EP3449325A1

EP3449325A1 - Method and device for defining a movement sequence for a robot

Info

Publication number: EP3449325A1
Application number: EP17718911.5A
Authority: EP
Inventors: Sami Haddadin
Original assignee: Kastanienbaum GmbH
Current assignee: Kastanienbaum GmbH
Priority date: 2016-04-24
Filing date: 2017-04-21
Publication date: 2019-03-06
Also published as: JP2019514705A; US20190168383A1; KR20190032280A; DE102016004841B4; SG11201809340WA; WO2017186601A1; CN109313436A; DE102016004841A1

Abstract

The present invention relates to a method and to a device for defining a movement sequence for a multi-axis manipulator (M) of a robot system, which manipulator (M) has a plurality of elements (G) which form different rotational axes, and an end element for interaction with an effector (E), wherein the effector (E) is intended to carry out at least one arbitrary operation in a working space (R), and wherein in order to carry out the at least one arbitrary operation the end element of the manipulator (M) is to be transferred into an arbitrary target pose (x_i) with respect to the working space (R), wherein the manipulator (M) moves in a plurality of steps (S_i;S_j) to the target pose (x_i) while approaching the end element, and for each step (S_i; S_j) at least one defined impedance pattern (K_x) and/or admittance pattern is defined with respect to at least one axis (A_A;A_G;A_E;A_R) which forms the axis (A_A;_AG;A_E;A_R) of a coordinate system (C_A;_CG;C_E;C_R) which is linked to the manipulator (M).

Description

Method and device for setting

a movement sequence for a robot

The present invention relates to a method and a device for determining a movement sequence for a robot, wherein the movement sequence is required in order to be able to carry out any desired operation in a working space assigned to the robot.

The method according to the invention serves to program a robot system, in particular, but not exclusively, of the lightweight design. Such robotic systems of lightweight construction are designed so that in addition to the necessary six degrees of freedom still have one or more degrees of freedom, which allow to open the so-called null space.

In order for the robot system to be able to carry out the desired operations during subsequent operation and to assume the appropriate poses for this purpose, the latter must be freely programmable with regard to movement sequence and force application or transmission at an end effector. In the abstract sense, the robot system initially represents a state-based automaton, which is freely programmable in several axes.

A common online, ie almost performed in real time programming method for robot systems of this type is the so-called "teach-in" method, in which approached the individual bases of the desired trajectories and then the respective position of the effector over in the robot system integrated encoder is determined and stored in a control unit.

Especially in robot systems of lightweight construction, the so-called direct "teach-in" method is used, in which the effector or the manipulator or robot arm is manually guided and moved directly by an operator, ie the manipulator is the required movement demonstrated in advance ,

This is only possible if, on the one hand, the robot arm has only such a weight and / or a corresponding sensitivity that it can still be moved by an operator, and, on the other hand, if there are no strong translating and thus self-locking gear mechanisms between the individual members of the robot arm or when using transmissions with high ratios a corresponding torque control is provided.

For the said direct "teach-in" method, it is therefore also known that the robot system is guided in its so-called gravitationally compensated state, in which the measured torques are fed back to the thereby active drives between the individual links, which causes the The self-locking of the robot system and any self-locking of the gear mechanism does not come into play, and therefore the robot system can only be moved depending on the external forces applied by an operator during manual guidance taking into account given schemes or programs to compensate for the friction. The performed "teach-in" movements are measured by the sensors already present in the area of the drive mechanisms and joints between the individual links of a robot arm, which can absorb both torques and translatory forces These are therefore not described analytically, but are determined exclusively by the manual guidance of the operator and thus by the course in the space.The existing sensors can thereby forces and torques Therefore, a robot system inherent in a high articulation via the provision of a plurality of degrees of freedom is hardly or only with a considerable programming effort feasible as a system that can be used over all degrees of freedom can be designed fully traceable, which in turn leads to the fact that the manual guidance of a manipulator of such a robot system is fraught with several disadvantages.

