DE102011122434B4 - Method for controlling movement of mechanical devices using sequentially interpolated traversing blocks - Google Patents

Abstract

A method of controlling a movement of a mechanical device using successively interpolated traversing blocks, by means of a path planning performed by a controller to ensure compliance with the limits in each traversing set and to reduce a speed and an acceleration up to a predetermined end position of the movement using at least one first method instruction, which calculates a still permissible final speed for each traversing block at least in one phase of a traversing block preparation in which stopping is guaranteed until the end of the traverse, wherein in the traversing processing phase the calculated final speed is used to determine the actual velocity trajectory, and starting from the current values of the position (s), velocity (v), and acceleration (a), the maximum jerk (j) set and dadu by means of the first procedural instruction new values of position (s), velocity (v) and acceleration (a) can be determined by interpolation; and by means of at least one second method instruction which verifies a validity of values determined by the first method instruction at least during a method block processing by checking with the aid of the second method instruction whether the new values of position (s), speed (v) and acceleration (a) are valid, and by means of at least a third procedural instruction, which initiates braking when exceeding a restriction and / or insufficient braking distance of a movement set by forming for the remaining distance to Verfahrsatzende sections, which for the reduction of acceleration and braking is required to the final velocity value determined by the first procedural instruction, the motion starting at an initial velocity and an initial acceleration and stopping at an endpoint.

Description

The present invention relates to a method for controlling a movement of a mechanical device, in particular an industrial robot, using sequentially and in particular contiguous and successively interpolated traversing sets, by means of a control device carried out path planning to ensure compliance with the valid in each traversing restrictions and for reducing a speed to v = 0 and an acceleration to a = 0 up to a predetermined end position of the movement.

It's supposed to be a stretch of length s be traversed, which is divided into n sections. In each of these so-called traversing blocks, restrictions apply for the maximum speed Vmax, the maximum and minimum acceleration a _max or. a _min , as well as the maximum and minimum jerk j _max or. _min ,

Within a traversing block, the acceleration profile is continuous and piecewise linear. This results in profiles for position, speed, acceleration and jerk, as in the 1 shown.

According to the prior art, the acceleration disappears in the transition of two traversing blocks, so that no transition acceleration takes place.

DE 10 2009 024 130 A1 . DE 10 2008 029 657 A1 . DE 10 2010 025 271 A1 EP 2 022 608 B1 . US 6 216 058 B1 . US 5,811,952 A each show a method of controlling a device with traversing blocks.

Accordingly, it is the object of the present invention to improve the dynamics of movement, for example, more smoothness and higher speeds and to reduce or prevent the excitation of the device or machine or robot by means of a corresponding web interpolation for the smoothest possible velocity course, so that under Adhering to predetermined restrictions, a time-optimal speed profile can be calculated in order to travel the route in as short a time as possible.

This object is achieved by the present invention by means of a method for controlling a movement of mechanical devices using sequentially interpolated traversing sets according to claim 1.

Advantageously, a brake ramp is calculated via the existing movement sections. The resulting value pairs for the braking deceleration and the speed are then preferably stored in a table. During the setpoint specification, the next interpolation point is calculated, taking into account the limit values of the following sections. The mechanism preferably works optimally for real-time control.

Accordingly, a method for controlling movement of a mechanical device, such as an industrial robot, using successively interpolated traversing sets, by means of a controller carried out path planning to ensure compliance with the valid restrictions in each traversing set and to reduce a speed to v = 0 and an acceleration to a = 0 up to a predetermined end position of the movement, using at least a first method instruction which calculates a still permissible final speed at which at least one phase of a movement set preparation is guaranteed for each movement set, at which a stop is guaranteed until the end of the travel; and by means of at least one second method instruction, which verifies a validity of values determined by the first method instruction at least during a method block processing, and / or by means of at least one third method instruction, which initiates a braking operation when a limitation and / or insufficient braking distance of a positioning block is exceeded; forming sections for the remaining distance up to the end of travel, which are required for the reduction of the acceleration and the deceleration to the final speed value determined by the first method instruction, the movement starting with an initial speed and an initial acceleration and stopping at an end point, as specified in claim 1.

Advantageous embodiments and further developments are the subject of the dependent claims.

It is considered a movable, in particular mechanical system or device which is intended to travel a distance in space. The movement starts with an initial speed and an initial acceleration and should stop at a preferably defined end point. External factors, such as As the mechanics and / or the mass of the system to be moved or the direction of motion specify the limits for acceleration and speed, which can not be exceeded or fallen below or may.

In addition, advantageously, the maximum rate of change of acceleration - the so-called jerk - limited.

The restrictions preferably comprise at least
a maximum speed v _max , which preferably has the unit [mm / s],
a maximum acceleration a _max , which preferably has the unit [mm / s ² ],
a minimum acceleration a _min which corresponds to a maximum delay and also preferably has the unit [mm / s ² ],
a maximum jerk j _max and
a minimal jerk _min , which in each case preferably has the unit [mm / s ³ ].

$$v\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}a\left(\tau \right)d\tau +v_0}$$

$$s\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}v\left(\tau \right)d\tau +s_0}$$

If the progression over time of the j: R ₊ → R, t → j (t) is known, then the values for the acceleration, the velocity and the position result as follows: $$a\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}j\left(\tau \right)}d\tau +a_0$$

$$v\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}a\left(\tau \right)d\tau +v_0}$$

$$s\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}v\left(\tau \right)d\tau +s_0}$$

There are a ₀ . v ₀ . s ₀ the values at the beginning of the movement. The position or the way or the distance s in this case preferably has the unit [mm].

In the following, however, the figures of the speed, acceleration, jerk and position are shown without units for the sake of simplicity and comprehensibility, with the above-mentioned units being able to be consulted at any time.

$$v\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}j*\tau +a_{0}d\tau +v_0=\frac{1}{2}j{t}^2+a_{0}t+v_0}$$

$$s\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}\frac{1}{2}}j*{\tau }^2+a_0*\tau +v_{0}d\tau +s_0=\frac{1}{6}j{t}^3+\frac{1}{2}{a}_0{t}^2+v_{0}t+s_0$$

