3-Wheel Swerve Drive - The Trouble with Tribots

Transcription

1 3-Wheel Swerve Drve - The Trouble wth Trbots Clem McKown - FRC Team August-2014 Executve Summary FRC's 2013 change n robot permeter rules (to 112 nch maxmum overall permeter from the earler maxmum 28 n x 32 n) opened new opportuntes for non-rectangular robots. In partcular, the new rules reduce the stablty penalty for a 3-wheeled robot desgn vs-à-vs the precedng rules because t allows an expanded wheelbase for a 3-sded chasss. The prmary expected beneft of a 3-wheeled swerve robot over a 4-wheeled s that t enables the use of two CIM motors per swerve module to yeld a drve-tran wth 6 CIM motors overall. 6 drve CIM motors have become the standard for hgh-performance tank drve robots wthn FRC. A 3-wheeled, 6-CIM swerve robot not only comples wth FRC's 2013 & 2014 motor lmts, but the mass reducton realzed by elmnatng one swerve module allows for the addton of CIM motors wthout excessvely compromsng other robot systems. Of course, there are expected to be drawbacks to a trangular, 3-swerve chasss as well as benefts. The team ntends to buld and test a prototype chasss to gan a better understandng of both the benefts and defcts of the concept. The purpose of ths paper s to defne the mathematcs for controllng a 3-swerve robot, both under chasss-centrc and feld-centrc control. Chasss Bass The proposed chasss desgn has three swerve modules arranged at the apexes of an equlateral trangle. The pvot axes are located 2.700" from the exteror surface of the chasss frame, a dstance whch allows safe rotaton of the pvot (1640's 2013 & 2014 desgn) wthout nterferng wth bumpers, etc. The chasss frame's apexes are truncated to flats also 2.700" from the pvot axs. The desgned total permeter s 111 n, provdng the same 1 n safety margn that 1640 used n ther 2013 & 2014 chasss. All swerve modules are mounted so that the calbraton 0 faces drectly away from chasss center-pont.

2 A dmensoned schematc of such a chasss s provded n Fgure 1. Conventons In ths document, lengths wll be expressed n nches (n or ") and angles n degrees ( ). Longtudnal precson wll be 0.001" unless stated otherwse. Rght-hand rule s used n all llustratons for determnng postve angle drecton. The mathematcs wll work equally well under left-hand rule, but ths must be appled unversally. Ths ncludes pvot numberng (1, 2, 3). If left-hand rule s used, then 2 & 3 swap postons. Swerve angles wll be based on sngle-drecton drve wth each module's drve drecton beng the swerve angle drecton (therefore drvng at 0 when the swerve angle s 0 ). Prototype modules also utlze the same angle sensors, and these are mounted n the same manner. A Trbot prototype chasss was desgned and bult usng 3/4" thck laser-cut plywood. An 8-slot crio was employed due to ready avalablty. Jaguar motor controllers were elected for the same reason. The desgn called for 2013 swerve modules, but 2012 modules were actually nstalled, agan due to ready avalablty. The 2012, 2013 & 2014 swerve modules share dentcal mountng bolt hole patterns (the 2012 havng an addtonal, unused mountng hole) and dentcal relatons between these mountng holes and the pvot, CIM and steerng axes, so crtcal geometry s unaffected. The 2012, 2013 & 2014 swerve The Trbot prototype mantans the same swerve module spacng and orentatons as provded n the Fgure 1 schematc on Page 1. Human Interface The Drver uses a wred Xbox controller havng dual, thumbdrven joystcks.

