机械自动爬楼装置的设计.pdf

1INTRODUCTION Wheelchair is a very important mobility assistance device for some aged and physical disabled persons Traditional wheelchair has high mobility on even terrain but when facing stairs the locomotion of the wheelchair will be limited seriously which brings great discommodity to the users For the purpose of improving the ability of stair climbing of traditional wheelchair many researchers have tried to equip the wheelchair with the travel mechanism of mobile robot to build wheelchair robot To the authors knowledge there are mostly three types of travel mechanisms applied in mobile robot which are appropriate for stair climbing they are wheeled type mechanism legged type mechanism and tracked type mechanism Wheeled type mechanism applied in wheelchair robot is usually in the form of wheel cluster 1 The wheelchair robot equipped with this type of mechanism can perform stair climbing but the climbing process may be uncomfortable for passengers as the orbiting motion of the wheel cluster and the security can not be assured without appropriate assistance Legged type mechanism can bring high ability of stair climbing to wheelchair robot but the structure of the mechanism is excessively complex 2 3 Compared to these two types of mechanisms wheelchair robot equipped with tracked type mechanism has better stationarity as the large contact area with the stairs and the structure of the mechanism is compact enough 4 but when the tracked type wheelchair robot climbs to the peak of the stairs if the tracked mechanism is in the form of single section the robot will have difficult in stable transformation of posture if the tracked mechanism is in the form of multi section the This work is supported by National Nature Science Foundation under Grant 60805048 contact between the track and the top floor will not be sufficient enough To improve the terrain adaptability of common tracked wheelchair robot especially at the peak of the stairs we propose a wheelchair robot equipped with new style variable geometry tracked mechanism General variable geometry tracked mechanisms usually retain the geometry to be convex polygon during transforming on the condition that the track tension keeps invariable or varies passively 5 6 so they can not adapt to convex terrain as example of the peak of the stairs very well On the contrary this new style variable geometry tracked mechanism can adapt to convex terrain and transform to concave geometry by active control of track tension so the wheelchair robot equipped with this mechanism will have better ability of stair climbing In this paper first the new style wheelchair robot and its stair climbing procedure are introduced Then the locomotion and transformation rule for the robot during different climbing phases is presented and the dynamic models of the robot whole body and its fundamental components are established Finally the dynamic simulation for stair climbing is performed and the simulation results are analyzed 2STAIR CLIMBING PROCEDURE OF THE NEW STYLE WHEELCHAIR ROBOT 2 1 The New Style Wheelchair Robot The mechanism of this wheelchair robot consists of a supporting frame a chair fixed on the top of the supporting frame and two variable geometry tracked mechanisms installed at the flanks of the supporting frame symmetrically as shown in Fig 1 a In the variable geometry tracked mechanisms two driving wheels are driven independently to realize moving and Dynamic Analysis for Stair Climbing of a New Style Wheelchair Robot Suyang Yu1 2 Xiaofan Li 1 Ting Wang 1 Chen Yao1 1 State Key Laboratory of Robotics Shenyang Institute of Automation Chinese Academy of Science Shenyang 110016 2 Graduate School Chinese Academy of Science Beijing 100049 E mail yusuyang Abstract In this paper a wheelchair robot equipped with new style variable geometry tracked mechanism is proposed Different from general variable geometry tracked mechanisms the key feature of this new style mechanism is that it can adapt to convex terrain and transform to concave geometry by active control of track tension based on which the ability of stair climbing of traditional wheelchair is improved For obtaining the dynamic characteristic of stair climbing which is crucial to the robot design the locomotion and transformation rule for the robot during different climbing phases is presented the dynamic models of the robot whole body and its fundamental components are established Finally the dynamic simulation for stair