For a constant jerk the following integrals can be specified directly: $$a\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}jd\tau +a_0=j*t+a_0}$$

$$v\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}j*\tau +a_{0}d\tau +v_0=\frac{1}{2}\mathrm{<figure-callout\; id="2"\; label="j\; t"\; filenames="DE102011122434B4\_0031.png"\; state="\{\{state\}\}">j\; </figure-callout>}{t}^{}{}^2+a_{0}t+v_0}$$

$$s\left(t\right)={\displaystyle \underset{0}{\overset{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102011122434B4\_0031.png"\; state="\{\{state\}\}">t</figure-callout>}}{\int }}\frac{1}{2}}j*{\mathrm{<figure-callout\; id="2"\; label="\tau "\; filenames="DE102011122434B4\_0031.png"\; state="\{\{state\}\}">\tau </figure-callout>}}^2+a_0*\tau +v_{0}d\tau +s_0=\frac{1}{6}\mathrm{<figure-callout\; id="3"\; label="j\; t"\; filenames="DE102011122434B4\_0033.png"\; state="\{\{state\}\}">j\; </figure-callout>}{t}^{}{}^3+\frac{1}{2}{a}_0{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="DE102011122434B4\_0031.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+v_{0}t+s_0$$

In compliance with the above restrictions, the route should advantageously be run in the shortest possible time. The entire movement is preferably divided into at least three phases. In the first phase, namely the acceleration phase, a certain maximum speed is initially set up, while in the second phase, namely the constant phase, this speed is then continued, and finally in the third phase, namely the deceleration phase, the movement or the speed to slowed down to a standstill or delayed or reduced. The acceleration should preferably be continuous over time and piecewise linear. This results in a piecewise constant jerk.

The path planning has the task, as already mentioned above, on the one hand to ensure compliance with the valid restrictions in each traversing set and on the other to reduce the speed to v = 0 and the acceleration to a = 0 to the predetermined end position or reduce.

Preferably, the compliance with the second condition, namely the speed and the acceleration to a predetermined position is substantially completely reduced in two steps, namely the step of Verfahrsatzvorbereitung and the step of Verfahrsatzabarbeitung realized.

In the positioning block preparation, the first method instruction, which may also be referred to as the "look-ahead algorithm", preferably determines a still permissible final speed for each traversing block by means of which the end of the total distance, i. until the last traversing block has been reached, the movement or the speed of the movement or acceleration can be completely decelerated or reduced. When moving the traversing blocks in the step of traversing processing, these values are then used to determine the actual course of the velocity.

Preferably, the actual speed at the end of all traversing sets should always be less than or equal to the speed of the first procedural instruction, so as to be able to ensure that the system or the movement of the device or machine can be delayed until reaching the end point to a standstill.

Consequently, the calculated final velocity is preferably used to determine the actual velocity profile in the phase of a procedural processing, wherein starting from the current values of the position (c_dCurrentPos), velocity (c_dCurrentVel) and / or acceleration (c_dCurrentAcc), the maximum jerk is determined by means of at least the first procedural instruction and thereby new values of the position (dNewPos), speed (dNewVel) and / or acceleration (dNewAcc) are determined by interpolation.

Accordingly, the first method instruction or the "look-ahead algorithm" preferably has the task, for each of the n movement records, wherein preferably a plurality of traversing sets and in particular at least one traversing block is used, in the traversing block buffer an end velocity v _LA which allows it to decelerate to v = 0 (and a = 0) until the end of the route. Thus, advantageously, it must be determined how much speed at a given initial speed v _start in one movement set in compliance with the applicable restrictions j _max . _min . a _min can be reduced. This preferably depends on the initial acceleration. At the beginning of a traversing block, which is, for example, in the acceleration phase, the following applies: a _start > 0. This means that first of all this acceleration has to be reduced and then a deceleration has to be established. Consequently, in this case, less speed can be reduced than if the movement were already in the deceleration process with a _start <0.

This means, in the case of the first procedural instruction, that preferably next to a terminal speed v _LA also a final acceleration a _LA is to be specified, so that advantageously for each traversing a final value pair of final speed and final acceleration ( v _LA . a _LA ) is determined. For this purpose, a continuous deceleration process is preferably formed by means of the first method instruction, wherein the following always applies: a _LA = 0.

In order to calculate the end value pair (v _LA , a _LA ) _i , i = 1,..., N, starting at the end point of the path at which v = 0 and a = 0 must apply ( v _LA , a _LA ) _n = (0, 0). Starting from these final conditions (v = 0, a = 0), an end value pair (v _LA , a _LA ) _n-1 with maximum velocity now becomes v determined for the Verfahrsatzende the penultimate traversing block, so that the limits of ( _n , a) = (0 _LA , a _LA .) _n = (0, 0) can be reached in compliance with the restrictions in the n-th movement rate.

This deceleration process is considered an acceleration process with regard to time in reverse, the permissible maximum acceleration being just the magnitude of the permissible maximum deceleration | a _min | equivalent. Preferably, the amounts of delays are always calculated by means of the first method instruction, so that all determined values for the acceleration or deceleration "a" have a positive sign.

As already mentioned above, an acceleration process consists of up to three sections or segments. Thus, in the calculations, the initial values preferably obtain the index 0 ( v ₀ . a ₀ ) and the end values prefers the index 3 ( v ₃ . a ₃ ).

At the beginning of the acceleration v ₀ = 0 and a ₀ = 0. Furthermore, the length of the nth set s ^{(n) must be included} in the calculation and the restrictions in the traversing block j _max . _min , | a _min | have to be considered. In addition, it must be determined what value a ₃ should take the acceleration at the end of the acceleration process.

weder die Beschränkungen des letzten noch des vorletzten Verfahrsatzes verletzen sollte, wird a₃ bevorzugt zunächst wie folgt gesetzt: $$a_3=\text{min}\left\{\left|a_{\text{min}}^{\left(n\right)}\right|,\left|a_{\text{min}}^{\left(n-1\right)}\right|\right\}.$$

Since the acceleration sought at the end of the acceleration process, ie $a_3=a_{LA}^{\left(n-1\right)}$

neither violate the restrictions of the last sentence nor of the penultimate one, will a ₃ preferably initially set as follows: $$a_3=\text{min}\left\{\left|a_{\text{min}}^{\left(n\right)}\right|.\left|a_{\text{min}}^{\left(n-1\right)}\right|\right\},$$

berechnet werden.With these requirements can now ${\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="DE102011122434B4\_0033.png"\; state="\{\{state\}\}">v</figure-callout>}}_3=v_{LA}^{\left(n-1\right)}$

be calculated.

