Construction and Kinematic Analysis of an Anthropomorphic Mobile Robot

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1 Constuction and Kinematic Analysis of an Anthopomophic Mobile Robot Scott Notman, Jack Peach, Michael Nechyba, Louis S. Bown, A. Aoyo Machine Intelligence Laboatoy Univesity of Floida Gainesville, FL FCRAR May 1-11, 21 FAMU

2 Constuction and Kinematic Analysis of an Anthopomophic Mobile Robot Scott Notman, Jack Peach, Michael Nechyba, Louis S. Bown, A. Aoyo Machine Intelligence Laboatoy Univesity of Floida Gainesville, FL Abstact This pape discusses the development, design, and initial constuction of an autonomous anthopomophic mobile obot cuently being developed at the Univesity of Floida s Machine Intelligence Laboatoy (MIL). Additionally, the fowad and invese kinematics of the five-degee of feedom manipulato ams ae solved. Figue 1 Design and Constuction The concept fo this obot evolved fom a pevious poject developed at the Univesity of Floida duing summe The pevious obot, Omnibot 2, was designed to aid the eldely and handicapped, as well as to entetain an audience and give tous of the MIL. Due to the Omnibot s success, a gant was povided by the Depatment of Electical and Compute Engineeing to design and build an impoved vesion of the platfom. This new platfom, called Pneuman, will impove Omnibot s featues, and will be capable of pefoming moe complex tasks. The initial mechanical platfom was conceived in Septembe 1999 (Figue 1). This design had 15 degees of feedom (DOF), and intended to use pneumatic cylindes and compessed ai fo a majoity of its actuatos. Thee wee 14 pneumatic cylindes and eight DC motos. Seven of the 15 degees of feedom used two pneumatic cylindes woking simultaneously to allow the DOF 18 degees of motion. This was accomplished by aanging the cylinde pais 9 degees out of phase. This allowed one of the cylindes to exet its maximum amount of foce while the othe cylinde could not exet any foce because its moment am would go to zeo at and 18 degees (Figue 2). Electonic cylinde contol modules wee developed, utilizing solenoid valves. These contol devices wee intefaced to a host pocesso implementing a PID contol algoithm. Cylinde Attachment Points Diection of Foce Exeted by Cylindes Figue 2 Axis of Rotation

Two SpaeAi tanks wee to povide pessuized ai to the pneumatic actuatos via a egulato. The tanks wee pessuized to 3 PSI and the egulato would dop the system pessue to 1 PSI.

Theefoe, DC motos ae cuently being used thoughout the entie obot. These two factos led to a thid evision of the platfom shown in Figue 4.

Figue 4 One last modification was made to the above platfom. The change includes the eplacement of the ams with moe dexteous ams that have 5 DOF and a dexteous hand.

3 Two SpaeAi tanks wee to povide pessuized ai to the pneumatic actuatos via a egulato. The tanks wee pessuized to 3 PSI and the egulato would dop the system pessue to 1 PSI. The egulated ai was sent though a seies of needle valves to adjust the flow ate. This allowed the cylindes to move at a easonable ate of speed. altenate method of actuation was sought. Theefoe, DC motos ae cuently being used thoughout the entie obot. These two factos led to a thid evision of the platfom shown in Figue 4. The initial concept design was evaluated and modified by two mechanical engineeing students duing the sping semeste of 2. Thei new design is shown in Figue 3. Figue 4 One last modification was made to the above platfom. The change includes the eplacement of the ams with moe dexteous ams that have 5 DOF and a dexteous hand. This final evision of the platfom is cuently being constucted at the MIL. A pototype of the new am is shown in Figue 5. Figue 3 This new platfom had two design flaws. Fist, the oveall mechanical stuctue was too heavy. Because the obot is autonomous, consideation should have been given to the weight of the stuctue. Unnecessay weight will limit to obot s mobility and shoten its battey life. Futhemoe, due to the significant ovehead equied to opeate and maintain the pneumatic actuation system, an Figue 5

