Analysis of Kinematic Constrained Mobile Robot Using ANT Colony Optimization

Transcription

1 Internatonal Journal of Artfcal Intellgence an Coputatonal Research, 3(1), 2011, pp Analyss of Kneatc Constrane Moble Robot Usng ANT Colony Optzaton Dayal R. Parh an Jagan Mohana Rao Ruppa Departent of Mechancal Engneerng, Natonal Insttute of Technology-Rourkela, Rourkela , Ina The kneatc of oble robots s ost popular n now away ays n the analyss fel. Ths kneatcs s anly base on the oble robot oblty, steerablty an Maneuverablty of the robot wheels. Ths analyss an control wll be useful for the trajectory plannng of a robot. There are fferent types of wheels confguratons are avalable lke fxe stanar wheels (fferental rve wheel), steerable stanar wheels, castor wheels, Swesh wheels, an sphercal wheels. In the present paper, we are escrbng about the fferental rve wheel kneatcs. Here we are explanng the evolutonary algorth (EA), the ant colony optzaton (ACO) algorth for obtanng the best global path n orer to reach the robot to the goal poston by avong the obstacles. Keywors: Kneatcs, Ant Colony Optzaton, Evolutonary Algorth, Dfferental Drve Robot. INTRODUCTION A oble robot s a self-operatng achne that can ove rrespectve to ts chosen path n the free space. By unerstanng the wheel constrants place on the robots oblty t s easer to unerstan the oble robot oton. It s a very ffcult to easure a oble robot current poston by rect way. It s an nterestng an challengng work to obtan the exact oble robot s poston an orentaton whle t s n oton. There are any wheel an axle confguratons that have been use for WMRs [1-12]. There are so uch of the research gven above s escrbe n a recent stuy of WMRs (Mur an Neuan [13]). Ths escrbe work evelops a forals that s use ntally to oel the kneatcs of each wheel, an secon to aalgaate the nforaton about nvual wheels to escrbe the kneatcs of the WMR by takng conseraton as a whole. A conton s evelope that eternes whether, gven the confguraton of the wheels n the WMR, eal rollng s possble. Qunlan an Khatb evelope a etho that prouces sooth trajectores an can be use for obstacle avoance. The present stuaton, robotcs s very portant part n anufacturng process. By conserng oble robots, autonoous navgaton leas to a great challengng work. Then, oble robotcs fel s an nterestng an challengng aspect for scence an *Corresponng author: rkparh@ntrkl.ac.n, jaganskl@gal.co engneerng, an t has any fferent Evolutonary Algorths (EA). The socal nsects behavors such as reproucng, foo huntng, nest bulng, garbage cleanng, an terrtory guarng shows that the socal nsects such as ants an bees have hgh swar ntellgence. Many optzaton algorths have been successfully apple to the optzaton, network routng an other scentfc applcatons. Aong the socal nsects any behavors, the ost of the cases we are recognze that the ants have the ablty to work as a whole for copleton of 33 a task that can t be one by a sngle ant. Also we can observe that, ths ablty of ants s a result of cooperatve effects. Ths cooperatve effects eans to the phenoenon that have the effect of two or ore nvual parts are anpulatng s hgher than the total of the nvual effects. In the present paper we are explanng the ant colony optzaton algorth for a oble robot can navgate n a free space by avong the objects n orer to reach the target poston through optu path wth less te an less effort. Here we are also escrbng the kneatcs constrants for a fferental rve robot. ANT COLONY OPTIMIZATION The navgaton proble of an MR can be ve n to 4 sub probles [32]: Worl percepton: It senses the worl sybolzng t nto features.