A manipulator of a lightweight robot usually provides seven degrees of freedom in terms of its mobility. However, the definition of a workspace in which the robot is to perform one or more operations is limited, for example using a Cartesian space, to six dimensions, thereby providing an additional degree of freedom for the manipulator, commonly referred to as null space. However, this results in a movement of the manipulator in a "teach-in" programming by the user is difficult to handle, since the manipulator can also move in coordinates, and purely coincidental, for the intended (s) task (n) not are relevant. Apart from the fact that such a behavior of the robot is in principle not desirable and can hardly be interpreted correctly by users who are not so familiar with the programming of such robot systems in the context of the programming, such behavior proves to be in the programming of the robot system as very inefficient.

Since the manipulator itself can not actively help to move due to a very passive behavior with respect to the movements in his joints within the correct coordinates of the assigned working space, it shows that a highly accurate positioning of the manipulator and thus the effector in the workspace is very difficult to perform.

For carrying out the "teach-in" method, the robot systems generally have an input device in the region of the robot arm, by means of which, for example, the gravitationally compensating mode of the robot system can be activated or deactivated.

As a result, the operator needs one hand to operate the gravity-compensating mode-activating input device and the other hand to manually guide the effector. This means that there is no longer any possibility for him to specifically influence those degrees of freedom which are not important when guiding the effector into the desired position, which would be advantageous for a highly accurate "teach-in" method. A user always needs both hands to realize an exact positioning.

A disadvantage of robotic systems that are supposed to perform defined operations in a workspace is also that For each individual operation, a separate programming or independent "teach-in" procedure must be carried out, although the operations may be identical in their nature, but must be carried out at different positions within the work space. that the same operation is that two elements, such as housing parts, connected to each other, for example, to be screwed .. The screwing process as such would be due to identically used screws and dimensions of the threaded holes on the housing parts respectively the same, with the positions of the threaded holes When using the programming or "teach-in" methods known from the prior art, these would therefore have to be carried out again for each individual threaded hole for the screwing operation. This requires a certain time and therefore costly programming effort.

On this basis, it is an object of the present invention to provide a robot system and a method for programming such a robot system, which eliminate the disadvantages mentioned above. Furthermore, it is an object of the invention to provide in this connection a method and a device for defining a defined movement sequence for a robot system, which allows a simple replicability and transferability of the operations to be performed by these movement sequences. This object is achieved with a method according to claim 1, a robot system according to claim 20 and a device according to claim 21.

The invention therefore relates to a method for determining a movement sequence for a multi-axis manipulator a robot system having a plurality of different axes of rotation forming members and an end member for cooperation with an effector, wherein the effector in a working space to perform at least any operation, and wherein the end member of the manipulator for performing the at least one arbitrary operation in any Target pose is to be transferred with respect to the working space, the method being characterized by

Moving the manipulator in several steps while approaching the end member to the target pose,

wherein for each step at least one defined impedance pattern and / or admittance pattern is defined with respect to at least one axis forming the axis of a coordinate system associated with the manipulator.

The multi-axis manipulators of lightweight robots are generally used as rigid bodies, elastic and / or viscoelastic elements, such as e.g. as a spring-mass system, modeled and regulated. Such a spring-mass system inherits a spring stiffness and / or impedance, whereby the spring stiffness can change via control loops and thus an impedance behavior with respect to the task space can be determined. This spring stiffness can be targeted via a control of the individual, arranged in the joints between two axle links drive units, influence and adequately dampen, thereby defining in principle

Yielding yield pattern. In other words, the movement behavior and interaction behavior of the manipulator in its entirety can be influenced in a targeted manner.

This possibility is now used according to the invention, in the programming of a desired movement sequence for a manipulator or in the "Teach-in" defined impedance pattern and / or admittance pattern on individual axes of one and the same coordinate system or of different coordinate systems. In the simplest form these are defined compliance patterns. According to the invention, this may be an arbitrary coordinate system comprising at least one of the axle members of the manipulator, another of the axle members of the manipulator, one or more joints between two axle members movably connected thereto, the effector attached to the end member of the manipulator is arranged, and / or the workspace in which the effector performs one or more operations is assigned directly. There may also be various arbitrary coordinate systems. In addition, it could also be a coordinate system whose axes can be identified automatically, for example, with reference to a manifold, ie, the system for performing the method learns by machine which coordinate system could be the most appropriate.

