Method and system for simulating a braking operation of a robot

Abstract

A method for simulating a braking operation of a robot wherein a dynamic model of the robot is used to determine, for a given initial state of the robot, a final state range with a plurality of possible final states of the robot as a result of the simulated braking operation.

Claims

1. A method for simulating a braking operation of a robot, the method comprising: determining a final state range of the robot out of a plurality of possible final states based on an initial state and a simulated braking operation using a dynamic model of the robot; wherein the final state range comprises a standstill pose range defining a plurality of possible standstill poses of the robot; wherein the standstill pose range is predicted based on: a movement pose of the robot during the simulated braking operation in which the robot is still moving, and a specified map that associates different movement poses with standstill pose ranges, each standstill pose range having a plurality of possible standstill poses; specifying, during the simulated braking operation, a variation range for at least one parameter of the dynamic model; and controlling at least one of a drive or a brake of the robot based on the simulated braking operation.

2. The method of claim 1, wherein the braking operation is simulated by interval arithmetic for at least one parameter of the dynamic model.

3. The method of claim 1, further comprising: determining, for at least two of the possible final states of the determined final state range, a design variable that is dependent on the determined final state range.

4. The method of claim 3, wherein the design variable is at least one of: a kinetic energy of the robot; or a parameter of a safety device in the surroundings of the robot.

5. The method of claim 1, further comprising: determining for a plurality of initial states of the robot a corresponding final state range comprising a plurality of possible final states of the robot based on the respective initial state and a simulated braking operation using a dynamic model of the robot; and determining a design variable that is dependent on the final states.

6. The method of claim 5, wherein the design variable is at least one of: a kinetic energy of the robot; or a parameter of a safety device in the surroundings of the robot.

7. The method of claim 1, wherein, during the simulated braking operation, at least one of: at least one axis of the robot is braked; or at least one axis of the robot is stationary.

8. A system for simulating a braking operation of a robot, the system comprising: a robot controller configured to simulate the braking operation of the robot by determining a final state range of the robot out of a plurality of possible final states based on an initial state and a simulated braking operation using a dynamic model of the robot; wherein the final state range comprises a standstill pose range defining a plurality of possible standstill poses of the robot; wherein the standstill pose range is predicted based on: a movement pose of the robot during the simulated braking operation in which the robot is still moving, and a specified map that associates different movement poses with standstill pose ranges, each standstill pose range having a plurality of possible standstill poses; the robot controller further configured to specify, during the simulated braking operation, a variation range for at least one parameter of the dynamic model, and to control at least one of a drive or a brake of the robot based on the simulated braking operation.

9. The system of claim 8, further comprising: a robot having at least three motion axes, a drive associated with each motion axis and configured to actuate motion of the robot about the respective axis, and a brake associated with each motion axis and configured to brake movement of the robot about the respective axis; the robot controller controlling at least one of the drives or the brakes based on the simulated braking operation.

10. A computer program product comprising a program code stored on a non-transitory, computer-readable medium, the program code, when executed on a computer, causing the computer to: determine a final state range of a robot out of a plurality of possible final states based on an initial state and a simulated braking operation using a dynamic model of the robot; wherein the final state range comprises a standstill pose range defining a plurality of possible standstill poses of the robot; wherein the standstill pose range is predicted based on: a movement pose of the robot during the simulated braking operation in which the robot is still moving, and a specified map that associates different movement poses with standstill pose ranges, each standstill pose range having a plurality of possible standstill poses; specify, during the simulated braking operation, a variation range for at least one parameter of the dynamic model; and control at least one of a drive or a brake of the robot based on the simulated braking operation.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and, together with a general description of the invention given above, and the detailed description given below, serve to explain the principles of the invention.

(2) FIG. 1 shows a robot and a system for simulating a braking operation of the robot according to an embodiment of the present invention; and

(3) FIG. 2 illustrates a method for simulating the braking operation according to an embodiment of the present invention.

DETAILED DESCRIPTION

(4) FIG. 1 shows a six-axis robot 1 and a system in the form of a computer 2 for simulating a braking operation of the robot according to an embodiment of the present invention which carries out a method, shown in FIG. 2, for simulating the braking operation according to an embodiment of the invention.

(5) By way of example, braking of an axis is considered, the position of which is indicated in FIG. 1 by a corresponding axial coordinate q.

(6) The equation
m.Math.l.sup.2.Math.{umlaut over (q)}=m.Math.g.Math.l.Math.cos(q)+A−B.Math.sgn({dot over (q)})−μ.Math.{dot over (q)}
with mass m, which is assumed to be concentrated in a point that is spaced apart from the axis by the distance l, the gravitational constant g, the drive torque A of the axis, a braking torque B that is direction-dependent owing to the sign function sgn(x)={1⇔x>0; −1⇔x<0; 0⇔x=0} and a coefficient of friction μ, as well as the first and second time derivation {dot over (q)}{umlaut over (q)}, is, in simplified terms, a dynamic model of the robot 1.

(7) In a step S10, a variation range [B.sub.1; B.sub.2>B.sub.1] and [μ.sub.1; μ.sub.2>μ.sub.1], respectively, is specified for each of the braking torque B and the coefficient of friction.

