DE102010052253B4 - Method and control means for controlling a robot arrangement - Google Patents

Method and control means for controlling a robot arrangement

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Publication number
DE102010052253B4
DE102010052253B4 DE102010052253.8A DE102010052253A DE102010052253B4 DE 102010052253 B4 DE102010052253 B4 DE 102010052253B4 DE 102010052253 A DE102010052253 A DE 102010052253A DE 102010052253 B4 DE102010052253 B4 DE 102010052253B4
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Prior art keywords
robot
time
process
section
process section
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DE102010052253.8A
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German (de)
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DE102010052253A1 (en
DE102010052253A8 (en
Inventor
Christian Sonner
Peter Klueger
Johannes Kurth
Manfred Hüttenhofer
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Kuka Deutschland GmbH
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Kuka Deutschland GmbH
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Priority to DE102010052253.8A priority Critical patent/DE102010052253B4/en
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Publication of DE102010052253A8 publication Critical patent/DE102010052253A8/en
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00Programme-controlled manipulators
    • B25J9/16Programme controls
    • B25J9/1679Programme controls characterised by the tasks executed
    • B25J9/1682Dual arm manipulator; Coordination of several manipulators
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00Programme-controlled manipulators
    • B25J9/16Programme controls
    • B25J9/1656Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1669Programme controls characterised by programming, planning systems for manipulators characterised by special application, e.g. multi-arm co-operation, assembly, grasping
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00Program-control systems
    • G05B2219/30Nc systems
    • G05B2219/34Director, elements to supervisory
    • G05B2219/34314Slow down, limit speed for energy saving
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00Program-control systems
    • G05B2219/30Nc systems
    • G05B2219/39Robotics, robotics to robotics hand
    • G05B2219/39144Scale moving time of all robots, machines to match slowest, no waiting
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00Program-control systems
    • G05B2219/30Nc systems
    • G05B2219/39Robotics, robotics to robotics hand
    • G05B2219/39361Minimize time-energy cost

Abstract

Method for computer-aided control of a robot arrangement having at least two robots (1, 2), comprising the steps of: determining at least one process section point (q, q) determining a process section time (T) for the process section point specifying a section time (T) for at least one robot (1) of the robot assembly based on the process section time (T); and - optimizing a workflow (q (s (t)) of this robot (1) on the basis of the predetermined section time (T + .DELTA.T), wherein a quality criterion of optimization based on an energy quantity (E) of the robot is determined and the workflow is optimized, by performing this numerically simulated for at least two different parameter values of parameters that co-determine the work flow, and determining as optimum process the one for which the quality criterion has the lowest value, and wherein the process section into one or more transfer sections (a) and / or one or more processing sections (b) divided and only the or the transfer sections are optimized, wherein in a transfer section, a trajectory and / or a web speed profile is variable, and for a processing section, a trajectory and / or a web speed profile is predetermined.

Description

  • The present invention relates to a method and a control means for the computer-aided control of a robot arrangement with at least two robots.
  • In robotic arrangements with two or more robots, a distinction can be made between coordinated and cooperative processes: while in cooperative processes the robots synchronously act as axes of a virtual hyperrobot, for example, to jointly move a payload held by the robots, robots perform subtasks in coordinated robotic operation a independent of other robots.
  • In order to avoid collisions, processes are subdivided according to in-house practice into process sections, which must first have been processed by all collision-prone robots before they can start a subsequent process section. If, for example, two robots alternately move payloads in the same workspace, such process sections can be specified by the exit of a robot from this workspace so that the respective other robot may only enter the - now free - working space in a subsequent process section.
  • However, workflows, particularly motions, of individual robots are typically timed, i. E. such that the robot handles the workflow in the minimum possible time, which may result from, for example, limitations in drive forces and moments, joint speeds and accelerations, and / or Cartesian velocities of reference points such as the TCP. In the coordinated process described above, which is clocked in process sections, this leads to the faster robot (s), i.e. those who process the respective process section in a minimal amount of time, wait for the slowest robot at the end of the process section and thus have consumed unnecessarily much energy in their time-optimized workflow.
