Novel Differential Drive Steering System with Energy Saving and Normal Tire Using Spur Gear for an Omni-directional Mobile Robot

Transcription

1 2 IEEE International onference on Robotics and utomation nchorage onention istrict May 3-8, 2, nchorage, laska, US Noel ifferential rie Steering System ith Energy Saing and Normal ire Using Spur Gear for an Omni-directional Mobile Robot Yuki Ueno, akashi Ohno, Kazuhiko erashima, Hideo Kitagaa, Kazuhiro Funato and Kiyoaki Kakihara bstract Holonomic omnidirectional mobile robots are useful because of their high leel of mobility in narro or croded areas, and omnidirectional robots equipped ith normal tires are desired for their ability to surmount difference in leel as ell as their ibration suppression and ride comfort. casterdrie mechanism using normal tires has been deeloped to realize a holonomic omnidiredctional robot, but some problems has remain. Here e describe effectie systems to control the caster-drie heels of an omnidirectional mobile robot. We propose a ifferential-rie Steering System (SS) using differential gearing to improe the operation ratio of motors. he SS generates driing and steering torque effectiely from to motors. Simulation and experimental results sho that the proposed system is effectie for holonomic omnidirectional mobile robots. I. INROUION n omnidirectional robot is highly maneuerable in narro or croded areas such as including residences, offices, arehouses and hospitals. his technology can be applied to an autonomous mobile robot in a factory, a heelchair and so on. Seeral kinds of omnidirectional mobile robots and their applications hae been deeloped []-[5]. Hoeer, these robots realized their omnidirectional motion by using special heels such as mechanum heels, ball heels, omni-disks and omni-heels. o improe the ride comfort, ibration suppression, slippage reduction and ability to surmount different in leel, omnidirectional robots equipped ith normal tires are needed. rai proposed an omnidirectional ehicle equipped ith normal tires [6]. Hoeer, it as a nonholonomic ehicle that had to adjust the direction of the heels before changing the moing direction of the ehicle. Holonomic omnidirectional ehicles, hich can moe in any direction ithout changing the direction of the tires beforehand, equipped ith normal tires include a dual-heel type and a caster-drie (actie-caster) type [7], [8]. he dualheel type has problems as follos. he number of heels is limited to to, and it is impossible to get high friction or to adapt to a rough terrain by a synchronous drie of many heels. Moreoer, a passie heel is needed to stabilize the posture of the ehicle. Y. Ueno,. Ohno and K. erashima are ith System and ontrol Labolatory, Production System Engeneering, oyohashi Uniersity of echnology, Hibarigaoka, empaku, oyohashi, ichi, Japan ueno,terasima@syscon.pse.tut.ac.jp K. Hideo is ith the epartment of Electrical ontrol Engineering, Gifu National ollege of echnology, Kamimakua, Motosu, Gifu, Japan hkita@gifu-nct.ac.jp K. Funato and K. Kakihara are ith the KER O., L, Yutakagaoka, oyokaa, ichi, Japan kfunato,kkakihara@ker-jp.com he caster-drie heel has an offset beteen the steering axis and the center of the heel. he heel can moe in any direction by controlling the steering axis and the driing heel independently by using to motors. Holonomic omnidirectional motion of a robot can be realized by using to or more caster-drie heels. Hoeer, the caster-drie heel also has a problem as follos. When the ehicle is in steady motion, including straight motion and rotation ith constant curature, only the driing motor orks and the steering motor becomes idle. When the ehicle changes its moing direction, high load is applied to the steering motor. herefore, high poer is required both for the driing and steering motors, hich means the ehicle s mass is increased. he aim of our research is therefore to deelop a holonomic omnidirectional mobile robot ith a caster-drie heel minimizing the motor poer by using the interference of the output of to motors. ne gearing mechanism is proposed to realize the interference. Furthermore, the proposed method