climbing is performed and the drive characteristic of the robot under different climbing conditions is obtained The simulation results provide theoretical foundation to the future work of driving system design and mechanical parameters optimization Key Words Wheelchair Robot Variable Geometry Tracked Mechanism Dynamics Drive Characteristic 4330 978 1 4244 5182 1 10 26 00 c 2010 IEEE steering of the robot two back flippers are driven synchronously to realize mechanism transformation and two front flippers are driven synchronously to realize active control of track tension two pairs of planetary wheels are attached at the tip of the flippers some idlers and guide wheels are installed to assist the mechanism to work The robot is also equipped with an inclinometer at the chair to read the pitch angle and two torque sensors at the revolute joints of the back and front flippers to detect the torque received by these two pairs of flippers a b Fig 1 The new style wheelchair robot a Structure of the wheelchair robot b Coordinate system of the wheelchair robot For further analysis of stair climbing the coordinate system of the robot is defined as shown in Fig 1 b In the coordinate system an inertial base frame Ow XwYwZw is fixed on the ground and OwZw is selected to be vertical with the horizontal plane OwYw is selected to be parallel with the lateral direction of the stairs Two frames O xyz and O XYZ are attached to the robot and O is selected at the mid position of the two driving wheels Oz and Ox are selected to be vertical and parallel with the chair in the lateral symmetry plane of the robot respectively OX OY and OZ are selected to be parallel with OwXw OwYw and OwZw respectively According to the coordinate system some points are defined to denote the elements of the robot mechanism and in coordinate plane xOz the immovable points to the supporting frame A B C G and F can be expressed as 0 0 A A x z cos sin BAB BAB xl zl cos sin CAC CAC xl zl 12 12 sin cos GB GB xxrr zzrr cos sin GFGF FGFG xlx zzl the movable points to the supporting frame D and E can be expressed as cos sin CCDD DCCD xlx zzl sin cos EBBE EBBE xxl zzl In coordinate plane XOZ these points can be expressed correspondingly as cossin sincos Xx R Y Zz In these expressions lIJ is the distance between points I and J r1 is the radius of the guide wheels r2 is the radius of the driving wheels the front planetary wheels and the idlers is the angle between the bundle of vectors AB CB FG and the negative direction of Ox is the angle between the vector CD and the positive direction of Ox is the angle between the vector BE and the negative direction of Oz is the angle between the chair and the positive direction of OX With these definitions all the geometrical quantities in this paper can be derived 2 2 Stair climbing Procedure To simplify the analysis it is assumed that there is no yaw angle when the robot climbs stairs then the stair climbing procedure can be divided into four phases In phase 1 the robot moves to confront the stairs with the back then the back and front flippers rotate anticlockwise to definite angles to make the chair retroverted as shown in Fig 2 a In phase 2 the robot starts to climb the first several stairs When the pitch angle of the chair reaches a definite value as the robot moves on the back and front flippers rotate anticlockwise sequentially to keep the obliquity of the chair as shown in Fig 2 b c In phase 3 the robot has climbed onto the stairs completely and goes on moving on the nose line of the stairs with a fixed configuration as shown in Fig 2 d The fourth phase can be divided into two steps When the back flippers pass over the nose of the last stair the first step of phase 4 starts In this step the robot stops moving and the back flippers rotate clockwise to make the tracked mechanisms transform to concave geometry with the assistant of the front flippers until the back planetary wheels support on the top floor as shown in Fig 2 e f Then the second step of phase 4 starts the robot keeps on climbing and the back and front flippers rotate anticlockwise until the robot loads on the upper floor completely as shown in Fig 2 g h 3CONFIGURATION ANALYSIS The wheelchair robot needs to hold the chair obliquity and track tension at proper values by rotating the back and front flippers to definite angles during stair climbing It means that the rotations of the two pairs of flippers are restricted by the chair obliquity as well as the track length thus