**2. Problem Area Definition**

The multi-robotic cell consists of a set of *n* robotic manipulators *M* = *{M1,* ... *, Mi,* ... *, Mn}*. In the organizational structure of cell control, manipulator M1 represents the master element and a set of manipulators *MS* ⊂ *M, MS* = *{M2,* ... *, Mi,* ... *, Mn}* represents the slave elements. Each manipulator *Mi* performs a set of *m* operations *O* = *{O1,* ... *, Oj,* ... *, Om}* cyclically. Each operation *Oj* is in one cycle

executed by manipulator *Mi*. The duration time of this operation is *Ti*,*<sup>j</sup>* ∈ *T* = ⎧ ⎪⎪⎪⎨ ⎪⎪⎪⎩ *T*1,1 ... *T*1,*<sup>m</sup>* ... ... ... *Tn*,1 ... *Tn*,*<sup>m</sup>* ⎫ ⎪⎪⎪⎬ ⎪⎪⎪⎭

.

It is clear that duration times *Tx,j* for *x* = (1, ... , *n*) of operation *Oj* for every manipulator *Mi* are different without using a synchronization algorithm. Duration time depends on a movement speed *Vi*,*<sup>j</sup>* ∈ *V* = ⎧ ⎪⎪⎪⎨ ⎪⎪⎪⎩ *V*1,1 ... *V*1,*<sup>m</sup>* ... ... ... *Vn*,1 ... *Vn*,*<sup>m</sup>* ⎫ ⎪⎪⎪⎬ ⎪⎪⎪⎭ of manipulator *Mi* endpoint, defined as a parameter of

a movement instruction.

The goal is to modify the movement speed of manipulators *MS* separately for every operation *Oj* in such a way that the duration times of the same operation for every slave manipulator *MSi* will be equal or very similar.

The main requirements for the synchronization algorithm design are listed in Figure 1.


**Figure 1.** Requirements for algorithm design.
