Effective Parameters for Helical Pole Climbing of the Wheel-based Modular Snake Robot

Transcription

1 Effectve Parameters for Helcal Pole Clmbng of the Wheel-based Modular Snake Robot Pongsakorn Polchankajorn and Thavda Maneewarn Insttute of FIeld robotcs (FIBO) Kng Mongkut s Unversty of Technology Thonbur Bangkok, Thaland fbo.kmutt.ac.th, fbo.kmutt.ac.th Abstract Ths research ams to study the factor that affect pole clmbng effcency of the modular snake robot on the cylndrcal pole wth constant radus. The wheel-based modular snake s clmbng the pole by formng tself nto a helcal or a spral shape around the pole and usng ts drvng wheel to propel tself upward along the helcal path. The jont confguraton of the robot can be found from the relaton of helcal ptch angle, helcal radus, and lnk length of the robot. Fve helcal clmbng confguratons wth dfferent helcal ptch angles and three spral clmbng confguratons wth dfferent spral s end radus were tested on the 18 degree of freedoms, 7 lnks modular hyperredundant robot. The expermental result showed that the clmbng velocty depends on the dstrbuton of the graspng force and the helcal ptch angle. The graspng force s affected by the helcal radus and the helcal ptch angle. Keywords-Modular Snake Robot; Helcal clmbng; Spral clmbng; Pole clmbng I. INTRODUCTION Clmbng robots have been developed for varous applcatons n the past twenty years. The desgns of clmbng robot are vared dependng on ther usages such as ppe nspecton, frut harvestng, wall cleanng etc. The mechansms for clmbng n a robot can be categorzed as statc and dynamc clmbng. In statc clmbng, graspng and bodyextendng actons are alternated, for example an nchworm clmbng moton suggested n [1, 2]. Ths type of clmbng robot usually has two actve grppers and can be used to clmb across a branch of ppes or trees. In dynamc clmbng, graspng and clmbng motons happen smultaneously. Ths type of clmbng results n contnuous moton, thus has been appled n pole clmbng applcatons as proposed n [3, 4]. In recent year, the modular and reconfgurable robots have been topc of nterest by many groups of robotc researchers [5-9]. Wth modular desgn, the robot can adapt tself to perform dfferent tasks n varous envronments ncludng pole clmbng. Choset [7] demonstrated the scenaro that a modular robotc snake could successfully grasp and roll up a cylndrcal pole. Hs team also nvented the Torodal Skn Drve (TSD) [8] that could drve the robot up the pole n helcal trajectory. Goldman and Hong [9] proposed the cost functon analyss for desgnng and controllng a modular clmbng robot. They also appled the helcal form for graspng and rollng up the pole. In ths paper, we am to study the parameters that affect the pole clmbng ablty of a modular robot n helcal confguraton. We are also nterested n the wheel-based modular snake robot due to the fact that the drecton of ts wheels can be adjusted to provde some frctonal support for the gravtatonal force that acts on the robot. In helcal confguraton, there are two parameters that sgnfcantly affect the clmbng ablty.e. helcal radus and helcal ptch angle. The helcal radus drectly affects the graspng force between the robot and the pole. On the other hand, the helcal ptch angle relates to the clmbng velocty. However, when the helcal ptch angle s ncreasng, the graspng force could be decreasng to the pont that the robot may lose ts clmbng ablty. In the next secton, we wll dscuss about the desgn of clmbng gat of the modular wheel-based snake robot. The knematcs of the proposed helcal and spral pole clmbng gat wll be explaned. The rest of the paper wll be organzed as follows. Secton II descrbes how the helcal pole clmbng works, the frame assgnments of the robot and the helcal and spral path equatons. Secton III descrbes the nverse knematcs and the dynamcs equaton of the robot. Secton IV descrbes the robot desgn and the clmbng experments. Fnally, the result of experments wll be dscussed and concluded n secton V and VI. II. CONCEPT OF POLE CLIMBING A. Desgnng pole clmbng gat for a modular snake robot A modular snake robot s desgned to