2 18 Internatonal Journal of Artfcal Intellgence an Coputatonal Research Path plannng: Uses the above sybolze features to create an orere sequence of objectve ponts that the robot ust attan. Path generaton: The goal s to obtan a path through the sequence of objectve ponts. Path trackng: It s n charge of controllng that the MR follows a path. In ACO algorths, artfcal ants are probablstc soluton constructon proceures, whch are base by artfcal pheroones an heurstc nforaton. Pheroones are represente as nuercal nforaton that s ofe n every teraton n orer to reflect the algorth s search space. The ACO Algorth There s a etale step by step forulzaton algorth s use for autonoous oble robot navgaton. Ths algorth can be sutable for any probles lke travellng salesan proble, scheulng proble, vehcle routng proble, etc. The escrpton of the algorth s as follows: 1. Intalzng the paraeters: ntally there are soe of the paraeters lke the total nuber of ants we are conserng here for solvng the partcular proble, the ntal pheroone concentraton of each ant at each ege. 2. Whle the ants are ovng fro the startng ege, f the ternaton crteron s not at reache then construct a soluton for the ants obtanng the optu path by takng the transton rule of probablty functon for gettng the new poston to the ant. Then we can upate the poston of the ants fro the current poston to the new poston by local upatng pheroone concentraton value along the obtane path of each ant. 3. After upatng locally we have to upate the pheroone level of each ant globally through the global upatng rule. Then we can observe one of the optu paths for the nuber of paths obtane by each ant. The proceure shoul be apple on an nvuals fro the total populaton base on the ftness value. Step by step proceure of the ACO: Step 1: Intalzng the pheroone concentraton τ j for each ege (,j). Step 2: The total nuber of ants = 1, 2, 3,.. K are kept at startng poston (orgn noe). Step 3: For every teraton, the selecton of next poston s base on the probablty functon gven n equaton (1). α τj () t pj () t = f j N α τj () t (1) j N Else the value of the value of the probablty functon f becoes zero. Where N s the set of feasble noes connecte to the noe rrespectve of the partcular ant an α s pheroone concentraton nfluence factor. Step 4: Deterne the shortest tour tll now for all ants an upate pheroone concentraton of each ege by usng the equaton (2). τ j (t) = τ j (t) * (1 σ) (2) Where the value of σ s the pheroone evaporaton rate value. Ths evaporaton shoul elnates the local optu values convergence. Step 5: Upate the global pheroone concentraton of each ant for the next teraton by usng the equaton (3). K k j ( 1)()() j j = 1 τ t + = τ t + τ t (3) Step 6: The gven algorth can be ternate by fferent ways lke It reaches the axu nuber of teratons When we observe that f all the ants follow the sae path. KINEMATICS OF A DIFFERENTIAL WHEELED MOBILE ROBOT There are fferent wheel rve confguratons lke fxe stanar wheels (fferental rve wheel), steerable stanar wheels, castor wheels, Swesh wheels, an sphercal wheels are avalable for the oble robot constructon. Out of that, the one of the ost splest for of robot constructon by usng the fferental rve wheels.e. the chasss wth two fxe wheels on both ses of the chasss. By observng the

3 Analyss of Kneatc Constrane Moble Robot usng ANT Colony Optzaton 19 kneatc constructon of ths fferental rve wheel we can obtan soe of the basc nforaton regarng the kneatcs of sple confguratons lke a car lke robot. Most of cases the castor wheel also be use along wth the fxe wheels only for the stablty purpose only. There s no effect of castor wheel on the kneatc constrants. Generally, n fferental rve wheels n orer to reuce the effect of slppage along wth that havng only rollng acton; the wheele oble robot shoul be rotate about a pont. The center pont shoul be a pont on the coon axs of rotaton of the two fxe wheels. The kneatc constrants can also be eonstrate geoetrcally usng the concept of a robot s nstantaneous center of rotaton (ICR). for the both the wheels, thus the velocty of a center of rotaton, an veloctes of left an rght wheels are as follows: v CR = ω.r (4) ( 2) ( ) v1 = ω.( r + (5) v2 = ω.( r 2 (6) In the above equatons, the value of r s the stance between the ICR to the pont between the fxe wheels. All the values v 1,v 2 an r are n ters of functon of te. Fro the equatons (4), (5), (6), the value of r an ω an velocty of center of rotaton (CR) pont are gven as: r v + v = * v1 v 2 2 (7) Fgure 1: The Path of Moton of the Dfferental Drve Robot Ths ICR geoetrc constructon eonstrates how robot oblty s a functon of the nuber of constrants on the robot s oton, not the nuber of wheels. By observng fro the above fg.1. v 1 an v 2 are the veloctes of the left an rght han se wheels when we are seeng fro the left se. Generally the fference between the bcycle an a fferental rve wheel s that the forer has two nepenent kneatc constrants whle the latter has only one although ther chasss have the sae nuber of nononrectonal wheels. Whle ovng the vehcle n te the left an rght wheels are gong to construct a path that oves aroun v v ω = (8) v CR v + v = (9) 2 Base on the veloctes of the left an rght wheel veloctes, there are fferent confguratons of robot otons are obtane. For the above entone fferental rve robot, there are four fferent types of confguratons shows as follows: 1. If the veloctes of both left an rght wheels are sae.e. v 1 = v 2, then the robot wll oves along a straght lne path.e. t oves forwar or backwar as shown n fg. 2, because the raus of curvature r becoes nfnte fro the equaton (7). ϕ the ICR wth the angular velocty rate ω =, sae Fgure 2: The Frst Movng Confguraton of a Dfferental τ Drve Robot when v 1 = v 2