3 The prmary joystck controls the robot's movement n Crab Mode. In Crab Mode, both x and y nformaton s used wth the joystck's angle provdng drectonal settngs and the joystck's dsplacement from neutral provdng speed settngs. The secondary joystck works wth the prmary to provde the turnng capabltes of Snake and Ocelot Modes. Only the x nformaton s used from the secondary joystck and ths ndrectly sets turnng radus. Chasss-centrc versus Feld-centrc control Chasss-centrc and feld-centrc refer to two dfferent drectonal references for the drver and the control logc. Team 1640 has htherto always used chasss-centrc control n whch a specfc axs of the chasss s determned to be "straght ahead". Joystck controls then operate on ths reference. Ths s easer to execute from an nstrument and software bass, as t does not requre the robot to "know" whch way t s facng relatve to the feld axes. On the other hand, t requred the drver to know whch way the robot s facng relatve to feld axs and to put her/hs mnd nto ths orentaton whle drvng. Ths ncreases the drver's mental burden. Feld-centrc control would allow the drver to move the robot around the feld usng the prmary joystck whle controllng the chasss orentaton relatve to the feld wth the secondary. The drver's reference space becomes the statonary feld, reducng (we thnk) drver's mental burden. From a robot standpont, lfe gets harder, as the robot now needs to "know" ts orentaton relatve to the feld. Gyroscopes are the way to know ths and only one axs s needed. Issue s that the gyroscope must reman stable for the match duraton (wth all ts hard knocks) to be effectve. Other than the change n reference, Crab Mode remans the same n chasss and feld-centrc control. The same s not true for Snake and Ocelot, as these undergo a reversal. In chassscentrc control, Snake Mode s statc whereas Ocelot requres dynamc drver nput. These relatonshps flp n feld-centrc control. Chasss-centrc control wll be derved frst; Feld centrc follows because t apples an addtonal level of calculaton and control to Chasss-centrc logc. Chasss Geometry Remanng consstent wth both Fgure 1 on Page 1, the actual prototype, and (as far as possble) prevous whte papers by ths author, three swerve modules are arranged around a chasss center-pont wth a unform dstance h between the chasss

4 center-pont and the pvot axes and an angle = 120 (2/3R) between each pvot axs around the chasss center-pont. Swerve modules are mounted so that each module's 0 calbraton axs faces drectly away from the chasss center-pont. Swerve modules are dentfed by numbers 1, 2 & 3 followng rght-hand rule. The lne from the chasss center-pont to the pvot axs of swerve module 1 defnes the 0 chasss axs. Note that based on Fgure 1, h = n. Chasss-Centrc Crab Mode In Crab Mode, the prmary joystck apples a Vector of Moton to the chasss descrbed n the prevous secton. Ths Vector of Moton provdes both angular drecton () and power/speed (V) nformaton. may be For Crab Mode, all swerves would be algned wth. For ndvdual swerve angles ( C ): C1 = eq. 1 C2 = eq. 2 C3 = eq. 3 All calculated swerve angles must be checked and f <0, add 360 to make >0. However, the rght tme to make ths correcton (and the opposte: f >360, subtract 360 to make <360 ) s after assessng all drve calculatons, ncludng Snake Mode. Drve power (V) s proportonal to the prmary joystck's dsplacement from neutral. In Crab Mode, all drves receve equal power. Chasss-Centrc Snake Mode Snake Mode drves the chasss n an arc wth chasss orentaton followng the path of the arc. The basc chasss orentaton and speed are based upon the Crab Mode prmary joystck nputs, whle the arc radus s ndrectly set va the secondary joystck x nput.

5 In the 2009 swerve whte papers, I ntroduced the concept of a "reference wheel", a useful tool for workng through the mathematcs around Snake Mode. The "reference wheel" concept wll be employed agan here. The "reference wheel" s not a real wheel, but a hypothetcal pvot wheel located at a dstance h from the chasss center-pont and orented along the vector of moton. The dagram at left shows a "reference wheel" and the real pvot wheels on a chasss. The secondary joystck steers by steerng the reference wheel drectly, creatng an angle,, between the vector of moton and the reference wheel's drve drecton. It can be easly shown that the trangle formed by the reference wheel, the chasss CP and the Turn CP s a rght trangle and has the angle at the Turn CP apex, whch allows calculaton of the Turn Radus, R CP. R CP h eq. 4 tan Equaton 4 blows up (dvson by zero) f = 0 (neutral joystck poston). So don't do Snake Mode calculatons f the secondary joystck s neutral. We need to now defne. (no subscrpt) has already been defned as the angular offset between the chasss axs and the vector of moton. s the angular offset from the vector of moton to each ndvdual pvot axs ( = 1, 2, 3). For calculaton: 1 = - eq. 5 2 = eq. 6 3 = eq. 7

