Control of Mobile Robots

Transcription

1 Conto of Mobie obots efeences: -. Siegwat and I.. Noubakhsh, Intoduction to Autonomous Mobie obots, MIT, 004 (Chaps.,3. - S. G. Tzafestas, Intoduction to Mobie obot Conto, Esevie,

2 Tpes of Mobie obots Aeia Mobie obots Undewate Mobie obots Gound Mobie obots Indoo Outdoo Legged Mobie obots Wheeed Mobie obots

3 Vaious Appications 3

4 Whee Configuations fo oing Vehices 4

5 Whee Tpes 5

6 Mobie obot efeence Fames (Coodinates obot position in goba efeence fame: x ξ I The otation matix maps the veocit fom the goba efeence fame to the oca efeence fame: ξ ( ξ I cos sin 0 ( sin cos To map the veocit fom oca efeence fame to the goba efeence fame: ξ I 1 ( ξ 1 T ( ( This definition in invese of the otation matix defined in Spong s book. x 6

7 Kinematic Mode of a Diffeentia-Dive obot Computing the veocities in oca efeence fame: Veocit of cente point P if the whee anges ae denoted b 1 and : otation of obot due to whee ange 1 is 1 /, then: 1 1 v v v X P 0 Y 7 Veocit vecto in oca efeence fame: Veocit in goba efeence fame: ω ξ 0 P v x ω ξ ξ sin cos ( 1 P P I v v P 1 1 ω ω ω

8 Whee Kinematic Constaints Two tpes of kinematic constaints on whee motions: oing contact in appopiate diection (no sippage. No atea sippage (the whee must not side othogona to the whee pane Sevea tpes of whees incuding fixed and steeed standad whees have some kinematic constaints on thei motions. Spheica o omnidiectiona whees do not put an kinematic constaints on the movements of the obot. 8

9 Constaints of a Fixed Standad Whee The position of the whee in oca efeence fame ae given b and α. The ange of whee ( is fixed. The veocit in the diection shown b vecto v must be equa to: [ ] γ γ x cos sin cos 9 The veocit pependicua to the whee must be zeo: γ γ [ ] α α x cos cos( sin( [ ] 0 sin cos sin x γ γ [ ] 0 sin sin( cos( x α α

10 Constaints of a Steeed Standad Whee The on diffeence with espect to the constant whee is the vaiabiit of the steeing ange of whee ((t. The constaints ae the same: x [ sin( α cos( α cos ] x [ cos( α sin( α sin] 0 One ma aso epace: ξ ( ξ I Note: d/dt does not have a diect impact on the instantaneous motion constaints of a obot. It is on b integating ove time that changes in steeing ange can affect the mobiit of a vehice. 10

11 obot Motion Kinematic Constaints When the combination of the whees of a obot esticts some movements of the obot, the obot ma not be abe to each a desied postue (position and oientation in its wokspace diect, but it might need to have some maneuves to each that postue. In this case, the obot is caed non-hoonomic. Fo exampe: Paking a ca can be done b side side, it needs to have a specia maneuve! Diffeentiabe Degees of Feedom (DDOF: The numbe of dimensions in the veocit space of a obot is the numbe of independent achievabe veocities. A obot is hoonomic if and on if DDOFDOF. Nonhoonom ma aso occu when the numbe of actuatos is ess than the degees of feedom, e.g., a diffeentia dive has actuatos, but 3 DOF. The hoonom of a obot can be detemined fom the oing and siding constaints of its whees. 11

12 Hoonomic and Nonhoonomic Constaints If the constaints obtained fo the obot motion can be expessed as: F( ξ, t 0 the constaints ae caed hoonomic. If thee exist some constaints in the fom of: f( ξ, ξ, t 0 the constaints ae hoonomic, if the can be integated to the above fom. Fo a unicce, the siding constaint is nonhoonomic: [ cos( α sin( α sin] ( ξ 0 I whie the oing constaint is hoonomic: [ sin( α cos( α cos] ( ξ I 1