Moreover, it can be provided according to the invention that determines the arbitrary coordinate system by the type of the effector, the pose to be taken and / or the type of operation to be performed. For example, if it is a screwing operation to be performed by the effector, a screwdriver, then the arbitrary coordinate system may be defined as a polar coordinate system in this context. It is also possible that the arbitrary coordinate system is designed to be time-variant, if, for example, the manipulator has to follow a predetermined movement for carrying out the imaginary operation, which is determined, for example, by a conveyor belt moving along the robot in the region of the working space. Within these arbitrary coordinate systems, according to the invention, it is then provided that the axis (s) selected for the application of the impedance patterns and / or admittance patterns relates to a translatory alignment or to a rotational alignment. In other words, during programming, it is therefore possible to use a targeted impedance behavior and / or admittance behavior with regard to a translatory partial or total movement of the manipulator and / or an impedance behavior and / or admittance behavior with respect to a rotary partial or total movement of the manipulator.

In a preferred embodiment of the method according to the

Invention it is provided that then

for a step, a defined impedance pattern and / or

Admittanzmuster is set with respect to an axis in a translational alignment, and

for a further step, defining a defined impedance pattern and / or admittance pattern with respect to an axis in a rotational orientation.

These steps can then be repeated (in an even or odd number) until the desired target pose is reached. Within these repetitions, the respectively identical impedance patterns and / or admittance patterns already defined for the previous steps can then be used for each individual step, or the impedance patterns and / or admittance patterns between the steps can be varied.

The method according to the invention is therefore characterized in that the programming of the desired sequence of movements can be carried out in several steps or loops by approaching the final pose in several stages. The number of steps can be chosen arbitrarily or results from the spatial circumstances. Thus, it is possible that in order to achieve one and the same pose in a work space, different motion sequences in different programming methods can result from manual guidance. If the space in which the manipulator moves during "teach-in" in accordance with the method according to the invention is free of obstacles, the manipulator could be guided more or less directly to the goal in just a few steps People working in a human-robot collaboration can manipulate the manipulator around these obstacles in several steps to the desired destination.

According to the invention, it is provided that the impedance patterns and / or admittance patterns are designed to be constant, time-variable and / or state-dependent during a step.

In order to carry out the method according to the invention, a robot system having a multiple degrees of freedom manipulator may comprise a control unit and an input device for programming the robot system, wherein the control unit and the input device are configured such that at least one impedance pattern and / or during programming of the robot system Admittance pattern is applied to an axis of a coordinate system. This means that at least one degree of freedom of the multiple degrees of freedom is controllable with regard to a mobility inherent in this degree of freedom.

The control unit is designed so that it is the one or more coordinate systems in advance in accordance with the previous specified parameters and the type of coordinate systems then chooses what makes the most sense for the required application. In addition to preferably Cartesian coordinate systems, cylindrical, spherical coordinate systems or coordinate systems defined by manifolds are also conceivable.

The operator is enabled by the robot system according to the invention or the method according to the invention, as required to apply individual joints of the robot system for programming purposes with defined impedance patterns and / or Admittanzmustern, for example. To attenuate defined Deflection pattern, and thus selectively To selectively influence the degrees of freedom of the robot system in order to adjust the degree of freedom of movement mobility for a movement to be performed during the programming of the robot system. In this way, the movements can be defined taking into account the predetermined coordinate systems either with regard to the rotational and / or translational alignment, as previously mentioned.

The invention has the advantage that, instead of always activating or deactivating the gravitation-compensated mode, a multi-stage, selectively programmable control method is proposed for the "teach-in", in which only a part of the multiple present in the robot system at any time Degrees of freedom can be changed by external forces, namely by the application of defined impedance patterns and / or admittance patterns, such as compliance patterns, which can be intentionally damped and / or blocked, as a result of which the number of available multiple degrees of freedom by an operator is increased of the robot system for a while programming the Robotic system can be reduced to performing movement, which results from the manual guiding. This is done by selectively or individually attenuating or blocking one or more degrees of freedom, so that a movement, in particular with regard to the interaction with the environment, is limited to the unobstructed degrees of freedom. Blocking is in this context not to be understood as an absolute lock; Preferably, a joint is subjected to an extremely hard damping, which means that such a high rigidity ultimately leads to a blockage of the joint, wherein minimal slight movements are still possible, while another joint is subjected to an extremely soft damping, which means that such low stiffness leads to a release of this joint.

