EP3408061A1

EP3408061A1 - Method and system for the path planning of a redundant robot

Info

Publication number: EP3408061A1
Application number: EP17700889.3A
Authority: EP
Inventors: Tobias Josef Jakob; Reinhard NEUREITER
Original assignee: KUKA Systems GmbH
Current assignee: KUKA Systems GmbH
Priority date: 2016-01-26
Filing date: 2017-01-18
Publication date: 2018-12-05
Also published as: WO2017129352A1; DE102016000754A1

Abstract

The invention relates to a method according to the invention for the at least partially automated path planning of a multi-axial robot (1) comprising the step of resolving (S20, S40, S50) a redundancy of the robot with respect to a path (B) specified in a workspace of the robot in such a way that a mixed quality criterion, which comprises an effective mass of the robot and a magnitude of a minimum collision force of the robot that can be detected on the basis of specified detection limit values for axial forces of the robot, is minimal.

Description

description

Method and system for path planning of a redundant robot

The present invention relates to a method and a system for path planning of a redundant robot and to a computer program product for carrying out the method.

Own WO 2013/004329 A1 discloses a method for controlling a

human-collaborating robot, in which an effective mass of the robot is minimized to resolve a redundancy of the robot in a path planning. As a result, the risk can already be advantageously reduced in a collision on the web.

In addition to the effective mass, WO 2013/004329 A1 optionally takes into account energy optimality as well as a distance to singular, desired and previous poses. The object of the present invention is to further improve the path planning of a redundant robot.

This object is achieved by a method having the features of claim 1. Claims 7, 13 provide a system or computer program product

Implementation of a method described here under protection. The subclaims relate to advantageous developments.

According to an embodiment of the present invention, a method for partially or fully automated path planning of a multi-axis robot comprises the step of resolving a redundancy of the robot with respect to one in one

Workspace of the robot predetermined pathway such that a mixed

Quality criterion, which, in particular proportionally, an effective mass of the robot and, in particular proportionate, an amount of a minimum collision force of the robot comprises, based on predetermined detection limits for axle forces of the robot Robot is detectable, is minimal or is or under or by minimizing a mixed quality criterion, which, in particular proportionate, an effective mass of the robot and, in particular proportionate, an amount of minimum collision force of the robot comprises, based on predetermined detection Limits for

Axes forces of the robot is detectable or under or by means of minimization, in particular combined or Pareto minimization, both an effective mass of the robot and an amount of minimum collision force of the robot, which is detectable based on predetermined detection limits for axial forces of the robot , It is thus proposed in an embodiment, in addition to the minimization of the effective mass, which is known from the above-mentioned WO 2013/004329 AI, to the correspondingly incorporated additional reference and the content of which is expressly fully made the subject of the present disclosure, at least one Collision force of the robot, which is detectable based on predetermined detection limits for axial forces of the robot to

take into account or together with the effective mass to minimize.

In this way, an advantageous path can be planned, in particular better, in particular earlier, responds to a collision on the web or a reaction time can be reduced. In a further development, the mixed quality criterion in addition to the effective mass and the amount of minimum collision force may include other cost functions or shares, in another development, it is only (proportionately) from the effective mass and the amount of minimum collision force.

As already explained in WO 2013/004329 A1, to which reference is additionally made, a pose of a robot can be clearly distinguished by its minimal,

in particular axis coordinates qe 5R ^{dof be} described, in particular by its joint or drive in particular engine positions, in particular angle.

In a, in particular Cartesian, working space of the robot, a path z (s) e R ^b or individual points z, e 9? ^b the web by means of a one or more, in particular three-dimensional position x and / or a one or more, in particular Three-dimensional orientation a of a robot-fixed reference, in particular a TCPs of the robot, are given or be.

If the number dof of the degrees of freedom or axes of the robot exceeds the

Dimension ö of the track or track points (dof> b), the robot is redundant with respect to the predetermined path in the workspace.

This may in particular be a so-called kinematic redundancy if the robot has seven or more axes. Likewise, a robot having six or fewer axes may be redundant with respect to a pathway

Dimension is less than the number of axes, which is called task redundancy. If, for example, as in the exemplary embodiment of WO 2013/004329 A1, to which reference is additionally made, only the two-dimensional position of its TCPs is specified for a flat three-axis robot, but not its orientation, this robot is redundant with respect to this path.

The redundancy may be due to a one- or multi-dimensional so-called

Redundancy parameter r reduced, in particular eliminated, be or be. If, for example, an axis coordinate, in particular a joint angle, is specified for a seven-axis robot, this robot is no longer redundant with respect to a path prescribed in the working space six-dimensionally - except for singular poses. reduces or eliminates its redundancy or the dimension of its null space to zero.

Thus, in one embodiment of a path z (s) or a path point z, and a corresponding value of a redundancy parameter r (s) or r, a corresponding vector of minimum, in particular axis coordinates q (s) and q, of the robot be assigned or be: g = g (z, r) (1)

Under path planning, the determination of the minimum coordinates or of the redundancy parameter is thus present in particular for position, in particular positional and / or orientation coordinates, predetermined in the working space of the robot. of the robot, in particular a robot-fixed reference, in particular its TCPs understood (z -> q or z -> r).

One or the effective mass m _{u of} the robot is or is defined or determined in an embodiment in WO 2013/004329 A1, to which reference is additionally made, in particular according to:

with the direction vector of the track or tangent unit vector u = to the

Orbit, which can be approximated by γ - * - ^, the dx

Jacobi matrix J or J _{v of} the translation, the mass matrix M and the kinetic

dq

1 T

Energy q M q of the robot.

One or the collision force r _{k of} the robot is or is defined or determined in one embodiment, in particular on the basis of a linear mapping of the path tangent or direction u, wherein the linear mapping in a development based on a pseudoinverse J * des Robot is defined or determined is, in particular by the pseudoinverse can be defined: wherein the pseudo inverses in one embodiment in accordance with the usual

J * , J ^T y (4) can be defined or determined with the weighting matrix A, which can be the mass matrix or the unit matrix in a further development. The

Pseudo inverse can thus be (with A = 1) in particular the so-called Moore-Penrose pseudoinverse:

This is based on the consideration that a collision force exerted on a potential obstacle by the robot in the robot-fixed reference, in particular the TCP, acts in the direction of the web direction or speed or of the tangent unit vector. Accordingly, equation (3) projects them

(Collision force) Direction to the minimum coordinates, in particular the axes or joints of the robot.

As can be seen in particular from equation (3), antiparallel pairs of forces or (rotational) moments are generally referred to as forces in the sense of the present invention for a more compact representation. Achskräfte can thus be in particular torques acting in or on axes, in particular joints (s) or drives, in particular motors, of the robot.

Accordingly, in an implementation in the minimum coordinates, too,

especially axis-specific, detection limit values for axle forces to be predefined or be:

In one embodiment, a predetermined limit value t _dii (in each case) indicates from which value on an axis / ^' a collision is detected on the basis of a force acting in the robot-fixed reference. In a further development, this can be the limiting value, in particular, for which a safety reaction of the robot, for example a STOP 0, STOP 1 or STOP 2 or a retraction, in particular on the track, is triggered or predetermined. In one embodiment, the amount of or the minimum collision force of the robot, which is detectable on the basis of predetermined detection limits for axial forces of the robot, the factor f, with which the tangent unit vector, in particular at least, must be multiplied, so that the projection of the tangent unit vector onto the minimum coordinates, in particular by means of a pseudoinverse, in particular the Moore-Penrose pseudoinverse, in, in particular at least or precisely, a component exceeds the axis-specific predetermined limit value x _d , i in magnitude: f = Mm {f \ 3 r _ki > T _{d <l}} (6) in words: f the amount is the minimum factor by which the (projected in the minimum coordinates or induced by a unit force in the path tangent direction of the body-fixed reference of the robot in the axes of the robot)

Collision (unit) force (at least) must be multiplied, so that in

at least / exactly one axis of the detection limits for this axis is reached or exceeded.

Accordingly, in one embodiment, the amount f of the minimum collision force of the robot, which is detectable on the basis of predetermined detection limits for axial forces of the robot, in particular be determined or defined by the fact that the amount, starting from an initial value is increased inter-operatively until, for the first time or within the framework of an iteration precision in (at least) one axis: t _ki ,> T _d , j.

The amount f of the minimum collision force and the effective mass m _{u of} the robot are or are in one embodiment in the form of a mixed quality criterion, in a development in particular in the form of a weighted sum G of the effective mass and the amount of minimum collision force and possibly other cost functions G ,, determines or minimizes:

G = a ^■ m _u + b ^■ f \ + (7)

preferably l; a, b (, _Cj )> gWt

As explained above, the redundancy of the robot by a

Redundancy parameter r be reduced or be. Accordingly applies in one

Execution:

G = a - mmz, r)) + b - f {q (z, r) ^ c _j - G _j = G {q {z, r)) {T)

Thus, in one embodiment, for one or more track points z, and

Redundancy parameter values η respectively determined values of the mixed quality criterion and then each of the pose or the redundancy parameter value are selected for the or the quality criterion has the smallest value. In particular, by specifying a search or permissible value range for the redundancy parameter in an embodiment for a subsequent path point, in each case starting from a preceding or current redundancy parameter value, advantageously a variation of the redundancy parameter can be limited in one embodiment and a particularly advantageous path can be planned , Accordingly, in one embodiment, the redundancy is generally such or below

Secondary condition resolved that a variation of a redundancy parameter to reduce the redundancy of the robot along the track smaller than one

predetermined variation limit is or remains.

According to one embodiment of the present invention, a system for at least partially automated path planning of a multi-axis robot, in particular hardware and / or software, in particular programmatically, for implementing a method described herein and / or has means for resolving a redundancy of the robot with respect to a in a working space of the robot predetermined path such that a mixed quality criterion, which includes an effective mass of the robot and an amount of minimum collision force of the robot, which is detectable based on predetermined detection limits for axial forces of the robot is minimal on. In one embodiment, the system includes means for resolving the redundancy such that a variation of a redundancy parameter to reduce the redundancy of the robot along the path is less than a predetermined variation limit; Means for determining the based on predetermined detection limits

detectable collision force based on a linear image of a track tangent; Means for determining the linear mapping based on a dummy inverse of the robot; Means for determining the blended quality score based on a weighted sum of the effective mass and the amount of the minimum

Collision force and / or means for determining the value of the mixed

Quality criterion for at least one point of the path predetermined in the working space of the robot for at least two poses in the null space of the robot, in particular for at least two values of a redundancy parameter of the robot for reducing the redundancy of the robot, and means for planning the path based on the pose or of the redundancy parameter for which the mixed quality criterion has the smaller value.

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

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, plan the lane.

In one embodiment, one or more of the steps described herein, in particular by the system or its means, partially or fully automated. In one embodiment, the system can control the robot on the basis of the path planned in this manner or in such a way that it travels once or several times, or for this purpose, in particular hardware and / or software, in particular program technology. Further advantages and features emerge from the subclaims and the exemplary embodiments. This shows, partially schematized ,:

1 shows a task-redundant robot in various poses; and

2 shows the sequence of a method according to an embodiment of the present invention. 1 shows, in a simplified embodiment for explanation, to which reference is additionally made to WO 2013/004329 A1, a three-armed robot 1 with a rocker mounted on a fixed base 1.1, an arm 1.2 hinged thereto and one at the swing away End hinged hand 1.3 with the TCP. All three hinges have parallel, on the plane of Fig. 1 perpendicular axes of rotation.

If the task of the robot 1 is to start a path B in the plane of the drawing with its TCP, regardless of its orientation, in the drawing plane, the robot is with its three

Degrees of freedom q = (qq ₂ with respect to the given position z = x = (xy) ^T redundant: it can be seen that at the same Cartesian TCP position (x, y) on the path B in the drawing plane of FIG. 1 or the working space of the robot different, redundant poses exist, of which three are shown by way of example in FIG.

2 shows the sequence of a method according to an embodiment of the present invention, which executes a controller 2 of the robot 1:

In a first step S10, the controller 2 discretizes the web B into individual Stützbzw. Track points (x, y) i (x, y) _n . In a second step S20, the controller 2 determines, for the initial support or track point (x, y) i, for a given search or value range, respectively

Redundancy parameter r, in the exemplary embodiment purely exemplary of

Joint angle qi of the rocker 1.1, respectively the value of the quality criterion G according to the above equations (1) to (7 '). So it is for different, by the

Redundancy parameter definable, poses of the robot 1 in whose zero space each determines its effective mass m _u and the factor f, with the

Tangent unit vector to the path B in the initial support or track point (x, y ^ must be multiplied at least to allow its projection in the

Minimum coordinates q = (oj q ₂ jf ₃ ) ^T using the Moore-Penrose pseudo-inverses in one degree of freedom exceeds the detection limit specified for this and axis, and the value of a mixed quality criterion for this pose the value of the weighted sum of effective mass and this factor f is determined. In a step S30, the controller 2 selects that pose as the starting pose or start redundancy parameter value defining it

Redundancy parameter value for which this quality criterion is or becomes minimal.

In a step S40, the controller 2 determines the values of the quality criterion for different poses or redundancy parameter values for a subsequent support or track point (x, y) in an analogous manner. This is or is the search or

Range of values, within which the redundancy parameter or the pose defined thereby is varied, thereby limiting that a variation of

Redundancy parameter (s) s compared to the previous support point (x, y) i-i is less than a predetermined variation threshold. This can advantageously an undesirable significant reorientation of the

Robot 1 can be prevented along the track.

Then, in a step S50, the controller 2 selects, for the support or track point (x, y) j in an analogous manner as a pose or start redundancy parameter value defining that pose or redundancy parameter value for which this quality criterion is minimal or will. In a step S60, the controller checks whether an end support point (x, y) _{n has been} reached. As long as this is not the case (S60: "N"), the controller 2 repeats the steps S40 - S60 in an analogous manner, otherwise (S60: "Y"), the path planning is completed. In this way, the controller 2 plans the path of the robot in the form of the sequence of poses or these defining redundancy parameter values r _x = Qu (/ = 1,..., N) along the path B predetermined in the working space of the robot and thus triggers it Redundancy with respect to the path B such that on the one hand - by minimizing the effective mass - reduces the risk of a potential collision and at the same time - by the simultaneous Pareto minimization of the amount f of the minimum collision force, based on the predetermined detection limit value for Achskräfte of the robot is detectable, a potential collision sensitive or

can be detected early, so that appropriate safety reactions can be initiated quickly. 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 it is the exemplary

The explanations are merely examples of the scope of protection

Applications and the structure should in no way limit. Rather, the expert is by the preceding description a guide for the

Implementation of at least one exemplary embodiment given, wherein various changes, in particular with regard to the function and arrangement of the described components, can be made without departing from the scope, as it is apparent from the claims and these equivalent

Feature combinations results. LIST OF REFERENCES

1 robot

1 .1 swingarm

1 .2 arm

1 .3 hand

2 control

B predetermined path in the work space

TCP Tool Center Point

u Tangent unit vector

Claims

claims

1 . Method for the at least partially automated path planning of a

multi-axis robot (1), with the step:

Resolving (S20, S40, S50) a redundancy of the robot with respect to a path (B) given in a working space of the robot such that a mixed quality criterion comprising an effective mass of the robot and an amount of minimum collision force of the robot based on predetermined detection limits for axle forces of the robot is detectable, is minimal.

2. The method according to claim 1, characterized in that the redundancy is resolved such that a variation of a redundancy parameter for reducing the redundancy of the robot along the track is smaller than a predetermined one

Variation limit is.

3. The method according to any one of the preceding claims, characterized in that on the basis of predetermined detection limits detectable

Collision force is determined on the basis of a linear image of a Bahntangente.

4. Method according to the preceding claim, characterized in that the linear mapping is determined on the basis of a dummy inverse of the robot.

5. The method according to any one of the preceding claims, characterized in that the mixed quality criterion is determined on the basis of a weighted sum of the effective mass and the amount of the minimum collision force.

6. The method according to any one of the preceding claims, characterized in that for at least one point in the working space of the robot

predetermined path for at least two poses in the zero space of the robot, in particular for at least two values of a redundancy parameter of

Robot to reduce the redundancy of the robot, the value of

and the path is planned on the basis of the pose or the redundancy parameter for which the mixed quality criterion has the smaller value.

7. System for at least partially automated path planning of a

multiaxial robot (1) adapted to carry out a method according to one of the preceding claims and / or means (2) for dissolving a redundancy of the robot with respect to one in a working space of the robot

Robot predetermined path (B) such that a mixed quality criterion, the effective mass of the robot and an amount of a minimum

Collision force of the robot, which is detectable on the basis of predetermined detection limits for axial forces of the robot, is minimal.

8. System according to claim 7, characterized by means (2) for dissolving the

Redundancy such that a variation of a redundancy parameter to

Reducing the redundancy of the robot along the path is less than a predetermined variation limit.

9. System according to one of the preceding claims, characterized by means (2) for determining the based on predetermined detection limits

detectable collision force based on a linear image of a

Path tangent.

10. System according to any one of the preceding claims, characterized by means (2) for determining the linear mapping based on a dummy inverse of the robot.

A system according to any one of the preceding claims, characterized by means (2) for determining the blended quality criterion based on a weighted sum of the effective mass and the amount of minimum collision force.

12. System according to one of the preceding claims, characterized by means (2) for determining the value of the mixed quality criterion for at least one point of predetermined in the working space of the robot track for at least two poses in the zero space of the robot, in particular for at least two values of a redundancy parameter of the robot for reducing the redundancy of the robot; and means for planning the path based on the pose

Redundancy parameter for which the mixed quality criterion has the smaller value.

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.