is shon to be effectie, because it is possible to surmount difference in leel and it absorbs the ibration by using normal tires. II. PRINIPLE. Omnidirectional Motion Using a aster-rie Wheel Fig. shos the caster-drie heel. o degrees of freedom can be generated in the steering axis using this mechanism. Longitudinal force is generated by the heel rotation. Lateral force is generated ith the rotation of the steering axis because of the friction beteen the floor and heel. he position and orientation of the heel can be represented by the position O (X,Y ) of the steering axis and the orientation θ as shon in Fig.. y rotating the driing heel ith the angular elocity, elocity ẋ = r is generated in the direction of the X axis. Here, r is the radius of the driing heel. y rotating the steering axis ith the angular elocity l, elocity ẏ = l l ould be generated at the center of the heel in the direction of the Y axis. Here, l is the offset distance beteen the steering axis and the center of the driing heel in the direction of X. Hoeer, reacting elocity ẏ = l l is generated at the steering axis in the direction of the Y axis, because the position of the driing heel is fixed by the friction ith the ground. herefore, the elocity (ẋ, ẏ )of the caster-drie heel can be controlled by changing and l. Fig. 2 shos an example of motion. he initial orientation θ of the heel is set to be θ = π/2 rad in the frame //$26. 2 IEEE 3763

2 Reolution center Y y x ' Z l r Grounding point O l θ O (x,y ) X Z' ounter gear Z Z Fig.. Model of the caster-drie heel Fig. 3. Principle of the proposed SS ' Motor Fig. 2. Lateral motion to right. O XY. he motion, as shon in Fig. 2, can be gien by changing and l appropriately. Een though the rotating heel itself cannot generate lateral motion to the right, the lateral motion of the robot, hich is fixed to the steering axis, is realized. No heel has to control the orientation of the robot by itself. he direct kinematic equation is denoted by the state ector x = [x,y ] and the input ector u =[, l ] as E eel Gear iming elt urn Unit: ẋ = u () here [ ] r cos θ l sin θ = r sin θ l cos θ he inerse kinamatic equation becomes here (2) u = ẋ (3) [ = r cos θ l sin θ r sin θ ] l cos θ Holonomic omnidirectional motion (ẋ, ẏ, θ) of a mobile robot can be achieed by using to or more caster-drie heels.. ifferential-rie Steering System (SS) We deeloped a useful method for constructing a casterdrie heel using a ifferential-rie Steering System (SS). he SS outputs driing and steering elocities from to motors using differential gearing. Fig. 3 shos the principle of the SS. he differential gearing mechanism is realized by using fie spur gears, referred to as,,, and. is engaged ith, and is engaged ith through the counter gear. and are fixed to each other. he SS is a 2-input/2-output system ithout fixing any component. () Fig.. Mechanism of the proposed SS and are independently drien by to motors. and proide output torque. Fig. shos the mechanism of the SS. orques of to motors are transmitted to the SS by a beel gear,, hich is fixed to the chassis E, proides the steering torque, and, hich leads to the driing heel ia the beel gear, proides the driing torque. Let,,, and be of the angular elocity of,,, and in Fig. 3, and Z, Z, Z and Z be the number of teeth of,, and, respectiely. When =,the steering angular elocity l becomes zero, and e obtain = Z Z Z = Z Z Z (5) = (6) When =, the driing angular elocity becomes zero because does not rotate beteen and, and e obtain = = (= )= (7) he direct kinematic equation, hich deries driing and steering output u = [, l ] from motor input u P = [, ], can be described as 376