Thus, the relative mobilities made possible by the joint mechanisms should, for example, be selectively damped between individual links of a robot arm, the degree of damping being set differently and being able to differ from joint to joint. This can be done by a corresponding control of arranged in the hinge points drive mechanisms. In a simple case, for example, a three-step method may be used in which the manipulator is first transferred to a gravitationally compensated (and / or centrifugal and / or coriolis force and / or inertia compensated) state, roughly surrounding the manipulator in the vicinity of the desired one To bring a pose. Thereafter, only the axes of rotation with respect to a coordinate system connected to the end effector are enabled to make a first correction of the end effector alignment. Thereafter, these rotation axes are almost blocked, ie provided with an extremely high rigidity, and only the Translatory axes with respect to this coordinate system released so that the final position of the end effector is set. These steps can be repeated in one or more loops until finally the final desired pose is achieved in the sense of a fine adjustment.

As a result, programming as such is substantially simplified, since the operator can more easily guide a multi-jointed robot system with an effector in relation to the degrees of freedom that are not relevant for the task, and can also set poses of the robot system by means of which trajectories can be defined , the previously known obstacles, such as, for example, a working space of a worker in the immediate vicinity of the robot system in subsequent operation, take into account accordingly.

The input device may be disposed on a member of the robotic system, preferably in the region of the end effector, or it may be an external tablet, so that the operator when manually guiding the desired

Permissibility pattern, quasi in real time, one-handed activate or deactivate and thereby also distinguish between individual joints of the manipulator.

Moreover, the method according to the invention for programming facilitates the one-handed guidance of, for example, 7-axis manipulators with a zero space, as a result of which the setting times can be further reduced while reducing the set-up costs.

In a particularly preferred embodiment, this is

Method according to the invention further characterized in that an overall impedance pattern generated after performing all the individual steps and / or Gesamtadmittanzmuster for the determined movement sequence with respect to the target pose is applied to at least one further target pose while maintaining a common target orientation in the context of impedance behavior and / or admittance behavior, wherein the position or translation of the further target pose relative to the position or translation of the original target pose within a common plane and / or angularly offset therefrom. It is thus possible to use a desired orientation of the robot arm, and thus of the effector, once again established by the "teach-in" in order, for example, to determine parallel objects located on one plane For example, when screwing a housing cover with several positions of the screw guides distributed over the cover, only the desired position or translation of the end effector with a screwdriver element with respect to the position of the respective threaded hole is taught the desired orientation resulting from the screwing movement to be carried out is maintained and the programming times can be further shortened as a result.

The method according to the invention offers a novel concept for programming or defining a movement sequence for a multiaxial manipulator of a robot system, in particular the lightweight construction, which is characterized by the selection of different compliance patterns or impedance profiles for restricting the movements with respect to a workspace. An overall compliance behavior of the manipulator is determined in relation to the workspace to be matched to a specific task. Be there for a desired interaction On the one hand, different coordinate systems and, on the other hand, different compliance characteristics necessary, can be switched back and forth in a simple manner during the "tech-in" process, in particular by direct input to the robot, between the individual impedance profiles and / or admittance profiles.

Further advantages and features of the invention will become apparent from the description of the embodiments illustrated with reference to the accompanying drawings. Show it:

1 shows an exemplary representation of a multi-axis manipulator of a robot system in which possible coordinate systems for the method according to the invention are indicated schematically;

FIG. 2 is a flow chart illustrating the essential steps of an embodiment of the method according to the invention; FIG.

3a is a diagram illustrating a stepwise method according to the invention in comparison with known methods; and

Fig. 3b is a diagram of the possible mutual

Interrelations of individual compliance patterns, with only stiffnesses being provided.

In FIG. 1, by way of example, a robot system with a manipulator M consisting of several axle links A is shown, which are connected to one another via joints G. At the end of the manipulator M, an effector E is provided which is to perform a specific operation in a working space R. The manipulator M, which is to assume a pose x, can be assigned a number of coordinate systems, which are shown schematically in FIG. 1, in the present case as Cartesian coordinate systems. However, other coordinate systems are also conceivable, such as, for example, coordinate systems associated with manifolds.