the equations of chair obliquity and track length can represent the locomotion and transformation rule for the robot during different climbing phases 3 1Configuration Analysis for Phase 1 In phase 1 the rotation of the back flippers which is restricted by the expected chair obliquity can be represented by the equation of chair obliquity in this phase as X x Y y Z z B C D E F G O A Ow Zw Xw Yw 2010 Chinese Control and Decision Conference4331 a b c d e r g h Fig 2 Stair climbing of the wheelchair robot a Transforming on the lower floor b c Climbing the first several stairs d Moving on the nose line with a fixed configuration e f Transforming to concave geometry g h Loading on the upper floor 132 0 E fZrr 1 where r3 is the radius of the back planetary wheels E Zis the coordinate of point E in coordinate plane XOZ The final form of 1 only contains the variables and The rotation of the front flippers which is restricted by the rotation of the back flippers can be represented by the equation of track length in this phase as 1122 123 1222 113 0 0 ADDF BFBEAE ADDF FGEGAE LA rLDrL FrLBrLErL LA rLDrL FrLGrLErL 2 where L is the length of the track I is the radius angle faced by the track segment surrounding wheel I LIJ is the length of the track segment between wheel I and J the detailed expressions of these intermediate variables are omitted in this paper The two expressions in 2 are corresponding to the two conditions that idlers B or guide wheels G work when the back flippers are at different rotation angles The final form of 2 only contains the variables and 3 2 Configuration Analysis for Phase 2 In phase 2 the analysis is against the condition that only the back planetary wheels support on the stairs which is more critical than other conditions in this phase as shown in Fig 2 b On this condition the equation of chair obliquity can be derived as 222 223 0 DEDE fLhXLZrhr 3 where h is the height of the stairs riser LD is the horizontal distance between the driving wheels and the supporting point In the early and late stages of phase 2 this equation can represent the variation of the chair obliquity and the rotation of the back flippers as the robot moves separately The final form of 3 only contains the variables D L and h In this phase the nominal track segments between the driving wheels and the back planetary wheels are two straight lines which are the same to those in phase 1 so the equation of track length in this phase is also 2 3 3Configuration Analysis for Phase 3 In phase 3 the equation of chair obliquity can be derived from 1 as 31 0ff 4 where is the stairs angle The final form of 4 only contains the variables and The equation of track length in this phase is still 2 as the same reason for phase 2 3 4Configuration Analysis for Phase 4 In the first step of phase 4 the robot stops moving and the back flippers rotate actively the rotation of the front flippers can be represented by the equation of track length in this step as 4122 123 4222 113 0 0 ADDF BFBEANEN ADDF FGEGANEN LA rLDrL FrLBrLErLL LA rLDrL FrLGrLErLL 5 where LIN is the length of the track segment between wheel I and the last stair nose the detailed expressions of these intermediate variables are omitted here The final form of 5 only contains the variables and In the second step of phase 4 the rotation of the back flippers can be represented by the equation of chair obliquity in this phase as 423 sincos 0 E flZlrr 6 where lis the length of the track segment still in stairs The final form of 6 only contains the variables l and In this step the nominal track segments between the driving wheels and the back planetary wheels are two fold lines which are the same to those in the first step so the equation of track length in this step is still 5 4DYNAMIC MODELING 4 1 Dynamic Modeling for Robot Whole Body The dynamic modeling of robot whole body is first against phase 2 To analyze the forces acting on the robot the robot whole body is divided into five parts the main body including the supporting frame the chair and the passenger the back flippers the back planetary wheels the front flippers and the front planetary wheels The forces 43322010 Chinese Control and Decision Conference b c a d e Fig 3 Forces acting on the robot whole body and its fundamental components a Forces acting on the robot whole body b Forces acting on the back planetary wheels c Forces acting on the back flippers d Forces acting on the front planetary wheels d Forces acting on the front flippers