The following is a first example:

There are three traversing blocks in the traversing buffer: s v _max a _max a _min j _{max min} Traversing block 1 30 10000 4000 -4000 50000 -50000 Traversing block 2 20 10000 3000 -3000 50000 -50000 Traversing block 3 50 10000 4000 -4000 50000 -50000

Then the values of the first procedure for speed and acceleration are as follows: v _LA a _LA Traversing block 1 706.8083379333484 3000 Traversing block 2 616.0990291262135 3000 Traversing block 3 0 0

To the end values or the end value pair of final speed and final acceleration of traversing block 1 to be determined, is preferably substantially the same procedure as in the determination of the end value pair for the positioning record 2 , This means that the calculated end values of the end value pair of the second traversing block are used as start values or initial values in the calculation of the end values of the first traversing block and consequently "accelerated backwards". The final acceleration is formed as described above: $$a_{LA}^{\left(1\right)}:=\text{min}\left\{\left|a_{\text{min}}^{\left(2\right)}\right|.\left|a_{\text{min}}^{\left(1\right)}\right|\right\}=\mathrm{3000th}$$

However, it is also possible that the desired acceleration a _LA can not be reached, as the following second example shows: s v _max a _max a _min j _{max min} Traversing block 1 30 10000 4000 -4000 50000 -50000 Traversing block 2 20 10000 4000 -4000 50000 -50000 Traversing block 3 20 10000 4000 -4000 20000 -50000

anstatt des vorläufigen Wertes a₃=4000 erreicht.Starting from (v _LA , a _LA ) ₃ = (0, 0) only one final acceleration of $a_3=a_{LA}^{\left(2\right)}=3634.241185664279$

instead of the provisional value a ₃ = 4000 reached.

When this case occurs, the maximum achievable acceleration is set as the final acceleration of the first procedural instruction (with the corresponding associated speed) of the current positioning record. The following values result: v _LA a _LA Traversing block 1 517.8025359433898 4000 Traversing block 2 330.1927248894627 3634.241185664279 Traversing block 3 0 0

In general, it is generally the case that the shorter the travel rate, the greater the speed and / or the smaller the jerk, the less acceleration can be built up or taken down within a defined distance.

However, this becomes problematic, for example, in the constellation, as shown in the third example: s v _max a _max a _min j _{max min} Traversing block 1 30 10000 1000 -1000 50000 -50000 Traversing block 2 10 10000 4000 -4000 20000 -20000 Traversing block 3 50 10000 4000 -4000 20000 -50000

After the first calculation result for final acceleration and velocity of the second traversing block $a_{LA}^{\left(2\right)}:=4000\text{and}{v}_{LA}^{\left(2\right)}:=625.6729729729\mathrm{73rd}$

errechnet, obwohl nur eine Beschleunigung von 1000 erlaubt ist.If these values are used to calculate the end values of the first traversing block, a final acceleration of $a_{LA}^{\left(1\right)}:=3694.848498478164$

calculated, although only an acceleration of 1000 is allowed.

The difference a _Δ = 3694.848498478164 - 1000 = 2694.848498478164 must therefore already be dismantled. For this purpose, the final acceleration of the second traversing set is subsequently reduced in order to be able to comply with the restrictions of the first traversing block. As new final acceleration is set: $$a_{LA}^{\left(2\right)}:=\text{min}\left\{\left|a_{\text{min}}^{\left(3\right)}\right|.\left|a_{\text{min}}^{\left(2\right)}\right|\right\}-a_{\Delta }=\mathrm{1305.151501521836.}$$

Now, as known, can be further calculated, the following end values are obtained: v _LA a _LA Traversing block 1 581.8476387081914 1000 Traversing block 2 561.3371315246402 1305.151501521836 Traversing block 3 0 0

A fourth example is intended to show what is required if the calculated final speed violates the permissible maximum speed, whereby the following two traversing blocks are considered: s v _max a _max a _min j _{max min} Traversing block 1 100 10000 6000 -6000 50000 -50000 Traversing block 2 250 1500 6000 -6000 20000 -50000

erhalten. Demnach verletzt die Endgeschwindigkeit des ersten Verfahrsatzes $v_{LA}^{\left(1\right)}$

die zulässige Maximalgeschwindigkeit des zweiten Verfahrsatzes. In diesem Fall sollte die berechnete Beschleunigung vorzugsweise nicht übernommen werden und die Geschwindigkeit nicht einfach auf die zulässige Maximalgeschwindigkeit gesetzt werden, also (v_LA, a_LA)₁ =(1500, 6000), da folglich, ausgehend von diesen Anfangswerten, die Beschleunigung bzw. die Verzögerung nicht abgebaut werden kann, bevor die Geschwindigkeit auf Null reduziert wurde.The final values for the first traversing block become provisional $v_{LA}^{\left(1\right)}:=1719.5348147814815\text{and}{a}_{LA}^{\left(1\right)}:=4600$

receive. Accordingly violates the final speed of the first traversing set $v_{LA}^{\left(1\right)}$

the permissible maximum speed of the second positioning record. In this case, the calculated acceleration should preferably not be adopted and the speed should not simply be set to the permissible maximum speed, that is, (v _LA , a _LA ) ₁ = (1500, 6000), since, starting from these initial values, the acceleration or acceleration is increased The delay can not be reduced before the speed has been reduced to zero.

zu setzen, da beim Starten mit diesen Werten in den letzten Verfahrsatz die Distanz von 250 folglich nicht ausreichen würde, um die Bewegung vollständig abbremsen zu können. Der Bremsweg betrüge im vorliegenden Fall 277.5.Furthermore, it is not enough the final acceleration of the positioning record 2 to zero and the final speed up $v=\text{min}\left\{v_{\text{Max}}^{\left(1\right)}.v_{\text{Max}}^{\left(2\right)}\right\}=1500$

Therefore, when starting with these values in the last traversing block, the distance of 250 would not be sufficient to completely decelerate the movement. The braking distance would be 277.5 in the present case.

Preferably, the procedure is instead as described below:

If a calculated speed of the first procedural instruction violates the permissible maximum speed, the last calculation is carried out again, but this time with a ₃ = 0, whereby the following values are obtained: v _LA a _LA Traversing block 1 1409.067567567568 0 Traversing block 2 0 0

If the maximum speed is still lower than the currently calculated value, the maximum speed is finally set as the look-ahead speed or as the speed of the first procedural instruction.

In the transition between two traversing blocks, the speed is always constant in this case or in this first procedural instruction. The terminal speeds determined by the first method instruction are preferably stored permanently.

Preferably, with the aid of the second method instruction (also referred to below as "DecCheck" algorithm), it is checked whether the new values of the position (dNewPos), the speed (dNewVel) and the acceleration (dNewAcc) are valid.

This means that in the positioning block preparation or in block preparation, a final speed (with associated final acceleration) was first determined for each traversing block, which represents the maximum permitted speed at the end of the respective traversing block, in order to decelerate the movement until the end of the overall route while in traversing processing these values are in turn used to determine the actual course of the velocity.

At the beginning of the movement, i. in the acceleration phase, a speed is to be built up. Based on the current position, velocity, and acceleration values (c_dCurrentPos, c_dCurrentVel, c_dCurrentAcc), the maximum positive jerk is set, which preserves the values in the next interpolation step. These are simply given by formulas (1) above by using the cycle time.