A first coordinate system C _A may, for example, refer to one of the axis members A and have corresponding axes A _A within this coordinate system C _A , which define this coordinate system C _A.

A second coordinate system C _E is directly related to the effector E and accordingly has axes A _E defining this coordinate system C _E.

A third coordinate system C _G may refer directly to a single joint G and is therefore defined by the axes A _G.

The fourth coordinate system C _R may be a coordinate system which relates to the working space R and is defined via the corresponding axis A _R. In the "teach-in" method according to the invention, the manipulator M is transferred into a pose x ± in several steps S ±, Sj (see FIGS. 2 and 3 a) by the effector E or the end member of the manipulator M carrying it is approximated to the final pose x ±, where the pose x ± corresponds to the working space R itself, which corresponds to the location of an operation to be performed in it, for example

Montagearbeitsplatz, and by the nature of the operation to be performed, for example. Screwing results. However, it can also be a simple positioning of the effector E in space act that does not derive directly from a task.

At least one defined impedance pattern and / or admittance pattern is defined for each step S ±, S _j , in the present case a compliance pattern resulting from an impedance or stiffness matrix K _x .

According to the invention, the impedance patterns and / or admittance patterns should be designed so that they relate to at least one axis of a selected coordinate system, ie, for example, to at least one axis A _{A of} the coordinate system C _{A of} one or more axis members A, on at least one axis A _{G of} the coordinate system C _{G of} one or more joints G, on at least one axis A _{E of} the coordinate system C _{E of} the effector and / or on at least one axis A _{R of} the coordinate system of one or more work spaces R.

FIG. 2 schematically shows a flow chart of an exemplary embodiment of the method according to the invention, which can be performed manually by an operator on a robot system for its programming.

In a first step 10, the manipulator M is brought into a compensated mode. For this purpose, by appropriate control of the drive units in the joints G corresponding counterforces and counter moments are generated to counteract the gravitational force, if necessary. A centrifugal and / or a Coriolis force and / or initiated inertial forces, whereby the dead weight and thus the inertia of the manipulator M and a any self-locking of the gear or joints is lifted, so that the manipulator M can show only a restorable behavior. The operator is now able to bring the robot arm or effector E approximately in the desired pose and / or to move to the desired position.

If, for example, a Cartesian coordinate system is taken into account as a relevant coordinate system, possible Cartesian task-related stiffness elements which, in the decoupled case, define the translational and rotational Cartesian stiffness, are obtained

The manipulator M can be free in certain directions move, define the associated with these n _t - TEN stiffness elements as k _{X / 1} = 0 for this purpose may be below specification or selection of a damping profile or compliance pattern a particular Cartesian task-related attenuation d _x, ± with respect to the directions limited to 6 - n _t . It should be noted that in practice a damping or

Impedance with respect to the null space should not be specified in more detail in order to interact with the task or

Operation under real conditions (eg by

Sensor noise). Nevertheless, it can also be provided that in the context of the method according to the invention an independent, for example, possibly time-variant yield pattern is assigned to the null space. Simply stated, a Cartesian stiffness matrix then results

in which reproduce the translational and rotational diagonal, positively defined stiffness matrices.

In a first step Si of the above-mentioned approximation, a compliance pattern with respect to an axis of a Cartesian coordinate system, for example the axis A _{A of} the coordinate system C _A , is then set in a translatory alignment. The corresponding stiffness matrix then results as

KT teach

A single execution of this step Si could already be sufficient to reach the target pose xi (step 20 in FIG. 2). However, the step Si could also be repeated one or more times (step 30 ^λ in FIG. 2).

In a further step S _{j of} the approximation, a defined coordinate A _{A of} the coordinate system then becomes Compliance pattern set in a rotational orientation. The corresponding stiffness matrix thus results as

K r teach

These steps of the "teach-in" method according to the invention can be repeated as often as necessary, but not always alternately (steps 30 ^λ , 30 ^{λ λ} in FIG. 2), until the pose Xi has finally been reached (step 40 in FIG Fig. 2).

