WO2017168187A1

WO2017168187A1 - Method and system for determining optimal positioning of a plurality of robots in a simulated production environment

Info

Publication number: WO2017168187A1
Application number: PCT/IB2016/000425
Authority: WO
Inventors: Moshe Hazan; Alex Greenberg; Zachi MANN
Original assignee: Siemens Industry Software Ltd.
Priority date: 2016-03-31
Filing date: 2016-03-31
Publication date: 2017-10-05

Abstract

Systems and a method for determining optimal positioning of a plurality of robots in a simulated production environment. It is provided a set of given states modeling positions of the plurality of the production items on the conveyor. Available initial positions of the plurality of robots are determined. Valid robot initial positions are determined from the available robot initial positions, wherein at least one robot of the plurality of robots is available for performing an assigned production task on the given production item of each given state through a collision-free robot trajectory, and wherein in the computation of the robot trajectory the motion of the given production item on the moving conveyor is taken into account. For each valid robot initial position, it is calculated a set of optimizing parameters values for defining the optimization levels of the assigned production tasks performed on the given items by the plurality of robots through the computed collision- free robot trajectories. At least one optimal robot initial position is determined by selecting at least one valid initial robot position wherein at least one specific optimizing parameter value meets a defined optimization level.

Description

METHOD AND SYSTEM FOR DETERMINING OPTIMAL POSITIONING OF A PLURALITY OF ROBOTS IN A SIMULATED PRODUCTION ENVIRONMENT

TECHNICAL FIELD

[0001] The present disclosure is directed, in general, to computer-aided design, visualization, and manufacturing ("CAD") systems, product lifecycle management ("PLM") systems, product data management ("PDM") systems, and similar systems, that manage data for products and other items (collectively, "Product Data Management" systems or PDM systems). More specifically, the disclosure is directed to production environment simulation.

BACKGROUND OF THE DISCLOSURE

[0002] In the planning of industrial processes, computer simulation techniques are used where a physical scene of a physical environment is modeled by a virtual scene of a three-dimensional (3D) virtual simulation environment. The physical or real scene may for example be a facility, a manufacturing or production plant, an industrial scene, or any other physical scene which may benefit from being modeled in a virtual environment for industrial simulation purposes.

[0003] In real production scenarios, it is often the case that some elements of the industrial scene have a stochastic behavior. For example, there are production systems in which the behavior of production items is known only in term of statistical metrics and such production items are subjected to some robotic tasks for which precise, safe and optimized planning is required.

[0004] Examples of production systems with certain elements behaving stochastically are pick and sort/place environments, where for example a production item may be positioned via dropping on a conveyor belt in a random manner due to underlying feeding mechanisms and a plurality of sorting robots are required to pick and sort them in their corresponding containers. In some examples, the conveyor geometry and speed and the dropping of items per time may be known in a deterministic manner, but the production item behavior in the production process may be known only in a stochastic manner. For example, the stochastic behavior of such production system may refer to the times and positions/orientations of the production items dropped on the moving conveyor belt during the production process. In other examples, also the dropping of items per time may be known only stochastically due to the complexity of some feeding mechanisms.

Examples of sorting robots include delta and parallel robots. In other examples, the plurality of robots interacting with the plurality of production items moving on the conveyor belts may be different than sorting robots and they thus may be any industrial robots performing any other kind of required production tasks as coating, molding, stamping, cutting, placing and others.

[0005] To design an optimized production system in which a plurality of robots are required to perform some production tasks on production items having stochastic behavior is still today a complex task since up-to-date techniques are ill-suited for the task.

[0006] Typically, in production systems where production items are moving on conveyors, there are detection systems, mostly vision, which identify the position and the orientation of the production items and provide them as inputs to logical modules that assign a given robot to perform the production task on the detected production item via robotic program algorithms.

[0007] For such production systems, a design of a 3D virtual production environment relying on statistical information of the production items positions and orientation is not satisfactory enough. In fact, the logic module decisions and the robot simulation validations are based on real-world physical attributes of the production items coupled with detailed knowledge of the robot position and their motion behavior.

