On the Modeling and Simulation of Collision and Collision-Free Motion for Planar Robotic Arm Galia V. Tzvetkova

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1 Iteratoal Joural of Egeerg Research & Scece (IJOER [Vol-, Issue-9, December- 25] O the Modelg ad Smulato of Collso ad Collso-Free Moto for Plaar Robotc Arm Gala V. Tzvetova Isttute of mechacs, Bulgara Academy of Sceces, SOFIA, BULGARIA Abstract Safety fuctog s cosdered as a mportat ssue wth overall desgg process of autoomous robotc systems. A geeral structure of collso detecto ad avodace system for plaar robotc arms s proposed. Smulato results of collso ad collso-free motos are preseted. Keywords Collso avodace, plaar robotc arms. I. INTRODUCTION Maufacturg, servce, research, eplorato ad may other areas of huma actvty requre a lot of hadlg operatos of a wde varety of objects, materals, parts, etc. The hadlg operatos ca be very smple ad fuzzy or very complcated ad precse. Robotc arms are the rght tool to automate these operatos ad to facltate the processes almost of ay area. At ths stage, robotc arms, most of them ow as mapulato robots, wor successfully may maufacturg areas. Usually, those areas are statc ad uchagg wor evromets, whch allow the robotc arms to perform ther operatos accordg to advaced doe programmg. The et stage challege for the robotc arms s ther capablty to wor cosderably cluttered ad chagg evromets that ca fluece ther proper fuctog. Besdes precse eecuto of the desred operatos, the et stage robotc arms must esure safety fuctog wth ther worg space. I cases of dyamc ad cluttered evromets, the robotcs arms have to adapt to uow advace stuatos. The most mportat case to cosder s esurg a safety wor amely, avodace of collsos ad accdets wth the surroudg objects. The author s purpose of ths paper s to beg a research o problems of safety fuctog of autoomous robotc mechasms varous worg evromets. II. FUNCTIONAL DESCRIPTION OF COLLISION PREVENTION SYSTEM The collso detecto ad preveto system cossts of three modules that perform the followg fuctos: : Moto Cotrol Ths module mplemets the moto cotrol accordg to set performace parameters. The moto cotrol cludes movg the arm ed-effectors (ЕЕ to desred postos of the worg space ad/or realzato of desred trajectores of the arm. 2: Detecto of Obstacle ad Dstace Measuremet Ths module checs for presece of acles wth the worg area of the robotc arm ad obtas the ecessary measuremets such as the global dstace betwee the arm EE ad a acle, as well as addtoal specfc dstace measuremets, thus esurg the complete measuremet formato for the safety wor of the arm. : Judgmet for Stuato ad Decso for Acto Ths module evaluates the worg scee of the arm, estmates the degree of dager of the curret stuato ad decdes how to safely cotue the curret process. The possble decsos ad actos are:. No dager stuato ad the moto ca cotue to the desred posto or alog the desred trajectory;.. Collso s possble correcto of the desred posto or the desred trajectory; STOP - evtable collso detected, mpossblty to correct the moto, operator assstace requred. The bloc structure of the collso detecto ad preveto system s preseted Fg.. Page 82

2 Iteratoal Joural of Egeerg Research & Scece (IJOER [Vol-, Issue-9, December- 25] FIG. BLOCK STRUCTURE OF THE COLLISION PREVENTION SYSTEM The system varables of the modules are descrbed as follows: G EE - set pot for thearm ed - effector (EE, g, g - set pots for cotroller ad cotroller 2, L L2 ( (q (,q ( - l moves towards set pot posto g, L (q (,q (- l 2 moves towards set pot posto g, 2 2 L2 P,...P,...P - EE succesve posstos P ; q Q q ( 2 2 F - chec for presece of OBSTACLES, 2 y - glob_ dst measuremet of global dstace to OBST 2 y - dst measuremet of dstace of l to, 2 L_ acle 2 y - dst measuremet of dstace of l 2 to ; L2_ acle OBSTACLE, Page 8

