Su cient Conditions for the Success of Robotic

Suucient conditions for the success of the robotic control of assembly are presented. The assembly is modelled as a discrete event system using Petri nets. The abstraction of assembly to the discrete event system highlights the changes in the state of contact as the key points to control in the assembly process. Using this abstraction , suucient conditions on the velocity commands are developed which guarantee successful parts mating. A method to derive robot velocity commands satisfying these conditions is derived. The method is then applied to a dual peg-in-the-hole problem. d : vector coordinate of edge f j : constraint function associated with j i (f) : i th ((nal) marking h : distance function surface and edge M : set of markings m : number of markings n : outward unit normal vector of surface P : set of places p : number of places p i : i th place () : edges (surfaces) of workpiece (env) 1 ; 2 : edges of surface q : generalized coordinate of the workpiece _ q : velocity vector T : set of transitions z : number of transitions z i : i th transition z k(j) (d(j)) : desired transition (next marking) for j