[0008] In the art, techniques based on rules of thumb are typically used for determining initial robot positioning which are based on best practices and validations in the physical production environment. [0009] According to other techniques, in order to avoid robot collisions and/or production items falling from conveyors, robotic simulation tools are used thanks to their capabilities of providing kinematics planning such as reachability and collision- avoidance. With such techniques, the pick-up times and pick areas may be unduly increased to compensate for unknown item locations and orientations, which can unfortunately lead to excessive robot number, unbalanced workload divided among the robots, and/or longer production times.

[0010] According to other techniques, tools of discrete event simulation are used to estimate the number of required robots based on stochastic behavior, but, unfortunately, such tools do not provide any hint regarding robot initial positioning which requires knowledge of the precise behavior of the production items.

[0011] Therefore improved techniques are desirable.

SUMMARY OF THE DISCLOSURE

[0012] Various disclosed embodiments include methods and corresponding systems and computer-readable mediums for determining optimal positioning of a plurality of robots in a simulated production environment. A method includes providing a set of given states modeling positions of the plurality of the production items on the conveyor. Available initial positions of the plurality of robots are determined. Valid robot initial positions are determined from the available robot initial positions, wherein at least one robot of the plurality of robots is available for performing an assigned production task on the given production item of each given state through a collision-free robot trajectory, and wherein in the computation of the robot trajectory the motion of the given production item on the moving conveyor is taken into account. The method also includes calculating for each valid robot initial position a set of optimizing parameters values for defining the optimization levels of the assigned production tasks performed on the given items by the plurality of robots through the computed collision-free robot trajectories. Additionally, the method includes determining at least one optimal robot initial position by selecting at least one valid initial robot position wherein at least one specific optimizing parameter value meets a defined optimization level.

[0013] The foregoing has outlined rather broadly the features and technical advantages of the present disclosure so that those skilled in the art may better understand the detailed description that follows. Additional features and advantages of the disclosure will be described hereinafter that form the subject of the claims. Those skilled in the art will appreciate that they may readily use the conception and the specific embodiment disclosed as a basis for modifying or designing other structures for carrying out the same purposes of the present disclosure. Those skilled in the art will also realize that such equivalent constructions do not depart from the spirit and scope of the disclosure in its broadest form.

[0014] Before undertaking the DETAILED DESCRIPTION below, it may be advantageous to set forth definitions of certain words or phrases used throughout this patent document: the terms "include" and "comprise," as well as derivatives thereof, mean inclusion without limitation; the term "or" is inclusive, meaning and/or; the phrases "associated with" and "associated therewith," as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, or the like; and the term "controller" means any device, system or part thereof that controls at least one operation, whether such a device is implemented in hardware, firmware, software or some combination of at least two of the same. It should be noted that the functionality associated with any particular controller may be centralized or distributed, whether locally or remotely. Definitions for certain words and phrases are provided throughout this patent document, and those of ordinary skill in the art will understand that such definitions apply in many, if not most, instances to prior as well as future uses of such defined words and phrases. While some terms may include a wide variety of embodiments, the appended claims may expressly limit these terms to specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] For a more complete understanding of the present disclosure, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, wherein like numbers designate like objects, and in which:

[0016] Figure 1 illustrates a block diagram of a data processing system in which an embodiment can be implemented;

[0017] Figure 2 illustrates a block diagram of a simulated production environment in accordance with a disclosed example embodiment;

[0018] Figure 3 illustrates a flowchart of a method for determining optimal robot positioning of a plurality of robots in a simulated production environment in accordance with disclosed embodiments.

DETAILED DESCRIPTION

[0019] FIGURES 1 through 3, discussed below, and the various embodiments used to describe the principles of the present disclosure in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the disclosure. Those skilled in the art will understand that the principles of the present disclosure may be implemented in any suitably arranged device. The numerous innovative teachings of the present application will be described with reference to exemplary non-limiting embodiments.

[0020] Previous techniques do not provide satisfactory results.

