Page - 120 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

purebackor front steeringcanberealizeddependenton thepositionofPICC. Thevirtualcoordinate system [xV,yV] isused to shift thezero positionand theprivileged direction. FRONT POyO xO θ3v3 y3 x3 P3|O θ2 v2 y2 x2 P2|O θ4 v4 y4 x4 P4|O θ1 v1 y1 x1 P1|O PV xV yV θFD rh vV PICC|V Figure3: Exemplarykinematicconfigurationwith four independently steerablewheels. θFD=atan2(PICC,x+PV,x,−PICC,y−PV,y) (1) Pα=(PICC,x+P1,x) 2+(PICC,y+P1,y) 2 (2) Pn,a=(PICC,x+PV,x) ·Pn,y−(PICC,y+PV,y) ·Pn,x (3a) Pn,b=(PICC,x+PV,x) ·Pn,x+(PICC,y+PV,y) ·Pn,y−Pα (3b) θn=atan2(Pn,a,Pn,b)+θFD , (3c) With θFD as the forward direction,PICC as the instantaneous center of curvature,Pv as the origin of the virtual coordinate system,Pn as the position of the wheel in the kinematic configuration, and Pα,Pn,a,Pn,b as auxiliary variables. The speed of the single wheels can be calculated based on the distanceof theoriginof thewheelsPn toPICCwith (4a)-(4c). rn= |PICC−Pn| (4a) rmax=max(rn) (4b) vn=vm · rn rmax (4c) withvn as the speedof thenthwheel andvm as the intended maximumspeedof the fastestwheel. 120