be able to perform varous types of locomoton such as crawlng, rollng and clmbng. In order to clmb a pole, the robot must apply suffcent graspng force around the pole whle movng ts body up the pole aganst the gravtatonal pull. The helcal confguraton can be used for ths type of moton, because the helcal form can provde graspng acton whle allowng the robot to move upward. For the non-wheel modular snake robot, the robot can roll ts body upward when t wraps tself around the pole n a helcal confguraton [7-9]. For the wheel-based modular snake robot, ts wheel can be adjusted to be perpendcular to the ground plane so that the robot can roll ts wheel upward vertcally as n the non-wheel robot [9]. However, we are nterested n the clmbng moton that the Ths work was supported n part by Junor Scence Talent Project, NSTDA /11/$ IEEE 232

2 wheels of the robot are algned wth the helcal path and drve the robot upward along the helcal path nstead of n the vertcal drecton. Ths clmbng gat has ts advantage snce the wheel can provde large frcton force perpendcular to ts rollng drecton. Ths frcton force can be partal supports aganst gravtatonal force. As long as the graspng force s suffcent, the wheel drvng force can be used to drve the robot upward wth less amount of force compared to the clmbng gat wth vertcal drven wheels or rollng body. Fgure 2. Crcular helx path and spral path. III. KINEMATICS AND DYNAMICS ANALYSIS Fgure 1. Robot s frame assgnment. Wth ths helcal clmbng gat, all wheels of the robot must be n contact wth the pole surface. In our desgn, each robot module conssts of three revolute jonts that can rotate around x, y and z axs. The wheel axs n each module s algned wth the x axs of the 4th frame. W and n desgnate the world frame and number of modules. The frame reference for each module can be descrbed by the transformaton matrx W 4 T. The transformaton equaton of the robot wth n modules can be wrtten as follow. W n W ( ) ( 0 ) ( ) T = T T T (1) 1 2 n B. Crcular helcal and spral path The crcular helcal path s the three dmensonal helx wth a constant radus. We can use 3 equatons to descrbe a three dmensonal helcal path as follow. xs ( ) = Rcos( s) (2) ys ( ) = bs (3) zs ( ) = Rsn( s) (4) Where R s the helcal path radus on xz plane (top vew) and 2π b s the helcal ptch angle. We can change helx path to spral path by changng the R constant to a functon that vared by the heght of the spral path (y axs). Example of functon R that use n the spral clmbng experment can be shown as follow. lr, mn, R max represent the heght of overall spral segment, the mnmum and the maxmum spral radus. R Spral l y( s) ys () > : Rmn +. Rmax Rmn 2 l 2 = l y( s) l ys () < : R 2 R R 2 l 2 ( ) ( ) max max mn (5) A. Helcal shape approxmaton In order to form a modular snake robot nto a helcal shape around the pole, the contnuous helcal and spral path equatons n secton II.B has to be dscretzed accordng to the robot physcal parameters such as type of jonts and the length of ts lnk. The helcal path can be descrbed by a helcal ptch angle and radus. For a gven lnk length ( L ) of each robot module and wth helcal radus R, the reference frame of each module can be assgned at the pont on the R -radus crcle at every θ step angle around y axs as shown n fgure 3. Fgure 3. Top vew of the helcal curve. For each reference frame, the axs vector x ( w P ) and z x ( w y P ) wth respect to the world frame can be assgned n the perpendcular and tangental drecton of a crcular pole surface and along the helcal path. The axs vector Y can be found from the cross product of vector of ( w P ) and ( w x y P ). Therefore, we can represent the rotaton matrx for each module reference frame as follow R= P P P (6) w w w w x y z Then we can transform the relaton of the rotaton matrx wth respect to the world frame to the rotaton matrx wth respect to frame -1 from the equaton. R= R R (7) 1 w T w 1 Algebrac method s used to solve for the jont angles of each robot's module by the Euler angle set equaton. α = atan2( m32, m22) (8) β = asn( m12 ) (9) γ = atan2( m, m ) (10)