1. 1. sämtliche Beschränkungen in diesem und allen folgenden Verfahrsätzen eingehalten werden; und
2. 2. bis zum Streckenende vollständig abgebremst werden kann.

These new values (dNewPos, dNewVel, dNewAcc) are preferably valid if it is ensured that:

1. 1. all restrictions in this and all following traverses are complied with; and
2. 2. can be braked completely to the end of the track.

Whether the "new" acceleration (dNewAcc) violates the maximum acceleration in the same traversing block is preferably checked immediately after its calculation. Thereafter, as mentioned above, it is checked with the aid of the second method statement whether the new values are valid.

In order to be able to determine whether the movement can be stopped until the end of the journey, it is preferable to form a delay process with the provisional new values (dNewPos, dNewVel, dNewAcc) as starting values.

Care must preferably be taken in this delay process that all restrictions are met, ie, that, for example, not the minimum acceleration a _min (or the maximum delay) of a traversing set is fallen below. This problem has also been explained in the description of the first procedural instruction, where iteratively there acceleration end values for each traversing set a _LA which allow the acceleration limit a _min to be complied with in each positioning record. This should therefore also be considered below.

The second method instruction (DecCheck algorithm) is advantageously fulfilled by means of two methods, namely a deceleration method and a braking distance calculation method (CalcBrakeDistance).

That is, preferably, the deceleration process with the new values of the position (dNewPos), the velocity (dNewVel), and the acceleration (dNewAcc) serving as start and initial values, respectively, using the deceleration method in which a final velocity is below a determined predetermined distance, and the braking distance calculation method in which a distance is determined below a predetermined final speed is formed.

Thus, in order to enable a deceleration process, in addition to the initial values for the velocity and the acceleration, the values with respect to a desired final acceleration and a distance at which the movement is to be delayed are also required. This corresponds to the input parameters of the deceleration method (Decelerate: StartVel, StartAcc, EndAcc, Distance).

A single deceleration process preferably can not be formed across traversing block boundaries, since in general the restrictions in the individual traversing blocks differ. Instead, a separate delay process is preferably formed for each positioning record.

Consequently, the movement is currently in the traversing block at position x and is the total distance of the traversing block s , then there is a track s - x available for the deceleration of the movement or the speed and / or the acceleration.

To determine which final acceleration should now be passed to the delay method, the delay becomes a _LA (or the negative acceleration), which was determined in the first procedural instruction, since this ensures that the restrictions for the minimum acceleration a _min can be complied with in each traversing block.

As a result of the calculation in the deceleration method, an end velocity (EndVel) is advantageously determined. Besides, preferably, the deceleration method also outputs the maximum speed (LimVel) achieved during the deceleration process. If, in fact, the initial acceleration (StartAcc) is positive, it must first be reduced before it can be delayed. However, as long as the acceleration "a" is positive, speed is still built up so that the maximum speed achieved is greater than the initial acceleration or speed.

Furthermore, it is conceivable that the desired final acceleration (EndAcc) is not achieved. This situation can already occur during the acceleration process in the first procedural instruction.

The following fifth example:

It's a stretch of length s = 30 and the restriction _min = -20000 given. The initial values are v ₀ = 800 and a ₀ = 3000th The desired final acceleration is a ₃ = 4000th Then there would be a stretch s = 320.8333 necessary to reach this final acceleration. Within the route s on the other hand, the acceleration could be reduced to a ₃ = 2293.160855222864. The final speed is then in this case v ₃ = 893.5353323018386. This final speed v ₃ is then in the present case at the same time the maximum speed reached.

The delay method thus returns the output parameters of the final speed (EndVel), the final acceleration (EndAcc) and the initial acceleration (VelVel).

This means that the final acceleration determined by the deceleration method is always greater than or equal to the acceleration a _LA is.

Accordingly, preferably determined by the delay method displacement rate end values for the speed ( v ₃ ) and the acceleration ( a ₃ ) with the determined end values ( v _LA . a _la ) of the first procedural instruction, where always: $${\text{a}}_3={\text{a}}_{\text{LA}},$$

This results in the following case distinctions: v ₃ > v _LA Values are invalid. v ₃ = v _LA ; a ₃ = a _LA Values are valid. v ₃ = v _LA ; a ₃ > a _LA There can be no statement about the validity of the values.

The first procedural instruction has determined the maximum speeds for the end positions of the individual traversing blocks, which guarantee a stop of the movement, ie a reduction of the speed and the acceleration to the value zero, up to the end of the travel. Any speed greater than the final speed according to the first procedure v _LA leads unfavorably to the fact that can not be braked within the track. Therefore, the preliminary values are invalid in this case.

Is the speed v ₃ on the other hand, less than or equal to the speed of the first procedural instruction, the accelerations must preferably be compared with each other. Are against it a ₃ and a _LA identical, then can be preferably decelerated within the entire route.

is a ₃ greater than a _LA On the other hand, no statement can be made about the validity of the values. Then the final velocity (End Vel) and final acceleration (End Acc) values determined by the deceleration method are passed to the next traversing block, which in turn forms a deceleration with these initial values. This means that at the beginning of the next traversing block the total distance of the subsequent traversing block is transferred to the next deceleration method so that, in turn, end values or final value pairs are obtained, which are compared with the corresponding values of the first procedural instruction. If, however, it is still not possible to decide on the validity of the provisional values, the system continues to use the next-second positioning record. This will continue until a decision can be made.

The second method of the second procedure is the brake distance calculation method (CalcBrakeDistance). While in the deceleration method a distance is specified and a final speed is determined, the braking distance calculation method requires a final speed and returns the distance required to decelerate to that final speed.

Like the deceleration method, the braking distance calculation method calculates the maximum speed (LimVel) achieved during deceleration. Similarly, a final acceleration must be specified, which should be reached at the end of the delay. This final acceleration can not be reached before the speed v ₃ is reached, the delay reached so far is returned.

The following sixth example:

It was v ₀ = 300, a ₀ = 0, a ₃ = -4000 = a _min . j _max = 50000 = - _min and s = 50. You put v ₃ = 0, then becomes a braking distance S _B = 17.2125 determined.

In addition to forming a delay process and then comparing the value pairs ( v ₃ . a ₃ ) and ( v _LA . a _LA ), can also be used for example with the braking distance calculation method on the value pair ( v _LA . a _LA ) to check whether the required distance is greater than or less than the remaining distance to the end of the traversing set.

If the distance is less than or equal to the remaining distance up to the end of the movement, the values are valid, otherwise they are invalid. For a _LA ≠ 0, however, this calculation is not always so easy to perform. Thus, the case may arise that the value pair of the first procedural instruction with the given starting values is not reached. Therefore, this method is preferably always applied only when a _LA = 0.