[0021] With embodiments, the optimal robot positioning may advantageously be validated in advance in a 3D virtual production scenario avoiding costly iterative trials on the shop floor. [0022] Embodiments enable to determine, in a virtual simulated production environment, optimal robot positioning for a plurality of robots performing production tasks on production items having a stochastic behavior in order to avoid collisions among robots and other objects of the virtual scene whilst fulfilling throughput and optimization requirements.

[0023] With embodiments, it is possible to determine the minimum number of robots, their optimal positioning for achieving collision-free movements and, optionally, also a balanced workload so that the production processes are optimized to reduce the production costs and/or the required production times.

[0024] Figure 1 illustrates a block diagram of a data processing system 100 in which an embodiment can be implemented, for example as a PDM system particularly configured by software or otherwise to perform the processes as described herein, and in particular as each one of a plurality of interconnected and communicating systems as described herein. The data processing system 100 illustrated can include a processor 102 connected to a level two cache/bridge 104, which is connected in turn to a local system bus 106. Local system bus 106 may be, for example, a peripheral component interconnect (PCI) architecture bus. Also connected to local system bus in the illustrated example are a main memory 108 and a graphics adapter 1 10. The graphics adapter 1 10 may be connected to display 1 1 1.

[0025] Other peripherals, such as local area network (LAN) / Wide Area Network / Wireless (e.g. WiFi) adapter 1 12, may also be connected to local system bus 106. Expansion bus interface 1 14 connects local system bus 106 to input/output (I/O) bus 1 16. I/O bus 1 16 is connected to keyboard/mouse adapter 1 18, disk controller 120, and I/O adapter 122. Disk controller 120 can be connected to a storage 126, which can be any suitable machine usable or machine readable storage medium, including but not limited to nonvolatile, hard-coded type mediums such as read only memories (ROMs) or erasable, electrically programmable read only memories (EEPROMs), magnetic tape storage, and user-recordable type mediums such as floppy disks, hard disk drives and compact disk read only memories (CD-ROMs) or digital versatile disks (DVDs), and other known optical, electrical, or magnetic storage devices.

[0026] Also connected to I/O bus 116 in the example shown is audio adapter 124, to which speakers (not shown) may be connected for playing sounds. Keyboard/mouse adapter 118 provides a connection for a pointing device (not shown), such as a mouse, trackball, trackpointer, touchscreen, etc.

[0027] Those of ordinary skill in the art will appreciate that the hardware illustrated in Figure 1 may vary for particular implementations. For example, other peripheral devices, such as an optical disk drive and the like, also may be used in addition or in place of the hardware illustrated. The illustrated example is provided for the purpose of explanation only and is not meant to imply architectural limitations with respect to the present disclosure.

[0028] A data processing system in accordance with an embodiment of the present disclosure can include an operating system employing a graphical user interface. The operating system permits multiple display windows to be presented in the graphical user interface simultaneously, with each display window providing an interface to a different application or to a different instance of the same application. A cursor in the graphical user interface may be manipulated by a user through the pointing device. The position of the cursor may be changed and/or an event, such as clicking a mouse button, generated to actuate a desired response.

[0029] One of various commercial operating systems, such as a version of Microsoft Windows™, a product of Microsoft Corporation located in Redmond, Wash, may be employed if suitably modified. The operating system is modified or created in accordance with the present disclosure as described.

[0030] LAN/ WAN/Wireless adapter 112 can be connected to a network 130 (not a part of data processing system 100), which can be any public or private data processing system network or combination of networks, as known to those of skill in the art, including the Internet. Data processing system 100 can communicate over network 130 with server system 140, which is also not part of data processing system 100, but can be implemented, for example, as a separate data processing system 100.

[0031] One or more of the processor 102, the memory 108, and a simulation program running on the processor 102 receive the inputs via one or more of the local system bus 106, the adapter 112, the network 130, the server 140, the interface 114, the I/O bus 1 16, the disk controller 120, the storage 126, and so on. Receiving, as used herein, can include retrieving from storage 126, receiving from another device or process, receiving via an interaction with a user, or otherwise.

[0032] Figure 2 illustrates a block diagram of a simulated production environment in accordance with a disclosed example embodiment.