3 B. Dynamc model The dynamc model of the robot can be derved from Lagrangan method assumng that the contact of all robot's wheels and the pole are under non-slpped condton. The general form of the lnk's equaton can be wrtten as follow. τ = M ( q) q + V( q, q ) + G( q) + J ( q ) λ (11) q = α β γ θ andτ = τ τ τ τ. Wth [ ] T α β γ θ Assume as the number of lnk. The angles α, β, γ, θ, τ α, τ β, τ γ, andτ θ are the roll angle, ptch angle, yaw angle, rollng angle of robot s wheel, roll torque, ptch torque, yaw torque, and wheel s torque, respectvely. J ( q ) λ s the non-holonomc constrant term that has the null space of lnear-velocty transform. T J ( q ) q = 0 (12) From the local matrx, each module of the robot has four control parameters and jont varables and one non- holonomc constrant. Therefore, the robot that conssts of n modules would have 4n control parameters and jont varables. The total number of non-holonomc constrants of the robot s n constrants. When the robot s formed nto the helcal confguraton, all non-holonomc constrants wll algn n the drecton perpendcular to the helcal curve. The spread out vew of the pole's surface when the robot s n helcal confguraton shows that all wheels drve nput are perpendcular to the non-holonomc constrants of the wheels, thus satsfes all n constrants for the n-modules robot. Fgure 4. Non-holonomc constrants n the spread out vew of the pole surface. IV. EXPERIMENT A. Wheel-based modular snake robot system The robot conssts of 7 modules. Each module has 3 revolute actuators (Robots DX-117) whch all axes are ntersect. All 3 revolute actuators are postoned controlled. Each module also has two drvng wheels. Both wheels are drven by a Robots RX-28 motor. The robot structure s made of alumnum alloy. The roll jont s supported wth superlene nylon to prevent lnk deflecton. The 10-cm dameter wheel s also made from superlene nylon and coated wth ant-slp substance. Each module s 19.1 cm long. The total weght of ths 7-module robot s approxmately 3 kg. Fgure 5 shows the complete wheel-based modular snake robot. T Fgure 5. The prototype wheel-based modular snake robot. In order to control the robot, the angular poston and the wheel velocty command s sent to the robot from a notebook computer to a mcrocontroller board on the robot va RS-232. The mcrocontroller converts these commands nto the protocol that s used by the dgtal servo motor and sends the command packet to all motors va a RS-485 bus. A current sensor s added nto each robot module to measure the current for ts drve motor. The mcrocontroller can collect data from the current sensor as well as the load feedback from a dgtal servo motor. Both data and power are sent to the robot va a 4 meters long cable. B. Clmbng experment The experment was performed to study the relatonshp between the parameters of the helcal clmbng path (.e. the helcal ptch angle and the helcal radus) and the clmbng performance (.e. clmbng velocty and graspng ablty). 1) Varyng the helcal path's ptch angle Ths experment was desgned to test the performance of helcal clmbng at dfferent helcal ptch angles. The relatonshp between the ptch angle, the graspng load, the drvng load and the clmbng velocty of the robot were focused n ths experment. The test was performed on the wheel-based modular robot whch was earler descrbed n secton A. The pole used n ths experment has 14 cm dameter and s covered wth carpet. The robot wheel radus s 5 cm. The helcal path of cm radus was chosen for ths experment (from the calculaton n secton III.A as shown n fg. 3). Accordng to the robot module dmenson and the pole radus, the helcal ptch angles were vared at 15, 17.5, 20, 22.5, 25 degree for ths experment. Table I shows the jont angle for each modules at varyng helcal ptch angle. TABLE I. JOINT ANGLE USED IN HELICAL CLIMBING EXPERIMENT Helcal ptch angle(degrees) Roll angle Ptch angle Yaw angle Durng the clmbng experment, data that can ndcate the status of the robot was collected e.g. the graspng load, the drvng load (.e. current readng from the drve motor) and the clmbng velocty. The clmbng tests were performed 5 tmes 234