  • The DE 196 25 637 A1 proposes to avoid collision in multi-robot operation to project collision areas in the space of the joint joint coordinates and plan there time-optimal collision-free trajectories. The end time of the faster robot is scaled to the end time of the slower robot to synchronously reach the same point in the joint coordinate space.
  • From the EP 1 705 541 B1 For example, a method for controlling robots is known to move respective ones of standard moving parts installed on respective ones of a plurality of robots to respective ones of synchronous operation positions set for each of the robots and simultaneously perform operations of the robots, comprising: a first movement time calculating step of calculating, for each of the robots, a respective one of first movement times when a respective one of the moving standard parts is moved from a respective one of the movement start positions to a respective one of the synchronous operation positions in a shortest time; a second movement time determination step in which a longest first movement time among the first movement times is determined as a second movement time; an operation plan generating step of generating, for each of the robots, an operation schedule of a speed change of each of the moving standard parts to move respective ones of the moving standard parts without stopping from respective ones of the movement start positions to respective ones of the synchronous operation positions in the second movement time; an operation completion judging step in which an operation completion state in which the robot can execute a next operation plan is judged; and a robot control step in which, when it is judged at the operation completion judgment step that all the robots to be operated simultaneously enter the operation completion state, simultaneously controlling a respective one of the plurality of robots according to a respective one of next operation plans of each of the robots operating in the operation plan Generating step is generated.
  • WANG F.-Y .; LEVER, PJA: "A CELL MAPPING METHOD FOR GENERAL OPTIMUM TRAJECTORY PLANNING OF MULTIPLE R080TIC ARMS", In: R080TICS AND AUTONOMOUS SYSTEMS, ELSEVIER SCIENCE PU8LISHERS, AMSTERDAM, NL, 8d. 12, No. 1/02, March 1, 1994 (1994-03-01), pages 15-27 propose a method that uses cell state space and cell mapping-based techniques to schedule globally optimal trajectories along predetermined geometric paths for coordinated multi-robotic arm systems.
  • The object of the present invention is to improve the control of robot arrangements with at least two robots.
  • This object is achieved by a method having the features of claim 1. Claim 6 provides a control means, claim 8, a computer program product, in particular a machine-readable data carrier or a storage medium, for performing a method according to the invention under protection, wherein an agent in the sense of the present invention equally hard and / or software technology can be formed, ie in particular corresponding Processing, computing, Memory and / or data transmission devices and / or programs, program modules, and the like may include. Advantageous developments are the subject of the dependent claims.
  • The present invention is based on the idea of utilizing the time difference between a time required by the slowest robot of a robot assembly to execute a process section and the time that a faster robot of the robot assembly would require in time-optimized operation to complete the workflow of the faster robot, especially with regard to its energy consumption. In contrast to a mere scaling of the minimum end time of the faster robot to that of the slower robot, optimization here can result in significant energy savings.
  • In general, a method according to the invention first comprises determining one or more process section points. In this case, an overall process which the robot arrangement is to carry out is preferably subdivided into two or more subprocesses or process sections. These can result, in particular, in the context of a collision avoidance, for example by the requirement that only one robot may always act in a common, preferably variable, workspace. Additionally or alternatively, process section points may also be synchronization points at which two or more robots simultaneously have to assume a certain configuration, for example to transfer a payload or to process a workpiece fixed by a robot by a tool which another robot guides. Process section points can result, for example, from the delivery cycle of a conveyor with which the robot arrangement interacts. For a more compact representation, an overall process without further subdivision can also represent a process section in the sense of the present invention whose single process section point then forms the end of the overall process.
  • In general, a process section point in the sense of the present invention is understood to mean in particular a point which describes a state of two or more robots of the robot arrangement, in particular poses of the robots, for example poses at the end of a machining process or a transfer movement. Is a workflow of a robot i the robot assembly by the course of its joint coordinates q i described above a process state parameter s 0 ≦ s ≦ s E , the overall process according to the joint coordinates q (s) = [q 1 (s), q 2 (s), ...] the robot of the robot assembly, so a process section point, for example by values of the process state parameter s or the associated joint coordinates or robot poses. Process section points can be determined manually, for example by clicking in a graphical representation of the process or input during a teaching of the process, and / or automatically, for example at predetermined intervals of the process state parameter.