[0033] The shown example embodiment is a simulated production scenario of picking and sorting where, over a conveyor belt 201 moving at a given speed, a plurality of production items 202 of different types T, K, Z are dropped onto a specific area 203 of the conveyor 201. The system generates, at each time interval, a single production item 202 from a predefined collection, and places it in a random or in a statistically described position and orientation on the conveyor width.

[0034] A plurality of robots 204, 205 are placed along the conveyor 201 to perform some assigned production operations on the production items 202 moving on the conveyor 201. The production operations performed on the items 202 by the robots 204, 205 are picking and sorting into the corresponding containers 208, typically positioned in the proximity of the picking robots 204, 205.

[0035] A detection system 206 recognizes a new production item 202 dropped onto the specific conveyor area 203 of the conveyor 201. The detection system 206 detects the item position and orientation and some item characteristics (e.g. color, shape, size and other characteristics for determining the item type T, K, Z) and notifies a logic module 207 that a new item 202 of a certain type at a specific position and orientation on the conveyor belt 201 is detected by transferring DS_Info data.

[0036] The detection system 206 may be any system that detects position and orientation and/any other characteristic of a production item 202. A typical example of detection system 206 is a vision system as for example LiDAR or Kinect.

[0037] The logic module 207, by processing the information received from the detection system 206, decides which robot 204, 205 is best for picking the detected item 202 and for sorting it into its specific container 208, in accordance with its identified characteristics.

[0038] Table 1 below is an example of the information stored by the logic module 207 for decision making in a simplified exemplary embodiment.

[0039] Each time that the detection system 206 notifies the logic module 207 about a new coming item 202 with the related information data DS_Info, the logic module 207 decides which robot 204, 205 is best at handling it and the relevant container 208. [0040] The decision of the logic module 207 relies on motion planning calculations of robotic tasks and other helpful information which include but it is not limited to the following:

- the position of the moving item 202, given the conveyor speed, when at least one or each robot 204, 205 finishes its current task;

- time necessary for the robot which will be located at the "Future robot position at the end of the current task" for reaching and picking the item 202;

- reachability of the moving item 202 from at least one robot 204, 205;

- collision- free trajectory of the robots 204, 205.

[0041] The dashed arrows in Figure 2 represent the logic module assignment of robots 204, 205, containers 208 and item type 202 according to taken decisions based on motion planning calculations and the above mentioned helpful information.

[0042] The decisions taken by the logic module 207 are based on accurate information derived from virtual kinematic simulation.

[0043] In other embodiments, the logic module 207 may conveniently receive inputs also from additional sources, e.g., sensors, HMI (human machine interface), and may also synchronize the work of additional peripheral devices. All the inputs received by the real logic module and by other modules on the shop floor can be simulated in the 3D virtual environment with the addition of corresponding virtual modules.

[0044] Advantageously, with embodiments, algorithms, providing accurate and automated simulation and analysis of the production process, may be generated for decision making, so that the production process can be optimized to meet several optimization criteria in accordance with the specific production planning requirements.

[0045] Examples of parameters useful for taking optimization criteria decisions include but are not limited to:

- number of items 202 handled by each robot 204, 205; - even distribution of workload among robots 204, 205;

- energy consumption of each robot 204, 205;

- number of items filling each container 208;

- scenarios in which items 202 are not handled by any robot 204, 205. [0046] Example implementation

Below it is outlined a possible implementation of a decision making algorithm for determining robot initial positioning in accordance with the example embodiment shown in Figure 2.

[0047] Definitions and Notations

- Let F denote the set of all frames, i.e. all possible 3D oriented positions (of

production items and/or of robots):

F = {< x, y, z, r_x, r_y, r_z > \x, y, z, r_x, r_y, r_z E R]

- Let P denote a finite set of production items, each identified by a unique integer number.

- Let C denote the set of all containers.

- Let § denote the set of all possible "system states":

§ = {< t, f, p, C > |t G WL⁺, f E F, p E P, C _= C}

where each state represents the elapsed time in seconds (t G ⁺), a 3D position (/ G F) of a production item (p G P), and a subset of containers (C ⁽C).