4 for each helcal ptch angle varaton. The results are shown n table II, fg. 6, fg. 7, fg.8, and fg. 9. TABLE II. ABILITY OF HELICAL GRASPING AND CLIMBING IN EACH HELICAL PITCH ANGLE Helcal ptch angle(degrees) Graspng Clmbng Fgure 8. The graph between mean and SD of clmbng velocty and helcal ptch angle. Fgure 6. The graph between mean and SD of clmbng load and helcal ptch angle. The expermental results n fgure 8 also showed the nverse relatonshp between the clmbng velocty and the helcal ptch angle. Contrary to the knematc relatonshp where the hgher ptch angle would resulted n more travellng dstance over tme, the graspng load decrease when the ptch angle ncrease (as shown n fg. 6) thus caused the clmbng ablty to drop. Table II shows that when the helcal ptch angle s larger than 20 degrees, the robot can only grasp the pole but cannot clmb the pole. When the robot tred to clmb the pole under these condtons, the wheel appeared to be slppng and the robot was no longer be able to grasp the pole and sld down eventually. Fgure 9. The graph of yaw s torque dstrbuton along the robot s body and the helcal ptch angle. Fgure 7. The graph between mean and SD of holdng torque n each axs of rotaton and helcal ptch angle. For a helcal path, the radus s constant throughout the robot's length. In a spral path as descrbed n secton II, the path's radus s vared along the path. The spral path s desgned to have a smaller path radus at each end to ncrease the graspng load. 2) Varyng the path's radus Ths experment was desgned to test the clmbng performance wth dfferent radus profle. From the prevous experment, fg 9 shows that the yaw holdng torque for each module were dstrbuted n parabolc form whch means that the graspng ablty was reduced at each end of the robot (.e. head and tal). Fgure 10. Smulaton of spral pose (left) and the real shape of helcal pose (center) and spral pose (rght). 235

5 In ths experment, the 15 degrees ptch angle was chosen. The radus of the spral path at the mddle was set to cm and both end raduses were vared at 11, 11.5 and 12 cm due to jont lmts of the robot. The clmbng test were performed 5 tmes for each confguraton except at the 12-cm case whch can be tested only 3 tmes because the yaw torque at the last module became too hgh and the motor were no longer be able to hold ts poston. Results from the experment are shown n fg and table III. Fgure 13. The graph between mean and SD of clmbng velocty of spral's end radus and helcal clmbng wth 15 degrees ptch angle. Fgure 11. The graph between mean and SD of clmbng load of spral's end radus and helcal clmbng wth 15 degrees ptch angle. Fgure 14. The graph between holdng torque of yaw angle and spral's end radus wth 15 degrees ptch angle. Fgure 12. The graph between mean and SD of holdng torque n each axs of rotaton and spral's end radus wth 15 degrees ptch angle. Fg. 11 and 12 shows the nverse relatonshp between the spral path's end radus and the holdng torque of yaw angle. When the spral end radus decreased, the yaw torque ncreased whch ndcated that the graspng ablty ncreased as well. When the graspng ablty ncreased, the robot could hold on to the pole tghter thus resulted n hgher clmbng velocty. Table III compares the clmbng velocty between the helcal (fx radus) and the spral (varyng radus) cases. The clmbng velocty s hgher wth the spral clmbng than the helcal clmbng at the same helcal ptch angle. Fgure 15. The comparson graph between helcal path s holdng torque and spral path's holdng torque wth 15 degrees ptch angle. 236