With the first procedural instruction, values for final velocities were determined in the positioning block preparation, with which it is possible to delay to the end of the distance. For these values, the associated acceleration was always zero.

With these values, the braking distance can advantageously be determined (dNewVel, dNewAcc, c_dConstEndVeILA, 0.0, dBrakeDist, dLimVel), whereby it is preferably compared whether the braking distance (dBrakeDist) is greater than or less than the distance up to the end of the traverse end (dRestDist). dBrakeDist = dRestDist Values are valid. dBrakeDist> dRestDist Switching to the delay method (DecCheckLow = FALSE).

If the braking distance is less than or equal to the remaining distance up to the end of the traversing stroke, the values are valid. However, conversely, the values need not be invalid when the braking distance is greater. The "braking distance criterion" is therefore sufficient, but not necessary for the validity of the values of position, speed and / or acceleration (dNewPos, dNewVel, dNewAcc).

If a _LA = 0 applies in a travel record, then preferably the brake distance calculation method is used, the deceleration method preferably not being used, and consequently the braking distance criterion is required. This means that if the braking distance is greater than the distance up to the end of the traversing stop, it is preferable to decelerate, but the values are then invalid.

By means of the second procedural instruction, a methodology has been developed which proves or refutes that with the provisional values of position, velocity and acceleration (dNewPos, dNewVel, dNewAcc) it is possible to decelerate until the end of the total distance. Furthermore, by means of this second procedural instruction, the minimum acceleration is essentially never a _min violates the individual traversing sets, so that consequently this restriction is essentially always adhered to.

In a preferred embodiment, the jerk is at least partially and more preferably always chosen freely, so that in general also j _max , and _min essentially always be adhered to. Consequently, only the restrictions are missing a _max and v _max ,

Since a continuous deceleration process is formed in the second process instruction, positive accelerations are preferably first completely degraded. The maximum acceleration is thus always assumed at the beginning of a traversing block in this process.

Accordingly, it is preferably checked at the beginning of each traversing set by means of the second method statement, whether the initial speed of each traversing set, the maximum acceleration a _max exceeds.

Furthermore, attention is paid to the maximum speed by, for example, always comparing the values of the initial acceleration (LimVel) with the values of the maximum speed (c_dMaxVel) after calling up the braking distance calculation method and / or the deceleration method.

Thus, in the second procedural instruction, preferably all constraints are considered. If a constraint is violated, for example, the second procedural instruction returns a value greater than zero. Otherwise, with the return value equal to 0 everything is fine. Return value meaning 0 No injury; Values are valid. 1 Braking distance is not enough. 2 Maximum speed has been exceeded. 3 Maximum acceleration has been exceeded.

If, during the course of the second process instruction, it is determined that the maximum acceleration or the maximum speed of a positioning record has been violated and / or the braking distance is insufficient, then a braking operation must therefore preferably be initiated.

However, in order to be able to decelerate correctly, sections are formed for the remaining distance up to the traversing set. That is, each traversing set may have a plurality but at least one section, and preferably at least two sections.

Consequently, there are also a variety of different method components or sections that are responsible for forming sections (BuildSections (), BuildAccSections (), BuildDecSections (), RemoveAcc (), BuildEndOfMove (), BuildFinalMove ()).

Preferably, in forming the sections, the initial values (c_dSi, c_dVi, c_dAi) and the back (c_dJi) are stored in each individual section. In addition, it must be preferred to know how long the process of each individual section lasts, so that the times (c_dTi), which indicate the start time at which the section "i" begins, are stored.

Before forming the sections, the current time (c_dTimeOffset) and position (c_dPosOffset) are also saved. This has the advantage that in the following calculations the initial values for the time and the position can be set to T = 0 and s = 0.

In order to obtain the correct values, the offset values are then added again. How many and which of the preferably seven sections are needed depends on several factors. If, for example, the maximum speed was violated in one traversing block, when forming the sections in this traversing block, it is therefore preferable to attempt to reach exactly this maximum speed.

Accordingly, an object of the present invention is to reduce speed as quickly as possible, whereby a plurality of cases with respect to the initial and final acceleration, as the following table shows, are distinguished. a ₀ a _LA > 0 = 0 = 0 = 0 <0 = 0 > 0 <0 = 0 <0 <0 <0

Furthermore, in a preferred embodiment, each time the third method instruction is called, the time (c_dTFinal), which stores the end of the period of the sections, is set, thereby returning the position, velocity, acceleration, and jerk values subsequent positioning record in the first interpolation step again used as initial values.

Further advantages, objects and characteristics of the present invention will be explained with reference to the following description of the appended drawings.

Components which at least substantially coincide in the figures with respect to their function may in this case be identified by the same reference symbols, these components not having to be identified and explained in all figures.

• 1 ein Diagramm zur beispielhaften Abbildung des zeitlichen Verlaufs von Geschwindigkeit, Beschleunigung und Ruck einer Bewegung;
• 2 ein Diagramm zur Abbildung des Bahnverlaufs eines Bremsvorganges mit positiver Anfangs- und verschwindender Endbeschleunigung (a₀>0, a_LA=0):
• 3 ein Diagramm zur Abbildung des Bahnverlaufs eines Bremsvorganges, bei welcher innerhalb der Sektionen die Bewegung verzögert wird;
• 4 ein Diagramm zur Abbildung des Bahnverlaufs eines Bremsvorganges mittels der Bildung lediglich einer zweiten Sektion;
• 5 ein Diagramm zur Abbildung des Bahnverlaufs eines Bremsvorganges mit negativer Anfangs- und negativer Endbeschleunigung (a₀<0, a_LA<0);
• 6 ein Diagramm zur Abbildung des Bahnverlaufs eines Bremsvorganges mit negativer Anfangs- und verschwindender Endbeschleunigung(a₀<0, a_LA=0);
• 7 ein Diagramm zur Abbildung des Bahnverlaufs eines Bremsvorganges mit verschwindender Anfangs- und verschwindender Endbeschleunigung (a₀=0, a_LA=0);
• 8 ein Diagramm zur Abbildung des Bahnverlaufs eines Bremsvorganges mit verschwindender Anfangs- und negativer Endbeschleunigung (a₀=0, a_LA<0);
• 9 ein Diagramm zur Abbildung des Bahnverlaufs eines Bremsvorganges mit positiver Anfangsbeschleunigung und dem Ziel die Maximalgeschwindigkeit zu erreichen, für den Fall a₀=0, a_LA=0;
• 10 ein Diagramm zur Abbildung des Bahnverlaufs eines Bremsvorganges mit positiver Anfangsbeschleunigung und dem Ziel die Maximalgeschwindigkeit zu erreichen, für den Fall a₀=0, a_LA<0;
• 11 ein Diagramm zur Abbildung der Ruckanpassung im letzten Verfahrsatz; und
• 12 ein Diagramm zur Abbildung von Zeiten beim Verfahrsatzübergang.