4 5 DOF Am Oveview The two ams discussed below ae five degee-offeedom (5 DOF) seial link manipulatos. Constucted fom aluminum and plastic, the ams wee designed to pefom simila to human ams. Uppe and lowe am lengths ae popotional to that of an adult human. Explosion of kinematics equations wee kept to a minimum by aligning the axis of otation fom joint to joint. As shown above in Figue 4, the ams ae mio images of each othe and ae identical in all othe espects. Joint Configuation When designing a highe nth ode DOF seial link manipulato, one must conside the kinematics equations behind each joint placement. The am was designed so that joint axis i intesects joint axis i+1, whee i is the numbe of joints in the am. Each new link is offset fom the pevious link by 9 as shown in Figue 6. Additionally, see Table 1 fo joint chaacteistics. Joints ShouldeA, ShouldeB, and ElbowA ae coincident at the shoulde. This alignment allows fo the am to otate as if a ball and socket joint wee implemented. ElbowB and WistA joints ae also coincident. Joints ShouldeA, ShouldeB, and ElbowB ae actuated by linea actuatos. The emaining joints, ElbowA and WistA, ae actuated by otay actuatos. Figue 6 Am kinematics. The aows indicate diection of otation. The thick lines epesent the links. ShouldeA ShouldeB Joint Max Toque Max Speed Range of Motion (Nm) (pm) (degees) ShouldeA ShouldeB ElbowA ElbowB WistA Table 1: Joint Chaacteistics Kinematic Analysis of Am DH Paametes Figue 7, shown below, indicates which fames coespond to each linkage. Note that fame {} is coincident with fame {1} when θ 1 =. Y 1 X 1 {1} Z 1 X 2 {2} Z2 Figue 7 The DH paametes ae shown in Table 2 below. {3} X 3 I α I-1 a i-1 d i θ I 1 θ 1 2 π/2 θ 2 3 -π/2 d 3 θ 3 4 π/2 θ 4 5 -π/2 θ 5 Table 2 The base fame {} is positioned at the shoulde. This is the am s point of attachment to the body of Pneuman. The oigin of fame {5} is located at the wist. A dexteous hand will be attached hee in the futue. {4} X 4 Z 4 Y 2 Y 3 Z 3 Y 4 {5} Y 5 X 5 Z 5 ElbowA ElbowB WistA Fowad Kinematics The oveall fowad kinematics fo the manipulato is given by the tansfom

5 whee T = px p y p z 1 11 = c 5 [c 4 (c 1 c 2 c 3 -s 1 s 3 )-c 1 s 2 s 4 ]-(c 3 s 1 +c 1 c 2 s 3 )s 5 12 = -c 5 (c 3 s 1 +c 1 c 2 s 3 )-[c 4 (c 1 c 2 c 3 -s 1 s 3 )-c 1 s 2 s 4 ] s 5 13 = -c 1 c 4 s 2 -(c 1 c 2 c 3 -s 1 s 3 )s 4 21 = c 5 [c 4 (c 2 c 3 s 1 +c 1 s 3 )-s 1 s 2 s 4 ]-(c 2 s 1 s 3 -c 1 c 3 )s 5 22 = -c 5 (c 2 s 1 s 3 -c 1 c 3 )-[c 4 (c 2 c 3 s 1 +c 1 s 3 )-s 1 s 2 s 4 s 5 ] 23 = -c 4 s 1 s 2 -(c 2 c 3 s 1 +c 1 s 3 )s 4 31 = c 5 (c 3 c 4 s 2 +c 2 s 4 )-s 2 s 3 s 5 32 = -c 5 s 2 s 3 -(c 3 c 4 s 2 +c 2 s 4 )s 5 33 = c 2 c 4 -c 3 s 2 s 4 p x = -d 3 c 1 s 2 p y = -d 3 s 1 s 2 p z = d 3 c 2 fame {} is at the lowe potion of the image and that the wist fame {5} is at the top of the image. Note that d 3 is the distance between ShouldeB (fame {2}) and ElbowA (fame {3}). Also note that the oigin of the fame fo ElbowA is the same as the oigin of the fame fo ElbowB (fame {4}). Invese Kinematics Afte the fowad kinematics solution was detemined, the closed fom invese kinematic solution was found fo the 5 DOF am. The solutions fo the joint angles ae θ 1 = Atan2[-p y, -p x ] Figue 7: 5 DOF Mathematica Simulation Two additional simulations wee pefomed. The fist, shown in Figue 8, illustates the eachable wokspace of the manipulato am with the following joint limitations: < θ 1 < 18 < θ 2 < 18 < θ 3 < 18 < θ 4 < 18 < θ 5 < θ 2 = Atan2 [ ± p + p, p ] θ 3 = Atan2[(- 12 c 1 c s 1 c s 2 ), 12 s 1-23 c 1 ] x y z θ4 = Atan2[( 2 2 ± ( + s ) 31 c2 ( 11c1 + 21s1) s2) + ( 32c2 ( 12c1 22s1 ) 2), ( 33 c 2-12 c 1 s 2-23 s 1 s 2 )] θ 5 = Atan2[(c 3 ( 21 c 1-11 s 1 )-( 11 c 1 c s 1 c s 2 )s 3 ), (c 3 ( 22 c 1-12 s 1 )-( 12 c 1 c s 1 c s 2 )s 3 )] The 5 DOF am was also simulated in Mathematica. An image is shown in Figue 7. Note that the base -1 Figue 8: Reachable Wokspace Note that each black dot indicates a andom vecto Q fo the joint angles, whee