- Let R denote a finite set of robots.

- Let < r , r₂, ... , r_n > be an ordering of all robots in R.

Let the robot positioning function be defined as follows: ^(< r^, ^,—, r_n > ) =< f_v f₂>—_> f_n ^{> sucn mat} f°^{r an}y 1≤ j≤ n, f_j E F is the position of robot r- given by function l_t.

- Let the Logic Module function be defined as follows:

L (< t, f, p, C >) = {< r, c > s. t. r E R, c E C} U 0

This function represents a logic module decision based on a system state. Each of such decision assigns a robot r G R to pick production item p E P and place it in container c G C. If there is no possible assignment, LM shall return 0.

[0048] The algorithm Input:

- R

- A finite set 5 c §. The finite set S represents a finite number of valid system states, meaning for each detection time, the position on the conveyor belt of each detected production item, and the set of possible containers into which the production item can be placed.

- A conveyor three-dimensional model [0049] The algorithm:

1. Find an initial set FP of k feasible positions:

FP = Ui_Sis_fc ^i(< ?i, r₂, ... , r_n > )

To compute FP , heuristically attempt to position the robots in various positions along the conveyor such that:

a. Each r £ R is able to reach the whole width of the conveyor.

b. For each Τχ, τ₂ G R, such that V\≠ r₂, there is no collision between Τχ and r₂.

2. i «- 1

3. While i≤ k do:

3.1. Relocate r_x ... r_n to positions given by i;(< r₁₍ r₂, ... , r_n >)

3.2. For each < t, f, p, c >G S, in incrementing order of the t element:

3.2.1. Let < r, c > be an assignment of robot and container given by L (< t,f, p, c >).

3.2.2. If LM(< t, f, p, c >) = 0, then there is no feasible solution for £_t, go to 3.2.6.

3.2.3. Compute motion of r to pick part p and place in container c.

3.2.4. Check for dynamic collision between r and p against all other objects in scene.

3.2.5. If a collision is found, the -£_t is marked as unfeasible, remove it:

FP <- FP \ i

3.2.6. i <- i + 1 [0050] The Output:

a. FP, the final set of feasible solutions.

b. Recommend the best position for each robot unit, according to one or more of the following optimizing criteria:

- number of production items handled by each robot;

- even workload among robots;

- energy consumption of each robot;

- number of production items placed in each container.

[0051] It is noted that the above example embodiment, it is an example of an algorithm implementation where production items moving on a conveyor are to be picked by sorting robots into a container. Those skilled in the art know that other embodiments for designing stochastic production flow are possible in which any type of industrial robots is performing other industrial tasks than picking and sorting. Other algorithm embodiments may include as inputs the statistic distribution of the states and their rates, the industrial robots and a description of the production environment and as outputs it is identified the position of the industrial robots in the production environment, optionally also the industrial robot minimal number, in order to fulfil throughput requirements and optimization criteria without collision movements.

[0052] Figure 3 illustrates a flowchart 300 of a method for determining optimal positioning of a plurality of robots in a simulated production environment in accordance with disclosed embodiments. Such a method can be performed, for example, by system 100 of Figure 1 described above, but the "system" in the process below can be any apparatus configured to perform a process as described.

[0053] The simulated production environment comprises a plurality of robots for performing production tasks on a plurality of production items being transported by a conveyor moving at a given speed. [0054] At act 305, a set of given states modeling position of the plurality of the production items on the conveyor is provided.

[0055] At act 310, available initial positions of the plurality of robots are determined.

[0056] At act 315, valid robot initial positions are determined by checking available robots for performing production tasks by computing collision free trajectories. The valid robot initial positions are determined from the available robot initial positions wherein at least one robot of the plurality of robots is available for performing an assigned production task on the given production item of each given state through a collision-free robot trajectory, wherein in the computation of the robot trajectory the motion of the given production item on the moving conveyor is taken into account.

[0057] At act 320, for each valid robot initial position, it is calculated a set of optimizing parameters values for defining the optimization levels of the assigned production tasks performed on the given items by the plurality of robots through the computed collision- free robot trajectories.