In the figures show:

• 1 a diagram for exemplifying the time course of speed, acceleration and jerk of a movement;
• 2 a diagram illustrating the trajectory of a braking process with positive initial and vanishing final acceleration (a ₀ > 0, a _LA = 0):
• 3 a diagram illustrating the trajectory of a braking process, in which the movement is delayed within the sections;
• 4 a diagram for illustrating the trajectory of a braking operation by means of the formation of only a second section;
• 5 a diagram illustrating the trajectory of a braking process with negative initial and negative final acceleration (a ₀ <0, a _LA <0);
• 6 a diagram illustrating the trajectory of a braking process with negative initial and vanishing final acceleration (a ₀ <0, a _LA = 0);
• 7 a diagram illustrating the trajectory of a braking process with vanishing initial and vanishing final acceleration (a ₀ = 0, a _LA = 0);
• 8th a diagram illustrating the trajectory of a braking process with vanishing initial and negative final acceleration (a ₀ = 0, a _LA <0);
• 9 a diagram for mapping the trajectory of a braking process with positive initial acceleration and the goal to reach the maximum speed, for the case a ₀ = 0, a _LA = 0;
• 10 a diagram for mapping the trajectory of a braking process with positive initial acceleration and the goal to reach the maximum speed, for the case a ₀ = 0, a _LA <0;
• 11 a diagram for mapping the jerk adjustment in the last traversing block; and
• 12 a diagram for the representation of times during the movement record transition.

1 shows a diagram for exemplary mapping of the time course of the speed v , the acceleration a and the jerk j a movement, the jerk j for movements can not be represented over the entire time of the movement by a closed Funktionssterm. Instead, the jolt j section-wise defined.

As in 1 can be clearly seen, the movement is divided into seven sections, within which the jerk j always constant. is. The movement starts at the time T ₀ = 0 and ends at the essentially fixed time T ₇ or at the section boundary T ₇ , The sections are therefore of t ₀ to t ₆ numbered. The i-th section is limited by the timings or section boundaries T _i and T _{i + 1} , i = 0, ..., 6.

The i-th section then has the length t _i = T _{i + 1} -T _I. Conversely, T _{i + 1} = T _i + t _i , i = 0, ..., 6.

The jerk j is now specified in sections by: $$\begin{array}{ccc}\text{j}\left(\text{t}\right)={\text{j}}_{\text{i}}.& {\text{T}}_{\text{i}}<\text{t}={\text{T}}_{\text{i + 1}}.& \text{i}=\text{0}.....\text{6}\text{,}\end{array}$$

$${\text{j}}_1={\text{j}}_3={\text{j}}_5=\text{0},$$

$${\text{j}}_2={\text{j}}_4={\text{j}}_{\text{min}}.$$

There are j ₀ , ... j ₆ real numbers. According to 1 applies, for example: $${\text{j}}_0={\text{j}}_6={\text{j}}_{\text{Max}}.$$

$${\text{<figure-callout id="1" label="j" filenames="DE102011122434B4\_0031.png" state="{{state}}">j</figure-callout>}}_1={\text{<figure-callout id="3" label="j" filenames="DE102011122434B4\_0033.png" state="{{state}}">j</figure-callout>}}_3={\text{<figure-callout id="5" label="j" filenames="DE102011122434B4\_0031.png" state="{{state}}">j</figure-callout>}}_5=\text{0}.$$

$${\text{j}}_2={\text{j}}_4={\text{j}}_{\text{min}},$$

To the acceleration a at any time t or at any time value t which one time t equals to receive, the jerk must j for example, be integrated over several sections. Lies t in the i-th section, ie T _i <t = T _{i + 1} , then $$a\left(t\right)=a_0+{\displaystyle \underset{0}{\overset{t}{\int }}j\left(\tau \right)}d\tau =a_0+{\displaystyle \underset{T_0}{\overset{T_1}{\int }}{j}_{0}d\tau +{\displaystyle \underset{T_1}{\overset{T_2}{\int }}{j}_{1}d\tau +...+{\displaystyle \underset{T_1}{\overset{T}{\int }}{j}_{1}d\tau }}}$$

i=0,...,6
die Änderung der Beschleunigung a im i-ten Abschnitt. Die Beschleunigung an den Abschnittsgrenzen wird dabei mit a_i=a(T_i) bezeichnet,
Für diese gilt: $$a_{i+1}:=a_i+d{a}_i=a_0+{\displaystyle \sum _{k=0}^{i}d{a}_k,}$$

i=0,...,6Where: $$d{a}_i:={\displaystyle \underset{T_i}{\overset{T_{\text{i}+1}}{\int }}{j}_{i}d\tau =j_i*t_i.}$$

i = 0, ..., 6
the change of acceleration a in the i-th section. The acceleration at the section boundaries is denoted by a _i = a (T _i ),
For these applies: $$a_{i+1}:=a_i+d{a}_i=a_0+{\displaystyle \underset{k=0}{\overset{i}{\Sigma }}d{a}_k.}$$

i = 0, ..., 6

Thus, the acceleration is a at any time t in the i-th section: $$\text{a}\left(\text{t}\right)={\text{a}}_0+{\text{there}}_0+{\text{there}}_1+...+{\text{there}}_{\text{i}-1}+{\text{j}}_{\text{i}}*\left(\text{t}-{\text{T}}_{\text{i}}\right)={\text{a}}_{\text{i}}+{\text{j}}_{\text{i}}*\left(\text{t}-{\text{T}}_{\text{i}}\right),$$

die Geschwindigkeitsänderung im i-ten Abschnitt und v_i :=v(T_i) =v_i-1, + dv_i-1 die Geschwindigkeit zum Zeitpunkt T_i. Für eine beliebige Zeit t ∈ [T_i, T_i+1] lautet die Geschwindigkeit $$v\left(t\right)=v_i+a_i\left(t-T_i\right)+\frac{1}{2}{j}_i{\left(t-T_i\right)}^2.$$