  • Then, a process section time is determined for the respective process section point. This is understood to mean, in particular, that time which the robot arrangement requires to reach the process section point while the respective process section is being processed by the robots of the robot arrangement. In a preferred embodiment, in each case a minimum section time is determined for two or more, in particular all robots of the robot arrangement, which require the respective robots at least for processing their respective process section. This minimum section time can preferably be achieved taking into account maximum permissible driving forces and moments, joint speeds and accelerations and / or Cartesian velocities of reference points, in particular the TCP, with a workflow planned at the optimum time. The process section time can then be determined on the basis of these minimum section times, in particular as the largest of the minimum section times. Similarly, a process section time may also be determined based on other process factors, such as the time it takes for a workpiece to reach a predetermined temperature requiring a paint, seal, or adhesive application for drying, or a tooling or spraying machine for processing a workpiece required. In general, the respectively longest of the times which robots, tools, workpieces and / or further processing means such as machine tools, conveyors or the like in each case require to achieve the process section point minimally can be determined as a process section time. In an advantageous development, the process period time thus determined from the minimum times can be increased by a predetermined value in order to provide a reserve for the slowest process agent and not to load it out. For this purpose, the respective minimum time of the individual processing means can be increased in the same way by a predetermined, preferably individual, value.
  • Now, on the basis of the process section time, a section time for one or more robots of the robot arrangement is specified, preferably only for robots whose minimum section time does not determine the process section time. In particular, the process section time itself can be specified as a section time. Similarly, it is possible to set the section times, for example to increase a given value compared to the process section time, so as not to burden even the slowest process agent. The section time can be specified, for example, as the total time that is available to the respective robot for processing the process section, or else as the time difference with respect to the previously determined minimum section time.
  • Then, a workflow is optimized for the robot (s) based on the given section time. In this case, a trajectory of the robot i, for example, by specifying its joint angle q i can be described via a path parameter s, be predetermined, for example, to guide the TCP on a given Cartesian path and so for example to avoid collisions, start a weld or apply adhesive or colorant in a given job path. In this case, the web speed profile s (t), with which the robot departs this predetermined path, can be optimized. If the trajectory of the robot is not predetermined because, for example, only one start and one end pose for capturing and depositing a payload are predetermined by the boundary conditions, while the transfer trajectory between these poses is still freely selectable, the trajectory itself can also be optimized. For example, in an optimizer, vertices or other parameters that generally describe the trajectory, such as the coefficients of splines or the like, may be used as variable optimization parameters. Additionally or alternatively, the web speed profile can also be optimized here, in particular in a single-stage process in which the trajectory over time is described.
  • For the purposes of the present invention, optimization is understood as meaning in particular the presetting of a workflow, for example a trajectory and / or a path velocity profile, for which one or more quality criteria achieve an extremal, in particular minimum value. Several quality criteria can be pareto-optimized together, preferably as a weighted sum. The quality criterion or criteria must not reach global extremal values for the optimized workflow, in particular if a determination is not possible closed or requires a high numerical effort. Accordingly, in a preferred embodiment, a workflow is optimized by performing this - preferably numerically simulated - for at least two different parameter values of parameters that determine the workflow, such as the interpolation points discussed above, and determining the optimum workflow for which the quality criteria have the lowest value.
  • Preferably, a quality criterion of the optimization is an energy quantity of the robot. This may in particular be an energy consumption of the robot or a size corresponding thereto, for example the integral of the square or the amount of drive power of the drives of the robot. It is clear from this that an energy quantity in the sense of the present invention does not necessarily have to have the physical dimension of an energy or work.
  • The energy quantity to be optimized may preferably also include energy consumption in the power supply of the robot, such as losses in converters, intermediate circuits or the like.
  • Additionally or alternatively, a quality criterion may preferably describe a load on the robot, for example maximum forces or moments occurring, in particular in joints, drives or the like. Also, a measure of vibrations of the robot, such as the amplitudes of elastic vibrations or the like, may form a quality criterion. Additional quality criteria can be taken into account additionally or alternatively.
