DE102015009892A1 - Method and system for controlling a robot - Google Patents

Abstract

A method according to the invention for controlling a robot (30), in particular a medical application, comprises the steps: - determining (S10-S40) a collision force ([Fc, x, Fc, y, Fc, z]) based on a model determined external force (Fe, [F'e, x, F'e, y, F'e, z]) resulting from an external load of the robot, a position error ([Δx, Δy, Δz]) of the robot and a pose (z) and / or velocity ([dx / dt, dy / dt]) of the robot; and detecting (S50) a collision of the robot based on this collision force.

Description

The present invention relates to a method and a system for controlling a robot as well as a robot arrangement with the system and a computer program product for carrying out the method.

In particular, in medical applications such as robot-assisted sonography, it may be desirable to detect a contact of the robot or robotic medical device and then provide a force feedback to a haptic input device of the robot.

F. Dimeas et al., Robotica, May 9, 2014, "Human-robot collision detection and identification based on fuzzy and time series modeling." propose two different methods for collision detection of robots: according to a method, a fuzzy inference system (FIS) of a position error, a commanded speed and the total torques measured at joints joint external joint moments, as the determination of external Forces from a dynamic model of the robot is problematic. According to another method, an autoregressive model ("AutoRegressive" AR), again without a dynamic model of the robot, detects joint torques, where a collision is detected based on a deviation of the joint predicted from the AR from the measured joint torques.

The object of the present invention is to improve the control of a robot.

This object is achieved by a method having the features of claim 1. Claims 7 to 9 protect a system or computer program product for carrying out a method described here or a robot arrangement with a system described here. The subclaims relate to advantageous developments.

• – Ermitteln einer Kollisions-Kraft auf Basis einer modellgestützt ermittelten externen Kraft, die aus einer externen Belastung des Roboters resultiert, eines Positionsfehlers des Roboters und einer Pose und/oder Geschwindigkeit des Roboters; und
• – Erfassen einer Kollision des Roboters auf Basis dieser Kollisions-Kraft.

According to an embodiment of the present invention, a method for controlling a robot, in particular a medical application, comprises the steps:

• - determining a collision force on the basis of a model-based determined external force resulting from an external load of the robot, a position error of the robot and a pose and / or speed of the robot; and
• Detecting a collision of the robot based on this collision force.

• – Mittel zum Ermitteln einer Kollisions-Kraft auf Basis einer modellgestützt ermittelten externen Kraft, die aus einer externen Belastung des Roboters resultiert, eines Positionsfehlers des Roboters und einer Pose und/oder Geschwindigkeit des Roboters; und
• – Mittel zum Erfassen einer Kollision des Roboters auf Basis dieser Kollisions-Kraft,

A system for controlling a robot, in particular a medical application, according to an embodiment of the present invention is, in particular hardware and / or software, in particular program technology, set up for carrying out a method described here and / or has:

• - Means for determining a collision force based on a model-based determined external force resulting from an external load of the robot, a position error of the robot and a pose and / or speed of the robot; and
• Means for detecting a collision of the robot on the basis of this collision force,

As a result, a collision of a robot can advantageously be detected in one embodiment. In particular, by taking into account a model-based determined external force resulting from an external load of the robot, instead of a measured G (esamtg) elenkkraft detection can be improved, in particular by a fuzzy system, which then no longer the functionality of a model for determining the external force must comply with.

In one embodiment, the robot has at least six, in particular at least seven, actuatable or actuated joints. In an embodiment in which a medical application of the robot is controlled, it carries a medical instrument, in particular an ultrasound head or the like.

For a more compact representation, an anti-parallel force pair or torque is generally referred to herein as a force. A force, in particular the determined collision force, the model-based determined external force and / or a feedback force explained below, may in particular comprise a Cartesian force with components in one or more Cartesian directions, in particular of an inertial or robot base fixed or robot end member fixed coordinate system, in particular be.

In one embodiment, a position error depends on a deviation between an actual, in particular measured, pose of the robot and a desired, in particular commanded, pose of the robot, in particular a deviation between an actual position and a desired position and / or orientation of a robot robot-fixed reference, in particular the TCPs, he can specify or be particular the deviation.

A pose of the robot depends in one embodiment on the position of its joints, in particular drives, and / or the position and / or orientation of a robot-fixed reference, in particular of the TCP, from, in particular specify or be. In general, a position and / or orientation of a robot-fixed reference, in particular of the TCP, is thus understood to be a pose of the robot for a more compact representation.

