An experiment on using the Pioneer3-DX robot in a multichannel measurement system

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8th WSEAS Internatonal Conference on SYSTEMS THEORY and SCIENTIFIC COMUTATION (ISTASC 8 Rhodes, Greece, August -, 8 An experment on usng the oneer3-dx robot n a multchannel measurement system G.

1 8th WSEAS Internatonal Conference on SYSTEMS THEORY and SCIENTIFIC COMUTATION (ISTASC 8 Rhodes, Greece, August -, 8 An experment on usng the oneer3-dx robot n a multchannel measurement system G. VASILIU *, A. FILIESCU *,AL.STANCU *, S. FILIESCU ** * Department of Automaton and Industral Informatcs ** Student n Electrcal Engneerng Unversty Dunarea de Jos of Galat Domneasca, 7, Galat, 88, ROMANIA Abstract: Increasng the precson of multchannel measurement systems requres a mnmum executon tme to select and analyze many probes, accessble from a depost located nsde the measurement system. Moble robot oneer3 handles all the movements of selected probes between the depost and measurement stand. Sldng-mode control of the robotc manpulator, and fuzzy technques for trajectory trackng, are used for a mnmum manpulaton tme and hgher securty n selecton and placement of probes. The dynamcal model of the moble robot wth one par of actve wheels, tme varyng mass and moment of nerta have been used n sldng-mode control. Two closed-loop, on-lne parameter estmators have been desgned to acheve robustness aganst parameter uncertantes. Two sldng-mode adaptve controllers correspondng to angular and translaton moton have been desgned. Keywords: Multchannel measurement system, oneer3-dx, Real-tme fuzzy control, Wheeled moble robot, Sldng-mode control.. Introducton to autoous, ntellgent, multchannel measurement systems Multchannel measurement systems are an mportant component of ntegrated steel manufacturng process. The nput of these systems are the physcal probes and the output s the nformaton concernng percentual concentraton of varous chemcal component. For a relatvely long perod of tme (days, weeks, such system can operate wthout the nterventon of a human operator. Usually, the overall precson of an ntellgent measurement system s ncreased f the result s corrected after comparng t wth several control probes. These control probes are stored n a structured probe-holder, nsde the measurement system. Fgure shows how the oneer 3-DX robot grasps the selected probe wth hs grpper. Fg.. oneer 3-DX grpper wth a steel probe. Fgure shows the same robot selectng the probe from a set of control probes. After the selecton, the robot carres the probes to the analsys stand and back to the probe holder. The probe holder s structured as a lbrary and every probe s assocated wth an ID code, a spatal poston and a n-dmensonal vector representng the composton. ISSN: ISBN:

Fgure 3 llustrates a compact block of probes, organzed as parallel matrx, every par of matrx are avalable n an moble stand D k.

2 8th WSEAS Internatonal Conference on SYSTEMS THEORY and SCIENTIFIC COMUTATION (ISTASC 8 Rhodes, Greece, August -, 8 Fg.. oneer 3-DX wheeled moble robot wth DOF robotc manpulator selectng a probe from the control set The avalable space n an autoous measurement system must be effcently used. Fgure 3 llustrates a compact block of probes, organzed as parallel matrx, every par of matrx are avalable n an moble stand D k. The optmal trajectory mnmzes the tme needed for the auxlary measurements of control probes. The precson of measurement for the current probe ncreases when the measurement s wthn a short tme nterval (necessary n order to approxmate the state of the system as stable wth a great number of auxlary probes, havng the composton confrmed by several laboratores. Once the destnaton ponts of robot trajectory s determned, the mnmum tme to transport all the selected probes can be obtaned usng the correspondng values for parameters lke: Dstance between the moble blocks wth probes; Velocty of the robot body; Angular velocty of the robotc arm; All these parameters must have correspondng numercal values adapted to the varable mass of the robot (when the robot grasps a new probe, the total mass ncreases, and when the probes are deposted back n the probe holder the mass decreases (the mass of a steel probe s.. kg. A smplfed dagram of movement problem s presented n fgure. COMACT BLOCK OF ROBES COMACT BLOCK OF ROBES Fg. 3. A compact block of probes organzed n parallel matrx. The ntal space between the moble stands D and D 3, after the dsplacement of stands D 3 D k becomes fnally the space between the moble stands D k and D k+. The unque space between all the stands of the probe holder and the moblty of all stands, represent the practcal soluton to keep a large number of probes n the lmted space of the measurement system. The space between two stands allows the access of the robot oneer 3-DX for handlng the selected control probe. In ths experment, fuzzy logc and sldng mode control s used to solve the problem of optmal trajectory of robot between the blocks wth measurement probes. IONEER3-DX ROBOT BODY ARM AND GRIER Fg.. Smplfed dsplacement of robot between the blocks of the probe holder. ISSN: ISBN:

3 8th WSEAS Internatonal Conference on SYSTEMS THEORY and SCIENTIFIC COMUTATION (ISTASC 8 Rhodes, Greece, August -, 8 The soluton of suspended blocks wth probes allows a substantal decrease (around procents of the necessary space between the moble blocks of probes. (In fgure, the dmensons of the robot body s double when ncludng the dmenson of the arm and grpper Actve zone of grpper ARM AND GRIER ROBOT BODY Fg.. Smplfed dagram of the robot body, arm, and actve zone of the grpper.. Fuzzy control of the robot For every possble process stuaton, the trajectory of the robot between the measurement stand and the locaton of the probe n the probe holder s determned, and can be represented as a lst of spatal coordnates (x,y. The optmum trajectory s assumed to be the one tracked n the least tme nterval. At any gven moment, the poston error of the current pont (x,y to the segment of the generalzed trajectory (Ax+by+C s determned by the dstance: Ax + By + C d ( A + B The outputs must be controlled so that the dstance from the current poston to the nearest pont of generalzed trajectory s mnmum. The error dot correspondng to the error derved from ( s: Δe e' ( Δt provded that Δt s small. Ths leads to three obvous domans of varaton for e(t: negatve (N, zero (Z and postve (. Note that, all the three membershp functons assocated wth e(t are fully determned by the parameter M, and the degree of membershp (DOM to a specfc doman can be easly calculated by lnear nterpolaton. By defnng a smlar set of membershp functons for the error dot (e (tδe/δt, one gets a total of 9 rules (3x3 of the followng type: If the error s postve and the error dot s postve, then v R must be HIGH and v L must be LOW. The entre rule base descrbng the fuzzy controller s presented n Table. Each cell of table contans a logc sentence and should be read as: If e(t s Negatve AND e (t s negatve, THEN V L must be HIGH and V R must be LOW Table. Rule base for the Fuzzy controller error dot e (t error e(t N Z N HL LH LM Z HL MM MH ML MH LH where H,M,L desgnate the sngleton values for HIGH, MEDIUM and LOW fuzzy domans of the outputs v L, v R respectvely. The truth value of the antecedent of the above sentence s mn(n(e,n(e, where N(e, N(e are the degrees of membershp of e(t and e (t to the doman N. The crsp output of the fuzzy controller s a combnaton of all the rules n the rule base as follows: v where: K out K z z S z mn(e, E' (3 ( ISSN: ISBN:

4 8th WSEAS Internatonal Conference on SYSTEMS THEORY and SCIENTIFIC COMUTATION (ISTASC 8 Rhodes, Greece, August -, 8 S s the correspondng sngleton value of the fuzzy output, and K s the total number of rules n the rule base. E, E are the degrees of membershp of e(t and e (t to the doman correspondng to the cell. Also generates the values of the left and rght wheel speed, v L and v R, for the next tme nterval untl the entre parabolc segment s fnshed. 3. Dynamc model and parameter uncertantes The vehcle dynamcs s fully descrbed by a three dmensonal vector of generalzed coordnates q ( t consttuted by the coordnates (( x ( t, y( t of the mdpont between the two drvng wheels, and by the orentaton angle Φ( t. The velocty constrant (non-holoc constrant of vehcle moton s x & sn Φ y& cos Φ. Defne by τ r and τ l the torques provded by DC motors to the rght and left wheel, respectvely. x x, x y, x3 Φ x x&, x y&, x Φ& (7 Defne the control nput correspondng to angular, u A τ r τ l and poston moton, u τ r + τ l, respectvely. x x + Tx x x( k + Tx x3 x3 + Tx x x Tx x + Tπ cos( x u (8 3 x x + Tx x + Tπ sn( x3 u x x + Tα ( ku A ( x x x x sn 3 cos( 3 (9 The control nput for angular moton has two terms: the frst one, denoted compensaton part u comp A (k, has to compensate the rotatonal dynamcs; the second one, denoted sldng mode part,, corresponds to system evoluton nsde of u sm A ( k sldng surface neghborhood. The whole control nput for angular moton s u comp sm u u A A + A ( Fg.. WMR confguraton varables for angular and poston moton. The vehcle s descrbed by the followng dynamcal model(see fgure where m, I, D, r are the robot mass, moment of nerta, dstance between wheels and wheels radus, respectvely τ r + τ l mx && my& Φ & + cos Φ r τ r + τ l my && mx& Φ & + sn Φ ( r D IΦ && ( τ r τ l r The real values of the parameters are tme-varyng wth upper bounded uncertantes α π Let real real max ( t α Δα ( t ; Δα Δα ( max ( t π Δπ ( t ; Δπ Δπ x R be the state vector, whose elements are Expressng the estmated value for angular moton control nput parameter, ˆ α α Δ ˆ α, the next sequence, correspondng to recursve least squares method, (Ljung, 999; Stoca and Ahgren,, can be used to provde an estmaton of the uncertanty scalar term Δ α ( k at the k th step Δ α ( k u A( k LΔα ( + u k k [ ( ] ( A Δα ( k L u ( k ( k Δ Δα Δα A Δα α ( ( k ( k L ( k u ( k ( k Δα Δα Δα A Δα (3 u k, sm u k u k. For ˆ π k π Δ ˆ π k, The control nput for poston moton, ( has only sldng-mode part, ( ( the correspondng parameter, ( ( smlar updatng law s used L Δ π ( k + Δ π ( k u ( k [ u ( k ] ( k Δ π ( k L u ( k ( k ( Δ π Δπ Δπ π Δπ ( ISSN: ISBN:

5 8th WSEAS Internatonal Conference on SYSTEMS THEORY and SCIENTIFIC COMUTATION (ISTASC 8 Rhodes, Greece, August -, 8 ( k u ( k u ( k S TΔ ˆ π Δ ˆ π Δ ˆ π( k + LΔπ + π ( + S where L Δ π, π have the same meanng as prevously and wll be defned later. Δ S. Sldng-mode adaptve control of angular moton The followng stable sldng surface has been chosen, n order to desgn the control nput for angular moton S A A( k + μ A (7 where ( ( ( ( x k δ e k A k x3 k arctg x ( ( k δe k (8 wth: μ (, δ, δ. arameter μ T and the poston errors, e, e, establsh the dynamcs of sldng surface. The nterval set of δ and δ assures the stablty of poston errors. For computng the control nput, the followng attractveness condton, (Furuta, 99; Yu and Xu,, has been used: S A ΔS A ( k + < ΔS A ( k + (9 where ΔS A ( k + S A ( k + S A ( The followng sldng surface s proposed: S ( k [ x ( k ] + [ x ( k ] ( [ x ( k δ e ( k ] + [ x ( k δ e ( k ] ( Startng wth the thrd equaton of model (, usng a trgoetrc equalty and the non-holoc constrant (, the followng equalty holds x x x ( ( x x tgtx k + ( x x x Moreover, ntroducng the expressons of the state varables, from state model (8, and usng the constrant(9, the above equalty becomes tg ( + Tπ u ([ x k ] + [ x ] ( Tx [ x ] [ x ] Tx ( Let defne S ( k cos ( Tx ( k (3 [ ] ([ x ( k ] + [ x ( k ] [ x ( k + δ e ( k ] + [ x ( k + δ e ( k ] ( The sldng moton on the surface concerns the reduced order system of the robotc model, wthout of 3 rd and th equaton. The same attractveness condton, for computng the poston moton control nput has been consdered S ΔS ( k + < ΔS ( k + ( ΔS ( k + S ( k + S (k ( An approxmate sldng mode evoluton on the surface can be assured. Consequently of sldngmode evoluton, the angular state x 3 tends to hold the followng expressons costx k x k δ e k ( 3( ( ( ( [ x δe ( k ] + [ x δe ( k ] ( Tx3 ( x δe ( k [ x δe ( k ] + [ x δe ( k ] sn (7 (8 Usng (, the followng expresson can be obtaned [ x ( k + ] + [ x ( k + ] [ ( Tx ] cos ([ ( ] [ ( ] ( ( ( x k + x k T π Δπ k u k Wth (7 and (, (3 and ( become S T Δ ( k + S ( k cos( Tx π Δπ ( k u S ( k + S ( k S T cos( Tx ( k π Δπ ( k ( ( k ( u ( k (9 (3 (3 Usng (9, (3 and upper bound of poston moton uncertanty, the second degree nequalty can be wrtten ISSN: ISBN:

6 8th WSEAS Internatonal Conference on SYSTEMS THEORY and SCIENTIFIC COMUTATION (ISTASC 8 Rhodes, Greece, August -, 8 If max ( π Δπ T u + S [ S ] < cos( Tx (3 > and S > S, then the sldng u sm control nput for poston moton s u ρ T where ( S S max [ cos( Tx ] ( π Δπ (33 ρ. The control nput stll can be computed usng onlne estmates for Δ π. Theore, the approxmate sldng mode condton s satsfed, S ( k +,.e. T cos Tx k π Δ ˆ π k u k + S k [ ( ( ] ( ( ( ( (3 From above, the control nput can be expressed as u ( k S ( k T cos( Tx ( k ( [ ] π ˆ π ( k Δ (3 When the system evolves n sldng-mode, can express the followngs x k x k δ e k (3 x ( ( ( x e ( k δ (37 Theore, output trackng error dynamcs assocated to the reduced order system can be expressed as: e ( k + e Te ( k ( k + e ( k Te ( k δ (38 e δ (39 For, the above errors are stable. δ, δ T For testng the proposed dscrete-tme sldngmode adaptve controller oneer 3-DX wth on board C and wreless adapter has been used n crcular trajectory trackng. The two motors use 38.3: gear ratos and contan -tck encoders. The followng parameters of model (3 were used: mkg, Dcm, I, kgm, T.3s.The moment of nerta has been computed assumng the mass unformly dstrbuted. A lnear-tme varyng mass addtonally to the nal one has been consdered from kg to kg. y(t 3 poston trajectory - 3 x(t 8 erence robot angular trajectory erence robot 8 t [sec] - control nput - 8 t [sec] trackng error angular poston poston angular - 8 t [sec] Fg.7. WMR closed loop response for crcular erence and ntal condtons x(33; x(33; x3( π /7; x(-.; x(.; x(.. The crcle trajectory trackng, shown n fgures 7, was obtaned for Δα max., Δπ max.33. The followng values have been chosen for the constants: μ., ρ ρ.99, δ δ 3. 33, ( ( A. Concluson Δ α Δπ. Dscrete-tme, sldng-mode adaptve controllers and parameter estmators for trajectory trackng appled to control angular and poston moton of oneer 3-DX one par of actve wheels moble robot, have presented n ths paper. The tmevaryng mass and moment of nerta dynamcal state space model have been undertaken n order to desgn the controllers. Two sldng-mode adaptve controllers have been desgned, for angular and poston moton, respectvely. The robustness s guaranteed by sldng-mode controllers and by onlne parameter estmators. Controllers parameters, on-lne updated, assure an approxmate sldngmode evoluton even f the attractveness condton s not satsfed and contrbute to an ncreased robustness. References [] Ljung, L., (999 System Identfcaton ( nd edton. rentce Upper saddle Rver, NJ. ISSN: ISBN:

7 8th WSEAS Internatonal Conference on SYSTEMS THEORY and SCIENTIFIC COMUTATION (ISTASC 8 Rhodes, Greece, August -, 8 [] Stoca,. and Ahgren., ( Exact ntalzaton of the recursve least squares algorthm. Internatonal Journal of Adaptve Control and Sgnal rocessng, vol., pp [3] Furuta, K., (99, Sldng mode control of a dscrete system. System & Control Letters, vol., pp.-. [] Yu, X., Xu, J.,X., ( Varable Structures Systems: Towards st Century, Sprnger_Verlag Berln Hedelberg. ISSN: ISBN:

On-line Parameter Estimation in Sliding-mode Control of Pioneer 3-DX Wheeled Mobile Robot

On-line Parameter Estimation in Sliding-mode Control of Pioneer 3-DX Wheeled Mobile Robot roceedngs of the 7th WSES Internatonal Conference on Systems Theory and Scentfc Computaton, thens, Greece, ugust -, 7 7 On-lne arameter Estmaton n Sldng-mode Control of oneer 3-DX Wheeled Moble Robot.