  • In particular, in order to determine the value of one or more of the aforementioned quality criteria in a simulation for different parameter values that determine the workflow of the robot, in a preferred embodiment of the present invention, its workflow is determined by means of a dynamic model, in particular a rigid body or a multi-body elastic model.
  • A workflow of a robot may include processing and / or transfer sections. In this case, a machining section may in particular comprise a tool or workpiece guide of the robot during a machining process, for example a robot-guided welding, gluing, painting, a machining or non-cutting machining or the like. In contrast, a transfer section may, in particular, have a predefined initial and final pose of the robot, wherein a robot path can be freely selected between the two poses, possibly taking into account boundary conditions such as collision freedom, maximum values for driving forces and moments, speeds and / or accelerations, and the like.
  • Typically, a trajectory and a web speed profile are predetermined for a processing section, in order, for example, to run an adhesive or varnishing web with a desired adhesive or varnish application at a predetermined application rate. An optimization is therefore not possible for such sections, without the affect the process to be carried out. In a preferred embodiment, it is therefore intended to subdivide the process section into one or more transfer sections and / or one or more processing sections and to optimize only the transfer section (s) so as to also optimize the entire process section. As a transfer section is thus generally understood in particular a process section or a part of a process section in which a trajectory and / or a web speed profile can be varied.
  • Usually, a controller of a robot arrangement is distributed: a global process or cell control carries out a control of the overall process, for example by specifying poses to be approached by the robots of the arrangement or trajectories to be traveled, while robot controls control the individual robots, for example paths between predetermined ( Support) interpolate poses.
  • A method according to the invention can likewise be carried out by a cell control, one or more robot controls or distributed by cell control and robot controls. In this case, it can be provided, in particular, that the specification of the section time for the robots of the robot arrangement is effected by a control of the robot arrangement, which additionally or alternatively determine process section points and can determine a process section time. The optimization of the workflow of a robot, in particular a simulation of its workflow for determining one or more quality criteria for different, the workflow determining parameter values, in addition to or alternatively to a determination of a minimum section time based on a time-optimal planned robot path preferably be done by the control of the respective robot , For this purpose, in a preferred embodiment, a simulation and an optimizer are implemented in the respective robot controller.
  • An inventive method may, at least in part, take place offline in advance and / or online during the work process. It is computer-assisted by at least one of the above-described steps being performed at least partially automated by a computer, in particular the cell or robot controller. In particular, the simulation and optimization can be carried out by executing corresponding numerical methods, as can the determination of minimum section times for time-optimized work processes, the determination of a process section time and the like.
  • Further advantages and features emerge from the subclaims and the exemplary embodiments. This shows, partially schematized:
    • 1 a process of a robot assembly according to an embodiment of the present invention; and
    • 2 Fig. 1 shows the sequence of a method according to an embodiment of the present invention.
  • 1 shows in the top row from left to right successive states of a robotic assembly with two robots 1 . 2 in a process controlled according to an embodiment of the present invention. In the bottom line of the 1 the curves of different state variables, in particular joint coordinates and their time derivatives, are plotted against the time t for the process indicated in the upper line.
  • In the process, the two robots set 1 . 2 alternating payloads 3 respectively. 4 on each other, in 1 filled or hatched symbolizes. For better understanding, in the greatly simplified embodiment, the in 1 upper robot 1 the automation cell two hinges with parallel, vertical axes of rotation (perpendicular to 1 ), which is a swingarm 1.2 with a base 1.1 or an arm 1.3 with the swingarm 1.2 connect, and their position by the joint coordinate or the angle q 1,1 between base and swingarm or the angle q 1,2 between the rocker and the arm, which can be summarized to the vector q 1 . Their first time derivative or joint velocity is denoted by ω 1, i = dq 1, i / dt (i = 1, 2), the second time derivative or joint acceleration corresponding to dω 1, i / dt. On the arm 1.3 is a gripper 1.4 for holding the payload 3 attached. The second robot has an analogous manner to a base 2.1 attached arm 2.3 with a gripper 2.4 for holding the payload 4 on, its joint angle to the base by the angle q 2 is described. Zero value and orientation result from the synopsis of the upper and lower lines of the 1 , ie the joint angles q 1 = ( q 1,1 . q 1,2 ) and q 2 take for in the left column the 1 pose shown the value 0 and are positively counted counterclockwise.
