DE102021201024B3 - Method and system for operating a robot - Google Patents

Abstract

A method for operating, in particular controlling and/or monitoring, a robot (1) comprises the steps: Specifying (S10) at least one pose of a robot-fixed reference of the robot; Determining (S20) a Jacobian matrix, the axis speeds of the robot to speeds of the robot-fixed reference maps;determining (S30) axis coordinates of the robot on the basis of the specified pose and determined Jacobian matrix; andoperating (S40) the robot on the basis of the determined axis coordinates;wherein the Jacobian matrix is determined on the basis of a previously calibrated transformation that maps the axis coordinates of the robot to a pose of the robot-fixed reference;and/orthe axis coordinates of the robot, taking into account predetermined limits for axis coordinates and/or or time derivations of these coordinates and/or poses of the robot-fixed reference and/or time derivations of these poses are determined.

Description

The present invention relates to a method for operating, in particular controlling and/or monitoring, a robot, as well as a system and a computer program product for carrying out the method.

Robots are often intended to approach or assume specified poses, in particular follow specified paths, and/or comply with specified limits, for example axis or TCP speed limits, using robot-fixed references, for example their TCP.

For this purpose in particular, it is often necessary to determine axis coordinates q of the robot that correspond to predetermined poses x of the robot-fixed reference.

However, while corresponding real poses x = F(q) of the robot-fixed reference can already be predicted with high precision for given axis coordinates q of the robot by means of calibrated transformations F, the determination of axis coordinates q _d of the robot has so far been done in such a way that its robot-fixed reference is real assuming a predetermined pose x _d precisely is difficult, which can affect the operation, particularly the control and monitoring, of the robot.

one from the DE 10 2019 219 930 B3 known method for performing a task by a robot considering a virtual constraint, comprising the steps of: monitoring for a conflict between a first task and a first virtual constraint in a first mode of operation; and switching the robot to a second mode of operation if a conflict is detected in the monitoring.

At one from the DE 10 2018 214 257 B3 known method for controlling a robot, at least one joint controller for adjusting a joint of the robot is adjusted on the basis of a pose of the robot and a predetermined force and position weighting of at least one Cartesian degree of freedom of a robot-fixed reference.

At one from the DE 10 2018 210 864 B3 known methods for controlling a robot on the basis of a Jacobian matrix, which transforms the joint speeds of the robot into a speed of a robot-fixed reference in a workspace of the robot, the robot is controlled on the basis of an inverse of the Jacobian matrix if a selection parameter has a first parameter value, and on the basis controlled by a transpose of the Jacobian matrix if the selection parameter has a second parameter value.

one from the DE 10 2017 010 244 A1 A known method for controlling a robot arrangement with at least one robot arm has the steps: primarily determining a trajectory in the axis space of the robot arrangement on the basis of a path with a plurality of Cartesian poses predetermined in advance at least one reference fixed to the robot arrangement; primarily determining control values in the axle space based on this trajectory; and controlling the robot assembly based on these control values.

the DE 10 2014 222 809 B3 relates to a method and a system for controlling a robot, which has at least one redundant degree of freedom, the method preventing the robot from colliding with the environment due to its redundancy and/or getting into an unfavorable position, without the tool center moving disadvantageously will.

the DE 10 2007 059 480 B4 relates to a method for pose monitoring of a manipulator with the steps: a) determining permissible poses of the manipulator in its working space; b) transforming these legal poses into legal regions in the coordinate space of the manipulator; c) checking whether in a pose to be checked at least one joint coordinate of the manipulator is outside of these permissible ranges; and d) issuing a message indicating whether at least one joint coordinate of the manipulator is outside the permissible ranges.

The object of the present invention is to improve the operation, in particular the control and monitoring, of a robot.

This object is achieved by a method having the features of claim 1. Claims 8, 9 protect a system or computer program product for carrying out a method described here. The dependent claims relate to advantageous developments.

• - Vorgeben wenigstens einer Pose x_d einer roboterfesten Referenz des Roboters;
• - Ermitteln einer Jacobimatrix J(q), die Achsgeschwindigkeiten dq/dt des Roboters auf Geschwindigkeiten dx/dt der roboterfesten Referenz abbildet, in einer Ausführung linear abbildet (dx/dt = ∂x/∂q.∂q/dt = J(q)· dq/dt);
• - Ermitteln von Achskoordinaten q_d des Roboters auf Basis der vorgegebenen Pose und ermittelten Jacobimatrix, insbesondere mit der Maßgabe, dass die roboterfeste Referenz die vorgegebene Pose, insbesondere möglichst präzise, einnimmt bzw. aufweist, wenn der Roboter diese Achskoordinaten q_d einnimmt bzw. aufweist; und
• - Betreiben, insbesondere also Steuern und/oder Überwachen, des Roboters auf Basis dieser ermittelten Achskoordinaten.

According to one embodiment of the present invention, a method for operating a robot comprises the steps, repeated several times in one embodiment:

• - Specification of at least one pose x _d of a robot-fixed reference of the robot;
• - Determination of a Jacobian matrix J(q), which maps axis speeds dq/dt of the robot to speeds dx/dt of the robot-fixed reference, in one embodiment linearly maps (dx/dt = ∂x/∂q.∂q/dt = J(q ) dq/dt);
• - Determination of axis coordinates q _d of the robot on the basis of the specified pose and determined Jacobian matrix, in particular with the proviso that the robot-fixed reference assumes or has the specified pose, in particular as precisely as possible, when the robot assumes or has these axis coordinates q _d ; and
• - Operating, ie in particular controlling and/or monitoring, the robot on the basis of these determined axis coordinates.

According to one embodiment of the present invention, the axis coordinates of the robot are calculated taking into account specified limits for axis coordinates and/or first and/or higher time derivatives dq/dt, d ² q/dt ² ,... of these coordinates and/or specified limits for poses the robot-fixed reference and/or first and/or higher time derivatives of these poses dx/dt, d ² x/dt ² ,... determined in one embodiment such that these limits are determined by the determined axis coordinates and/or the approach to these determined axis coordinates be respected.

In particular, this is based on the idea of already considering or complying with such limits at the level of the inverse kinematics or reverse transformation. As a result, in one embodiment, the operation of the robot can be improved, in particular carried out more safely and/or more efficiently.

In one embodiment, the axis coordinates of the robot are determined on the basis of speeds. As a result, Jacob matrices can be used particularly advantageously in one embodiment.

In one embodiment, the axis coordinates of the robot are determined on the basis of a speed reduction in order to take the specified limits into account. In a development, in an iterative determination of the axis coordinates q _d , those axis coordinates q _s that would lead to a violation of the limits are reduced to such an extent that the limits are, in particular, just kept, in particular set to corresponding limit values, and in a development the other axis coordinates are reduced accordingly. As a result, in one embodiment, the operation of the robot can be improved, in particular carried out more safely and/or more efficiently.

In a further development, the axis coordinates of the robot are determined on the basis of a saturation-in-the-null-space algorithm (SNS algorithm), in particular in order to take into account the specified limits, as described, for example, in the article by F. Flacco, A. De Luca, O. Khatib, Motion Control of Redundant Robots under Joint Constraints: Saturation in the Null Space, 2012 IEEE International Conference on Robotics and Automation, River Centre, Saint Paul, Minnesota, USA, May 14-18, 2012, p. 285 -292 is described, to which additional reference is made and the content of which is fully incorporated into the present disclosure.

zu deren grundsätzlicher Struktur bzw. deren grundsätzlichem Aufbau auf Gl. (13) in diesem Aufsatz Bezug genommen wird. Dabei bezeichnet J die Jacobimatrix, q_d die zu ermittelnden Achskoordinaten, dq_d/dt (im Aufsatz: q̇_SNS) deren erste Zeitableitung, dq_s/dt (im Aufsatz: q̇_N) die erste Zeitableitung derjenigen Achskoordinaten, die zur Einhaltung der Grenzen auf entsprechende Grenzwerte gesetzt werden (vgl. insbesondere den Algorithmus 1 im Aufsatz), W die Matrix, die diese Achskoordinaten q_s bzw. Zeitableitung, dq_s/dt aus den q_d bzw. dq_d/dt selektiert, s einen entsprechenden Skalierungsfaktor zur Reduzierung der Geschwindigkeit, dx_d/dt (im Aufsatz: x) eine erste Zeitableitung der vorgegebenen Pose und # eine (Pseudo-)Inverse, nicht notwendigerweise die im Aufsatz verwendete. Die hier verwendete erste Zeitableitung der vorgegebenen Pose wird in einer Ausführung auf Basis der Differenz zwischen der vorgegebenen Pose und einer Pose, die mittels der Transformation aus den Achskoordinaten ermittelt wird, ermittelt, in einer Ausführung mittels Multiplikation mit einer Verstärkungsmatrix K (dx_d/dt = K·(x_d - F(q))).In one embodiment, the axis coordinates q _d are determined according to the following equation or equation structure: $$q_{\text{i.e}}={\displaystyle \int \text{i.e}{q}_{\text{i.e}}/\text{German}}={\displaystyle \int \left[\text{i.e}{q}_s/\text{dt+}{\left(J\cdot W\right)}^{\#}\cdot \left(\text{s}\cdot \text{i.e}{x}_{\text{i.e}}/\text{German}-J\cdot \left(\text{i.e}{q}_{\text{s}}/\text{German}\right)\right)\right]},$$

for their basic structure or their basic structure on Eq. (13) is referred to in this paper. J denotes the Jacobian matrix, q _d the axis coordinates to be determined, dq _d /dt (in the essay: q̇ _SNS ) its first time derivative, dq _s /dt (in the essay: q̇ _N ) the first time derivative of those axis coordinates that are required to comply with the limits be set to corresponding limit values (cf. in particular Algorithm 1 in the essay), W the matrix that contains these axis coordinates q _s or time derivative, dq _s /dt which q _d or dq _d /dt selects, s a corresponding scaling factor to reduce the speed, dx _d /dt (in the essay: x) a first time derivative of the specified pose and # a (pseudo) inverse, not necessarily the one in the essay used. The first time derivative of the specified pose used here is determined in one embodiment on the basis of the difference between the specified pose and a pose that is determined from the axis coordinates by means of the transformation, in one embodiment by means of multiplication with an amplification matrix K (dx _d /dt = K (x _d - F(q))).

As a result, in one embodiment, the specified limits can be taken into account particularly effectively in the inverse kinematics. It can be seen in particular that if no speeds have to be reduced or set to corresponding limit values to comply with the specified limits (s=1; W=0, q _s =0), the first time derivative dq _d /dt of the axis coordinates to be determined by dq _d /dt = J ^#̇ dx _d /dt.

In addition or as an alternative to this aspect of determining the axis coordinates taking into account predetermined limits, according to one embodiment of the present invention, the Jacobian matrix is determined on the basis of a previously calibrated transformation that maps the robot's axis coordinates to a pose of the robot-fixed reference. In one embodiment, this transformation is an absolutely accurate transformation or an absolutely accurate model of the robot.

In particular, this is based on the idea that by using a pre-calibrated transformation to determine the Jacobian matrix, precision can already be increased at this level. As a result, in one embodiment, the operation of the robot can be improved, in particular carried out more safely and/or more precisely.

In one embodiment, parameters of this transformation are, in particular are, calibrated in advance using measurements on at least one (real) robot, particularly preferably the robot to be operated. In a further development, a method can be used as described in U. Wiest's dissertation, "KineMATIC CALIBRATION OF INDUSTRIAL ROBOTS", PhD Thesis Computer Science, University of Karlsruhe, 2001, to which additional reference is made and the content of which is fully included in the present disclosure is incorporated. In general, in one embodiment, several parameters p of the transformation F(q, p) → x are calibrated in advance on the basis of a plurality of measured poses x _i and associated axis coordinates qi, in particular in such a way that the sum of the squared errors Σ(F(q _i , p) - x _i ) ² is minimized.

As a result, the precision can be improved in one embodiment.

In one embodiment, the axis coordinates are determined iteratively and/or by means of integration, in a further development such that a time derivation of the axis coordinates is determined on the basis of the Jabobi matrix, in particular on the basis of a saturation-in-the-null-space algorithm, and from this by means of integration the axis coordinates are determined, and/or that the difference between the specified pose and the pose on which the previously calibrated transformation maps the determined axis coordinates is used as the input value of an iteration loop. In one embodiment, the iteration can also take into account a predefined speed of the robot-fixed reference. In one embodiment, this input value, possibly plus a predefined speed of the robot-fixed reference, is used as the first time derivation of the predefined pose in the SNS algorithm.

In one embodiment, in a first iteration loop or a first iteration run, a starting value for the axis coordinates to be determined is mapped to a pose of the robot-fixed reference by the transformation. Based on a difference between the specified pose of the robot-fixed reference and this pose, on which the transformation has mapped the start value for the axis coordinates to be determined, a first time derivation of the specified pose is determined, in one embodiment by multiplication with a matrix. In one embodiment, a predetermined speed of the robot-fixed reference is added to this first time derivation. Then, using an SNS algorithm, axis speeds are determined on the basis of this first time derivative of the specified pose, possibly supplemented by the specified speed of the robot-fixed reference, and highly integrated to a next iteration value for the axis coordinates to be determined.

In one or more further iteration loops, based on a difference between the specified pose of the robot-fixed reference and the pose to which the transformation applies the iteration value determined in the previous iteration loops for the axis coordinates to be determined in of the current iteration loop, a new first time derivative of the specified pose is determined, in one embodiment by means of multiplication with the matrix. Then, using the SNS algorithm, new axis speeds are determined on the basis of this first time derivative of the specified pose, possibly supplemented by the specified speed of the robot-fixed reference, and highly integrated to a new iteration value for the axis coordinates to be determined, which in turn is then used in the next iteration loop as in the iteration value determined in the previous iteration loop (this next loop) is used for the axis coordinates to be determined.

In one embodiment, this iteration is terminated when a termination criterion is reached, in one embodiment a predetermined number of iteration runs or iteration loops run through and/or a predetermined tolerance for the above-mentioned difference between the predetermined pose and the pose on which the transformation is based falls below a predetermined maps the iteration value determined in the previous iteration loop for the axis coordinates to be determined.

An integration can thus consist in particular of adding the new axis speeds of the current iteration loop, multiplied by a time increment, to the last iteration value for the axis coordinates to be determined and thereby obtaining the new iteration value for the axis coordinates to be determined.

In addition, reference is made to B. Siciliano, L. Sciavicco, L. Villani, G. Oriolo, "Robotics: Modelling, Planning and Control", Springer Science & Business Media (2010), in particular Chapter 3, and its content in full included in the present disclosure.

As a result, in one embodiment, the operation of the robot can be improved, in particular carried out more safely, efficiently and/or more precisely.

In one embodiment, the robot has at least three, in particular at least six, in one embodiment at least seven, (movement) axes or joints, in one embodiment rotary axes or joints, and/or a robot arm, in particular a robot arm with at least three in particular at least six, in one embodiment at least seven, joints, in one embodiment rotary joints or (movement, in particular rotary) axes, can in particular be such. In one embodiment, the robot-fixed reference is stationary with respect to a distal link of the robot (arm) and can in particular be the TCP. The present invention is particularly suitable for such applications, in particular due to the kinematics and/or conditions of use.

In one embodiment, a pose x has a one-, two- or three-dimensional position and/or a one-, two- or three-dimensional orientation of the robot-fixed reference. In one embodiment, it is specified by a robot controller and/or on the basis of a specified task, in particular a path, and/or manual input. Axis coordinates q _i , q=[q ₁ ,...,q _n] depend in one embodiment on the pose of the two robot limbs relative to one another, which are movably connected to one another or adjusted relative to one another by the corresponding axis indicate directly or indirectly. In one embodiment, axis speeds depend on the relative speed of the two robot links, and in particular can indicate this directly or indirectly.

As mentioned above, the operation of the robot can in particular include controlling the robot and/or monitoring the robot, in particular controlling being able to be regulating in particular.

• Mittel zum Vorgeben wenigstens einer Pose einer roboterfesten Referenz des Roboters;
• Mittel zum Ermitteln einer Jacobimatrix, die Achsgeschwindigkeiten des Roboters auf Geschwindigkeiten der roboterfesten Referenz abbildet;
• Mittel zum Ermitteln von Achskoordinaten des Roboters auf Basis der vorgegebenen Pose und ermittelten Jacobimatrix; und
• Mittel zum Betreiben, insbesondere Steuern und/oder Überwachen, des Roboters auf Basis der ermittelten Achskoordinaten; wobei
• das Mittel zum Ermitteln der Jacobimatrix Mittel zum Ermitteln der Jacobimatrix auf Basis einer vorab kalibrierten Transformation, die Achskoordinaten des Roboters auf eine Pose der roboterfesten Referenz abbildet, aufweist; und/oder
• das Mittel zum Ermitteln von Achskoordinaten Mittel zum Ermitteln von Achskoordinaten des Roboters unter Berücksichtigung von vorgegebenen Grenzen für Achskoordinaten und/oder Zeitableitungen dieser Koordinaten und/oder Posen der roboterfesten Referenz und/oder Zeitableitungen dieser Posen aufweist.

According to one embodiment of the present invention, a system for operating, in particular controlling and/or monitoring, a robot, in particular hardware and/or software, in particular programming, is set up to carry out a method described here and/or has:

• means for specifying at least one pose of a robot-fixed reference of the robot;
• Means for determining a Jacobian matrix which maps axis speeds of the robot to speeds of the robot-fixed reference;
• Means for determining axis coordinates of the robot based on the specified pose and determined Jacobian matrix; and
• Means for operating, in particular controlling and/or monitoring, the robot on the basis of the determined axis coordinates; whereby
• the means for determining the Jacobian matrix comprises means for determining the Jacobian matrix based on a pre-calibrated transformation that maps axis coordinates of the robot to a pose of the robot-fixed reference; and or
• the means for determining axis coordinates has means for determining axis coordinates of the robot, taking into account predetermined limits for axis coordinates and/or time derivatives of these coordinates and/or poses of the robot-fixed reference and/or time derivatives of these poses.

In one embodiment, the means for determining axis coordinates of the robot has means for determining the axis coordinates of the robot based on a saturation-in-the-null-space algorithm and/or speeds, in a further development based on a reduction in speeds Consideration of the given limits.

In one embodiment, the system has means for calibrating parameters of the transformation in advance using measurements on at least one robot, in particular the robot.

A means within the meaning of the present invention can be configured as hardware and/or software, in particular a processing unit, in particular a microprocessor unit (CPU), graphics card (GPU ) or the like, and/or one or more programs or program modules. The processing unit can be designed to process commands that are implemented as a program stored in a memory system, to acquire input signals from a data bus and/or to output output signals to a data bus. A storage system can have one or more, in particular different, storage media, in particular optical, magnetic, solid-state and/or other non-volatile media. The program can be designed in such a way that it embodies or is able to execute the methods described here, so that the processing unit can execute the steps of such methods and thus in particular can operate the robot. In one embodiment, a computer program product can have, in particular be a, in particular non-volatile, storage medium for storing a program or with a program stored thereon, with the execution of this program causing a system or a controller, in particular a computer, to execute a Method or one or more of its steps to perform.

In one embodiment, one or more, in particular all, steps of the method are carried out fully or partially automatically, in particular by the system or its means.

In one implementation, the system includes the robot.

• 1: ein System nach einer Ausführung der vorliegenden Erfindung;
• 2: ein Verfahren zum Betreiben des Roboters nach einer Ausführung der vorliegenden Erfindung; und
• 3: eine Iteration zum Ermitteln von Achskoordinaten des Roboters nach einer Ausführung der vorliegenden Erfindung.

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

• 1 : a system according to an embodiment of the present invention;
• 2 Figure 1: a method of operating the robot according to an embodiment of the present invention; and
• 3 : an iteration for determining axis coordinates of the robot according to an embodiment of the present invention.

1 shows a system according to an embodiment of the present invention with a robot (arm) 1 and a controller 2 for controlling and/or monitoring this robot (arm) 1, which executes a method according to an embodiment of the present invention or is set up for this purpose.

2 Fig. 1 shows a method of operating the robot 1 according to an embodiment of the present invention.

In a step S10, a pose x _d of a robot-fixed reference of the robot 1 is specified, which is 1 is indicated by TCP.

In a step S20, a Jacobian matrix J is determined on the basis of a transformation F(q,p), the parameters p of which have been calibrated beforehand, for example numerically by differentiation (J _app = [F(q + Δq,p) - F(q ,p)]/Δq). If an analytical Jacobian matrix of the previously calibrated transformation is available, this can preferably be used.

In a step S30, axis coordinates q _d of the robot 1 are determined on the basis of a saturation-in-the-null-space algorithm, as explained in principle in the above-mentioned article, so that predefined limits for axis coordinates and/or time derivatives of these coordinates and/or poses of the robot-fixed reference and/or time derivations of these poses are taken into account or adhered to.

im Block SNS ermittelten Zeitableitungen dq_d/dt in der in 3 skizzierten Weise in einer Iterationsschleife zu den Achskoordinaten q_d integriert, beispielsweise die neuen Achskoordinaten q_d,i aus den Achskoordinaten q_d,(i-1) der vorherigen Iterationsschleife, den Zeitableitungen (dq_d/dt)_i und einem Zeitinkrement Δt ermittelt, zum Beispiel q_d,i = q_{d, (i-1)} + (dq_d/dt)_i·Δt oder dergleichen. Dabei wird die Zeitableitung dx_d/dt der vorgegebenen Pose mittels Multiplikation der Differenz zwischen der vorgegebenen Pose x_d und einer Pose F(q), die mittels der Transformation aus den Achskoordinaten ermittelt wird, mit einer Verstärkungsmatrix K ermittelt (dx_d/dt = K·(x_d - F(q))). Durch die Skalierung s·x_d/dt, (0 ≤ s ≤ 1) wird diese Zeitableitung reduziert, um vorgegebene Grenzen zu berücksichtigen bzw. einzuhalten. Entsprechend werden die Achskoordinaten q_d auf Basis von Geschwindigkeiten dq_d/dt, x_d/dt und gegebenenfalls (dx/dt)_d ermittelt.In this case, according to the above equation $$\mathrm{i.e}{q}_{\text{i.e}}/\text{German}=\text{i.e}{q}_{\text{s}}/\text{dt+}{\left(J\cdot W\right)}^{\#}\cdot \left(\text{s}\cdot \text{i.e}{x}_{\text{i.e}}/\text{German}-J\cdot \left(\text{i.e}{q}_{\text{s}}/\text{German}\right)\right)$$

time derivatives dq _d /dt determined in the block SNS in the in 3 integrated as outlined in an iteration loop to the axis coordinates q _d , for example the new axis coordinates q _d,i determined from the axis coordinates q _d,(i-1) of the previous iteration loop, the time derivatives (dq _d /dt) _i and a time increment Δt, for example q _d,i = q _{d, (i-1)} + (dq _d /dt) _i *Δt or the like. The time derivative dx _d /dt of the specified pose is determined by multiplying the difference between the specified pose x _d and a pose F(q), which is determined using the transformation from the axis coordinates, with a gain matrix K (dx _d /dt = K (x _d - F(q))). This time derivation is reduced by the scaling s*x _d /dt, (0≦s≦1) in order to take into account or comply with specified limits. Correspondingly, the axis coordinates q _d are determined on the basis of speeds dq _d /dt, x _d /dt and, if applicable, (dx/dt) _d .

The iteration is terminated when a termination criterion is reached, for example reaching a predetermined maximum number of runs, falling below a predetermined tolerance for or due to the difference (x _d −F(q)) or the like. In one embodiment, the iteration can also take into account a specified speed (dx/dt) _d of the robot-fixed reference, as in 3 indicated by dashed lines, in particular by adding this to K (x _d - F(q)) (dx _d /dt = K (x _d - F(q) + (dx/dt) _d ).

The axis coordinates q _d determined in this way are then used to control and/or monitor the robot 1 (step S40). For example, the axes are correspondingly adjusted to these axis coordinates or axis drives are correspondingly controlled, in particular regulated.

Reference List

1

robot(arm)

2

steering

TCP

robot-fixed reference

q = [q1,...q6]

axis coordinates

Claims (9)

Method for operating a robot (1), comprising the steps: specifying (S10) at least one pose of a robot-fixed reference of the robot; determining (S20) a Jacobian matrix which maps axis speeds of the robot to speeds of the robot-fixed reference; determining (S30) axis coordinates of the robot on the basis of the specified pose and determined Jacobian matrix; and Operating (S40) the robot based on the determined axis coordinates; whereby the Jacobian matrix is determined on the basis of a previously calibrated transformation, maps the axis coordinates of the robot to a pose of the robot-fixed reference, with parameters of the transformation having been calibrated in advance using measurements on the robot. procedure after claim 1 , characterized in that the axis coordinates of the robot are determined on the basis of speeds and / or that the axis coordinates of the robot under Considering predetermined limits for axis coordinates and / or time derivations of these coordinates and / or poses of the robot-fixed reference and / or time derivations of these poses are determined. procedure after claim 2 , characterized in that the axis coordinates of the robot are determined on the basis of a reduction in speeds in order to take into account the specified limits. Method according to one of the preceding claims, characterized in that the axis coordinates of the robot are determined on the basis of a saturation-in-the-null-space algorithm. Method according to one of the preceding claims, characterized in that the operation includes controlling and/or monitoring the robot (1). Method according to one of the preceding claims, characterized in that the axis coordinates are determined iteratively and/or by means of integration. Method according to one of the preceding claims, characterized in that the robot is controlled and/or monitored on the basis of the determined axis coordinates. System for operating a robot (1), which is set up to carry out a method according to one of the preceding claims. Computer program product with a program code, which is stored on a computer-readable medium, for carrying out a method according to one of the preceding Claims 1 until 7 .

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