Accordingly, in one embodiment, a speed of the robot depends on the speed of its joints, in particular drives, and / or the translational and / or rotational speed of a robot-fixed reference, in particular of the TCP, it can indicate or be particular. In general, for the purpose of a more compact representation, a speed of a robot-fixed reference is also understood here to be the speed of the robot.

• – Ermitteln (jeweils) eines oder mehrerer, insbesondere wenigstens zweier, insbesondere wenigstens dreier, Zugehörigkeitsgrade einer oder mehrerer Komponenten der modellgestützt ermittelten externen Kraft, (jeweils) eines oder mehrerer, insbesondere wenigstens zweier, insbesondere wenigstens dreier, Zugehörigkeitsgrade einer oder mehrerer Komponenten des Positionsfehlers des Roboters und (jeweils) eines oder mehrerer, insbesondere wenigstens zweier, insbesondere wenigstens dreier, Zugehörigkeitsgrade einer oder mehrerer Komponenten der Pose und/oder Geschwindigkeit des Roboters auf Basis von einer Fuzzy-Menge bzw. Zugehörigkeitsfunktionen eines Fuzzy-Systems; und
• – Ermitteln einer oder mehrerer Komponenten der Kollisions-Kraft auf Basis des Fuzzy-Systems in Abhängigkeit von diesen Zugehörigkeitsgraden.

In one embodiment, the method, in particular its step of determining a collision force, comprises the steps:

• Determining (in each case) one or more, in particular at least two, in particular at least three, degrees of membership of one or more components of the model-based determined external force, (respectively) one or more, in particular at least two, in particular at least three, degrees of membership of one or more components of the position error the robot and (each) one or more, in particular at least two, in particular at least three, degrees of membership of one or more components of the pose and / or speed of the robot on the basis of a fuzzy set or membership functions of a fuzzy system; and
• Determining one or more components of the collision force on the basis of the fuzzy system as a function of these degrees of membership.

• – Mittel zum Ermitteln (jeweils) eines oder mehrerer, insbesondere wenigstens zweier, insbesondere wenigstens dreier, Zugehörigkeitsgrade einer oder mehrerer Komponenten der modellgestützt ermittelten externen Kraft, (jeweils) eines oder mehrerer, insbesondere wenigstens zweier, insbesondere wenigstens dreier, Zugehörigkeitsgrade einer oder mehrerer Komponenten des Positionsfehlers des Roboters und (jeweils) eines oder mehrerer, insbesondere wenigstens zweier, insbesondere wenigstens dreier, Zugehörigkeitsgrade einer oder mehrerer Komponenten der Pose und/oder Geschwindigkeit des Roboters auf Basis von Zugehörigkeitsfunktionen eines Fuzzy-Systems; und
• – Mittel zum Ermitteln einer oder mehrerer Komponenten der Kollisions-Kraft auf Basis des Fuzzy-Systems in Abhängigkeit von diesen Zugehörigkeitsgraden.

Accordingly, the system, in particular its means for determining a collision force, in one embodiment:

• - means for determining (in each case) one or more, in particular at least two, in particular at least three, degrees of membership of one or more components of the model-based determined external force, (respectively) one or more, in particular at least two, in particular at least three, degrees of membership of one or more components the positional error of the robot and (respectively) one or more, in particular at least two, in particular at least three, degrees of membership of one or more components of the pose and / or speed of the robot on the basis of membership functions of a fuzzy system; and
• - Means for determining one or more components of the collision force based on the fuzzy system as a function of these degrees of membership.

A degree of membership can be determined in a manner known per se on the basis of a membership function of the fuzzy system. In other words, the component (s) of the model-based determined external force, position error, pose and / or velocity are fuzzified and from these fuzzified quantities or degrees of membership, in particular rule-based by the fuzzy system, in particular again defuzzified, component (s). the collision force determined. For this purpose, in addition to the above-mentioned publication F. Dimeas et al., Robotica, May 9, 2014, "Human-robot collision detection and identification based on fuzzy and time series modeling." , And the contents of which are fully incorporated in the present disclosure. For example, a first membership function of a component of the model-based determined external force / position error / pose / velocity (each) may have a degree of membership to a first fuzzy set, e.g. B. "small" and another degree of membership to a second fuzzy set, z. B. "large" assign, possibly also one or more other degrees of membership to other fuzzy sets, z. B. "medium" o. Ä.