[0058] At act 325, it is determined at least one optimal robot initial position by selecting at least one valid initial robot position wherein at least one specific optimizing parameter value meets a defined optimization level.

[0059] In some embodiments, the optimizing parameters may be, but not limited to, the number of production items handled by each robot, workload of each robot, energy consumption of each robot, and/or number of items placed in each container. Examples of defined optimization levels may be, but not limited to, minimizing differences of number of handled items by each robot, minimizing workload differences among robots, minimize energy consumption of each robot, and/or minimizing differences of item number of each container.

[0060] In some embodiments, the set of given states modeling positions and orientation of the production items may be determined from a statistical distribution model or, in other embodiments, may be totally random. For example, such given states may be conveniently generated by a discrete stochastic event based simulation engine so that accurate positions and orientation of involved production items are provided.

[0061] In some embodiments, the computed robot trajectory is performed by a robot simulation engine. Conveniently, for each state, robotic motion aspects as well as feasibility aspects, e.g. collision avoidance and others, can be verified.

[0062] Hence, in some embodiments, statistical coverage and discrete event simulation may be combined with precise kinematic evaluation of each event. Advantageously, the capability of discrete event simulation to generate states for the precise kinematic simulation enables to simulate, validate and optimize the production line in virtual 3D world by identifying feasible options and determining optimal robot initial positions, number of robots and/or their programs.

[0063] Advantageously, for production planning optimization, embodiments allow to analyze the impact of changing other parameters such as, for example, the conveyor speed, the initial available initial positions of the robots, the number of robots or even by fully reprograming the decision making algorithms.

[0064] Of course, those of skill in the art will recognize that, unless specifically indicated or required by the sequence of operations, certain steps in the processes described above may be omitted, performed concurrently or sequentially, or performed in a different order.

[0065] Those skilled in the art will recognize that, for simplicity and clarity, the full structure and operation of all data processing systems suitable for use with the present disclosure is not being illustrated or described herein. Instead, only so much of a data processing system as is unique to the present disclosure or necessary for an understanding of the present disclosure is illustrated and described. The remainder of the construction and operation of data processing system 100 may conform to any of the various current implementations and practices known in the art. [0066] It is important to note that while the disclosure includes a description in the context of a fully functional system, those skilled in the art will appreciate that at least portions of the mechanism of the present disclosure are capable of being distributed in the form of instructions contained within a machine-usable, computer-usable, or computer- readable medium in any of a variety of forms, and that the present disclosure applies equally regardless of the particular type of instruction or signal bearing medium or storage medium utilized to actually carry out the distribution. Examples of machine usable/readable or computer usable/readable mediums include: nonvolatile, hard-coded type mediums such as read only memories (ROMs) or erasable, electrically programmable read only memories (EEPROMs), and user-recordable type mediums such as floppy disks, hard disk drives and compact disk read only memories (CD-ROMs) or digital versatile disks (DVDs).

[0067] Although an exemplary embodiment of the present disclosure has been described in detail, those skilled in the art will understand that various changes, substitutions, variations, and improvements disclosed herein may be made without departing from the spirit and scope of the disclosure in its broadest form.

[0068] None of the description in the present application should be read as implying that any particular element, step, or function is an essential element which must be included in the claim scope: the scope of patented subject matter is defined only by the allowed claims.

Claims

WHAT IS CLAIMED IS:

1. A method for determining optimal positioning of a plurality of robots in a simulated production environment; wherein the simulated production environment comprises a plurality of robots for performing production tasks on a plurality of production items being transported by a conveyor moving at a given speed,

the method performed by a data processing system and comprising:

a) providing (305) a set of given states modeling positions of the plurality of the production items (202) on the conveyor (201);

b) determining (310) available initial positions of the plurality of robots (204,

205);

c) determining (315) valid robot initial positions from the available robot initial positions, wherein at least one robot of the plurality of robots (204, 205) is available for performing an assigned production task on the given production item (202) of each given state through a collision-free robot trajectory, and wherein in the computation of the robot trajectory the motion of the given production item (202) on the moving conveyor (201) is taken into account;

d) calculating (320) for each valid robot initial position a set of optimizing parameters values for defining the optimization levels of the assigned production tasks performed on the given items (202) by the plurality of robots (204, 205) through the computed collision-free robot trajectories; and

e) determining (325) at least one optimal robot initial position by selecting at least one valid initial robot position wherein at least one specific optimizing parameter value meets a defined optimization level.