The steps, which are once focused only on the translational alignment and once only on the rotational orientation, therefore constitute much simpler "teach-in" steps.

Preferably, the method according to the invention can be used to transfer a once determined and set pose Xi to another target pose X, which differs from the pose xi only by another position but has a common target orientation (step 50 in Fig. 2).

For example. is in the pose x a screw to be screwed through the effector E of the manipulator M in a component. At other points of the component are s- 1 screws, which are also to be screwed.

After the transfer to the gravitationally compensated state, for example, a change is made between the translational and the rotational states, as mentioned above. The Stiffness matrix is about the selection of

Compliance pattern custom, i.

_, - l T ₍

If the pose x _{± is} reached, it is quasi stored as a reference.

Thereafter, switching to a mode in which the manipulator M is guided to the other s - 1 positions of the other screws, and then only the position is stored, since the orientation is indeed the same. The corresponding matrix then appears as

For any further pose X is then then

It becomes clear that any number of additional poses xi, X ... x _s can be programmed in a systematic way by using the previous compliance patterns defined by the stiffness matrices.

3a illustrates in an exemplary manner the advantage of the method according to the invention in comparison to known "teach-in" methods individual steps in which the effector E of a manipulator M to take a pose at a certain target point B in a workspace R. It should be emphasized that the target point B at which an operation is ultimately to be performed by the effector E of the manipulator M is not known as an input parameter for the programming of the motion sequence which the manipulator M is to run through for this purpose.

To start a movement of a manipulator M from an initial state at the position A, which may be located anywhere in the room, which is completely separated and decoupled from the working space R, in which the position B is located.

In a pure motion programming (dotted line), the manipulator M would end with its effector E at any point Β ^λ , which inevitably can not coincide with the desired position, since it is either unknown or insufficiently known. Since B is not known in advance or only inadequately, but only implicitly by the result to be achieved (pose, operation at point B), no environment model can be generated that could be used for pure motion programming.

In a "teach-in" programming in which the manipulator M is performed only in a gravitationally compensated state (dashed line), the effector E always ends in a position Β ^{λ λ} , which is too inaccurate and therefore from the desired position B. However, a minimal deviation is already sufficient that the desired operations, such as screwing in a screw, can not be carried out without error and in a reliably replicable manner. Operation, ie ultimately guiding the manipulator to perform in the present case as much more difficult.

According to the invention, the guidance of the manipulator M is therefore subdivided into a plurality of steps S 1 to S 4, which can assume a different duration, wherein each step then has one defining a compliance pattern

Stiffness matrix Kl is assigned to K4. In this way, the effector E can approach the position B exactly (solid line) in order to assume the pose x _B necessary for the imaginary operation.

In the application of the different stiffness matrices K1 to K4, possibly with simultaneous compensation with respect to gravity, inertia, centrifugal forces and / or Coriolis forces, these can in turn be matched to each other via steps S1 to S4, i. the resulting individual compliance patterns are all interrelated, as illustrated in FIG. 3b.

It becomes clear that the targeted selection of the number of steps on the one hand and the targeted selection of the impedance pattern and / or admittance pattern, in the simplest case of compliance patterns on the other hand, a gradual realization of the desired pose (s) is possible in advance in the programming of the course of motion is not included due to a lack of knowledge.

Claims

claims

A method of determining a sequence of motions for a multi-axis manipulator (M) of a robot system comprising a plurality of different axes of rotation forming members (G) and an end member for cooperation with a

Effector (E), wherein the effector (E) in a workspace (R) to perform at least any operation, and wherein the end member of the manipulator (M) for performing the at least one arbitrary

Operation in any desired pose (χ ±) with respect to the working space (R) to be transferred,

marked by

Moving the manipulator (M) in several steps (S ± Sj) as the end member approaches the target pose (xi),

wherein for each step (S ±; Sj) at least one defined impedance pattern (K _x ) and / or admittance pattern is established with respect to at least one axis (A _A ; A _G ; A _E ; A _R ) defining the axis (A _A ; A _G ; A _E ; A _R ) one with the manipulator (M)

linked coordinate system (C _A , C _G , C _E , C _R ) forms.

The method of claim 1, wherein the at least one axis (A _A ; A _G ; A _E ; A _R ) is translational

Orientation and / or relates to a rotational orientation.