Q = [θ 1, θ 2, θ 3, θ 4, θ 5 ] T The final simulation in Figue 9 epesents the possible oientations of the manipulato. -1 1 -.5.5 1.5 -.5-1 -1 -.5.5 1 Figue 9: Possible Oientations Again, each black dot indicates a andom vecto Q fo the joint angles.

6 Q = [θ 1, θ 2, θ 3, θ 4, θ 5 ] T The final simulation in Figue 9 epesents the possible oientations of the manipulato Figue 9: Possible Oientations Again, each black dot indicates a andom vecto Q fo the joint angles. Actuatos Afte weighing the pos and cons of a numbe of actuato schemes, it was found that DC motos would povide the needed toque with the least complexity. Howeve, DC motos pesent poblems when implemented in obotic systems. These complex systems ely on pecision and epeatability. DC motos poduce backlash, which thows off pecision and theeby epeatability. To help emedy this poblem a evolute seies elastic actuato (SEA) has been devised (Figue 1). The evolute SEA will educe backlash and will povide foce feedback at the joint. The SEA also pomotes obustness and compliance thoughout the am. Figue 7 depicts a basic epesentation of a SEA. A sping is placed inline with the tansmission shaft to educe unwanted backlash and poblems that may aise due to a sudden impact of a link with an object. Two bands of suplus motos wee puchased; one having a stall toque of 32 oz.-in. and the othe 2 Figue 1: Seies elastic actuato (SEA) oz.-in. Although these motos would suffice, gea eduction at specified joints was imminent. Two joints that did not equie any gea eduction othe than that of the geabox wee ElbowA and WistA. Diectly diven, these two joints poved moe than the equied ange of motion and max speed. Table 3 descibes the chaacteistics of the DC motos. Joint Voltage Stall Toque Max Speed (volts) oz in (pm) ShouldeA ShouldeB ElbowA ElbowB WistA Table 3: DC moto chaacteistics. Rotay Actuato One of the poblems encounteed when designing the otation aspects of the uppe am was to align the ShouldeB joint pependicula with the ElbowB axis. A pulley dive system was implemented to ovecome this poblem. The advantage of a pulley dive system is its compactness compaed to the linea actuato. In a pulley dive system thee is no need fo a leve am o a lead scew. Anothe advantage ove the lead scew is that it inceases the available pm at the joint it actuates. The SEA s axis of otation is coincident with that of the joint s axis. Below in Figue 11 the moto pulley is igidly attached to the moto shaft. The cable is wapped aound the moto pulley and patly aound the joint pulley. Both ends of the cable ae teminated on the joint pulley. One is static while the opposite end is attached to a cable-tensioning device. The cable-

tensioning device is necessay to keep the cable taut at all times.