3 here P = [ ] u = = P u P (8) [ Z Z Z Z +Z Z Z Z Z Z +Z Z Z Z Z +Z Z Z Z Z Z Z +Z he inerse kinematic equation becomes u P = P u () here [ ] Z P = Z () Z Z Next, e derie the motor poer ratio of the SS. Joint torques,, and of,, and, respectiely, are gien by [ ] [ Z Z = Z Z Z Á Z Z Á Z ] [ Z ] ] (9) (2) here the positie direction of each torque is same as that of angular elocity in Fig. 3. For an omnidirectional mobile robot ith the SS, steady motion including straight motion and rotation ith constant curature is achieed by l (= ) =.When l =( =), the joint torques are gien from (2) by = Z Z Z Z (3) = 2Z Z () = (5) he poer ratio of to motors is gien from (5) and (3) by P : P = : = ( Z Z Z Z Z )( Z ): c Z Z = : (6) On the other hand, hen = ( = ), the joint torques are gien from (2) by = Z Z Z Z (7) = (8) = 2(Z ) Z (9) he poer ratio is gien from (7) and (7) by III. OPERIONRIO OF MOORS o examine the operation ratio of motors, e compare the SS to a conentional caster-drie heel. We define the operation ratio δ of motors as (Sum of motor poer in motion) δ = (22) (Sumofratedpoerofmotors) he ratio (P : P ) of the rated poer of to motors used in the SS is set to be :. he ratio of rated poer used in the conentional method is also set to be :, as denoted in Wada [8]. We calculate the operation ratio δ in the case of driing motion ( =).LetP be the sum of motor output poer needed to achiee the motion. he result of the conentional P method is P = P = P and δ = P +P =.5. he result of the SS is P = P = P 2 and δ = P P +P =. Next, e calculate δ in the case of steering motion ( = ). he result of the conentional method is P = P = P and δ =.5. he result of the SS is P = P = P 2 P P +P =. and δ = he output poer of motors can be decreased by using the SS as a caster-drie heel because of its high operation ratio of motors. his means that the size of the robot can be smaller by using the SS. IV. ONSRUION OF OMNIIREIONL MOILE ROO We constructed a prototype model of a ehicle ith four SS heels to check the feasibility of the proposed mechanism, as shon in Fig. 5. Effectieness of the proposed SS as confirmed by this apparatus. Fig. 6 and able I sho a figure and the specifications of a platform of the omnidirectional mobile robot ith four SS heels, respectiely. he proposed omnidirectional robot has the capability of climbing a slope of 2 deg and exceeding a difference of 7 mm hile carrying a load of kg. Offset distance, l, can be adjusted in this unit by trial and error. If the offset distance is larger, the straight run P : P = : = Z Z Z Z : = Z Z : (2) Z Z When Z Z Z is equal to Z, the poer ratio yields P : P =: (2) Fig. 5. laboratory Photograph of the four-heeled ehicle built in the authors 3765

4 LE I SPEIFIION OF HE VEHILE Size ( W H) (mm) Weight 8 (kg) Motor poer 5 (W) 8 Max. elocity 6(km/h) Max. acceleration 2. (m/s 2 ) Max. slope angle 2 (deg) Max. step difference 7 (mm) Max. loading eight (kg) ementer of heel 2 (mm) Offset distance 8-56 (mm) Y Y (x b,y b ) (x b,y b ) (x a,y a ) (x a,y a ) X θ a θ O (x,y ) (x d,y d ) (x,y ) d d (x c,y c ) (x,y ) c c O Fig. 7. Model of the ehicle X Fig. 6. Platform of the proposed omnidirectional mobile robot becomes stable and the demand alue of angular elocity of the steering becomes smaller. In this case, larger torque is needed in the steering axis. On the other hand, hen the offset distance is smaller, the straight run is unstable, but the mobility is improing. In addition, the torque in the steering axis is smaller, hile the angular elocity of the steering axis becomes larger. here is a contrastie relationship beteen torques, angular elocity and stability of the heel. herefore, it is necessary to think about the offset distance from the experiment. From that reasons, the offset distance can be adjusted beteen 8 mm and 56 mm in consideration of the motor capacity. In this paper, offset distance is tentatiely gien as 25 mm.. Kinematic Model of a Four-heeled Vehicle caster-drie heel generates to degrees of freedom on the demensional plane. o generate omnidirectional moement on the ideal flat floor, a ehicle must hae at least to heels to control three degrees of freedom in total, hich includes to translation degrees of freedom and an attitude degree of freedom. Hoeer, a real road surface contains a nonideal floor. In consideration of ehicle stability on the nonideal floor, e adopted a control system for a fourheeled ehicle. Fig. 7 shos a schematic model of the four-heeled ehicle. he kinematic model is described follos: ẋ ẏ θ (x a sin θ + y a cos θ ) (x a cos θ y a sin θ ) (x b sin θ + y b cos θ ) = (x b cos θ y b sin θ ) (x c sin θ + y c cos θ ) (x c cos θ y c sin θ ) (x d sin θ + y d cos θ ) (x d cos θ y d sin θ ) ẋ a ẏ a ẋ b ẏ b ẋ c ẏ c ẋ d ẏ d (23) x y x& r y& r s s x& y& Fig. 8. r lr l P P lock diagram of the single heel hen, the inerse kinematic model is described as follos: ẋ a y a cos θ x a sin θ ẏ a x a cos θ y a sin θ ẋ b y b cos θ x b sin θ ẏ b ẋ c = x b cos θ y b sin θ ẋ y c cos θ x c sin θ ẏ ẏ c x c cos θ y c sin θ θ ẋ d y d cos θ x d sin θ ẏ d x d cos θ y d sin θ (2) herefore, hen ẋ, ẏ and θ (= ) are gien, the elocity(ẋ a, ẏ a, ẋ b, ẏ b, ẋ c, ẏ c, ẋ d, ẏ d )offourheelsis calculated by using (2), here ẋ, ẏ and indicate the elocity in the X-direction, Y-direction and the angular elocity of the ehicle, and x a, y a, x b, y b, x c, y c, x d and y d indicate the coordinate of each heels on the local coordinate system, respectiely. V. SIMULION N EXPERIMEN. Simulation of the Single Wheel o check the kinematic model of the SS, e simulated the motion of the heel. Fig. 8 shos a block diagram of the control system. If ordered elocity ẋ r and ẏ r ere gien, the angular elocities of gears and are calculated s θ 3766

5 .8.6 Wheel 2 3 Yposition (m) t =. s t =. s 5 6 t =.2 s Xposition (m) x (m/s) time (s) Fig. 9. y (m/s) l time (s) Simulation results of the single heel by using (). θ is the steerage angle of the heel hich is the integral calculus alue of steerage angular elocity l. Hoeer, in fact, the heel angle is detected from the absolute encoder attached to the steering axis. ranslational motion toard the +X direction ith a maximum elocity of 6 km/h (=.67 m/s) and a maximum acceleration of.5 m/s 2 as examined. he initial alue of θ as set as.57 rad (=9 deg) in this case. Fig. 9 shos the simulation result, here, x, y,,, and l indicate the elocity in the X-direction, Y- direction, the angular elocity of gear and the gear, the angular elocity of the heel and the steering axis, respectiely. s shon from the simulation result, the heel can moe to reference directions instantly and independently of the initial angle of the heel. In addition, graphs of the angular elocity of to motors, and, sho that the SS can be generated driing and steering torques by using to motors simaltaneously as indecated by l and.. Simulation and Experiment ith the Four-heeled Vehicle o erify the mobility of the ehicle, e examined its X- axis direction translation moement. Initially the heels are pointed in different directions, and the alue of θ as set to be.57 rad in this case. Fig. shos the simulation result of the four-heeled ehicle. he rectangle, triangle and four smaller rectangles in the graph indicates the ehicle body, front of the ehicle Y position (m).5 t =.3 s t =.6 s X position (m) PL Unit Fig.. Motor rier Motor rier Fig.. t =. s t =.7 s Simulation result of the ehicle SS ontroller - Motor Encoder Motor Encoder -2 SS2 ontroller SS3 ontroller SS ontroller ontrol system of the ehicle t =.5 s t =.8 s SS bsolute Encoder θ θ 2 θ 3 θ riing l Steering and heels, respectiely. From the results, the ehicle can moe to goal direction instantly, despite the difference in the ays the heels point, by soling inerse kinematics of (2) and (3). Fig. is a block diagram of the control system of the ehicle. programmable logic controller (PL) unit is used for controlling the ehicle. he PL unit has arious exclusie units such as the PU unit, logic input and output unit and analog input and output unit. Each heel angle is detected from an absolute encoder attached to the steering axis by using the input unit. o control motors, an exclusie motor drier is used. he rotation speed of motors is controlled by the motor drier, and reference for the reolution speed is gien by analog oltage from the analog output unit. he PU unit is used for resoling the kinematic equation from the angle of each heel and reference elocities and obtaining each motor s angular elocity. he calculated angular elocity is transformed to analog oltage and transmitted to the motor drier, and the ehicle is controlled. When experiments are 3767