The method of claim 2, wherein

for a step (Si), a defined impedance pattern and / or admittance pattern with respect to an axis

(A _A ; A _G ; A _E ; A _R ) in a translational orientation

is determined, and for a further step (S _j ) a defined

Impedance pattern and / or admittance pattern with respect to an axis (A _A ; A _G ; A _E ; A _R ) is set in a rotational orientation.

4. The method of claim 3, wherein at least one of the steps (S ±; Sj) or all steps (S ±; Sj) n times

be repeated until the target pose (xi) is reached.

, The method of claim 4, wherein for each step (Si;

S _j ) of the nth repetition the respectively defined

Impedance pattern and / or admittance pattern is maintained or varied.

Method according to one of Claims 3 to 5, in which the impedance patterns and / or admittance patterns are designed to be constant, time-variable and / or state-dependent during a step (Si; S j).

Method according to one of claims 1 to 6, further comprising the step:

- Setting at least one arbitrary

Coordinate system with respect to the manipulator (M). 8. The method of claim 7, wherein an arbitrary

Coordinate system (C _A ) with respect to an axle member (A) of the manipulator (M) is set.

9. The method of claim 7 or 8, wherein an arbitrary coordinate system (C _G ) with respect to a joint (G) between two Achsgliedern (A) of the manipulator (M) is set.

10. The method of claim 7, 8 or 9, wherein a

arbitrary coordinate system (C _E ) with respect to the effector (E) is determined.

11. The method of claim 7, 8, 9 or 10, wherein an arbitrary coordinate system (C _R ) with respect to the

Workspace (R) is set.

12. The method according to any one of claims 8 to 11, wherein the arbitrary coordinate system in dependence of the target pose (xi) determined.

13. The method according to any one of claims 8 to 12, wherein the arbitrary coordinate system is designed time-varying. 14. The method according to any one of claims 8 to 13, wherein the arbitrary coordinate system determined in dependence on the operation to be performed.

15. The method according to any one of claims 1 to 14, further comprising the step:

- Transfer of the manipulator (M) in one

gravitationally compensated condition and / or

Centrifugal force compensated state and / or

Coriolis force compensated state and / or

inertia-compensated state.

16. The method according to any one of claims 1 to 15, wherein a after performing the steps (S ±; S _j ) generated

Total impedance pattern and / or total admittance pattern for the motion sequence to be determined with respect to the target

Pose (xi) is applied to at least one further target pose (Xj) while maintaining a common orientation within the context of the impedance behavior and / or admittance behavior, the position of the further target pose (Xj) relative to the position of the target pose (Xj). x ±) within one common plane and / or angularly offset to this.

A computer program comprising program instructions that cause a processor to execute and / or control the steps of the method of any one of claims 1 to 16 when the computer program is run on the processor.

18. A data storage device on which a computer program according to claim 17 is stored.

19. Computer system with a

Data processing apparatus, wherein the

Data processing device is configured such that a method according to any one of claims 1 to 16 is carried out on the data processing device.

20. Robot system with a multi-axis manipulator (M) and with an end member (E) of the manipulator (M) for

Carrying out an operation comprising means for

Execution of the method according to one of claims 1 to 16.

21 device for determining a movement sequence for a multi-axis manipulator (M) of a robot system, the multiple, different axes of rotation forming links

(G) and an end member for cooperation with an effector (E), wherein the effector (E) in a working space (R) to perform at least any operation, and wherein the end member of the manipulator

(M) for carrying out the at least one arbitrary

Operation in any desired pose (xi) with respect to the working space (R) to be transferred, wherein the device is designed such that the following Steps are executable:

Moving the manipulator (M) in several steps (S ± S _j ) as the end member approaches the target pose (x ±), wherein for each step (S ±; S _j ) at least one defined impedance pattern (K _x ) and / or admittance pattern with respect to at least one axis (A _A ; A _G ; A _E ; A _R ) defining the axis (A _A ; A _G ; A _E ; A _R ) of an axis associated with the manipulator (M) Coordinate system (C _A , C _G , C _E , C _R ) forms.

22. Robot with a manipulator (M) and with a

Apparatus according to claim 21.