4 20 Internatonal Journal of Artfcal Intellgence an Coputatonal Research 2. If the veloctes of the both wheels are fferent, then the robot wll get the curve oton about the pont ICR as shown n fg. 3. Fgure 5: The Fourth Movng Confguraton of Dfferental Drve Robot when v 1 = v 2 Fro the above all confguratons, we are observe that the fxe wheel oble robot s anly epens on the veloctes of the both left an rght wheels. If there a sall fference n the veloctes, t causes the foraton of fferent path trajectores of oble robot. Fgure 3: The Secon Movng Confguraton of Dfferental Drve Robot when v 1 < v 2 3. If the velocty of the rght wheel s becoes the value of zero, then the robot wll take a turn about the pont CR wth a raus of /2 as shown n fg. 4. Fgure 4: The Thr Movng Confguraton of Dfferental Drve Robot when v 2 = 0 4. If both the wheels oves n opposte recton.e. v 1 = v 2, then the robot wll turn about the CR wth a raus of r = 0.e. the ICR s conces wth the CR as shown n fg. 5. CONCLUSIONS In the present research work, t has been explane about ant colony optzaton an kneatcs of fferental rve wheele robot. The an objectve of ths task s that to fn the optu path for the robot that anly epens upon the varous confguratons of the oble robot wheels. Fro the above scusson, we are observe that fferent path trajectores are obtane wth the varatons of veloctes of the avalable oble robot wheels. References [1] Whtaker, L. E. (1962), Star Clbng Devce. U. S. Patent No. 3,058,754. [2] Sth, M. H. an Coles, L. S. (1973), Desgn of a Low Cost, General Purpose Robot. Proc. of 3r IJCAI. Stanfor, Calforna. pp [3] Holls, R. (1977), Newt: A Moble, Cogntve Robot. Byte 2(6): [4] Everett, H. R. (1979), A Secon-generaton Autonoous Sentry Robot. Robotcs Age 7(4): [5] Gralt, G., Sobek, R. an Chatla, R. (1979), A Multlevel Plannng an Navgaton Syste for a Moble Robot; A Frst Approach to Hlare. Proc. of the IJCAI. Tokyo, Japan. pp [6] Moravec, H. P. (1980), Obstacle Avoance an Navgaton n the Real Worl by a Seeng Robot Rover. Ph. D. Thess. Departent of Coputer Scence, Stanfor Unv. [7] Ija, J., Kanayaa, Y. an Yua, S. (1981a), Eleentary Functons of a Self-contane Robot

5 Analyss of Kneatc Constrane Moble Robot usng ANT Colony Optzaton 21 Yaabko 3.1. Proc. of the 11th ISIR. Tokyo: Socety of Boechanss Japan, Japan Inustral Robot Assocaton. pp [8] Ija, J., Kanayaa, Y. an Yua, S. (1981b), A Moble Robot wth Sonc Sensors an ts Unerstanng of a Sple Worl. Techncal Report No. ISE-TR Insttute of Inforaton Scence an Electroncs, Unv. of Tsukuba, Japan. [9] Baler, Jr., C. (1982), Avatar: A Hoe Bult Robot. Robotcs Age 4(1): [10] Helers, C. (1983a), The Wanerng Roboteers. Robotcs Age 5(3): [11] Helers, C. (1983b), En Helenleben (or, A Hero s lfe, wth Apologes to R. Strauss). Robotcs Age 5(2): [12] Ichkawa, Y., Ozak, N. an Saakane, K. (1983), A Hybr Locooton Vehcle for Nuclear Power Plants. IEEE Trans. Systes Man Cybernet. SMC-13(6): [13] Mur, P. F. an Neuan, C. P. (1987), Kneatc Moelng of Wheele Moble Robots. J. Robotc Systes 4(2):