2. The method of claim 1 further comprising:

- the state set of step a) is determined from a statistical distribution model or is determined in a totally random manner.

3. The method of claim 2 or 3 further comprising: - the computed robot trajectory of step c) is performed by a robot simulation engine.

4. The method of any of the previous claims, wherein the optimizing parameters are selected from the group consisting of one or more of the following:

- number of production items handled by each robot (204, 205);

- workload of each robot (204, 205); and

- energy consumption of each robot (204, 205).

5. The method of any of the previous claims, further comprising:

- varying the number of the plurality of robots (204, 205).

6. The method of any of the previous claims, wherein the production task performed by the plurality of robot is selected from the group consisting of:

- picking a production item (202) of a certain type and placing it in a corresponding container;

- coating a production item (202) of a certain type with a specific coating material; and

- any production task dependent on the production item characteristics.

7. A data processing system comprising:

a processor, and

an accessible memory, the data processing system particularly configured to:

a) provide (305) a set of given states modeling positions of the plurality of the production items (202) on the conveyor (201);

b) determine (310) available initial positions of the plurality of robots (204, 205); c) determine (315) valid robot initial positions from the available robot initial positions, wherein at least one robot of the plurality of robots (204, 205) is available for performing an assigned production task on the given production item (202) of each given state through a collision-free robot trajectory, and wherein in the computation of the robot trajectory the motion of the given production item (202) on the moving conveyor (201) is taken into account;

d) calculate (320) for each valid robot initial position a set of optimizing parameters values for defining the optimization levels of the assigned production tasks performed on the given items (202) by the plurality of robots (204, 205) through the computed collision-free robot trajectories; and

e) determine (325) at least one optimal robot initial position by selecting at least one valid initial robot position wherein at least one specific optimizing parameter value meets a defined optimization level.

8. The data processing system of claim 7, wherein the the state set of item a) is determined from a statistical distribution model or is determined in a totally random manner.

9. The data processing system of claim 7 or 8, wherein the computed robot trajectory of item c) is performed by a robot simulation engine.

10. The data processing system of any of the claims 7 to 9, wherein the optimizing parameters are selected from the group consisting of one or more of the following:

- number of production items handled by each robot (204, 205);

- workload of each robot (204, 205); and

- energy consumption of each robot (204, 205).

11. The data processing system of any of the claims 7 to 10, further comprising:

- varying the number of the plurality of robots (204, 205).

12. The data processing system of any of the claims 7 to 1 1, wherein the production task performed by the plurality of robot is selected from the group consisting of: - picking a production item (202) of a certain type and placing it in a corresponding container;

- any production task dependent on the production item characteristics.

13. A non-transitory computer-readable medium encoded with executable instructions that, when executed, cause one or more data processing systems to:

14. The non-transitory computer-readable medium of claim 13, wherein the the state set of item a) is determined from a statistical distribution model or is determined in a totally random manner.

15. The non-transitory computer-readable medium of claim 13 or 14, wherein the computed robot trajectory of item c) is performed by a robot simulation engine.

16. The non-transitory computer-readable medium of any of the claims 13 to

15, wherein the optimizing parameters are selected from the group consisting of one or more of the following:

- number of production items handled by each robot (204, 205);

- workload of each robot (204, 205); and

- energy consumption of each robot (204, 205).

17. The non-transitory computer-readable medium of any of the claims 3 to

16, further comprising:

- varying the number of the plurality of robots (204, 205).

18. The non-transitory computer-readable medium of any of the claims 3 to

17, wherein the production task performed by the plurality of robot is selected from the group consisting of:

- any production task dependent on the production item characteristics.