  • The process of alternately picking up payloads 3 . 4 through the robots 1 . 2 and their alternating Aufeinaderstapelns on a stack arranged between the two robots according to the invention is divided into alternately successive process sections. In a first process section [ t 0 . T ] becomes the robot 2 from a filing pose in which he has a payload 4 deposited on the pile, transferred to a receiving pod, in which he has another payload 4 from a conveyor (not shown). The first robot 1 transports a payload in this first process section 3 from another conveyor (not shown) on the stack and puts them there. In a subsequent second process section [T, 2T ≅ t 0 ] transported reversely the robot 2 a payload 4 from the conveyor to the stack, while now the robot 1 from the storage float is transferred to the receiving pod to another payload 3 take. This is followed by a first process section, etc. This ensures that the two robots 1 . 2 Do not collide with each other in the common workspace above the stack. This subdivision can be done manually or automatically, for example, during the planning of the overall process.
  • Now, for example, in advance during a process flow planning, for each process section, ie the above-described first and second process section, each time by a robot control of the time-optimal workflow or the time-optimal motion q i (t) for the respective robot i = 1, 2 determined.
  • For the robot 2 results in the embodiment of the bottom line of 1 illustrated course of its joint angle q 2 and its first and second time derivative, respectively dq 2 / dt . 2 / dt over time t , The robot accelerates 2 , as in 1 dash-dotted lines, in the first half of the process section with a limited by its maximum permissible drive torque acceleration and brakes in the second half with the same amount, negative acceleration by a corresponding counter torque to a standstill, resulting in a corresponding, common in the rail planning speed trapezoidal profile which degenerates in the embodiment to a velocity triangle profile and in 1 dashed lines is drawn. This results in the time-optimized workflow of the robot 2 minimum required time, which is the same for both process sections, and the respective minimum section time T 2 represents.
  • In the same way can for the robot 1 a minimum section time T 1 be determined, which is smaller than the minimum section time in the embodiment, for example due to stronger drive motors and / or lesser masses and thus greater allowable accelerations T 2 of the robot 2 ,
  • The robot controller R i of the respective robot i = 1, 2 determines first, for example, after teaching the recording and storage poses, the minimum section time explained above T i , for example, by simulation and numerical optimization, and transmits them to the cell controller Z (see. 2 ).
  • In the cell control Z This will become a process section time T as the maximum of the minimum section times T i determined (T = MAX (T 1 , T 2 ) = T 2 ) and the difference .DELTA.T i = T - T i between this process section time T and the respective minimum section time T i transferred to the individual robot i = 1, 2 (see. 2 ).
  • In the individual robot controls R i the respective process section becomes one or more transfer sections s a and / or one or more processing section s b divided into 1 are indicated by the sections "a" and "b", respectively. In the exemplary embodiment, these are two short processing sections b for picking up or dropping the payload by closing or opening the gripper, in which the workflow, in particular the movement, of the respective robot must not be changed. Between the editing sections b this results in a transfer section a in which the workflow, in particular the movement, of the robot between the recording and storage pose is freely selectable and can be optimized.
  • The control R 1 of the robot 1 now optimizes the workflow, here the movement, of the robot in this transfer section a under the boundary condition that this is completed after T 1 + ΔT 1 , ie this time difference suggests the transfer movement (T (s a, E ) → T (s a, E ) + ΔT 1 ). The index "E" denotes the end position.
  • In the embodiment, the robot controller R 1 the movement q 1 (t) ie the trajectory q 1 (s) and the web speed profile s (t) , for the transfer section a optimize. The quality criterion is a characteristic value for the robot 1 required energy, such as an integral over the square of its drive torques, minimized under the constraint that the movement must be completed within the time available. It turns out that the robot 1 first his arm 1.3 pivots to the moment of inertia about the axis of rotation of the base 1.1 to minimize, then the base swiveled by 180 ° and finally the arm 1.3 swings out again to reach the filing pose.