The fuzzy system is in one embodiment a FIS ("fuzzy inference system"), in particular Sugeno or Mamdani. In one embodiment, it includes the membership functions that map the inputs to degrees of membership, rules or a rule base that maps the fuzzified inputs to outputs, and / or (inverse) membership functions that defuzzify the fuzzified outputs. In one embodiment, the FIS evaluates its output by weighting the rule base with the degrees of membership. This weighting then comes in another fuzzy set for defuzzification and this results in the output of the FIS (Mamdani). In another embodiment (Sugeno) the defuzzification is carried out by means of the weighting of the rule base and by means of the evaluation of a linear function of the input variables.

It has surprisingly been found that a fuzzy system with the input variables mentioned external force, position error and pose or speed is particularly advantageous for detecting collisions, since in particular non-collision-related variations in the external force can be advantageously filtered.

In one embodiment, a component of the collision force in at least a first Direction (respectively) depending on one or more membership degrees of a component of the model-based determined external force in this first direction, one or more degrees of membership of a component of the position error of the robot in that first direction, and / or one or more degrees of membership of a position of a robot-fixed reference in FIG determined this first direction.

Accordingly, in one embodiment, the system or its means for determining at least one component of the collision force comprises means for determining a component of the collision force in at least a first direction (respectively) depending on one or more degrees of membership of a component of the model-based determined external Force in said first direction, one or more degrees of membership of a component of the positional error of the robot in this first direction, and / or one or more degrees of membership of a position of a robot-fixed reference in that first direction.

A first direction may in particular be a robot (member) or space-fixed and / or Cartesian direction, in particular of the working space of the robot. In one embodiment, a first direction is the vertical direction, a horizontal direction, or a direction inclined to the vertical and horizontal. In one embodiment, a first direction is a collision direction, in particular an anticipated and / or main collision direction, and / or perpendicular to a potential, in particular predetermined, collision plane. For example, in an ultrasound examination of a patient lying horizontally, the vertical is the expected main collision direction.

It has been found that, for an advantageous determination of a component of the collision force in certain directions, in particular in a (main) collision direction, advantageously in addition to the position error and the component of the external force, the position of a robot-fixed reference in this direction is particularly suitable.

Additionally or alternatively, in one embodiment, a component of the collision force in at least one second direction (respectively) is dependent on one or more degrees of membership of a component of the model-based determined external force in that second direction, one or more degrees of membership of a component of the position error of the robot in this second direction and / or one or more degrees of membership of a speed of a robot-fixed reference in this second direction.

Accordingly, in one embodiment, the system or its means for determining at least one component of the collision force additionally or alternatively comprises means for determining a component of the collision force in at least one second direction (respectively) in dependence on one or more degrees of membership of a component model-assisted external force in this second direction, one or more degrees of membership of a component of the position error of the robot in this second direction, and / or one or more degrees of membership of a velocity of a robot-fixed reference in that second direction.

It has been found that, for an advantageous determination of a component of the collision force in certain directions, in particular obliquely to a (main) collision direction, advantageously in addition to the position error and the component of the external force, the velocity of a robot-fixed reference in this, in particular for ( Main) inclined direction of collision, direction is particularly suitable.

The second direction may in particular be a robot (member) or space-fixed and / or Cartesian direction, in particular of the working space of the robot. In one embodiment, the second direction is a horizontal direction, the vertical direction, or a direction inclined to the vertical and horizontal. In one embodiment, the second direction is inclined to the first direction, in particular perpendicular to this. In one embodiment, two second directions are perpendicular to each other and / or two first directions perpendicular to each other.

In one embodiment, the fuzzy system, in particular one or more of its membership functions and / or rules and / or its linear function, is parameterized by means of a neural network, in particular based on the method of least squares and / or the method of backward propagation descending gradient.

Accordingly, in one embodiment, the system comprises means for parameterizing the fuzzy system, in particular one or more of its membership functions and / or rules, by means of a neural network, in particular based on the method of least squares and / or the method of backward propagation descending gradient.

As a result, in one embodiment, the method or system can advantageously be adapted to different robots and / or applications, in particular rapidly, autonomously and / or robustly.

In one embodiment, the external force is modeled based on a dynamic model of the robot. Accordingly, in one embodiment, the system includes means for model-based determination of the external force based on a dynamic model of the robot.