Both ends of the sping ae igidly attached the individual FSR sufaces. Note that the moto shaft will not be attached diectly to A.

Figue 11: Rotay actuato dive system Sensos Joint Angles Infomation egading joint angle position will be obtained by potentiometes.

7 tensioning device is necessay to keep the cable taut at all times. An intelligent tensioning device such as an inline memoy-shape alloy extension sping may be implemented in a late vesion of the otay actuato. Both ends of the sping ae igidly attached the individual FSR sufaces. Note that the moto shaft will not be attached diectly to A. A pulley system will inteface between A and the moto shaft theeby inceasing output toque. Figue 11: Rotay actuato dive system Sensos Joint Angles Infomation egading joint angle position will be obtained by potentiometes. The sensos will be aligned with the axes of otation fo all of the joints, poviding an analog voltage popotional to the joint angle. Foce Feedback Mechanism Robot manipulato ams ae pecise when it comes to movement, yet ae poo at sensing applied foce. When a manipulato am is exposed to an object eithe intentionally o unintentionally, it has no way of sensing the applied foce unless equipped with a foce senso. Foce sensos ae used to egulate am motion, but may also be used to deal with contact foces. In ode to ovecome this shotfall in ou obot ams, foce-sensing esistos (FSR) have been imbedded within the otay SEA to povide sufficient foce feedback. The static mechanics in Figue 12 ae as follows: The moto is igidly attached to link A. A is igidly attached to the moto shaft. B is igidly attached to link B. Two FSR ae igidly attached to opposite sides of the inne wall of B. Figue 12: Seies elastic actuato (SEA) with moto Now, a dynamic desciption of Figue 13: Zeo-foce opeation: o When the moto otates, A and B ae coincident and will otate togethe. Foce-sensing opeation: o When the moto otates, A will otate yet esisting foce on link B will not allow B to otate. Theefoe, the sping will compess. o When the sping compesses, the FSR senses a change in foce applied. This change in applied foce is linealy elated to the change in otation between A and B. Figue 13: SEA Dynamics

Softwae and Electonics The electonics system of Pneuman may be boken down into blocks. The main pocesso is a ZF Linux 486 PC/14 embedded compute. It is unning the Red Hat Linux 5.2 opeating system.

8 Softwae and Electonics The electonics system of Pneuman may be boken down into blocks. The main pocesso is a ZF Linux 486 PC/14 embedded compute. It is unning the Red Hat Linux 5.2 opeating system. This compute intefaces to six PC/14 cads. Thee of the PC/14 cads geneate the pulse width modulation (PWM) signals, moto diection signals, and have analog to digital inputs fo all of the motos on Pneuman. The fouth cad contains fou National Semiconducto LM629 PID motion contolle IC s. This cad contols the dive motos that use an optical encode fo feedback. The fifth cad is an RC Systems VX86 voice synthesize cad. This cad allows Pneuman to talk. The final PC/14 cad is a PCMCIA to PC/14 bus adapto cad that allows the use of a wieless netwoking cad. The PC/14 PWM cads wee custom designed fo Pneuman (Figue 14). The boads have thee main systems, including PWM components, digital input/output (IO) components, and an analog to digital convete. The goal fo the boads is to povide a complete PID contolle fo each moto implemented in softwae. This will be possible by using the analog inputs fo angle position sensos, and contolling the motos via a moto dive boad with PWM and diection signals. Figue 14: PWM Boad The fist system is esponsible fo geneating PWM using thee standad 8254 pogammable times. Each time chip contains thee individual times, fo a total of nine times on each PC/14 boad. Each time has a count egiste associated with it. Depending on the mode of opeation, when the count egiste counts down to zeo, an event may occu. One of the times is set to opeate as a ealtime inteupt (RTI) poviding a signal that coesponds to the peiod of the PWM signals. Note that all eight of the PWM signals geneated must have the same peiod. This RTI signal is connected to the tigge inputs of all the othe times. Futhemoe, all of the othe times (eight) ae opeating in one-shot mode. This means that once the tigge is asseted, the outputs of these times ae asseted until thei count egistes have eached zeo, theeby de-asseting the output. Additionally, the values in the count egistes ae loaded with diffeent values via the PC/14 bus, theeby changing the time that the outputs ae high. Thus, this may be used in combination with the RTI as mentioned above fo hadwae PWM. The next system povides eight digital IO s fo the diection of each moto, eight outputs to contol the A to D, and eight inputs to ead the A to D values. This system uses a standad 8255 PPI IC. The final component of the boad uses an Analog Devices ADC88 IC. This paticula IC povides eight input channels as well as eight bits of esolution fo each channel. The PC/14 LM629 PID moto contolle boad was also custom designed fo Pneuman (Figue 15). The boads have fou contolle IC s. The 486 compute intefaces to these IC s via the PC/14 bus. They ae dedicated motion contol pocessos that use a quadatue incemental position feedback signal. Optical encodes mounted diectly to each dive wheel povide these signals. Thee ae fou eight-bit PWM outputs fo diectly diving an H- bidge moto dive. Each IC may opeate in position o velocity mode. Position mode will be useful fo doing navigation though dead eckoning.