  • Is, however, the trajectory q 1 (s) predetermined for the transfer section, for example, to avoid a collision with obstacles, not shown, can for this trajectory, the web speed profile s (t) for the condition that the required energy E of the robot 1 is minimized (E = E min ), optimized and so in turn the energy consumption can be reduced.
  • In principle, the energy optimization explained above can also be applied to the robot 2 be performed. However, this leads to the already initially determined time-optimal workflow, since only with this the specified section time can be met. In general, therefore, it is provided in an advantageous embodiment to carry out the optimization only for those or those robots whose minimum section time does not determine the process section time.
  • The process section time does not have to correspond to the largest minimum section time. For example, in the example above, based on the minimum section time of the robot 2 determined process time to be increased by a predetermined value to the load of the robot 2 by reducing the time-optimal trajectories. This can be carried out in an advantageous development only for one of the two alternating process sections, in which then, for example, the drive motors of the robot 2 can cool as a result of submaximal loading.
  • LIST OF REFERENCE NUMBERS
  • 1, 2
    robot
    1.1, 2.1
    Base
    1.2
    wing
    1.3, 2.3
    poor
    1.4, 2.4
    grab
    3, 4
    payload
    q 1,1
    Joint angle base - rocker (robot 1)
    q 1,2
    Joint angle rocker arm (robot 1)
    q 2
    Joint Angle Base - Arm (Robot 2)
    d / dt
    Derivative by time t
    T
    Process section time
    a
    transfer section
    b
    machining section
    Z
    cell controller
    R 1 , R 2
    robot control

Claims (8)

  1. Method for computer-aided control of a robot arrangement having at least two robots (1, 2), comprising the steps of: - determining at least one process section point (q 1, E , q 2, E ); - determining a process section time (T) for the process section point; - Specification of a section time (T) for at least one robot (1) of the robot assembly based on the process section time (T); and - Optimizing a workflow (q 1 (s (t)) of this robot (1) on the basis of the predetermined section time (T 1 + ΔT), wherein a quality criterion of the optimization based on an energy quantity (E) of the robot determined and optimized the workflow is performed by numerically simulating for at least two different parameter values of parameters that co-determine the workflow, and determining as optimum process the one for which the quality criterion has the lowest value, and wherein the process section is divided into one or more transfer sections (a) and / or one or more processing sections (b) subdivided and only the or the transfer sections are optimized, wherein in a transfer section, a trajectory and / or a web speed profile is variable, and for a processing section, a trajectory and / or a path velocity profile is predetermined.
  2. Method according to the preceding claim, characterized in that a path velocity profile (s (t)) and / or a trajectory (q 1 (s)) is determined on the basis of the predetermined section time to optimize the workflow of a robot.
  3. Method according to one of the preceding claims, characterized in that a minimum section time (T i ) for at least two robots (i = 1, 2) of the robot arrangement is determined, and that the process section time (T) based on these minimum section times (T i ) is determined.
  4. Method according to one of the preceding claims, characterized in that the optimization of the workflow of a robot takes place at least partially by its control (R i ).
  5. Method according to one of the preceding claims, characterized in that the specification of the section time for a robot by a controller (Z) of the robot assembly takes place.
  6. Control means (Z, R i ) for computer-aided control of a robot arrangement having at least two robots (1, 2), comprising: a process section point means (Z) for determining at least one process section point (q 1, E , q 2, E ); a process section time means (Z, R i ) for determining a process section time (T) for the process section point; a section time means (Z) for specifying a section time (T) for at least one robot (1) of the robot arrangement based on the process section time (T); and optimizing means (R i ) for optimizing a work flow (q 1 (s (t)) of this robot on the basis of the predetermined section time, thereby characterized in that the control means is arranged to carry out a method according to one of the preceding claims.
  7. Control means after Claim 6 , characterized in that one of its means is at least partially implemented in a controller (R i ) of a robot of the robot arrangement and / or in a controller (Z) of the robot arrangement.
  8. Computer program product with a computer program stored thereon for carrying out a method according to one of the preceding Claims 1 to 5 ,
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PCT/EP2011/005477 WO2012069129A1 (en) 2010-11-23 2011-10-28 Method and control element for controlling a robot arrangement

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