For speed v and position s Analogous quantities are introduced. So is: $$\begin{array}{l}d{v}_i:={\displaystyle \underset{T_1}{\overset{T_{i+1}}{\int }}a\left(\tau \right)d\tau ={\displaystyle \underset{T_1}{\overset{T_{i+1}}{\int }}{a}_1+j_i\left(\tau -T_i\right)d\tau ={\left[a_i\tau +\frac{1}{2}{j}_i{\left(\tau -T_i\right)}^2\right]}_{t_i}^{T_{i+1}}}}\\ =a_i{T}_{i+1}+\frac{1}{2}{t}_i^2-a_i{T}_i=a_i{t}_i+\frac{1}{2}{j}_{\mathrm{<figure-callout\; id="2"\; label="i\; t\; i"\; filenames="DE102011122434B4\_0031.png"\; state="\{\{state\}\}">i\; </figure-callout>}}{t}_i^{}{}_2^{}\end{array}$$

the velocity change in the ith section and v _i : = v (T _i ) = v _i-1 , + dv _i-1 the velocity at time T _i . For any time t ∈ [T _i , T _{i + 1} ] is the velocity $$v\left(t\right)=v_i+a_i\left(t-T_i\right)+\frac{1}{2}{j}_i{\left(t-T_i\right)}^2,$$

The position change in the i-th section is obtained by $$\begin{array}{l}{d}_{s_i}:={\displaystyle \underset{T_i}{\overset{T_{i+1}}{\int }}v\left(\tau \right)d\tau ={\displaystyle \underset{T_i}{\overset{T_{i+1}}{\int }}{v}_i+a_i\left(\tau -T_i\right)+\frac{1}{2}{j}_i{\left(\tau -T_i\right)}^{2}d\tau }}\\ ={\left[v_i\tau +\frac{1}{2}{a}_i{\left(\tau -T_i\right)}^2+\frac{1}{6}{j}_i{\left(\tau -T_i\right)}^3\right]}_{T_i}^{T_{i+1}}=v_i{t}_i+\frac{1}{2}{a}_{\mathrm{<figure-callout\; id="2"\; label="i\; t\; i"\; filenames="DE102011122434B4\_0031.png"\; state="\{\{state\}\}">i\; </figure-callout>}}{t}_i^{}{}_2^{}+\frac{1}{6}{j}_{\mathrm{<figure-callout\; id="3"\; label="t\; t\; i"\; filenames="DE102011122434B4\_0033.png"\; state="\{\{state\}\}">t\; </figure-callout>}}{t}_i^{}{}_3^{}\end{array}$$

The position at the section boundaries is s _i : = s (T _i ) = s _I-1 + ds _I-1 and for any time t ∈ [T _i , T _{i + 1} ] finally $$s\left(t\right)=s_i+v_i\left(t-T_i\right)+\frac{1}{2}{a}_i{\left(t-T_i\right)}^2+\frac{1}{6}{j}_i{\left(t-T_i\right)}^3,$$

In the 2 is a diagram for mapping the braking process with positive initial and vanishing final acceleration shown. This means that the current acceleration a ₀ > 0 and the acceleration from the first method statement a _LA = 0.

The movement is thus in the process of forming the sections just in an acceleration process, so that first the existing acceleration must be reduced. That is, the movement is thus in the second segment, where: T ₂ = 0th

Now, the third method statement and preferably the method BuildAccSections (StartVel, StartAcc, TargetVel) is called, in order to get the current values for the velocity (= v ₂ ) and the acceleration (= a ₂ ).

Since no particular speed is reached, but only preferably as quickly as possible, the acceleration is to be reduced, the target speed or the end speed is set to zero (TargetVel = 0). Consequently, it is calculated what time and distance is needed to take effect of j ₂ = _min to a ₃ = 0 to arrive. The final values are then T ₃ . s ₃ . v ₃ , a ₃ = 0.

The speed of the first method instruction a _LA = 0 also includes a speed v _LA which should preferably be reached at the end of the traversing block. Ie, that of a speed v ₃ to a speed v _LA < v ₃ is delayed.

In order to plan the deceleration process, it is therefore preferred to use the third method instruction (StartVel, StartAcc, EndVel) with the starting values v ₃ (= v ₄ ), a ₃ = 0 (= a ₄ ) and the desired final speed v _LA used. This will initially the starting values T ₄ = 0 and s ₄ = 0, whereby only later the correct values are stored.

Consequently, so far the distances have been calculated, which for the reduction or the reduction of the acceleration v _LA , ie the speed of the first procedural instruction needed. If the two sections and the current position are added together, the distance of the current positioning block is essentially obtained. However, it is possible that a small difference could arise, for example, for the following reason: The formation of sections became necessary, as described above, because in a further acceleration with the values in the next interpolation step, an excessively long braking distance would have been required v _LA decelerate. With the current values, however, a delay is still possible. The limiting case in which a delay on v _LA is still possible until the end point of the traversing block is reached somewhere between the current values and the values in the next step.

After the time t ₃ For this section, times and positions are adjusted at the beginning of each section. The values at the end of the last calculated section are stored (additionally in the sizes c_dS, c_dV, c_dA, c_dJ, c_dTFinal).

Subsequently, the second procedure is deactivated.

Whenever the final acceleration of the first process instruction a _LA = 0, the final velocity v _LA be reached exactly. Is against a _LA negative, as in 3 is shown, then the acceleration within the sections is delayed as much as possible to try at the end of the traversing block a _LA to reach. There is no third section in this case.

To make the sections 4 to 6 The third procedure (BuildDecSections with StartVel, StartAcc, EndAcc, Distance) is called, which then transfers the current values for the velocity and the acceleration. It is a _LA the final acceleration and the remaining distance is the distance that results from subtracting from the total distance of the movement rate the current distance which was consumed in the function of the third procedure instruction (BuildAccSections ()).

It would also be conceivable that it is not possible to form all sections (DecSections), since the acceleration can not be reduced to a = 0 until the end of the positioning record. In this case, only the second section, as in 4 shown, formed.

If the initial acceleration is negative, which can happen, for example, if it is delayed over several traversing blocks, then those in the 5 and 6 Cases shown occur.

The case a ₀ <0, a _LA <0 ( 5 ) is similar to the case a ₀ > 0, a _LA <0 (similar to 2 ), except that here the acceleration sections (AccSections) are omitted, so that only the sections 4 to 6 gives.

Another case shows 6 , In general, the speed in the web interpolation is always slightly below the speed calculated by the first method instruction. In the case a ₀ <0, a _LA = 0, this leads to the desired final speed v _LA is reached before the end of the traversing is reached. The rest of the route will then continue at this speed. However, no sections are formed up to the end of the movement, but there is an exit from the precalculated sections and a setting on exit from the sections of the values.

In the 7 and 8th in each case the case is shown that in a traversing the maximum speed is to be achieved or has already been achieved.

If sections are to be formed, these can - if a _LA = 0 - be planned until the end of the movement (see 7 ). This trajectory is calculated analogously to that in 2 , only now no acceleration needs to be broken down, leaving the sections 0 to 2 omitted.