6 TABLE III. VELOCITY COMPARISON BETWEEN HELICAL AND SPIRAL CLIMBING (M/MIN) Helcal ptch Spral Velocty Velocty angle(degrees) radus(cm.) V. DISCUSSION From the result of experments n the prevous secton, we found that the man contrbuton that affects the pole clmbng performance of the wheel-based modular snake robot s the magntude and the dstrbuton of force that the robot uses to grasp the pole. Snce the robot conssted of n modules, the graspng force dstrbuton drectly relates to number of modules, the length of each modules and the pole radus. Wth the helcal (fx radus path) confguraton, the graspng load s large at the mddle module and small at both ends. When the path radus s too large, the robot cannot produce suffcent amount of graspng force especally at the end modules, thus the robot cannot clmb the pole. Wth the spral (varyng radus) path, the radus of the path are smaller at both ends n order to ncrease the graspng force at the end modules. The clmbng speed can be ncrease by decreasng the end radus as long as the jont lmt and the torque lmt of the robot allows. Another problem that was notced durng the helcal clmbng experment s that the wheels of the head module dd not always touch the pole surface. We assume that t could be the result of accumulated error from all jonts of the robot whch can be shown by the Cartesan error that s affected by the jont error from Jacoban relatonshp n equaton 14. x q1 y = J... p z q 18 (14) The error of each jont was found from the angular readng data durng the pole clmbng experment compare wth the angle calculated from the helcal curve. However, the Cartesan accumulate error ranged from 10 cm to 13 cm, whch was much larger than the actual error from our drect observaton. The dfference may be resulted from the deflecton n the rollng jont that occurred n the real robot whch was not consdered n the knematc calculaton. VI. CONCLUSION In ths paper, a pole clmbng n helcal and spral confguraton of the wheel-based modular snake robot was studed. The pole graspng condton was realzed by formng the robot nto a helcal and spral shape. The wheel-base desgn s chosen n order to decouple the graspng and clmbng acton. Wheels are used to propel the robot upward along the pole surface n helcal path. All wheel axes need to be parallel to the pole surface whch can be realzed by performng nverse knematc calculaton from the predefned helx path accordng to the robot model. Non-slp contact between the robot and the pole can be created by formng the helcal path wth the suffcently small radus (accordng to the pole's radus) and the suffcent statc frcton coeffcent between the wheel and the pole surfaces. Clmbng experments were performed to study the relatonshp between dfferent helcal path parameters (.e. ptch angle and radus) and clmbng performance (.e. clmbng velocty). Wth the constant helcal path radus, when the helcal ptch angle ncreased, the graspng ablty of the robot decreased as shown by the lower graspng force (whch s drectly related to yaw torque) and the slower clmbng velocty. The profle of the yaw torque along the robot's body showed a parabolc relatonshp whch meant that the graspng torque are lower at both end modules than at the mddle module. By applyng the spral path whch the helcal radus are smaller at both ends than n the mddle, to compensated the Cartesan error of each jont, the graspng force along the robot's body can be more unformly dstrbuted. The experment showed that the spral clmbng can ncrease the clmbng velocty and graspng ablty wth same actuator s ablty. Therefore, man factors that contrbute to the pole clmbng performance are the magntude and the dstrbuton of the graspng torque n all robot's modules. Accordng to the knematc relatonshp, the hgher ptch angle should yeld more clmbng dstance as long as the non-slp contact condton can be mantaned. Results from ths study can be used for desgnng a better wheel-based modular snake and modular robot s gat that can clmb and crawl n varous envronments and the ncluson of a force-control scheme nto the system n the future. REFERENCES [1] Zad Mohd. Rpn, Tan Beng Soon, A.B. Abdullah and Zahurn Samad, 2000, "Development of a Low-Cost Modular Pole Clmbng Robot", TENCON 2000: [2] M. Almonacd, R. J. Saltarén, R. Aracl, and O. Renoso, 2003, Moton Plannng of a Clmbng Parallel Robot, IEEE Transactons on Robotcs and Automaton. [3] Baghan A., Ahmadabad M.N., Harat A., 2005, Knematcs Modelng of a Wheel-Based Pole Clmbng Robot (UT-PCR), IEEE Internatonal Conference on Robotcs and Automaton. [4] W. Chonnaparamutt, H. Kawasak, S. Uek, S. Murakam, and K. 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