In one embodiment, the dynamic model maps a pose, speed and / or acceleration of the robot and forces acting thereon, in particular according to a relation M (q) .d ² q / dt ² + h (q, dq / dt) = T _mot - T _e with the mass matrix M, the joint coordinates or the position and orientation of a robot-fixed reference q or their time derivatives, the force vector h, the driving forces T _mot and the external forces T _e . It can equally be implemented in Cartesian or joint coordinate space. The driving forces T _mot and / or the vector q and its time derivatives can be detected or -mittel in particular by means of sensors.

As mentioned above, in particular, the combination of a model-based determination of external forces based on a dynamic model with the determination of a contact force based on these external forces on the basis of a fuzzy system (s) can improve detection of a collision.

Alternatively or additionally, in particular downstream of the dynamic model, a (time) predictive model, in particular an autoregressive model, in particular an AR model, can be provided in order to determine the external forces in a model-supported manner. As a result, a time delay through the fuzzy system can be compensated for, at least partially.

Accordingly, in one embodiment, the external force is determined on the basis of a predictive model, in particular an autoregressive model. Accordingly, in one embodiment, the system comprises means for model-based determination of the external force based on a predictive model, in particular an autoregressive model.

The predictive model, in one embodiment, maps an external force, determined in an embodiment based on the dynamic model, to a (predicted) external force. In addition to a predictive model is in addition to the above-mentioned publication F. Dimeas et al., Robotica, May 9, 2014, "Human-robot collision detection and identification based on fuzzy and time series modeling." , And the contents of which are fully incorporated in the present disclosure.

In one embodiment, after detection of a collision based on the collision force is switched to another determination to determine a feedback force, this other determination can be carried out in an embodiment even parallel to the determination of the collision force to the To improve switching, in particular to reduce a delay caused thereby.

Accordingly, in one embodiment, a feedback force is determined after detecting a collision of the robot without the fuzzy system and / or the predictive model based on, in particular the same, dynamic model of the robot.

Accordingly, in one embodiment, the system includes means for switching upon detection of a collision based on the collision force to another determination to determine a feedback force, or means for determining a feedback force after detecting a collision of the robot without Fuzzy system and / or the predictive model based on, in particular the same, dynamic model of the robot.

In one embodiment, the feedback force is a feedback force of a haptic input device of the robot or a force, which is impressed on an operating element of an input device of the robot, in particular by at least one actuator, in order to force the operator a contact of the robot, in particular to convey a guided by this tool, in particular medical instrument. Accordingly, in one embodiment, the system or the robot assembly includes a haptic input device and means for applying the feedback force to an operating element of the input device to force feedback to a user a contact of the robot, in particular a guided by this tool, in particular medical instrument mediate, on.

By switching after detecting the contact or the determination of the feedback force without fuzzy system and / or predictive model, distortions, in particular filtering, of the force, which may be useful for detecting a collision, advantageously reduced in one embodiment, and so a force feedback can be improved.

Additionally or alternatively, prior to detecting a collision of the robot, the feedback force may be at least substantially equal to zero based on the determined collision force. Also, this can be a force feedback can be improved.

Alternatively, in one embodiment, the feedback force may be prior to detecting a collision of the robot are also determined on the basis of the determined collision force, in particular this correspond.

A robot assembly according to an embodiment of the present invention includes a robot and a system for controlling the robot described herein.

A means in the sense of the present invention may be designed in terms of hardware and / or software, in particular a data or signal-connected, in particular digital, processing, in particular microprocessor unit (CPU) and / or a memory and / or bus system or multiple programs or program modules. The CPU may be configured to execute instructions implemented as a program stored in a memory system, to capture input signals from a data bus, and / or to output signals to a data bus. A storage system may comprise one or more, in particular different, storage media, in particular optical, magnetic, solid state and / or other non-volatile media. The program may be such that it is capable of embodying or executing the methods described herein, so that the CPU may perform the steps of such methods and, in particular, operate or control the robot.

In one embodiment, one or more of the steps described herein are at least partially automated, in particular by the system or means described herein.

The invention is particularly advantageous in medical applications in which a robot-guided medical instrument temporarily contacts a patient, in particular in robot-assisted sonography or other imaging methods, so that they represent a preferred use and for which therefore particular protection is claimed. For here in particular a reliable, early and / or gentle detection of a contact and / or a subsequent precise power feedback is important. However, it can equally be used in other applications and is therefore not limited to medical applications.

Further advantages and features emerge from the subclaims and the exemplary embodiments. This shows, partially schematized:

1 a robot assembly having a robot and a system for controlling the robot 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 a robot assembly with a robot 30 who has an ultrasound head 31 leads, and a system for controlling the robot 30 or a medical application of the robot in the form of a robot controller 10 that with a haptic input device 20 for controlling the robot 30 is communicating or signal-connected.

The robot controller 10 introduces hereafter with reference to 1 . 2 explained method according to an embodiment of the present invention and for this purpose has a corresponding computer program product.

In a first step S10, the controller determines 10 from joint angles and driving forces, in particular torques, of the robot 30 based on a dynamic model 11 of the robot 30 an external force F _e resulting from external loading of the robot. For this purpose, the driving forces are subtracted from the total joint forces determined from the dynamic model on the basis of the joint angles and their time derivatives and this difference is projected into the Cartesian space by means of the Jacobian matrix, in which the force F _e three components in the x, y and z directions a coordinate system whose z-axis is oriented vertically or counter to the direction of gravity.

Subsequently, in a step S20, the latter is based on the dynamic model 11 determined external force F _e by an ARMA model 12 component-wise a probable external force [F ' _{e, x} , F' _{e, y} , F ' _{e, z} ] determined.

Thus, based on the dynamic model 11 and the predictive model 12 model-based an external force [F ' _{e, x} , F' _{e, y} , F ' _{e, z} ] determined from an external load of the robot 30 results.

In a next step S30, for the components F ' _{e, x} , F' _{e, y} and F ' _{e, z of} this external force are respectively given by FIS 13X . 13Y respectively. 13Z , the subsystems of a FIS 13 form degrees of membership B on the basis of membership functions Bi of the fuzzy system 13 determines how this is done in 1 is indicated schematically.

In an analogous manner, in step S30 in the subsystems 13X . 13Y also for horizontal components Δx, Δy of a position error and horizontal components dx / dt, dy / dt of a speed of the TCPs of the robot 30 each based on membership functions Bi of the fuzzy system 13 Membership degrees B determined.

In an analogous manner, in step S30 in the subsystem 13Z also for a vertical component Δz of the position error and a vertical component z of a position or position of the TCP of the robot 30 each based on membership functions Bi of the fuzzy system 13 Membership degrees B determined.

The subsystems determine from these ascertained degrees of membership B 13X . 13Y . 13Z of the fuzzy system 13 in a step S40, a vertical component F _{c, z} or horizontal components F _{c, x} , F _{c, y of} a collision force are rule-based.

The rules and / or membership functions Bi of the fuzzy system 13 are parameterized in advance by a neural network.

As long as the thus determined collision force [F _{c, x} , F _{c, y} , F _{c, z} ] remains below a predetermined threshold, there is a switching means 14 the controller 10 in a step S50 to the haptic input device 20 a feedback force F _fb equal to zero. Alternatively, the thus determined collision force [F _{c, x} , F _{c, y} , F _{c, z} ] itself as a feedback force F _fb to the haptic input device 20 be issued.

On the other hand, if the collision force [F _{c, x} , F _{c, y} , F _{c, z} ] exceeds the predetermined threshold value, the switching means outputs 14 to the haptic input device 20 in step S50, a feedback force F _fb that controls 10 based on the dynamic model 11 without the predictive model 12 or the fuzzy system 13 determines, in a simple case, directly the external force F _e . It can also output a corresponding, for example optical and / or acoustic, signal

If the amount falls below one, in particular the same, threshold value, the switching means switches 14 back again and the controller 10 detects the next collision of the ultrasonic head in the manner described above 31 ,

Although exemplary embodiments have been explained in the foregoing description, it should be understood that a variety of modifications are possible. It should also be noted that the exemplary embodiments are merely examples that are not intended to limit the scope, applications and construction in any way. Rather, the expert is given by the preceding description, a guide for the implementation of at least one exemplary embodiment, with various changes, in particular with regard to the function and arrangement of the components described, can be made without departing from the scope, as it turns out according to the claims and these equivalent combinations of features.