In 8th is first moved in the second procedure with constant (maximum) speed, as indicated by the dashed line. If the second procedural instruction returns a value greater than zero in the course of the interpolation, sections are formed up to the end of the movement.

In the 8th and 10 In addition, the case is shown that the section formation is called with positive start acceleration, where the goal is to reach the maximum speed.

Consequently, if a ₀ > 0 and a _LA = 0, then sections can be formed as usual until the end of the movement. In the case with a ₀ > 0 and a _LA <0, as in the 10 First, the acceleration sections (AccSections), ie the sections 0 to 2 formed to reach the maximum speed. Then, first in the mode of the second procedural instruction and later again sections are formed, namely the sections 4 to 6 , This case therefore essentially corresponds to the case 8th ,

Also worth mentioning are two other special cases. It may thus be possible for a traversing block to be traversed completely in the mode of the second method instruction (DecCheck mode) without sections having to be formed. This is especially true at the beginning of a movement as the system accelerates. In order to ensure a correct transition from one positioning block to the next traversing block, however, the values for the time, velocity and acceleration must be calculated, which apply exactly at the traversing block transition (ie at position c_dDistance). Of course, this position will generally not lie on an interpolation point, but between two interpolation points.

If, during the calculation of the next interpolation point, it is determined that the new position is greater than the position at the traversing block transition (dNewPos> c_dDistance), then sections are still formed only for the last or remaining part of the traversing block, whereby the method statement contains the current values for the speed and the acceleration as well as the remaining distance are transmitted up to the end of the traversing end (c_dDistance; c_dCurrentPos).

The other special case concerns the very last traversing block in the traversing block, for which v _LA = 0 and a _LA = 0 always apply. In 6 the situation was shown that should be decelerated to a constant speed v _LA > 0 and the remaining distance of the traversing set is to be traversed in the mode of the second procedural instruction at this speed. However, this solution does not work if v _LA = 0, because here the remaining distance can not be made up, since it was already completely decelerated. Instead, the sections must advantageously be planned so that the remaining distance can be traversed with the existing conditions.

All these conditions can be met if the jerk in the last section or in the last traversing block, as in the 11 shown, adjusted.

12 shows a diagram for mapping times in the movement set transition. For path interpolation, in each interpolation step, the interpolation calculation method is called with the current position, velocity, acceleration, and jerk values, and returns the values for the next step. The step size is determined by the cycle time. The interpolation calculation method is passed the current time. At the time at which sections are formed, this time is preferably buffered temporarily (offset value). This is particularly necessary because the start time of the sections has been set to T = 0 and not, as should be preferred, to the current time.

If you move later within the calculated sections, the offset value will be subtracted from the current time. The same procedure is used for the position.

When forming the sections, therefore, the position difference between the current position and the stored position is added to the stored position value. If the position exceeds the total distance of the positioning record during the interpolation at any time, it is noted that the movement has arrived at the end of the positioning block and is actually already in the next positioning block. At this point, an "intermediate step" is preferably inserted in the interpolation. Each time the third method statement is called (BuildSections method), the time (c_dTFinal) is set, which stores the end of the period of the sections. If sections are formed up to the end of the traversing block, then this point in time also marks the end of the traversing block. Consequently, the values for the position, the velocity, the acceleration and the jerk at the end of the motion set can be returned. Preferably, the remaining time, which is missing until the next regulatory interpolation point, is also temporarily stored. The next sentence preferably now uses in the first interpolation step not the usual cycle time, but this stored residual time and thus determines the values for the position, the velocity, the acceleration and the jerk. This means that the movement has arrived in the new traversing block.

LIST OF REFERENCE NUMBERS

a

acceleration

a _max

maximum acceleration

a _min

minimal acceleration

j

shock

j _max

maximum jerk

_min

minimal jerk

s

position

t

Time

t ₀ , t ₁ , t ₂ , t ₃ , t ₄ , t ₅ , t ₆

sections

T ₁ , T ₂ , T ₃ , T ₄ , T ₃ , T ₆

timings

v _max

Maximum speed

v, v _2, v _{3, V4,} v _5, v ₆ v ₇

speed

Claims (8)

A method of controlling a movement of a mechanical device using successively interpolated traversing blocks, by means of a path planning performed by a controller to ensure compliance with the limits in each traversing set and to reduce a speed and an acceleration up to a predetermined end position of the movement using at least one first method instruction, which calculates a still permissible final speed for each traversing block at least in one phase of a traversing block preparation, in which stopping is guaranteed until the end of the traverse, wherein in the traversing processing phase the calculated final speed is used to determine the actual velocity trajectory, and starting from the current values of the position (s), velocity (v), and acceleration (a), by means of the first procedural instruction set the maximum jerk (j _max ) and thereby determining new values of position (s), velocity (v) and acceleration (a) by interpolation; and by means of at least one second method instruction which verifies a validity of values determined by the first method instruction at least during a method block processing by checking with the aid of the second method instruction whether the new values of position (s), speed (v) and acceleration (a) are valid, and by means of at least a third procedural instruction, which initiates a braking operation when a restriction and / or insufficient braking distance of a traversing set, by forming the remaining distance to the traversing end sections, which for the Reduction of the acceleration and deceleration are required to the determined by the first method instruction Endgeschwindigkeitswert, wherein the movement starts with an initial speed and an initial acceleration and stops at an end point. Method according to Claim 1 , characterized in that the constraints comprise at least a maximum speed (vmax), a maximum acceleration (a _max ), a minimum acceleration (a _min ), a maximum jerk (j _max ) and a minimum jerk (j _min ). Method according to one of Claims 1 or 2 , characterized in that the mechanical device is an industrial robot. Method according to Claim 1 or 2 , characterized in that a deceleration operation with the new values of the position (s), the speed (v) and the acceleration (a) serving as start values is made using a deceleration method in which a final speed is determined below a predetermined distance is formed, and a braking distance calculation method in which a distance is determined below a predetermined final speed. Method according to Claim 4 , characterized in that by means of the deceleration method determined traverse rate end values for the velocity (v ₃ ) and the acceleration (a ₃ ) with the determined end values (v _LA , a _La ) of the first procedural instruction are compared, where always applies: a ₃ ≥a _LA . Method according to one of the preceding claims, characterized in that at the beginning of each traversing set by means of the second method statement is checked whether at a predetermined initial speed (v _start ) of the respective traversing set, the maximum permissible acceleration (a _max ) is exceeded. Method according to one of the preceding claims, characterized in that the jerk (j) is at least partially selected freely. Method according to one of the preceding claims, characterized in that with each call of the third method instruction, the time which stores the end of the period of the sections is set, whereby the values for the position (s), the speed (v), the acceleration (a) and the jerk (j) are returned, which the subsequent traversing block again uses as initial values in the first interpolation step.

Images