acting on the robot whole body are shown in Fig 3 a In Fig 3 a the point O0 O1 E O2 and D denote the mass centers of the five parts respectively FIPAX and FIPAZ are the inertial forces produced by transfer of the driving wheels FIPAn and FIPAt are the inertial forces produced by rotation of the main body FIPBn and FIPBt are the inertial forces produced by rotation of the back flippers FIPCn and FIPCt are the inertial forces produced by the front flippers GP and MIP are the gravity forces and the inertial moments where the subscript P denotes one of the points O0 O1 E O2 and D NA FA NN FN are the normal and tangential forces acting on the robot from the ground and the stairs Assuming that FA NA where denotes the coefficient of static friction the dynamic equation of robot whole body can be derived according to the D Alembert s principle as 00 222 00 0 0 TT wAwA T T ANN MXZB CGg KNNF 7 where wA X and wA Z are the transfer acceleration of the driving wheels in coordinate plane XwOZw and are angular velocity and acceleration of the chair the front flippers and the back flippers respectively M0 B0 C0 G0 and K0 are the coefficient matrices and the detailed procedures of formulation are omitted here The dynamic equations of robot whole body for the other phases of stair climbing can be derived correspondingly by giving some other assumptions of the relationship between the forces acting on the robot from the ground and the stairs and modifying K0 in 7 By substituting the state of locomotion and transformation of the robot solved out numerically from the configuration equations into these dynamic equations the forces acting on the robot from the ground and the stairs can be solved out then the driving moment of the driving wheels can be given by 2 AAN MFFr 8 4 2Dynamic Modeling for Fundamental Components To obtain the driving moments of the flippers first the dynamic models of the back planetary wheels the back flippers the front planetary wheels and the front flippers against phase 2 are established the forces acting on these four components are shown in Fig 3 b e In Fig 3 b e TE1 TE2 TD1 TD2 are the track tension around the back and front planetary wheels RE RE RD RD are the constrained forces between the planetary wheels and the flippers where 21ED TT EXEX RR EYEY RR DXDX RR DYDY RR MB and MC are the driving moments of the back and front flippers Then the dynamic equations of these four components can be derived as 11 22 11 1211 0 T wAwA T TT NNEEXEZE MXZB CGg QFNTKRRT 22 22 222 2 0 T wAwA T T EXEZ B MXZB CGgQRR KM 33 22 3331 32 0 T wAwA T D T DXDZD MXZB CGgQT KRRT 44 22 44 44 0 T wAwA T T DXDZC MXZB CGg QRRKM 9 where Mi Bi Ci Gi Qi and Ki are the coefficient matrices The dynamic equations of these fundamental components for the other phases of stair climbing can be derived correspondingly by modifying Q1 in 9 By substituting the state of locomotion and transformation of the robot obtained from the configuration equations the forces acting on the robot from the ground and the stair obtained from the dynamic equation of robot whole body and the expected track tension into the dynamic equations of components the driving moments of the back and front flippers can be acquired by solving the equations recurrently TE1 TE2 FN NN REZ FIEAt FIEBn FIEAn FIEBt REX FIEAX FIEAZ GE MIE R EX R EZ FIO1At FIO1AX FIO1AZ GO1 FIO1Bt FIO1An FIO1Bn MIO1 RBX RBZ MB TD1 FIDAZ GD TD2 RDX RDZ FIDAt FIDAn FIDAX FIDCn MID GO2 FIO2AZ FIO2AX R DX R DZ MID FIO2At FIO2An FIO2Ct FIO2Cn MC RCZ RCX NN FN FIEBtGE FIEAt FIEAX MIE FIEAZ E FIEBn FIEAn FIO1At FIO1Bt GO1 FIO1An FIO1Bn FIO1AZ FIO1AX O1 MIO1 NA GO0 FIO0AZ FIO0At FIO0AX MIO0 FIO0An O0 MIO2 FIO2Cn GO2 FIO2AZ FIO2AX FIO2At FIO2Ct FIO2An FIDCn FIDAn FIDAt FIDAX MID FIDAZ GD O2 D FA 2010 Chinese Control and Decision Conference4333 5DYNAMIC SIMULATION To perform the dynamic simulation for stair climbing the modular simulation platform in matlab simulink is established The platform is composed of four modules configuration module track tension module body dynamic module and components dynamic module The relationship between these modules is shown as Fig 4 In the simulation platform the configuration module can obtain the state of locomotion and transformation of the robot during stair climbing with the input parameters by solving the equations of chair obliquity and track length and send it to the other three modules The track tension module can calculate the optimum track tension needed for the robot accord