LIST OF REFERENCE NUMBERS

10

robot control

11

dynamic model

12

AR

13, 13X-13Z

FIS ("Fuzzy Inference System")

14

switching

20

Haptic input device for remote control of the robot

30

robot

31

ultrasound probe

B

membership degree

B _i

membership function

F _e , [F ' _{e, x} , F' _{e, y} , F ' _{e, z} ]

external force

[F _{c, x} , F _{c, y} , F _{c, z} ]

Collision force

F _fb

Feedback force

[Δx, Δy, Δz]

position error

[dx / dt, dy / dt]

horizontal speed

z

vertical position

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited non-patent literature

• F. Dimeas et al., "Robot-Robot Collision Detection and Identification based on Fuzzy and Time Series Modeling", Robotica, May 9, 2014 [0003]
• F. Dimeas et al., "Robot-Robot Collision Detection and Identification based on Fuzzy and Time Series Modeling", Robotica, May 9, 2014 [0016]
• F. Dimeas et al., "Robot-Robot Collision Detection and Identification based on Fuzzy and Time Series Modeling", Robotica, May 9, 2014 [0035]

Claims (9)

Method for controlling a robot ( 30 ), in particular a medical application, with the steps: determining (S10-S40) a collision force ([F _{c, x} , F _{c, y} , F _{c, z} ]) on the basis of a model-based determined external force (F _e , [F ' _{e, x} , F' _{e, y} , F ' _{e, z} ]) resulting from an external load of the robot, a position error ([Δx, Δy, Δz]) of the robot and a pose (z) and / or velocity ([dx / dt, dy / dt]) of the robot; and detecting (S50) a collision of the robot based on this collision force. Method according to Claim 1, comprising the steps of determining (S30) at least one degree of affiliation (B) of at least one component (F ' _{e, x} , F' _{e, y} , F ' _{e, z} ) of the model-based determined external force, at least one degree of affiliation (B) at least one component (Δx, Δy, Δz) of the positional error of the robot and at least one degree of membership (B) of at least one component (z, dx / dt, dy / dt) of the pose and / or speed of the robot based on membership functions (B _i ) of a fuzzy system ( 13 . 13X - 13Z ); and determining (S30) at least one component (F _{c, x} , F _{c, y} , F _{c, z} ) of the collision force on the basis of the fuzzy system as a function of these degrees of membership. A method according to claim 2, characterized in that a component (F _{c, z} ) of the collision force in at least a first, in particular vertical, direction depending on at least one degree of membership of a component (F ' _{e, z} ) of the model-based determined external force in the first direction, at least one degree of membership of a component (Δz) of the positional error of the robot in the first direction and / or at least one degree of membership of a position (z) of a robot-fixed reference in the first direction is determined; and / or a component (F _{c, x} , F _{c, y} ) of the collision force in at least one second, in particular horizontal, direction as a function of at least one degree of membership of a component (F ' _{e, x} , F' _{e, y} ) the model-based determined external force in the second direction, at least one degree of membership of a component (Δx, Δy) of the position error of the robot in the second direction and / or at least one degree of membership of a speed ([dx / dt, dy / dt]) of a robot-fixed reference is determined in the second direction. Method according to one of the preceding claims 2 to 3, characterized in that the fuzzy system ( 13 . 13X - 13Z ) is parameterized by means of a neural network. Method according to one of the preceding claims, characterized in that the external force based on a dynamic model ( 11 ) of the robot and / or a predictive model, in particular an autoregressive model ( 12 ), is determined. Method according to one of the preceding claims, characterized in that a feedback force (F _fb ), in particular a haptic input device ( 20 ) of the robot after detection of a collision of the robot without the fuzzy system and / or the predictive model based on a dynamic model ( 11 ) of the robot is determined and / or detected before detection of a collision of the robot on the basis of the determined collision force ([F _{c, x} , F _{c, y} , F _{c, z} ]) or, at least substantially, is equal to zero , System ( 10 . 20 ) for controlling a robot ( 30 ), in particular a medical application, which is set up to carry out a method according to one of the preceding claims and / or comprises: means ( 10 ) for determining a collision force ([F _{c, x} , F _{c, y} , F _{c, z} ]) on the basis of a model-based determined external force (F _e , [F ' _{e, x} , F' _{e, y} , F ' _{e, z} ]) resulting from an external load of the robot, a position error ([Δx, Δy, Δz]) of the robot and a pose (z) and / or velocity ([x / dt, dy / dt]) the robot; and funds ( 10 ) for detecting a collision of the robot based on this collision force. Robot arrangement with a robot ( 30 ) and a system ( 10 . 20 ) for controlling the robot according to any one of the preceding claims. A computer program product having a program code stored on a computer-readable medium for performing a method according to any one of the preceding claims.

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