3 Iteratoal Joural of Egeerg Research & Scece (IJOER [Vol-, Issue-9, December- 25] ( F CC - crteroof closeess, closss Y - evaluato - - glob_dst CC OBST closss Decsofor a degree of dager, y o collsodager cotuatoof moto, y collsos possble trajectory corecto, 2 y - - -STOP mpossblemoto,ecessty of operator's help; III. MATHEMATICAL BASIS The dyamc model of -dof robotc arm s well ow as []: D(θ θ C(θ, θθ τ ( Where θ, θ,θ, τ R are -vectors of jots posto, velocty, accelerato ad put drvg torque, matr of erta forces,, matr of cetrfugal ad corols forces? C(θ θr D(θ R The state vector 2 ( R cossts of robotc arm jot agles ad veloctes [ θ, θ ] : T ( 2( ( ( 2(... ( ( t The equato ( s trasformed state space form: ( A ( Bu( (2 I A, B D ( θ C( θ, θ ad the cotrol put s u( τ(. A state space equato for a separate l ca be wrtte as: wth (,,2,..., as tal codtos for the ls, ad ( acle, deoted as OBST, ( A ( B u ( V l ( ( OBST V j matr of coectos. j j j, j l j - the closest dstace betwee l j ad detected A. Free of Obstacle Cotrol Equato (2 s preseted dscrete form as [2]: The matres A ad A B u (4 B are calculated accordg to ow formulas: (T L - pi - - t A A, B H(T ( d B (5 T ad T s dscretzato terval for the system varables. T Page 84

4 Iteratoal Joural of Egeerg Research & Scece (IJOER [Vol-, Issue-9, December- 25] Closg the ope system (4 by a feedbac ga matr K [ 2] ad after some route trasformatos, the state of the closed system becomes: The cotrol put s calculated as [2]: u G [ A B K] B u (6 G EE G K (7 G u s the cotrol put that esures free movemet of the arm ed-effectors (EE to the desred posto whe o acles est wth the worg space of the robotc arm. B. Obstacle cosderato ad moto correcto The closed system s descrbed, after tag to accout acle estece, as: The cotrol put cotas a secod compoet u : T F(T Φ( C d F ad u EE [ A B K] B G F Z (8 cosderg estece of acle aroud the EE or the l j. Combg (7, (8 ad (9 oe ca get the model: u G u (9 u s the compoet of the cotrol vector that realzes trajectory correcto after G Z A B Ku B u F z ( The followg relato s cosdered for the purpose of cotrol correcto as a result of estece of potetal collso for l j ad a acle, detected the ear closeess: Z u j, F z j, l j, B ( l, s the closest measured dstace betwee the l j ad the acle. Based o the above equato t s j calculated: Z j Z u j, ( F z ( B l j, B (2 u, s the cotrol put to correct the moto because of acle presece ear l j. IV. BASIC SIMULATIONS FOR 2 DOF PLANAR ROBOTIC ARM The results from a computer program smulato are show Fg. 2(a,b,c,d []. Fg.2a shows a potetal collso stuato. The secod l s very close to the acle. Fg.2b shows collso occurrece, whe the secod l crashes the acle. Fg. 2c shows acle avodace from the robotc arm ed-effectors. Fg.2d shows collso-free moto after the collso avodace. Page 85

5 Iteratoal Joural of Egeerg Research & Scece (IJOER [Vol-, Issue-9, December- 25] Potetal Collso Collso Occurrece Collso Avodace Fg. 2a Fg.2b Fg.2c Collso-Free Moto Fg. 2d V. CONCLUSION A geerc fuctoal model for collso avodace ad collso free-moto of robotc arms s proposed. Basc smulato result for two dof plaar robotc arm s preseted. Further detalzato of research s uder plag. REFERENCES [] M. W. Spog, S. Hutchso, ad M. Vdyasagar, Robot Modelg ad Cotrol, by Joh Wley & Sos, 26. [2] K. Ogata, System Dyamcs, 4th Edto, Pearso Educato, Ic., 24. [] G.V.Tzvetova, Networ Modelg of System Goals Attamet, Proceedgs for the rd Iteratoal Iovatos ad Real-Tme Applcatos of Dstrbuted Sesor Networs Symposum., Shreveport Coveto Ceter, Shreveport, Lousaa, USA, November 26-27, 27. Page 86