DE102018210864B3 - Method and system for controlling a robot - Google Patents

Abstract

In a method according to the invention for controlling a robot (10) based on a Jacobian matrix that transforms joint speeds (dq / dt) of the robot into a velocity of a robot-fixed reference (TCP) in a working space of the robot, the robot is based on an inverse of the Jacobian matrix regulated if a selection parameter (c) has a first parameter value (c ₁ ), in particular in a first parameter range, and controlled on the basis of a transpose of the Jacobian matrix, if the selection parameter has a second parameter value (c ₂ ), in particular in a second parameter range lies.

Description

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

In robotics it is known to have joint or axis speeds q of the robot through a Jacobian matrix J to transform into a velocity ẋ of a robot-fixed reference in a working space of the robot: $$\dot{x}=\underset{J\left(q\right)}{\underset{\}}{\left(\frac{\partial \dot{x}}{\partial \dot{q}}\right)\dot{q}}}$$

Furthermore, it is known per se to control robots based on an inverse J ^{-1 of} this _{Jacobian matrix} , in a very simple example about nominal joint positions q _cmd based on desired or predetermined nominal poses x _{cmd of} the robot-fixed reference: $$q_{cmd}=J^{-1}\cdot x_{cmd}$$

However, inversion of the Jacobian matrix becomes problematic in the vicinity of singular poses of the robot.

Furthermore, it is known per se to control robots based on a transposed J ^{T of} the _{Jacobian matrix} , in a very simple example - neglecting the dynamics, in particular masses, of the robot - for example, desired joint forces τ _cmd based on desired or predetermined desired _values the stresses exerted F _cmd at the robot-fixed reference: $${\tau }_{cmd}=J^T\cdot F_{cmd}$$

The DE 10 2015 009 151 A1 relates to a method for automatically determining an input command for a robot that is input to the robot by manually applying an external force, wherein the input command is determined on the basis of the fraction of joint forces impressed by the external force that controls movement of the robot in only one seeks to effect for this input command specific subspace of the joint coordinate space of the robot.

In a method of switching a controller of a robot into a hand-held mode of operation for moving the robot by manually applying forces and / or torques to the robot according to the DE 10 2015 008 144 A1 As a result of the switching and as a function of detected and / or desired joint forces and / or torques and / or a pose of the robot, an error response is triggered.

One from the DE 10 2013 010 290 A1 A known method of monitoring a kinematically redundant robot comprises the steps of: detecting joint forces acting in joints of the robot, determining an external force between a robot-fixed reference and an environment based on the detected joint forces, determining another monitoring quantity at least in the Substantially independent of an external force acting on the robot-fixed reference, on the basis of the detected joint forces, and monitoring the determined external effective force and the determined further monitoring variable.

The DE 10 2011 003 506 A1 relates to an industrial robot with a robot arm and a control device, wherein the robot arm comprises a plurality of successively arranged, with respect to axes movable members, provided for moving the links provided electric drives and a fastening device provided for attaching an end effector. The control device is connected to the electric drives and is adapted to control the electric drives for movement of the links at least in a partial operating mode by means of a control device which determines based on a applied by the robot arm target force applied by the drives target torques. The Control device has at least one integral component and is set up to limit the integral component on the basis of at least one criterion, in particular dynamically.

The DE 692 07 627 T2 relates to a hybrid control system for controlling the displacement and force of a manipulator having means for providing an end effector displacement error signal indicative of any difference between an actual displacement of an end effector of a robotic manipulator and a desired displacement thereof, means for calculating a displacement error signal for a selected one A joint, wherein the means for calculating comprises means for multiplying the end effector displacement error signal by a pseudo-inverse of a matrix product of a selection matrix and a Jacobian matrix, means for providing an end effector force error signal representing any difference between an actual force exerted by the Endbetätigungsglied is exercised, and a desired force to be exerted by the same, indicates a means for calculating a Kr Aft error signal for a selected joint of the Endbetätigungsgliedkraftfehlersignal, and a control signal means responsive to the joint displacement error signal and the joint force error signal to provide a control signal to cause the Endbetätgliedglied moves in accordance with the desired displacement and exerts the desired force.

The US Pat. No. 6,456,901 B1 relates to a hybrid control system for a robot, comprising: a singularity detector, a task-level controller receiving a motion plan and determining a first set of control commands defined in the task space; and a joint level controller that receives the motion plan and determines a second set of control commands defined in the joint space.

The object of the present invention is to improve the operation of robots.

This object is achieved by a method having the features of claim 1. Claims 9, 10 protect a system or computer program product for carrying out a method described herein. The subclaims relate to advantageous developments.

According to an embodiment of the present invention, a robot based on a Jacobian matrix is controlled, which transforms joint speeds of the robot into a velocity of a robot-fixed reference in a working space of the robot.

The velocity (see ẋ in Eq. (1)) can in particular be a one-, two- or three-dimensional translatory and / or one, two or three-dimensional rotational speed of the robot-fixed reference, in one embodiment of the TCP ("Tool Center Point "), in particular be.

• - auf Basis einer bzw. der Inversen der Jacobimatrix geregelt, falls ein Auswahlparameter einen ersten Parameterwert aufweist, in einer Ausführung falls der Auswahlparameter in einem ersten Parameterbereich liegt,

und, in einer Ausführung gleichartig bzw. in strukturell gleicher Weise bzw. mit derselben Regler- bzw. Regel(ungs)struktur,

• - auf Basis einer bzw. der Transponierten der Jacobimatrix geregelt, falls der Auswahlparameter einen zweiten Parameterwert aufweist, in einer Ausführung falls der Auswahlparameter in einem zweiten Parameterbereich liegt.

According to an embodiment of the present invention, the robot becomes

• if the selection parameter has a first parameter value, in an embodiment if the selection parameter lies within a first parameter range, on the basis of one or the inverse of the Jacobian matrix,

and, in an embodiment similar or structurally the same or with the same controller or regulation (ungs) structure,

• - Regulated on the basis of one or the transpose of the Jacobian matrix, if the selection parameter has a second parameter value, in an embodiment if the selection parameter is in a second parameter range.

As a result, in an embodiment for different boundary conditions of the robot in which the selection parameter has different parameter values or lies in different parameter ranges, in each case an advantageous behavior of the robot can be realized. In particular, the inverse of the Jacobian matrix can be used for the first parameter value or parameter range and thereby in one embodiment an advantageous (re), in particular precise (re), control, in particular a hybrid force and position control, and at the same time for the second parameter value or parameter range the transposed of the Jacobian matrix used and thereby in an embodiment an advantageous (re), in particular stable (re), regulation, in particular force control, realized, in particular in the vicinity of singular poses of the robot, in ambient contact of the robot or the like, without the present Invention is limited thereto.

In one embodiment, the robot, in particular instead of on the basis of the inverse or transpose of the Jacobian matrix and / or this structurally similar or structurally thereto the same way or with the same controller or rule (ungs) structure, regulated on the basis of a transfer matrix, if the selection parameter has a third parameter value, in one embodiment lies in a third parameter region which in one embodiment connects the first and second parameter regions, the transition matrix depending on the selection parameter such that the transition matrix equals the inverse of the Jacobian if the selection parameter has the first parameter value, in one embodiment lies in the first parameter range, and the transfer matrix is equal to the transpose of the Jacobian matrix, if the selection parameter has the second parameter value, in one embodiment lies in the second parameter range, or the transfer m atrix is specified or determined accordingly.

In this way, in one embodiment, the different control of the robot on the basis of the inverse or transpose of the Jacobian matrix, in particular control technology, advantageously, in particular stable (he), realized.

In one embodiment, the transition matrix progressively transitions from the inverse of the Jacobian to the transposed of the Jacobian when the selection parameter transitions steadily from the first parameter value or the first parameter range to the second parameter value and the second parameter range, respectively specified or is determined accordingly or so.

As a result, in one embodiment, the transition between the different control of the robot on the basis of the inverse and the transpose of the Jacobian matrix, in particular control technology, advantageously, in particular stable (he), be realized.

In one embodiment, the robot is controlled on the basis of a predetermined proportional gain, in an embodiment based on a proportional gain of a following error or a control difference between a predetermined nominal and a detected or current actual size, in particular for a force, pose and / or a first and / or higher time derivation thereof.

mit der Proportionalverstärkung in Form der Diagonalmatrix K_P1.For example, in the first, simple example mentioned above, nominal joint velocities _q̇ cmd can be _commanded on the basis of a following error between desired or predetermined nominal poses x _cmd and detected or current actual poses x _act : $${\dot{q}}_{cmd}=J^{-1}\cdot \underset{{\mathrm{<figure-callout\; id="1"\; label="K\; P"\; filenames="DE102018210864B3\_0018.png"\; state="\{\{state\}\}">K\; </figure-callout>}}_P}{\underset{\}}{\left[\begin{array}{cccc}{P}_{1.1}& 0& ...& 0\\ 0& P_{1.2}& & \\ ⋮& & \ddots & \\ 0& & & {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="DE102018210864B3\_0018.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{1,}n}\end{array}\right]}}\cdot \left(x_{cmd}-x_{act}\right)$$

with the proportional gain in the form of the diagonal matrix K _P1 .

In one embodiment, the robot is controlled on the basis of a predetermined first proportional gain, if the selection parameter has the first parameter value, is in an embodiment in the first parameter range, and, in a similar embodiment or structurally the same or with the same controller or The control structure, controlled on the basis of a predetermined second proportional gain, if the selection parameter has the second parameter value, lies in one embodiment in the second parameter range.

As a result, in one embodiment, a control-related behavioral change of the robot as a result of a control of the robot based on the inverse or transpose Jacobi matrix are at least partially reduced or compensated and so realized in a design a homogeneous (re) s (control) behavior of the robot.

In one embodiment, the robot, in particular instead of on the basis of the first or second proportional gain and / or this structurally similar or structurally same way or with the same regulator or control (ungs) structure, regulated on the basis of a transfer gain, if the Selection parameter one, in particular the above-mentioned, third parameter value, in particular in one, in particular the above-mentioned, third parameter range, wherein the transfer gain depends on the selection parameter such that the transfer gain is equal to the first proportional gain if the selection parameter has the first parameter value in one embodiment in the first parameter range, and the transfer gain is equal to the second proportional gain if the selection parameter has the second parameter value an execution in the second parameter range, or is respectively specified or determined or determined.

As a result, in one embodiment, the control of the robot based on the different proportional gains, in particular control technology, advantageously, in particular stable (he), realized.

In one embodiment, the transition gain steadily transduces from the first proportional gain to the second proportional gain as the selection parameter steadily transitions from the first parameter value and the parameter range, respectively, to the second parameter value and the second parameter range, respectively.

As a result, in one embodiment, the transition between the control of the robot on the basis of the first and second proportional gain, in particular control technology, advantageously, in particular stable (he), can be realized.

The selection parameter can be one-dimensional or multi-dimensional. In one embodiment, it hangs, in a development continuous and / or linear or proportional, from a pose of the robot, in particular at least one joint or axis position or coordinate, a following error and / or a distance of the robot to a singular pose , Jacobian singular values, in particular a quotient of the largest singular value of the Jacobian divided by its smallest singular value, and / or an insertion depth and / or a travel of an end effector of the robot, for example a closing path of a gripper or a welding gun, and / or a state, in particular Travel, a cooperating with the robot machine, such as a closing path of a press in which the robot positions a workpiece, from.

In this way, in one embodiment, (advantageous) transitions can be detected particularly advantageously, in particular simply, reliably, and / or precisely, without the present invention being restricted thereto.

Additionally or alternatively, in one embodiment, the first, second and / or third parameter range or its limit (s) depends on an operator input or can be set or changed by an operator.

As a result, in one embodiment, the transitions can be optimally adapted to different operating conditions.

In one embodiment, the robot is based on the Jacobian matrix, in particular on the basis of the inverse of the Jacobian matrix, on the basis of the transposed Jacobian matrix based on the transfer matrix, on the basis of the first proportional gain, on the basis of the second proportional gain and / or on the basis of the transfer gain (respectively , in a similar embodiment or structurally thereto the same way or with the same regulator or control (ungs) structure) force-controlled, position-controlled or hybrid force and position-controlled.

With or with such arrangements, the invention can be used with particular advantage, in particular due to the (controller) stability in control based on the transposed Jacobian, the precision in control based on the inverse of the Jacobian and the (controller) stability in regulation on Base of the transfer matrix.

According to one embodiment of the present invention, a system, in particular hardware and / or software, in particular program technology, is set up and / or has a method for carrying out a method described here Means for controlling the robot based on an inverse of the Jacobian if a selection parameter has a first parameter value, in an embodiment if the selection parameter is in a first parameter range, and based on a transpose of the Jacobian if the selection parameter has a second parameter value in one Execution if the selection parameter lies within a second parameter range.

• Mittel zum Regeln des Roboters auf Basis einer Überführungsmatrix, falls der Auswahlparameter einen dritten Parameterwert aufweist, insbesondere in einem dritten Parameterbereich liegt, wobei die Überführungsmatrix von dem Auswahlparameter derart abhängt, dass die Überführungsmatrix gleich der Inversen der Jacobimatrix ist, falls der Auswahlparameter den ersten Parameterwert aufweist bzw. in dem ersten Parameterbereich liegt, und die Überführungsmatrix gleich der Transponierten der Jacobimatrix ist, falls der Auswahlparameter den zweiten Parameterwert aufweist bzw. in dem zweiten Parameterbereich liegt; und/oder
• Mittel zum Regeln des Roboters auf Basis einer vorgegebenen ersten Proportionalverstärkung, falls der Auswahlparameter den ersten Parameterwert aufweist, in einer Ausführung in dem ersten Parameterbereich liegt, und auf Basis einer vorgegebenen zweiten Proportionalverstärkung, falls der Auswahlparameter den zweiten Parameterwert aufweist, in einer Ausführung in dem zweiten Parameterbereich liegt; und/oder
• Mittel zum Regeln des Roboters auf Basis einer Überführungsverstärkung, falls der Auswahlparameter einen dritten Parameterwert aufweist, insbesondere in einem dritten Parameterbereich liegt, wobei die Überführungsverstärkung von dem Auswahlparameter derart abhängt, dass die Überführungsverstärkung gleich der ersten Proportionalverstärkung ist, falls der Auswahlparameter den ersten Parameterwert aufweist bzw. in dem ersten Parameterbereich liegt, und die Überführungsverstärkung gleich der zweiten Proportionalverstärkung ist, falls der Auswahlparameter den zweiten Parameterwert aufweist bzw. in dem zweiten Parameterbereich liegt; und/oder
• Mittel zum Kraft- und/oder Positionsregeln des Roboters auf Basis der Jacobimatrix, insbesondere auf Basis der Inversen der Jacobimatrix, auf Basis der Transponierten der Jacobimatrix, auf Basis der Überführungsmatrix, auf Basis der ersten Proportionalverstärkung, auf Basis der zweiten Proportionalverstärkung und/oder auf Basis der Überführungsverstärkung.

In one embodiment, the system or its agent has:

• Means for controlling the robot based on a transfer matrix if the selection parameter has a third parameter value, in particular in a third parameter range, the transfer matrix being dependent on the selection parameter such that the transfer matrix is equal to the inverse of the Jacobian if the selection parameter is the first parameter value or in the first parameter range, and the transfer matrix is equal to the transposed ones of the Jacobian matrix, if the selection parameter has the second parameter value or lies in the second parameter range; and or
• Means for controlling the robot based on a predetermined first proportional gain, if the selection parameter has the first parameter value, in one embodiment lies in the first parameter range, and based on a predetermined second proportional gain, if the selection parameter has the second parameter value, in an embodiment in US Pat second parameter range is; and or
• Means for controlling the robot based on a transfer gain if the selection parameter has a third parameter value, in particular in a third parameter range, wherein the transfer gain depends on the selection parameter such that the transfer gain is equal to the first proportional gain if the selection parameter has the first parameter value or in the first parameter range, and the transfer gain is equal to the second proportional gain if the selection parameter has the second parameter value or lies in the second parameter range; and or
• Means for controlling the force and / or position of the robot on the basis of the Jacobian matrix, in particular based on the inverse of the Jacobian matrix, on the basis of the transposed Jacobian matrix, on the basis of the transfer matrix, on the basis of the first proportional gain, on the basis of the second proportional gain and / or on Base of the transfer gain.

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, preferably 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 thus, in particular, control the robot. In one embodiment, a computer program product may have, in particular, a storage medium for storing a program or a program stored thereon, in particular non-volatile memory, wherein execution of this program causes a system or a controller, in particular a computer, to perform a described here Execute method or one or more of its steps.

In one embodiment, one or more, in particular all, steps of the method are completely or partially automated, in particular by the system or its (e) means. In one embodiment, the system includes the robot.

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 particular rotation axes or joints, which are adjusted in one embodiment by, in particular electrical, drives of the robot or are adjustable, which have in one embodiment electric motors and / or transmission, in particular a robot arm with the axes or joints, in particular drives.

The present invention is particularly advantageous for such robots because of their capabilities or uses.

• 1: ein System zum Regeln eines Roboters nach einer Ausführung der vorliegenden Erfindung;
• 2: eine Übergangsfunktion eines Auswahlparameters; und
• 3: ein Verfahren zum Regeln des Roboters nach einer Ausführung der vorliegenden Erfindung.

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

• 1 a system for controlling a robot according to an embodiment of the present invention;
• 2 : a transition function of a selection parameter; and
• 3 A method of controlling the robot according to an embodiment of the present invention.

1 shows a system for controlling a robot 10 according to an embodiment of the present invention.

The robot has drives 11 for adjusting its six axes, which in 1 are indicated by their joint angles q = [q ₁ , ..., q ₆ ] ^T. At the end flange of the robot carries a force-moment sensor 12 and an end effector 13 , whose TCP in 1 also indicated.

The system has a robot controller 20 for controlling the robot 10 on that one in 3 has indicated structure, wherein 3 at the same time illustrates a method of controlling the robot according to an embodiment of the present invention.

The present invention will be explained below for the sake of a more compact and clearer illustration, by way of a very simple example.

From given target forces F _cmd and using the force-moment sensor 12 recorded current actual forces F _act becomes a rule difference .DELTA.F determined.

In a block or step 21 is based on the current pose or joint angle q = [q ₁ , ..., q ₆ ] ^T , which are detected, for example, by means of joint angle sensors, first determines the Jacobian matrix J (q).

mit den Singulärwerte σ₁,..., σ₆ der Jacobimatrix.For these, a singular value decomposition (SVD) is carried out in a manner known per se: $$J=U\cdot \underset{\Sigma }{\underset{\}}{\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102018210864B3\_0018.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1& 0& ...& 0\\ 0& {\sigma }_2& & \\ ⋮& & \ddots & \\ 0& & & {\sigma }_6\end{array}\right]}}\cdot V$$

with the singular values σ ₁ , ..., σ _{6 of} the Jacobian matrix.

In the exemplary embodiment, the quotient c = σ _max / σ _{min of} the largest singular value σ _max of the Jacobian divided by its smallest singular σ _{min is} used as selection parameter, which describes the condition of the Jacobian or its singular matrix Σ.

ermittelt. Zweckmäßige Werte können beispielsweise 5 ≤ c₁ ≤ 20 und 50 ≤ c₂ ≤ 200 sein, insbesondere c₁ = 10 und c₂ = 100.An in 2 shown transition function λ (c) is according to $$\lambda \left(c\right)=\{\begin{array}{ccc}0& \Leftarrow & c\le c_1\\ \frac{c-c_1}{c_2-{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="DE102018210864B3\_0018.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}& \Leftarrow & c_1<c<c_2\\ 1& \Leftarrow & c\ge c_2\end{array}$$

determined. Suitable values may be, for example, 5 ≦ c ₁ ≦ 20 and 50 ≦ c ₂ ≦ 200, in particular c ₁ = 10 and c ₂ = 100.

mit $${\Sigma }_{transition}\left(\lambda \right)=\left[\begin{array}{cccc}\frac{{\sigma }_1}{{\left({\sigma }_1-\lambda \cdot {\sigma }_1+\lambda \right)}^2}& 0& \cdots & 0\\ 0& \frac{{\sigma }_2}{{\left({\sigma }_2-\lambda \cdot {\sigma }_2+\lambda \right)}^2}& & \\ ⋮& & \ddots & \\ 0& & & \frac{{\sigma }_6}{{\left({\sigma }_6-\lambda \cdot {\sigma }_6+\lambda \right)}^2}\end{array}\right]$$

$$J_{transition}\left(c\le c_1\right)=J_{transition}\left(\lambda =0\right)=V\cdot {\Sigma }_{transition}\left(\lambda =0\right)\cdot U^T=V\cdot {\Sigma }^{-1}\cdot U^T=J^{-1}$$

$$J_{transition}\left(c\ge c_2\right)=J_{transition}\left(\lambda =1\right)=V\cdot {\Sigma }_{transition}\left(\lambda =1\right)\cdot U^T=V\cdot {\Sigma }^T\cdot U^T=J^T$$

und andererseits eine Überführungsverstärkung gemäß $$\begin{array}{l}{K}_{Ptransition}\left(\lambda \right)=\left[\begin{array}{cccc}\left(1-\lambda \right)\cdot P_{\mathrm{1,1}}+\lambda \cdot P_{\mathrm{2,1}}& 0& \cdots & 0\\ 0& \left(1-\lambda \right)\cdot P_{\mathrm{1,2}}+\lambda \cdot P_{\mathrm{2,2}}& & \\ ⋮& & \ddots & \\ 0& & & \left(1-\lambda \right)\cdot P_{\mathrm{1,6}}+\lambda \cdot P_{\mathrm{2,6}}\end{array}\right]\hfill \\ K_{Ptransition}\left(c\le c_1\right)=K_{Ptransition}\left(\lambda =0\right)=\left[\begin{array}{cccc}{P}_{\mathrm{1,1}}& 0& \cdots & 0\\ 0& P_{\mathrm{1,2}}& & \\ ⋮& & \ddots & \\ 0& & & P_{\mathrm{1,6}}\end{array}\right]=K_{P1}\hfill \\ K_{Ptransition}\left(c\ge c_2\right)=K_{Ptransition}\left(\lambda =1\right)=\left[\begin{array}{cccc}{P}_{\mathrm{2,1}}& 0& \cdots & 0\\ 0& P_{\mathrm{2,2}}& & \\ ⋮& & \ddots & \\ 0& & & P_{\mathrm{2,6}}\end{array}\right]=K_{P2}\hfill \end{array}$$

ermittelt.Now, on the one hand, a transfer matrix J _transition according to $$J_{transitiOn}=V\cdot {\Sigma }_{transitiOn}\left(\lambda \right)\cdot U^T$$

With $${\Sigma }_{transitiOn}\left(\lambda \right)=\left[\begin{array}{cccc}\frac{{\sigma }_1}{{\left({\sigma }_1-\mathrm{<figure-callout\; id="1"\; label="\lambda \; \cdot \; \sigma "\; filenames="DE102018210864B3\_0018.png"\; state="\{\{state\}\}">\lambda \; </figure-callout>}\cdot {\sigma }_{}{}_1+\lambda \right)}^2}& 0& \cdots & 0\\ 0& \frac{{\sigma }_2}{{\left({\sigma }_2-\lambda \cdot {\sigma }_2+\lambda \right)}^2}& & \\ ⋮& & \ddots & \\ 0& & & \frac{{\sigma }_6}{{\left({\sigma }_6-\lambda \cdot {\sigma }_6+\lambda \right)}^2}\end{array}\right]$$

$$J_{transitiOn}\left(c\le c_1\right)=J_{transitiOn}\left(\lambda =0\right)=V\cdot {\Sigma }_{transitiOn}\left(\lambda =0\right)\cdot U^T=V\cdot {\Sigma }^{-1}\cdot U^T=J^{-1}$$

$$J_{transitiOn}\left(c\ge c_2\right)=J_{transitiOn}\left(\lambda =1\right)=V\cdot {\Sigma }_{transitiOn}\left(\lambda =1\right)\cdot U^T=V\cdot {\Sigma }^T\cdot U^T=J^T$$

and on the other hand, a transfer gain according to $$\begin{array}{l}{K}_{PtransitiOn}\left(\lambda \right)=\left[\begin{array}{cccc}\left(1-\lambda \right)\cdot P_{1.1}+\lambda \cdot P_{2.1}& 0& \cdots & 0\\ 0& \left(1-\lambda \right)\cdot P_{1.2}+\lambda \cdot P_{2.2}& & \\ ⋮& & \ddots & \\ 0& & & \left(1-\lambda \right)\cdot P_{1.6}+\lambda \cdot P_{2.6}\end{array}\right]\hfill \\ K_{PtransitiOn}\left(c\le c_1\right)=K_{PtransitiOn}\left(\lambda =0\right)=\left[\begin{array}{cccc}{P}_{1.1}& 0& \cdots & 0\\ 0& P_{1.2}& & \\ ⋮& & \ddots & \\ 0& & & P_{1.6}\end{array}\right]=K_{P1}\hfill \\ K_{PtransitiOn}\left(c\ge c_2\right)=K_{PtransitiOn}\left(\lambda =1\right)=\left[\begin{array}{cccc}{P}_{2.1}& 0& \cdots & 0\\ 0& P_{2.2}& & \\ ⋮& & \ddots & \\ 0& & & P_{2.6}\end{array}\right]=K_{P2}\hfill \end{array}$$

determined.

ermittelt, in einem Block bzw. Schritt 22 mit aktuellen Ist-Gelenkgeschwindigkeiten dq/dt verglichen und die Antriebe 11 auf Basis dieser Regeldifferenz geregelt.Then, target joint velocities become uniform according to $${\left(\frac{dq}{dt}\right)}_{cmd}={\dot{q}}_{cmd}=\underset{J_{transitiOn}\left(\lambda \right)}{\underset{\}}{V\cdot {\Sigma }_{transitiOn}\left(\lambda \right)\cdot U^T}}\cdot K_{PtransitiOn}\left(\lambda \right)\cdot \left(F_{cmd}-F_{act}\right)$$

determined, in a block or step 22 with current actual joint speeds dq / dt compared and the drives 11 regulated on the basis of this control difference.

in strukturell gleicher Weise auf Basis der Überführungsmatrix J^T der Jacobimatrix und einer zweiten Proportionalverstärkung K_P2 geregelt wird, falls der Auswahlparameter c in dem zweiten Parameterbereich c ≥ c₂ liegt: $$c\ge c_2\Rightarrow {\dot{q}}_{cmd}=\underset{J^T}{\underbrace{V\cdot {\Sigma }_{transition}\left(\lambda =1\right)\cdot U^T}}\cdot \underset{K_{P2}}{\underbrace{K_{Ptransition}\left(\lambda =1\right)}}\cdot \Delta F$$

und in strukturell gleicher Weise auf Basis der Transponierten J_transition der Jacobimatrix und einer Überführungsverstärkung K_Ptransition geregelt wird, falls der Auswahlparameter c in dem dritten Parameterbereich c₁ < c < c₂ liegt: $$c_1<c<c_2\Rightarrow {\dot{q}}_{cmd}=\underset{J_{transition}}{\underbrace{V\cdot {\Sigma }_{transition}\left(\lambda \right)\cdot U^T}}\cdot K_{Ptransition}\left(\lambda \right)\cdot \left(F_{cmd}-F_{act}\right)$$

wobei die Überführungsmatrix J_transition stetig von der Inversen der Jacobimatrix in die Transponierte der Jacobimatrix und die Überführungsverstärkung K_Ptransition stetig von der ersten Proportionalverstärkung in die zweite Proportionalverstärkung übergeht, wenn der Auswahlparameter stetig von dem ersten Parameterbereich zu dem zweiten Parameterbereich übergeht.It can be seen in this very simple example that the robot is controlled on the basis of the inverse J ^{-1 of} the Jacobian matrix and a first proportional gain K _P1 if the selection parameter c in the first parameter range c ≤ c ₁ lies: $$c\le {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="DE102018210864B3\_0018.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\Rightarrow {\dot{q}}_{cmd}=\underset{J^{-1}}{\underset{\}}{V\cdot {\Sigma }_{transitiOn}\left(\lambda =0\right)\cdot U^T}}\cdot \underset{{\mathrm{<figure-callout\; id="1"\; label="K\; P"\; filenames="DE102018210864B3\_0018.png"\; state="\{\{state\}\}">K\; </figure-callout>}}_P}{\underset{\}}{K_{PtransitiOn}\left(\lambda =0\right)}}\cdot \Delta F$$

is structurally controlled in the same way on the basis of the transfer matrix J ^{T of} the Jacobian matrix and a second proportional gain K _P2 if the selection parameter c in the second parameter range c ≥ c ₂ lies: $$c\ge c_2\Rightarrow {\dot{q}}_{cmd}=\underset{J^T}{\underset{\}}{V\cdot {\Sigma }_{transitiOn}\left(\lambda =1\right)\cdot U^T}}\cdot \underset{K_{P2}}{\underset{\}}{K_{PtransitiOn}\left(\lambda =1\right)}}\cdot \Delta F$$

and is governed structurally in the same way on the basis of the transposed J _{transition of} the _{Jacobian matrix} and a transfer _gain K _Ptransition , if the selection _parameter c in the third parameter range c ₁ <c <c ₂ lies: $$c_1<c<c_2\Rightarrow {\dot{q}}_{cmd}=\underset{J_{transitiOn}}{\underset{\}}{V\cdot {\Sigma }_{transitiOn}\left(\lambda \right)\cdot U^T}}\cdot K_{PtransitiOn}\left(\lambda \right)\cdot \left(F_{cmd}-F_{act}\right)$$

wherein the _{transition matrix} J _transition steadily _transitions from the inverse of the _{Jacobian matrix} into the transpose of the _{Jacobian matrix} and the transition _gain K _Ptransition steadily from the first proportional _gain to the second proportional _gain as the selection parameter transitions steadily from the first parameter domain to the second parameter domain.

Although exemplary embodiments have been explained in the foregoing description, it should be understood that a variety of modifications are possible.

mit einer vorgegebenen Mindesteintauchtiefe u, die beispielsweise zwischen 1 mm und 20 mm liegen kann, ermittelt werden. Auf diese Weise wird beim hybrid kraft- und positionsgeregelten Fügen bei einem anfänglichen Eintauchen, d.h. einem Übergang von Kraft- zu Formschluss, stetig von J^-1 auf J^T übergegangen.For example, instead of the quotient c = σ _max / σ _min , an immersion depth d of a robot-guided bolt in a bore can also be used, and the transition function λ (d) can be used $$\lambda \left(d\right)=\{\begin{array}{ccc}0& \Leftarrow & d\le 0\\ \frac{d}{u}& \Leftarrow & 0<d<u\left(6\text{'}\right)\\ 1& \Leftarrow & d\ge u\end{array}$$

with a predetermined minimum immersion depth u, which may for example be between 1 mm and 20 mm, are determined. In this way, in the case of an initial dipping, ie a transition from force to form fit, the hybrid force- and position-controlled joining changes continuously from J ^-1 to J ^T.

LIST OF REFERENCE NUMBERS

10

robot

11

drive

12

Force-torque sensor

13

end effector

20

control

21, 22

Control block / process step

c

selection parameter

q = [q ₁ , ..., q ₆ ] ^T

joint angle

dq / dt

(Actual) joint angular velocity

(dq / dt) _cmd

Target joint angular velocity

F _cmd

Target force

F _act

Actual force

.DELTA.F

Control difference

TCP

Tool Center Point

λ

Transition function

Claims (10)

A method of controlling a Jacobian-based robot (10) that transforms robot's joint speeds (dq / dt) to a robot-fixed reference (TCP) velocity in a robot's working space, the robot being controlled based on an inverse of the Jacobian matrix, if a selection parameter (c) has a first parameter value (c ₁ ); and the robot is controlled based on a transpose of the Jacobian matrix if the selection parameter has a second parameter value (c ₂ ). Method according to Claim 1 characterized in that the robot is controlled based on a transfer matrix if the selection parameter has a third parameter value, the transfer matrix depending on the selection parameter such that the transfer matrix equals the inverse of the Jacobian if the selection parameter has the first parameter value, and the transition matrix is equal to the transpose of the Jacobian if the selection parameter has the second parameter value. Method according to the preceding claim, characterized in that the transfer matrix progressively transitions from the inverse of the Jacobian matrix to the transposed one of the Jacobian matrix as the selection parameter transitions steadily from the first parameter value to the second parameter value. Method according to one of the preceding claims, characterized in that - the robot is controlled on the basis of a predetermined first proportional gain, if the selection parameter has the first parameter value; and - the robot is controlled based on a predetermined second proportional gain if the selection parameter has the second parameter value. Method according to the preceding claim, characterized in that the robot is controlled on the basis of a transfer gain if the selection parameter has a third parameter value, the transfer gain being dependent on the selection parameter such that the transfer gain is equal to the first proportional gain if the selection parameter is the first one Parameter value, and the transfer gain is equal to the second proportional gain if the selection parameter has the second parameter value. Method according to the preceding claim, characterized in that the transfer gain continuously transitions from the first proportional gain to the second proportional gain as the select parameter progressively transitions from the first parameter value to the second parameter value. Method according to one of the preceding claims, characterized in that the selection parameter of a pose of the robot, a following error and / or a distance of the robot to a singular pose, singular values of the Jacobian matrix and / or an insertion depth and / or a travel of an end effector of the robot and / or a state of a robot cooperating with the robot. Method according to one of the preceding claims, characterized in that the robot is force and / or position-controlled. A system for controlling a Jacobian-based robot (10) that transforms robot's joint speeds (dq / dt) to a robot-fixed reference (TCP) velocity in a working space of the robot, the system implementing a method according to any one of the preceding claims is set up. 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 1 to 8th ,

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