6 Y position (m) X position (m) x (m/s) ime (s) 6 Fig y (m/s).5 - : Moing direction : Reference : Experiment - 2 ime (s) 6 Experimental result of the ehicle performed, the x-y position of the ehicle can be computed from the encoder signal. Fig. 2 shos the experimental result of the four-heeled ehicle. In addition, ẋ, ẏ,, 2,, 2 indicates the elocity in the X-direction, Y-direction, the angular elocity of motors in heel- (motor:- and - 2) and the angular elocity of motors in heel- (motor:- and -2), respectiely. We examined autonomous moing by using a elocity pattern that as generated beforehand. he pattern of motion as at the first translation moement forard, the second translation moement rightard and finally the translation moement to 5 degrees in the left rear side. From the result, e see that there is a little error trajectory ith respect to the reference. It is considered to be the result of the large amount of friction beteen the tire and the floor because the error trajectory is generated hen the moe direction changes. We should be able to aoid this problem in future by adding a feedback control system. On the other hand, hen the control system of a ehicle consists of a manual control system such as a joystick or poer assist system, the ehicle does not require strict trajectory control, because the operator is doing fine adjustment of the ehicle themseles. he error of the angle of the ehicle in the translation moement affects its operability, so e need to improe stability of the straight-run in the future. VI. ONLUSIONS N FUURE WORKS. onclusions In this paper, a noel ifferential-rie Steering System (SS) is proposed for the caster-drie heel of a holonomic omnidirectional mobile robot, and omnidirectional mobile robot based on the proposed mechanism is nely built. he SS can proide a high operation ratio of motors compared to a conentional caster-drie heel. Numerical analysis and experiments by building a prototype noel ehicle shoed the effectieness of the SS.. Future Works Future orks include the folloing: Posture control on rough terrain. Ealuation of ibration test on the ground. pplication to an omnidirectional heelchair. VII. KNOWLEGMENS We ould like to express my gratitude to Prof. Miyoshi and r. Yoshiyuki Noda for their adice to deelop this research. his ork as supported by the 2st entury OE Program Intelligent Human Sensing, and also G-OE Frontier of Intelligent Sensing, and furthermore by ichi Science & echnology Foundation Research id Project of 28 and 29 year. We ould like to address the sincere thanks. REFERENES [] M. West and H. sada, esign of a holonomic omnidirectional ehicle, Proc. IEEE Int. onf. Robot. utomat., 992, pp [2] F. G. Pin and S. M. Killough, ne family of omni-directional and holonomic heeled platforms for mobile robots, IEEE rans. Robot. utomat., 99, ol., pp [3] R. amoto and S. Hirose, eelopment of Holonomic Omnidirectinal Vehicle Vuton-II ith Omni-iscs, Journal of Robotics and Mechatronics, 22, Vol., No.2, pp [] K. erashima, H. Kitagaa,. Miyoshi and J. Urbano, Frequency Shape ontrol of Omni-directional Wheelchair to Increase User s omfort, Proc. IEEE 2 Int. onf. on Robotics and utomation, Ne Orleans, 2, pp [5] J. Urbano, K. erashima, Skill-ssist ontrol of an Omni-directional Wheelchair by Neuro-Fuzzy Systems Using ttendant s Force Input, International Journal of IJII(International Journal of Innoatie omputing, Information & ontrol), Vol.2, No.6, ec., 26, pp [6]. rai, E. Nakano, H. Hashino and K. Yamaba, he ontrol and pplication of Omni-irectional Vehicle (OV), Proc. 8th IF World ongress, 98, pp [7] M. Wada,. akagi and S. Mori, Mobile Platform ith a ualheel aster-drie Mechanism for Holonomic and Omnidirectional Mobile Robots, Journal of Robotics Society of Japan, 2, Vol.8, No.8, pp [8] M. Wada and S. Mori, Holonomic and omnidirectional ehicle ith conentional tires, Proc. IEEE Int. onf. on Robotics and utomation, 996, pp [9] K. adakuma, R. adakuma and J. erengeres, eelopment of Holonomic Omnidirectional Vehicle ith Omni-all : Spherical Wheels, Proc. IEEE/RSJ International onference on Intelligent Robots and Systems, 27, pp [] S. Kim, H. Kim and. Moon, Local and Global Isotropy of aster Wheeled Omnidirectional Mobile Robot, Proc. IEEE International onference on Robotics and utomation, 25, pp