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Description of motion of a mobile robot...

Ali generalized velocities can be noted on the basis of eąuation (2.2) as qi =    xa    = ^ (di + ^2) cos (3 =    ~{e\ +    Ć2)cos/?    = Cne 1    + C21Ć2    + G\

92    =    VA    = ^(di + 0-2) sin/? =    ^(ei +    e₂) sin/? =    C^ei + C22Ż2 +    G₂

93    = P = 7^-(di - 0:2) = rj-(ći - e.2) = Ci3ei + C23Ć2 + G3    (2.6)

ZL\    Zl\

94    =    di    = ei = C14Ć1 + C24Ć2    + G4

95    =    d2    = e.2 = Cisei + C25Ć2    + G5

That means that the coefficients Cij and Gj assume the following values

C21 ^:

Cu = - cos/? r

c 12 = - sin/J

^{Ca =} ih

014 = 1 C15 = O - cos /?

C₂₂ = - sin /5

^{023 =}

C24 = O C25 = 1

Gi =0

G₂ = 0

G₃= o (2-7) G4 = O

g₅ = 0

The generalized forces, defined out of eąuation (2.3) and the coefficients defined by formula (2.7),finally yield

@1 = CnQl + CuQ2 + Gi3<53 + Gi4<54 + Cis^s = Ml — Nifi

(2.8)

02 = C₂lQl + C22Q2 + C23Q3 + C2aQa + ^25^5 = M2 — N₂f₂

In the analysed case, Maggie’s eąuations have the following form

(2mi+m₄)(0 (di+d₂) + 2m₄(^-) rl₂(d₂ - di)d₂ + J*idi +

+(2mi/i + 7714/2 + 2/a;i +    — d2) = Mi — N\f\

ZL\

(2mi+m₄)(0 (di+d₂) + 2ra₄(^-) W₂(di - d₂)di + /₂₂d₂ +

— (2ui\li + TUąI^ + 2/_xi + ^4) 77T^- (dl — d2) = M2 — /V₂/2 ZL\

It should be mentioned that if relationships (2.5) are introduced into eąuations (1.5), and d = (di+d2)/2 is taken into account, then elimination of the