6 Turn raduses for all swerve wheels may now be calculated: R sn h cos RCP hsn h 1 2 eq. 8 2 tan tan 1 and drve power factors for each wheel: R V V (Note h s n numerator & denomnator and dvdes out) eq. 9 R max A choce s now needed. What wll be the range of? In the frst "Pvot-Wheel Drve" whte paper of 2-August-2009, a lmted (chasss algned wth vector of moton) snake mode was presented wth a range from -90 to +90. At the lmts of the range, the turn radus s zero and the turn center-pont and chasss center-pont are the same. Swerve angle calculatons were complcated by the need to swtch calculatons based on whether the turn center-pont s nsde or outsde the wheel-base. In "Pvot-Wheel Drve - Crab wth a Twst" whte paper of 29-March-2010, a general (random algnment between the chasss and vector of moton) snake mode (referred to as Twst 1 n the paper) was presented, but where 's range s lmted to -45 to 45. By lmtng the range of, the turn center-pont never comes nsde of the h-radus crcle around the chasss center-pont; the equatons are thereby smplfed. The control logc for DEWBOTs IX & X both follow the mathematcs presented n ths latter paper, ncludng the lmted range. The math for both cases wll be presented here. For the case that: [sgn of ] R CP /h [sgn of ] sn (Turn center-pont s not nsde wheelbase - always true for ) 1 hcos 1 cos sgnof sn sgn of sn eq. 10 R 1 sn tan tan For the case that: [sgn of ] R CP /h < [sgn of ] sn (Turn center-pont s nsde wheelbase) 1 hcos 1 cos 180 tan 180 tan eq. 11 RCP hsn 1 sn 1 2 sn 2 tan tan

7 Note that h s now out of the equatons., and V were not dependent on h. Fnally, to calculate the actual steerng set-ponts: = C + (add or subtract 360 as needed for range) eq. 12 A workng Mcrosoft Excel model of snake mode control logc was developed. Chasss-centrc Ocelot Mode Presently, ocelot mode requres that the drver dynamcally rotate the vector of moton (usng the prmary joystck) to mantan a steady course whle snake steerng. Ths should work wth the control equatons presented here, although care needs to be taken to keep the turn center-pont away from the chasss center-pont. Otherwse the robot wll spn n a statonary locaton. I understand that the current ocelot drve (4-wheel) bascally rolls along the h radus crcle whch passes through the pvot axes. Feld-centrc Control Feld-centrc control requres that the robot be able to sense the drecton of the feld axs relatve to chasss orentaton (). Typcally ths requres a gyroscope (deally at the chasss center-pont) although other optons exst. Ths sensng need be only one axs. If usng a gyroscope, concerns are: 1. Stablty of the gyroscope over the match duraton 2. Intalzng and calbratng the control system to the feld axs at match start. We need to understand what chasss orentaton behavor we want n feld-centrc control. We know from chasss-centrc experence that the orentaton relatve to the feld changes as we drve. We could accept ths; usng the gyroscope to control speed and drecton relatve to the feld but allow orentaton to drft as we drve and then control t usng the secondary joystck only as and when needed, or we could use the gyroscope data to control chasss Trbot Snake Drve orentaton unless the secondary joystck s 1.0 used to change t. 0.9 Feld-centrc Crab Mode There needs to be an addtonal pece of nformaton: ( ), the angular dsplacement of the feld axs from the chasss axs (0-360 ). Motor power factor V1 V2 V Reference steerng angle

8 The joystck steerng drecton, ( ), s now relatve to the feld axs, not the chasss axs. For crab mode, swerve set-ponts can be calculated: C1 = + eq. 13 C2 = eq. 14 C3 = eq. 15 As wth chasss-centrc crab mode, these values need to be checked and adjusted to range. All drve motors are drven at the same power on crab mode based on prmary joystck dsplacement from neutral. Feld-Centrc Chasss Orentaton The acton of the secondary joystck s fundamentally dfferent n feld-centrc control than t s n chasss-centrc. In chasss-centrc control, ths nput drves the robot n snake turns. In feldcentrc, the secondary joystck rotates the chasss to change chasss orentaton whle drvng n crab mode. Ths s an ocelot twst and ths drve mode s automatc n feld-centrc control. In chasss-centrc, ocelot twst drvng requres dynamc drver control. In feld-centrc control, t s snake turnng whch requres dynamc drver control. They are flpped. The whte paper "Pvot-Wheel Drve - Crab wth a Twst" of 29-March-2010 dealt wth ocelot mode (referred to as Twst 2 n the paper), but not effectvely. A dfferent approach s used here. Actually, an ocelot twst s handled just lke a snake turn, but wth a crtcal dfference: In a snake turn, for a gven joystck nput, the angle between the vector of moton and the chasss axs remans fxed and the vector of moton rotates about a turn center-pont. Swerve set-ponts durng a snake turn are statc - they are determned by the joystck nput only and do not change untl the joystck nput changes. An ocelot twst, for a gven joystck nput, mantans a constant vector of moton relatve to the feld axs. Whle the turn logc and mathematcs are the same as snake, an actual turn s prevented by contnually adjustng wheel drectons to keep the robot's course constant. Ths s a dynamc steerng system.

9 As wth snake turnng, a "reference wheel" s used for steerng. The steerng angle ( ) range for ths wheel should defntely be constraned to ±45. s determned drectly by the secondary joystck x nput (just as n snake) and determnes (for a fxed speed nput) the rotatonal speed of the ocelot twst. Note that ocelot twstng wll slow the robot's overall velocty and ths effect ncreases as devates from 0. Varables & calculatons: was defned n the Feld-Centrc Crab Mode secton as the angle between the chasss axs and the feld axs. Ths s provded n real tme va on-board nstrumentaton. It s dynamc. was defned n the Feld-Centrc Crab Mode secton as the steerng drecton relatve to the feld axs. Ths s provded from the prmary joystck. Statc (as long as joystck nput not changed). C1, C2 and C3 have been defned n equatons 13, 14 & 15 n the Feld-Centrc Crab Mode secton. These are the swerve angle set-ponts for Feld-Centrc Crab Mode. Dynamc. R CP (n) s calculated usng equaton 4 n the Chasss-Centrc Snake Mode secton. Even though we're not actually turnng, we run the math as f we are. Statc (as long as joystck nput not changed). (defned n the Chasss-Centrc Snake Mode secton) remans the angular offset between the vector of moton and each ndvdual pvot axs ( = 1, 2, 3). Dynamc. The calculaton of these values changes under feld-centrc control:

10 1 = - - eq = eq = eq. 18 R (n) are the ndvdual wheel dstances from the "turn center-pont" ( = 1, 2, 3) and are calculated usng equaton 8. Dynamc. V are the ndvdual wheel power factors ( = 1, 2, 3) and may be calculated usng equaton 9. Dynamc. ( ) are the ndvdual swerve angle "correctons" (from the base C 's) needed to affect the ocelot twst ( = 1, 2, 3). Calculated from equaton 10 and are not condtonal as long as Dynamc. ( ) are the swerve angle set-ponts ( = 1, 2, 3). Calculated usng equaton 12. Dynamc. So almost all of the mathematcs are recycled from snake mode. A robust Mcrosoft Excel model of feld-centrc ocelot mode control logc was developed, but t's a lttle heavy to paste n a Mcrosoft Word document. An observaton s warranted, though. The plots of versus and V versus are very characterstc and regular for a gven. Examples below. There may be an opportunty to reduce some calculaton burden wth look-up tables. Somethng to keep n mnd. versus Power vs Power 0.60 V1 V2 V More on the above two charts The above charts provde an ndcaton that 's could be stored n a look-up table as a functon of and. Ths n fact seems to be the case.

11 The next set of charts (top of the followng page) examnes the affect of negatng on and V. If there s a smple relatonshp between negated 's (a reasonable expectaton), then the lookup tables could be cut to half the sze (for the same performance). When s negated, the affect on both and V s a phase shft n of 180. So, a look-up table havng only postve (or only negatve) 's can be used to cover the entre turnng range, but for negatve 's, the look-up would need to be shfted by 180 (and checked for range). Lookng at postve 's only n the range from 5 to 45 usng 5 ncrements of and 3 steps of, and V were calculated and shown below. These fgures are not dependent upon h. The tables of calculated values of and V are provded at the end of ths paper. A Fnal Twst n our Story The fnal twst s a statonary twst around the chasss center-pont. Swerve angles would all be 90 or 270, dependng upon the drecton of the twst. We do ths now (DEWBOT X). We ll need to do t wth a 3-swerve robot as well. Ths s referred to as Twst 3 n "Pvot-Wheel Drve - Crab wth a Twst" of 29-March-2010.

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