Backing up a Truck Adriano Cruz ©2005 NCE/UFRJ e IM/UFRJ

Truck Adriano Cruz NCE and IM - UFRJ Problem Description Docking point (x f, y f )   x,y 0 <= x,y <= <=  <= <=  <= 30 rear front

Truck Adriano Cruz NCE and IM - UFRJ Problem Description n Three state variables: n  : angle of the truck with the horizontal n (x,y): position of the rear centre of the truck. n Only backing up n Truck moves backward a fixed distance at every stage. n Parking lot: plane [0,100]x[0,100]

Truck Adriano Cruz NCE and IM - UFRJ Goal n The goal is to make the truck arrive at the loading dock at a right angle (  f =90 0 ) and to align the position (x,y) of the truck with the desired loading dock (x f,y f )

Truck Adriano Cruz NCE and IM - UFRJ Inputs and Outputs n Input variables – 0 <= x <= 100 – -90 <=  <= 270 –It is assumed enough clearance between the truck and the loading dock so y can be ignored. n Output variable – -30 <=  <= 30 – steering-angle –Positive values represent clockwise rotations of the steering wheel.

Truck Adriano Cruz NCE and IM - UFRJ Movement Equations n If the truck moved backward from (x,y) to (x’,y’) then x’ = x + r cos(  ’) y’ = y + r sen(  ’)  ’=  +  n r is the fixed driving distance of the truck for all movements.   x,y

Truck Adriano Cruz NCE and IM - UFRJ Fuzzy Rules  X  RB R Below LE Left NB Neg Big RU R Upper LC L Center NM Neg Med RV Right Vert CE Center NS N Small VE Vertical RC R Center ZE Zero LV Left Vert RI Right PS P Small LU L Upper PM Pos Med LB L Below PB Pos Big

Truck Adriano Cruz NCE and IM - UFRJ Membership functions - Inputs    x  x  LELCCERIRC    RBRUVELBLURVLV 

Truck Adriano Cruz NCE and IM - UFRJ Membership functions - Outputs    NSZEPBPS  NBPM

Truck Adriano Cruz NCE and IM - UFRJ Comments n Fuzzy sets CE, VE and ZE are narrower than the other sets in order to allow finer control near the loading dock. n Wider fuzzy sets at the endpoints permitted rough control far from the loading dock

Truck Adriano Cruz NCE and IM - UFRJ Rule Map  / x LELCCERCRI RBPSPM PB RUNSPSPMPB RVNMNSPSPMPB VENM ZEPM LVNBNMNSPSPM LUNB NMNSPS LBNB NM NS

Truck Adriano Cruz NCE and IM - UFRJ Inference Method RV ()() CE (x)(x) PS ()()  x  VE ()() CE (x)(x) ZE ()()  x Centroid If  =RV and x=CE then  =PS If  =VE and x=CE then  =ZE R13 R18

Truck Adriano Cruz NCE and IM - UFRJ Sensitivity Analysis n Rules randomly selected are removed from the rule base. n Docking Error (DE) n Trajectory Error (TE)

Truck Adriano Cruz NCE and IM - UFRJ Docking Error

Truck Adriano Cruz NCE and IM - UFRJ Standard Deviation DE

Truck Adriano Cruz NCE and IM - UFRJ Trajectory Error

Truck Adriano Cruz NCE and IM - UFRJ Standard Deviation ET