E.), ISBN: , InTech, Available from: InTech Europe University Campus STeP Ri Slavka Krautzeka 83/A Rijeka, Croatia Phone: +385 (51) ax: +385 (51) InTech China Unit 405, Office Block, Hotel Equatorial Shanghai No.65, Yan An Roa (West), Shanghai, , China Phone: ax: