DE102021211819B3 - Method for generating a speed profile for a path control - Google Patents

Abstract

The invention relates to a method for generating a speed profile for a path control, comprising generating a limit speed profile (1) for a plurality of path segments of a specified path, dividing the limit speed profile (1) into zones (1a-1g), each of which has constant limit values for speed , acceleration or jerk, determining a plurality of transition conditions at a transition from a first zone (1a-1g) to a second zone (1a-1g) based on a limit value of the second zone (1a-1g) and calculating a first Speed profile (2) for the first zone (1a-1g) to reach a predetermined desired speed (vsoll), the first speed profile (2) having a multiplicity of predetermined interpolation points for determining a current path. If the first velocity profile violates one of the plurality of transition conditions, a second velocity profile (3.1-3.5) is generated for the transition from the first zone (1a-1g) to the second zone (1a-1g) at each interpolation point of the first velocity profile (2) calculated, the second speed profile (3.1-3.5) being calculated in each case as a function of a determined speed in an interpolation point and an associated transition condition, from the first speed profile (2) to the second speed profile (3.1-3.5) at a directly preceding interpolation point calculated, switched when the second velocity profile (3.1-3.5) computed at a current interpolation point violates one of the plurality of transition conditions, and interpolation points are determined along the second velocity profile (3.1-3.5) to determine the current trajectory.

Description

The present invention relates to a method for generating a speed profile for a path control, as well as a computing unit and a computer program for carrying out the method. The process allows modifications to the velocity profile during runtime while maintaining defined limit values for velocity, acceleration and jerk.

Background of the Invention

Path controls are used in numerically controlled machines and systems, which control the position of a moving object along a predefined path. Within the framework of path control, the movements to the next position to be approached (motion profile), the type of path to be traveled through and the speed for the movements to this position are specified. The trajectory is usually broken down into trajectory segments, which consist of straight lines or circular segments, for example. Since real machines and systems are subject to certain limitations with regard to the maximum speed, acceleration and jerk (change in acceleration), the processing of a single path segment from a starting point to an end point cannot take place at a specified constant speed, since this is the starting point of the path segment, where the object's velocity is zero, would result in a jump in velocity with infinite acceleration. Continuous speed profiles are therefore required in which these speed jumps are smoothed/rounded off.

EP 2 996 003 A1 shows a method for generating a condition-based motion profile in which a piecewise constant setpoint profile for the jerk is converted into a piecewise linear profile using a moving average filter. This results in a corresponding rounding of the acceleration and velocity profile.

Such filtering has the disadvantage that there are two different viewing levels (before and after the filter) at runtime, which require separate management. This leads to complex and therefore error-prone algorithms with regard to the synchronization between the interpolated movement and non-movement-specific machine functions. In addition, acceleration and jerk cannot be completely decoupled using the method described above, so that the maximum possible jerk is not achieved in some cases. In addition, different jerk limit values for acceleration and deceleration are not possible with this method.

The pamphlet DE 10 2009 049 172 A1 discloses a method for controlling a manipulator. A movement variable is automatically determined for a specific path section with a predetermined course of a movement variable on the basis of movement variables permissible in this path section.

The pamphlet DD 2 89 832 A5 discloses an analog circuit arrangement for sequence control at track section transitions in track controls.

Other common methods in which - at least in sections - completely pre-calculated speed profiles are run have the main disadvantage that the partly iterative calculations required for this are very computationally intensive and a subsequent influencing of the movement profile, for example by using an override function are adapted, a complete recalculation of the speed profile is required, which in practice would lead to an intolerable delayed reaction due to the computing time required for the recalculation.

Disclosure of Invention

According to the invention, a method for generating a speed profile for a path control as well as a computing unit and a computer program for carrying out the method with the features of the independent patent claims are proposed. Advantageous configurations are the subject of the dependent claims and the following description.

In particular, the invention provides a method for generating continuous speed profiles for path controls, which overcomes the disadvantages mentioned above and can generate smooth and (substantially) smooth, speed-optimized speed profiles. The method according to the invention also allows speed and acceleration to be varied during runtime.

The advantages of the method are achieved in particular by determining in advance a large number of transition conditions between individual zones of a limit speed profile, which are checked during the runtime in each interpolation step. If a violation of a transitional condition is detected, there is a switchover from a first speed profile with which a predetermined target speed in a can be reached in the current zone, to a second speed profile, which takes into account the permissible speed in a subsequent zone and complies with the transition conditions. This ensures that a specified path can always be traveled at the maximum possible speed while complying with all permissible limit values of a machine/system.

The method according to the invention is advantageously divided into two calculation parts, namely a preparation part to be calculated in advance, which does not have to be real-time capable, and an interpolation part to be called cyclically at runtime, which can advantageously be processed in real time, i.e. each step is completed within a deterministic time period (while moving).

The preparation part is used to generate a limit speed profile along a specified path, on the basis of which the current speed and acceleration on the path are determined in the subsequent interpolation part.

At the beginning of the preparatory part, the start and finish positions of a lane are usually already set. The path dynamics that can be used to drive along the specified path are also already known. The path is usually segmented to ensure that the dynamics of the individual axes of a machine/system are used as well as possible and not exceeded. Constant limit values for speed, acceleration, deceleration and jerk (each separately for acceleration and deceleration) are usually specified for each of these path segments based on the properties of the machine/system or the process in general. However, these limit values, which are determined segment by segment, are only valid within the respective path segments and can lead to limit value violations if several consecutive path segments are traveled.

Therefore, in the preparatory part of the method, based on the segmentally determined constant limit values for the individual path segments, a limit speed profile is generated for several consecutive path segments of a given path. This limit speed profile is then divided into zones, each of which is characterized by a constant limit value for speed, acceleration or jerk. In other words, a limit speed profile is generated that is valid for several consecutive path segments and contains areas with constant limit values for speed, acceleration or jerk, which represent the individual zones of the speed profile.

The limit speed profile preferably contains one or more zones which have a constant speed as a limit and/or one or more zones which have a constant negative jerk for building up a deceleration (negative acceleration) as a limit and/or one or more zones that have constant deceleration as a limit, and/or one or more zones that have a constant positive jerk to reduce deceleration as a limit. The zones are calculated in such a way that the variable jerk, deceleration or speed characteristic of the section reaches its maximum permissible limit value.

In addition, the preparation part of the method includes determining a plurality of transition conditions at a transition from a first zone to a second zone based on a limit value of the second zone. A first and second zone should be understood to mean any two zones that follow one another.

Each transition condition can be a pair of velocity and acceleration values. This means that the transition conditions define the acceleration with which, depending on the speed, a zone may be left at runtime without the risk of violating the limit speed profile in the subsequent zones. In addition, the transition conditions define the maximum deceleration depending on the speed with which a zone may be left without the speed in the following zones violating the zero line, as this would result in a change of direction on the track.

The interpolation part of the method includes a one-dimensional interpolation along the specified path, which forms the basis for a subsequent n-dimensional geometry calculation of the individual axes of a machine/plant. The interpolation part is called cyclically in a fixed cycle (interpolation cycle) and calculates a currently interpolated path including the current speed, the current acceleration and the current jerk for each cycle.

At the beginning of the first zone, a first speed profile for the first zone is calculated/initialized in order to reach a predetermined target speed. The predetermined setpoint speed can be, in particular, a act externally (e.g. by a machine operator) specified or overwritten setpoint speed. The first speed profile is preferably calculated using the (usual) known jerk-limited seven-phase profile, which makes it possible to reach the predetermined target speed while maintaining the limit values for maximum speed, acceleration and jerk in a minimum of time.

• - Phase 1: Positiver konstanter Ruck zum Aufbau der Beschleunigung
• - Phase 2: Positive konstante Beschleunigung zum Beschleunigen
• - Phase 3: Negativer konstanter Ruck zum Abbau der Beschleunigung bis zum Erreichen einer konstanten Geschwindigkeit
• - Phase 4: Konstante Geschwindigkeit
• - Phase 5: Negativer konstanter Ruck zum Ausbau einer Verzögerung (negativen Beschleunigung),
• - Phase 6: Konstante Verzögerung zum Abbremsen,
• - Phase 7: Konstanter positiver Ruck zum Abbau der Verzögerung.

The seven-phase profile consists of a total of 7 phases, with which each point-to-point movement can be represented with standstill at the beginning and end. The individual phases have the properties listed below:

• - Phase 1: Positive constant jerk to build up acceleration
• - Phase 2: Positive constant acceleration to accelerate
• - Phase 3: Negative constant jerk to reduce acceleration until a constant speed is reached
• - Phase 4: constant speed
• - Phase 5: Negative constant jerk to increase deceleration (negative acceleration),
• - Phase 6: Constant deceleration to slow down,
• - Phase 7: Constant positive jerk to reduce deceleration.

Each of the calculated partial profiles consists of an individual sequence of these phases, whereby phases of the same type can occur several times within a partial profile (e.g. a partial sequence in the order phase 5 → phase 6 → phase 5 or phase 7 → phase6 → phase7 ). The seven-phase profile can be extended by additionally considering the derivative of the jerk (referred to as “snap” in English). This creates a model with thirteen phases, for example, in that a further phase for jerk build-up and reduction is inserted between two phases of the seven-phase profile.

Alternatively or additionally, the individual phases can be described by other mathematical models, i.e. other mathematical descriptions of the equations of motion can be selected, for example based on a sinusoidal curve.

The first speed profile includes the analytical relationship between distance, speed, acceleration and jerk and has a large number of predetermined interpolation points for determining a current path, i.e. current target values for distance, speed and acceleration are calculated in each interpolation cycle based on the course of the first speed profile and jerk determined. In addition to the constant limit values for speed, acceleration and jerk, the limit speed profile and the currently valid transition conditions from the first zone to the second zone are taken into account. The cycle time of the interpolation cycle is preferably 1 ms.

If the first speed profile violates one of the plurality of transition conditions, a second speed profile is calculated at each interpolation point of the first speed profile for the transition from the first zone to the second zone, with the second speed profile depending on a determined speed in an interpolation point and a associated transition condition is calculated. In other words, the current speed is determined in each interpolation cycle based on the course of the first speed profile and, based on this speed, the course of the second speed profile is calculated in such a way that the transition condition applicable to the current speed is maintained as far as possible. Thus, in each interpolation cycle, in addition to the first speed profile, there is another second speed profile that changes from cycle to cycle and represents a current speed profile from the first zone to the second zone, taking into account the multitude of transition conditions.

Preferably, the second speed profile is calculated analogously to the first speed profile using the seven-phase profile or the alternatives described above. It is also possible that the second speed profile is always calculated, i. H. even if the first velocity profile does not violate any of the transition conditions.

The first and/or the second speed profile are preferably selected from a set that contains: speed profile for reaching a target speed, speed profile for reaching a transition condition, speed profile along the limit speed profile and speed profile for reaching a local speed minimum or standstill.

However, a change from the first speed profile to the second speed profile only takes place when the second speed profile, which is based on a current interpolation point has been calculated, one of a variety of transition conditions is violated. In this case, there is a change from the first speed profile to a new speed profile which is based on the second speed profile which was calculated at a directly preceding interpolation point. In other words, an object is moved on the basis of the first speed profile until a transition condition is violated during the transition from the first zone to the second zone.

This means that the maximum speed is maintained for as long as possible and only reduced as much as necessary at the zone transition. Due to the short cycle time, the second speed profile determined at the preceding interpolation point already largely corresponds to the achievable optimum speed while complying with the transition conditions. In addition to the described transition speed profile from a first to a second zone, the second speed profile can also be a speed profile along the limit speed profile and/or a speed profile to a local speed minimum or to a standstill.

To determine the current path after the change from the first to the second speed profile, interpolation points are defined along the second speed profile, at which the current values for path, speed, acceleration and jerk are then determined until the transition from the first to the second zone is reached will.

The method according to the invention generates smooth, jerk-limited and approximately time-optimal speed profiles for path controls without filtering the movement variables speed, acceleration and/or jerk. Due to the fact that the transition conditions are determined once and that a completely new precalculation is no longer necessary, there is only a small amount of additional computing effort in the event of changes at runtime, which is further reduced by the zone-based calculation of the movement variables. This enables an encapsulated view of motion segments at runtime and avoids time-consuming iterative calculation steps.

Current target values for the positions of individual axes of a machine or system are preferably calculated at each interpolation point of the first and second speed profile based on the determined current path and sent to the relevant machine or system. In other words, the current path is transformed to the individual axes of a machine or system, which results in the target values for the positions of the individual axes, which are then sent to the corresponding drives of the machine/system.

The limit speed profile is preferably generated by means of a forward calculation and a backward calculation of permissible maximum speeds for the plurality of path segments. As a result, a sequence of path segments can be determined along which a continuous maximum speed can be used. In addition, the combination of a forward calculation and a backward calculation ensures that the speed at the end of a path safely reaches zero.

The forward calculation of the permissible maximum speeds for the multiple path segments preferably firstly includes a check as to whether a permissible maximum speed of a second path segment is being observed when a transition from a first path segment to the second path segment is approached at a permissible maximum speed of the first path segment. A first and second path segment should be understood to mean any two consecutive path segments. The permissible maximum speed of the first and second path segment is preferably the predefined constant limit values for the permissible speed in the individual path segments, which comply with the limit values of the individual axes of the machine.

If the permissible maximum speed of the second path segment is exceeded, the maximum speed of the first path segment is reduced at the beginning of the second path segment, i.e. at the transition from the first to the second path segment. The maximum speed at the start of the second path segment is preferably lowered to such an extent that the constant limit value for the permissible speed of the second path segment is reached but not exceeded.

Preferably, a minimum speed at one end of the second path segment is then determined based on the maximum speed at the beginning of the second path segment. If the maximum speed was reduced at the start of the second path segment, the minimum speed at the end of the second path segment is determined on the basis of the reduced maximum speed, otherwise the maximum speed originally present is used.

If the minimum speed at the end of the second path segment is greater than zero, the above steps are repeated in a third path segment and subsequent path segments until the minimum speed at an end of a path segment reaches zero. This means that based on the possibly reduced maximum speed of the second path segment at the transition from the second path segment into a further, third path segment, a check is made as to whether the maximum speed of the third path segment is being exceeded. If this is the case, the maximum speed is lowered again at the beginning of the third path segment, preferably until the constant limit value for the permissible speed of the third path segment is reached but not exceeded. Based on this reduced maximum speed, the minimum speed that can be achieved at the end of the third path segment is then determined. If a speed of zero can be reached at the end of the third path segment, the forward calculation is complete, otherwise the steps described are repeated in a further path segment until the determined minimum speed is zero at the end of a path segment or the end of the path is reached at which the speed is forced to zero.

The forward calculation preferably also includes a check as to whether a permissible maximum acceleration of the second path segment is maintained when a transition from the first path segment to the second path segment is approached with a permissible maximum acceleration of the first path segment. If the permissible maximum acceleration of the second path segment is exceeded, the maximum acceleration of the first path segment is reduced at the beginning of the second path segment, i.e. at the transition from the first to the second path segment. The maximum acceleration at the start of the second path segment is preferably lowered to such an extent that the constant limit value for the permissible acceleration of the second path segment is reached but not exceeded.

The minimum speed at the end of the second path segment is then preferably determined on the basis of the maximum speed and the maximum acceleration at the start of the second path segment. If the maximum speed and/or the maximum acceleration was reduced at the start of the second path segment, the minimum speed at the end of the second path segment is determined on the basis of the reduced maximum speed and/or the reduced maximum acceleration, otherwise the maximum speed and/or maximum acceleration originally present is used.

These steps are repeated in a third path segment and possibly in further following path segments if the minimum speed at the end of the second path segment is greater than zero. The forward calculation is complete when the velocity reaches zero at the end of a path segment.

The backward calculation of the permissible maximum speeds for the plurality of path segments preferably firstly includes a determination of a path segment at the start of which the maximum speed was last reduced during the forward calculation. If one or more reductions in the maximum speed at the beginning of a path segment occurred during the forward calculation, the backward calculation begins with a speed reduction at the beginning of the last path segment found during the forward calculation.

The new permissible maximum speeds for all path segments preceding the determined path segment (back to the start of the first path segment) are then calculated on the basis of the lowered maximum speed at the start of the determined path segment. The acceleration is preferably set to zero at the beginning of the backward calculation and the constant limit values of the individual path segments for speed, acceleration and jerk are taken into account during the backward calculation.

If there was at least one drop in speed during the forward calculation, the backward calculation for the end of the first path segment results in a maximum speed that is lower than the maximum speed originally assumed at the beginning of the forward calculation.

If the newly calculated permissible maximum speeds for the individual path segments are determined by means of the backward calculation, the limit speed profile can be generated from this. The limit speed profile can subsequently be divided into the previously described zones of constant permissible speed, constant permissible acceleration or constant permissible jerk, whereupon the transition conditions at the zone transitions can be determined. In other words, a limit speed profile is generated by means of the forward and backward calculation, which is valid for several consecutive path segments and areas with constant limit values for contains velocity, acceleration or jerk. Based on these areas, the speed limit profile is divided into individual zones at the transitions of which zone transition conditions must be observed in order not to violate the speed limit profile in the subsequent zone.

Since it is always possible to decelerate to a standstill starting from the last speed reduction, any further path segments that may follow no longer have any influence on the preceding path segments and therefore also do not influence the generation of the limit speed profile.

If the maximum speed at the beginning of a path segment is not reduced during the forward calculation, the backward calculation can be omitted.

The plurality of transition conditions preferably includes value pairs for speed and acceleration, the value pairs for speed and acceleration at the transition from the first zone to the second zone being selected in such a way that the limit values of the second zone (and further subsequent zones) are not exceeded. If, for example, the second zone is a zone with a constant permissible deceleration, then a pair of values is already determined by the course of the limit speed profile at the zone transition, namely by the maximum possible speed at the end of the zone with the maximum possible deceleration there (negative acceleration).

Further pairs of values preferably indicate at which maximum speed the zone may be left with the maximum possible acceleration and at which maximum speed the zone may still be left with an acceleration value of zero. In order to describe the connection between possible speed and acceleration at the zone transition as precisely as possible, it can be useful to determine further pairs of values. Values that were not explicitly determined during the preparatory part can be evaluated at runtime using intermediate interpolation.

The first speed profile is preferably adapted to the predetermined target speed and a predetermined target acceleration in each interpolation point. In other words, the course of the first speed profile can change if a change in the predetermined setpoint speed is detected at an interpolation point. The adapted first speed profile is preferably adapted to the path that is still available within the current zone.

A computing unit according to the invention, e.g. a control unit of a production machine or system, is set up, in particular in terms of programming, to carry out a method according to the invention.

The implementation of a method according to the invention in the form of a computer program or computer program product with program code for carrying out all method steps is advantageous because this causes particularly low costs, especially if an executing control unit is also used for other tasks and is therefore available anyway. Suitable data carriers for providing the computer program are, in particular, magnetic, optical and electrical memories, such as hard drives, flash memories, EEPROMs, DVDs, etc. It is also possible to download a program via computer networks (Internet, intranet, etc.).

Further advantages and refinements of the invention result from the description and the attached drawing.

It goes without saying that the features mentioned above and those still to be explained below can be used not only in the combination specified in each case, but also in other combinations or on their own, without departing from the scope of the present invention.

The invention is shown schematically in the drawings using an exemplary embodiment and is described in detail below with reference to the drawings.

character list

• 1 shows an embodiment of the computing unit according to the invention,
• 2 shows an example of a forward calculation for determining a limit speed profile using the method according to the invention,
• 3 shows an example of a backward calculation to determine the limit speed profile based on the in 2 described forward calculation,
• 4 shows an example of the division of the in 3 determined limit speed profile in the individual zones,
• 5 shows an example of different transition conditions at a zone transition the limit speed profile according to the method according to the invention,
• 6 shows an example for the calculation of a current path according to the method according to the invention using a flowchart, and
• 7 shows an example for the determination of a second speed profile with the method according to the invention.

Detailed description of the drawing

1 shows an embodiment of a computing unit 10 according to the invention, which has a plurality of sub-units 1, 2, 3.

In a first sub-unit 1, the non-real-time calculations for determining a limit speed profile, transition conditions and a first speed profile are carried out as part of a preparatory part. The splitting of the limit speed profile into individual zones, each with a constant permissible speed, acceleration or jerk, also takes place in the first sub-unit 1.

The variables determined are sent to the second sub-unit 2, which carries out the calculations at runtime, preferably in a fixed interpolation cycle, which can be 1 ms, for example. In each interpolation cycle, the second sub-unit adjusts the first speed profile to an externally specified target speed (eg by a machine operator) and then calculates the current path using the first speed profile, taking into account the transition conditions and the limit speed profile. For this purpose, the sub-unit 2 calculates a second speed profile in each interpolation cycle, which allows a time-optimized transition from a first zone into a second zone of the limit speed profile. The calculation steps carried out in subunit 2 in the interpolation part of the method according to the invention are described below with reference to FIG 6 explained in more detail.

The second sub-unit 2 sends the path calculated in each interpolation cycle, including the current speed, the current acceleration and the current jerk, to a third sub-unit 3, which calculates the position values for the individual axes (in particular driven by electric motors) of a machine/system (not shown). ) is calculated and these values are sent to a drive controller 4 of the machine/system.

2 shows an example of a forward calculation (index v) for determining a limit speed profile 1 with a preferred embodiment of the method according to the invention. A relationship between a speed on the ordinate and a time (which is required for a given distance) is plotted on the abscissa. A limit speed profile represents the maximum speed with which a specified path can be traversed without exceeding the machine/system-related and technological limit values for speed, acceleration and/or jerk. Starting from the end of a movement segment of a path with an assumed point in time t _k,v , a limit speed profile 1 is determined, which represents the maximum speed that can be used while maintaining the limit values for speed, acceleration and jerk determined segment by segment. A movement segment should be understood to mean a movement with speed, acceleration and jerk on a path segment.

The movement segment under consideration is to be moved at a specified speed V _{k_soll} . This speed was previously determined in such a way that it adheres to the above limit values for the track segment under consideration.

During the forward calculation, it is checked whether the following movement segments, which begin at the times t _k,v , t _k+1,v or t _k+2v , allow the speed v(t) to be braked to a standstill without the to violate the determined limit values of these subsequent path segments. In the present example, the speed v(t) cannot be slowed down to a standstill in the first subsequent movement segment up to t _{k+1, v} currently considered, first movement segment to the subsequent, second movement segment is permissible. At time t _k+1,v , the maximum velocity v _loc,min,1 should prevail, but taking into account the maximum values for deceleration and jerk, it can only be decelerated to velocity v _loc,1,v . Therefore the speed v(t _k+1 ) has to be lowered to the speed v _loc,min , ₁ and the transition is marked as “violated”. At time t _k+1,v it is preferably also checked whether the acceleration a at the transition from the first to the second path segment is permissible, and if it is exceeded it is also reduced.

Since the speed v(t) cannot be reduced to zero in the second movement segment either, it must also be checked there whether the speed v(t _k+2 ) at the transition from the second to the third movement segment leads to an over exceeding the permissible speed v(t) in the third track segment. At time t _k+2,v the maximum velocity v _loc,min,2 should prevail, but taking into account the maximum values for deceleration and jerk it can only be decelerated to velocity v _loc,2,v . Therefore, at time t _k+2,v there is a further reduction in speed to speed v _loc,min,2 and this transition is also marked as “violated”. Starting from the speed v _loc,min,2 , the speed v(t) can then be braked to a standstill in the third movement segment.

A sequence of movement segments has thus been found, at the end of which the speed can be reduced to zero, and the forward calculation is complete for the movement section under consideration. If t _k+2,v is not the end of the path, a next movement section begins at point t _k+2,v , ie the forward calculation for the next movement segment starts again at this point.

3 shows an example of a backward calculation (index r) to determine the limit speed profile based on the in 2 described forward calculation. The calculation starts at the point t _k+2,r . This corresponds to the last transition marked as "violated" in the forward calculation. The backward calculation starts with the limit speed v _loc,min,2 determined there within the forward calculation and an acceleration value of zero and uses the limit values for speed, acceleration and jerk applicable between t _k+1,r and t _k+2,r to determine the maximum possible speed at time t _k+1,r to v _loc,1r .

Based on the maximum possible speed v _loc,1,r at t _k+1,r , the maximum possible speed at the point is subsequently calculated using the limit values for speed, acceleration and jerk applicable between t _k,r and t _k+1,r t _k,r to v _end,max calculated. Since there were two speed reductions within the area under consideration during the forward calculation, the backward calculation at point t _k,r results in a limit speed v _end,max that is lower than the speed v _{k_soll} originally assumed at the beginning of the forward calculation, and a negative one Acceleration.

Based on the maximum possible speed v _end,max at t _k,r and this negative acceleration, the speed profile for reaching v _k,soll,r is then calculated using the applicable limit values for speed, acceleration and jerk for the path segment considered at the beginning.

The limit speed profile 1 for the movement segments under consideration is thus found. Since, starting from the last speed reduction to the speed v _loc , _min,2, in the forward calculation it is always possible to decelerate to a standstill and since this speed must not be exceeded, any further movement segments that may follow no longer have any further influence on the movement segments considered .

4 shows an example of the division of the in 3 determined limit speed profile 1 in individual zones 1a-1g. The division takes place in such a way that each zone 1a-1g corresponds exactly to a section of the determined limit speed profile 1 with a constant limit value. The illustrated limit speed profile 1 consists of a zone with constant speed 1a, zones with constant negative jerk 1b, 1c to build up a deceleration (negative acceleration), zones with constant deceleration 1d and 1f and zones with constant positive jerk 1e, 1g to reduce it a delay together. The zones 1a-1g are formed in such a way that the variable jerk, deceleration or speed characteristic of the section reaches its maximum permissible limit value.

5 shows an example of different transition conditions at a zone transition t _z of any section of the limit speed profile 1 according to a preferred embodiment of the method according to the invention. In particular, the transition conditions define with which acceleration a = a _lim depending on the speed a zone may be left at runtime without the risk of violating the limit value according to limit speed profile 1 in the following zones. Furthermore, in 5 Pairs of values for speed and acceleration are shown, which indicate the maximum speed at which the zone can still be left with an acceleration value a = 0 and the maximum speed at which the zone can be left with a maximum possible acceleration a = a _max . The other pairs of values shown make it possible to describe the relationship between permissible speed and acceleration at the zone transition t _z in even greater detail. The more transition conditions present at a zone transition t _z , the more optimally the corresponding speed profile can be calculated.

6 shows an example of the calculation of a current path in the interpolation part of a preferred embodiment of the method according to the invention using a flow chart rens. At the start of the calculation, there is already a limit speed profile for several path segments of a specified path, which is divided into zones that each have constant limit values for speed, acceleration or jerk. There are also transition conditions that must be met at a transition from one zone to a subsequent zone in order not to violate the limit value of the subsequent zone. In other words, a large number of transition conditions at a transition from a first zone to a second zone have already been determined based on a limit value of the second zone.

The following flow starts in a step S100.

At the beginning, a first zone, z=1, is selected (S101) and a first speed profile, V=V ₁ , preferably determined using the jerk-limited seven-phase profile described above and initialized as the current speed profile (S102). In other words, a first speed profile V=V1 _is calculated for a first zone z=1 to reach a predetermined setpoint speed v set , the first speed profile being present in phases in the form of equations of motion and having a large number of predetermined interpolation points for determining a current path.

A first interpolation cycle, i=1, is started (S103) and a check _is first made as to whether the setpoint speed v setpoint (i) has changed compared to the setpoint speed in the last interpolation cycle v _setpoint (i-1). If this is the case, branch "1", then the first speed profile V ₁ is adapted to the changed target speed (S104), otherwise, branch "0", it remains unchanged (S105).

In the subsequent step S106, the current values for distance x(i), speed v(i), acceleration a(i) and jerk j(i) are then calculated using the first speed profile V ₁ determined in the initialization. If the first speed profile V ₁ violates one of the transition conditions at the end of the first zone (V ₁ (i _max ) > ÜB(i _max )), branch "1", a second speed profile V ₂ is generated in the same interpolation cycle as a function of the current speed v( i) and the current acceleration a(i) is calculated using the associated transition conditions (S107). Otherwise the interpolation is continued on the first speed profile V ₁ up to the end of the zone, branch "0". In step S107, a second speed profile for the transition from the first zone to the second zone is calculated at each interpolation point of the first speed profile, with the second speed profile being calculated depending on a determined speed in an interpolation point and an associated transition condition.

It is then checked whether the speed of the second speed profile V ₂ in the zone transition violates the transition condition ÜB(i). If the speed of the second speed profile V ₂ violates the transition condition ÜB(i), branch "1" in the zone transition, the current speed profile V changes to the second speed profile V ₂ (i-1), which was determined in the previous interpolation cycle i-1 was, instead of (S109), otherwise, branch "0" is further interpolated along the first velocity profile V ₁ (S108). In other words, a change from the first speed profile V ₁ to the second speed profile V ₂ calculated at a directly preceding interpolation point (i-1) takes place when the second speed profile V ₂ calculated at a current interpolation point i , one of the transition conditions is violated.

Since the interpolated second speed profile V ₂ (i-1) was valid in the last interpolation cycle i-1, but the second speed profile of the current cycle V ₂ (i) led to a violation of the transition condition ÜB, the optimum with regard to the maximum permissible speed lie between these two speed profiles V ₂ at the zone transition. Since the usual cycle times for the interpolation are small (1 ms is a typical value), the second speed profile of the last cycle V ₂ (i-1) is already very close to the optimum and can be approximated to the actual speed optimum with simple modifications if necessary .

If further interpolation points are still present in the first zone, i<i _max , a change is made to the next interpolation point i+1 (S110). If a switchover to the second speed profile of the last interpolation cycle V ₂ (i-1) has taken place in step S109, the further determination of interpolation points along the second speed profile V ₂ takes place. After reaching the last interpolation point of the first zone (i=i _max ), the next zone (S111) is entered, in which the first speed profile V ₁ is initialized again. The calculation is continued until all zones of the path segments considered have been traversed (z=z _max ), then the end of the method is reached (S112).

In the last zone z _max , the second speed profile V ₂ corresponds to a speed profile that enables braking to a standstill.

In 7 an example is shown which illustrates switching between the first and second speed profiles V ₁ and V ₂ . The straight solid line represents the limit speed profile 1 of the zone, namely a limit speed profile 1 with constant deceleration. The horizontal dashed line shows the specified target speed v set _, which in the present example remains constant throughout the interpolation along the first speed profile. The arrows on the exemplary zone transition t _z symbolize the determined zone transition conditions.

At the beginning of the zone, the speed and acceleration are both zero (standstill).

At the beginning of a zone, a first speed profile V ₁ is generally assumed to reach the target speed, which is calculated during the initialization. In particular, the setpoint speed comes from an external specification. The first speed profile can again be the jerk-limited seven-phase profile already mentioned.

Cyclic interpolation is now carried out along this first speed profile V ₁ . A second speed profile (transition speed profile) V _2-1 -V _2-5 is calculated in each interpolation cycle and checked against the zone transition conditions (arrows at the zone transition t _z ). The second speed profile V _2-1 -V _2-5 is also based on the seven-phase profile already described and can be selected from a number of predefined profiles which, in addition to the above-mentioned speed profile for reaching a target speed, also include a speed profile for reaching a transition condition, along a speed profile of the limit speed profile and a speed profile for reaching standstill

When calculating a speed profile for a transition condition, the transition conditions at the zone transition are taken into account in the order "maximum permissible acceleration", "achievable constant speed" and "maximum permissible deceleration". This means that a transition profile to the maximum permissible acceleration at the zone transition is first calculated. If this transition speed profile violates a transition condition, then a transition speed profile is calculated next to the achievable constant speed at the zone transition. If this transitional speed profile also violates a transitional condition, then a transitional speed profile to the maximum permissible deceleration is determined as the last step.

With regard to the transition speed profiles V _2-1 and V _2-2 shown, which have a constant speed (a = 0) at the zone transition t _z , this means that a first calculated transition speed profile to the maximum permissible acceleration at the zone transition led to an injury and then a transition speed profile to the achievable constant speed was determined. In both cases, this does not lead to a violation of the transition conditions, since the speed at the corresponding interpolation points is below the speed up to which a zone transition with zero acceleration (a = 0) is permissible, but above the speed at which a zone transition is permissible with maximum acceleration (a = a _max ) is possible.

Since the transition speed profiles V _2-1 and V _2-2 do not violate the zone transition conditions, the interpolation continues along the first speed profile V1.

The speeds at the interpolation points of the transition speed profiles V _2-3 to V _2-5 are above the speed that allows a zone transition with constant speed (a = 0), so that these transition speed profiles have a constant deceleration (a = a _lim ) show at the zone transition. For the transition speed profiles V _2-3 and V _2-4 , this means that the two initially determined transition speed profiles to the maximum permissible acceleration and achievable constant speed led to a violation of the transition conditions and only the transition speed profile with the maximum permissible deceleration starting from the relevant interpolation points does not lead to a violation of the transition conditions.

However, the transition speed profile with maximum permissible deceleration V _2--5 violates the zone transition condition a = a _lim , since the deceleration achieved at the end of the zone is too low and thus the limit speed profile 1 at the zone transition is exceeded (see lightning bolt shown). The transition speed profile V _2-4 determined in the previous step does not yet violate the conditions and still exists at the current time. There is therefore a change to the transition speed profile V _2-4 , on which the zone can then be completely interpolated. In addition to switching to a transition speed profile V _2-1 -V _2-5 , a change to a speed profile along the limit speed and/or a change to a speed profile to a standstill.

In summary, the method according to the invention makes it possible to generate smooth, jerk-limited and approximately time-optimal velocity profiles for path controls without the need for filtering the movement variables velocity, acceleration and/or jerk. The zone-based calculation of the movement variables eliminates the need for further complex advance calculations for the interpolation time in the event of changes in the setpoint speed and/or the setpoint acceleration occurring during the runtime. At the same time, there is no need for complex synchronization algorithms because there is no filtering. The method enables an encapsulated view of motion segments at runtime and does not require any further complex iterative calculation steps.

Claims (11)

Method for generating a speed profile for a path control, comprising the steps: - generating a limit speed profile (1) for a plurality of path segments of a specified path, - dividing the limit speed profile (1) into zones (1a-1g), each of which has constant limit values for speed, acceleration or jerk, - determining a plurality of transition conditions at a transition from a first zone (1a-1g) to a second zone (1a-1g) based on a limit value of the second zone (1a-1g), - calculating a first velocity profile (2) for the first zone (1 a-1 g) to reach a predetermined setpoint speed v set ) _, the first speed profile (2) having a large number of predetermined interpolation points for determining a current path, and if the first speed profile has one of the large number violated by transition conditions: - Calculation of a second velocity profile (3.1-3.5) for the Ü Transition from the first zone (1a-1g) to the second zone (1a-1g) at each interpolation point of the first speed profile (2), the second speed profile (3.1-3.5) each depending on a determined speed in an interpolation point and an associated transition condition is calculated, - change from the first speed profile (2) to the second speed profile (3.1-3.5), which was calculated at a directly preceding interpolation point, if the second speed profile (3.1-3.5), which was calculated at a current interpolation point, violates one of the plurality of transition conditions, and - determining interpolation points along the second speed profile (3.1-3.5) to determine the current path. procedure according to claim 1 , current setpoints for the positions of individual axes of a machine or system being calculated at each interpolation point of the first and second speed profile (2, 3.1-3.5) based on the determined current path and sent to the machine or system. procedure according to claim 1 or 2 , wherein the limit speed profile (1) is generated by means of a forward calculation and a backward calculation of permissible maximum speeds for the plurality of path segments. procedure according to claim 3 , wherein the forward calculation of the permissible maximum speeds for the multiple path segments includes the following steps: - Checking whether a permissible maximum speed of a second path segment is maintained when a transition from a first path segment to the second path segment is approached with a permissible maximum speed of the first path segment, - Lowering the maximum speed of the first track segment at a start of the second track segment if the permissible maximum speed of the second track segment is exceeded, - determining a minimum speed at an end of the second track segment based on the maximum speed at the start of the second track segment, and - repeating the above steps in a third path segment and subsequent path segments starting from the maximum speed at the start of the second path segment if the minimum speed at the end of the second path segment is greater than zero, until the minimum speed at one end of a path segment reaches zero. procedure according to claim 4 , further comprising the steps: - checking whether a permissible maximum acceleration of the second path segment is observed when a transition from the first path segment to the second path segment is approached with a permissible maximum acceleration of the first path segment, - reducing the maximum acceleration of the first path segment at the beginning of the second path segment if the permissible maximum acceleration of the second path segment is exceeded, and - determining the minimum speed at one End of the second path segment based on the maximum speed and the maximum acceleration at the beginning of the second path segment. procedure according to claim 4 or 5 , wherein the backward calculation of the permissible maximum speeds for the several path segments comprises the following steps: - determining a path segment at the start of which the maximum speed was last reduced during the forward calculation, - calculating new permissible maximum speeds for all path segments preceding the determined path segment, starting from the reduced one maximum speed at the start of the path segment determined, and - generation of the limit speed profile from the newly calculated permissible maximum speeds. Method according to one of the preceding claims, wherein the plurality of transition conditions comprises pairs of values for velocity and acceleration and the pairs of values at the transition from the first zone (1a-1h) to the second zone (1a-1h) are selected such that a limit speed profile of the second and subsequent zones (1a-1h) is not exceeded. Method according to one of the preceding claims, in which the first speed profile (2) _is adapted to the predetermined desired speed (v desired ) and a predetermined desired acceleration at each interpolation point. Arithmetic unit (10) which is set up to carry out a method according to one of the preceding claims. Computer program that causes a computing unit (10) to use a method according to one of Claims 1 until 8th perform when it is executed on the computing unit (10). Machine-readable storage medium with a computer program stored on it claim 10 .

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