9 Velocity mode will insue that the wheels ae all opeating at the same speed. contol of the platfom. The debug module povides a sceen image of all the data gatheed by the system and allows an oveide of any contol paametes. Pocess Manage Comm Image Poc Move Contol Data Analysis Debug Shaed Memoy Figue 16: Softwae Achitectue Softwae Subsystem Figue 15: PID PC/14 Boad The code on the embedded 486 compute is being developed in the C pogamming language fo the Linux 5.2 opeating system. The code consists of six modules, all of which ae individual pocesses (Figue 16). The main executable is a pocess manage that initializes memoy space fo the othe pocesses and executes the equested modules. The communication module is necessay fo contol of the seial pots. The esults fom the pocesses ae then sent to the othe modules via a shaed memoy space. The movement contol module keeps pecise ecods of the cuent states of all the actuatos. This data is used to detemine what contol is necessay to move to a desied position. The data analysis module will contain the pimay functions fo all of the data pocessing. This module enables autonomous contol of the entie system. All the othe modules contain the data input and output functions, poviding the data analysis module with all the necessay paametes. A debug module is included in the design, enabling human intevention into the Conclusion Building Pneuman has povided the MIL with an excellent oppotunity to design and constuct a physical platfom. Afte Pneuman is finished, this student built platfom will be a pat of the MIL and will foste othe students eseach. It will povide tous of the labs fo pospective engineeing students. Because this platfom is available to othe students, they can implement thei new ideas with ease and see them in thei final fom. Although simulations ae useful fo detemining the feasibility of a concept, the constuction of a pototype povides moe infomation and expeience with obotics. This, along with the gatification of seeing student ideas become implemented in a physical obot make Pneuman an excellent leaning tool. This is evident fom the wok pesented, and will be obvious when the platfom is finished.

10 Refeences [1] Caig, J. J., Intoduction to Robotics: Mechanics and Contol, 2 nd ed., Addison- Wesley, Reading, MA [2] Notman, Scott, A. Aoyo, E. Schwatz, Omnibot 2: Development of an Autonomous Mobile Agent fo the Disabled and Eldely, Floida Confeence on Recent Advances in Robotics, Dania, Floida, 2. [3] Notman, Scott, S. M. Kanowitz, A. Aoyo, E. Schwatz, Development Of An Anthopomophic Mobile Agent, Floida Confeence on Recent Advances in Robotics, Dania, Floida, 2. [4] Williamson, M. M., Seies Elastic Actuatos, Maste s Thesis, Massachusetts Institute of Technology Atificial Intelligence Lab, Cambidge, MA, 1995.

Sliding Mode Control for Half-Wave Zero Current Switching Quasi-Resonant Buck Converter

Sliding Mode Control for Half-Wave Zero Current Switching Quasi-Resonant Buck Converter Sliding Mode Contol fo Half-Wave Zeo Cuent Switching Quasi-Resonant Buck Convete M. Ahmed, Student membe, IEEE, M. Kuisma, P. Silventoinen Abstact This pape focuses on the pactical implementation of sliding