(8) Then, in a step S20, a braking operation of the robot 1 is simulated using the dynamic model, up to a standstill, and specifically using interval arithmetic, such that, for example in the case of numerical time integration of the differential equation specified above, an addition B+μ is determined by the interval [B.sub.1+μ.sub.1, B.sub.2+μ.sub.2].

(9) Accordingly, in this case, a standstill pose range [q.sub.1, q.sub.2>q.sub.1] results, having a plurality of possible standstill poses q.sub.i, for the robot. It is thus possible, for example, for a minimum coefficient of friction μ.sub.1 from the variation range [μ.sub.1, μ.sub.2], together with a minimum braking torque B.sub.1 from the variation range [B.sub.1; B.sub.2], to lead to a maximum overrun q.sub.2 and, vice versa, for a maximum coefficient of friction μ.sub.2 from the variation range [μ.sub.1; μ.sub.2], together with a maximum braking torque B.sub.2 from the variation range [B.sub.1, B.sub.2], to lead to a minimum overrun q.sub.1.

(10) Then, in a step S30, a required safety range is determined, in each case, for the minimum overrun q.sub.1 and the maximum overrun q.sub.2, and in step S40 a safety range of the robot 1 is constructed, in accordance with the larger of said safety ranges.

(11) In a modification, in step S10 a map Q is specified, which associates different pairs of movement poses q.sub.k and speeds {dot over (q)}.sub.p of the robot with standstill pose ranges [q.sub.1(q.sub.k, {dot over (q)}.sub.p), q.sub.2(q.sub.k, {dot over (q)}.sub.p)>q:(q.sub.k, {dot over (q)}.sub.p)] having a plurality of possible standstill poses q.sub.i(q.sub.k, {dot over (q)}.sub.p)], in each case:
Q:(q.sub.k,{dot over (q)}.sub.p).fwdarw.[q.sub.1(q.sub.k,{dot over (q)}.sub.p),q.sub.2(q.sub.k,{dot over (q)}.sub.p)]
for example in the form of specified deviations
Q:(q.sub.k,{dot over (q)}.sub.p).fwdarw.[q.sub.k−α.Math.,{dot over (q)}.sub.p,q.sub.k+α.Math.{dot over (q)}.sub.p]
having the constant α.

(12) Then, in step S20 of the modification, a braking operation of the robot 1 is again simulated using the dynamic model, but having singular values for the braking torque B and the coefficient of friction μ. As soon as the speeds {dot over (q)} of the robot are in a specified range approaching standstill, in the simulation, the simulation can be interrupted and, in step S20, the standstill pose range [q.sub.1; q.sub.2] can be predicted on the basis of the current simulated movement pose and the specified map Q.

(13) Thus, for example proceeding from a movement pose q.sub.E, in which the speed {dot over (q)}.sub.E of the robot is in the above-mentioned range for the first time, the standstill pose range [q.sub.1, q.sub.2] results, using the above-mentioned map Q [q.sub.E−α.Math.{dot over (q)}.sub.E, q.sub.E+α.Math.{dot over (q)}.sub.E].

(14) Then, in step S30, a required safety range is determined, in each case, for the minimum overrun q.sub.1 and the maximum overrun q.sub.2, and in step S40 a safety range of the robot 1 is constructed, in accordance with the larger of said safety ranges.

(15) As is in particular clear therefrom, in one embodiment of the present invention, in general the aspect of predicting the standstill pose range on the basis of a movement pose of the robot and a specified map, which associated different movement poses with a plurality of possible standstill poses in each case, and the aspect of the simulation in which a variation range is specified for at least one parameter of the dynamic model, can also be combined, in one embodiment, in the example, for example in that, in step S20, [B.sub.1; B.sub.2] is simulated for the variation ranges [μ.sub.1, μ.sub.2], using interval arithmetic, until the speeds {dot over (q)}.sub.p of the robot are in the specified range, and the standstill pose range [q.sub.1; q.sub.2] is predicted on the basis of movement poses, from the movement pose range determined in the process, and from the specified map Q. Although embodiments given by way of example have been explained in the preceding description, it is noted that a plurality of modifications are possible. It should furthermore be noted that the embodiments given by way of example are merely examples which are not intended to restrict the scope of protection, the applications, and the structure, in any way. Instead, the above description provides guidance for a person skilled in the art to implement at least one embodiment given by way of example, it being possible for various amendments to be made, in particular in view of the function and arrangement of the described components, without departing from the scope of protection as emerges from the claims and the combinations of features equivalent thereto.

(16) While the present invention has been illustrated by a description of various embodiments, and while these embodiments have been described in considerable detail, it is not intended to restrict or in any way limit the scope of the appended claims to such detail. The various features shown and described herein may be used alone or in any combination. Additional advantages and modifications will readily appear to those skilled in the art. The invention in its broader aspects is therefore not limited to the specific details, representative apparatus and method, and illustrative example shown and described. Accordingly, departures may be made from such details without departing from the spirit and scope of the general inventive concept.

LIST OF REFERENCE SIGNS

(17) 1 robot 2 computer (system) q joint angle (pose)