DE102011011932A1 - Navigation system for e.g. position determination of security patrol robot, has ultrasound transmitting stations positioned in surface, where ultrasonic transmission range of station is partially overlapped with that of adjacent station - Google Patents

Abstract

The system has multiple ultrasound transmitting stations positioned in or near a surface, where a desired number of mobile objects simultaneously moves on the surface. Each of the transmitting stations and the mobile objects are equipped with respective timers, which are synchronized. The mobile objects receive ultrasound transmitted by the transmitting stations, where ultrasonic transmission range of the transmitting station is partially overlapped with the ultrasonic transmission range of the adjacent transmitting station.

Description

State of the art

• 1) The following patents describe devices and methods for determining the exact position of a robot by means of ultrasound: DE 102004018670 A1 . JP 000005341031 AA . JP 000008054926 AA . JP 000060107580 AA . US 000005440216 A . US 000005491670 A . US 000005646494 A . US 000005682313 A . EP 000001435555 A2 . US 000005652593 A . US 2003/0142587 A1 . US 2009/0073045 A1

One or more fixed stations whose positions are known are described. These send or receive ultrasound.

In addition, each describes a mobile robot that receives or transmits ultrasound. The distances between the fixed station and the robot are calculated on the basis of the propagation speed of the ultrasound and the measured time between the transmission and the reception of the ultrasound.

From the determined distances of the robot to one or more fixed stations, the exact coordinates of the current position and the direction of travel can be calculated in the robot.

• 2) Um eine Überlagerung der Signale bei den in 1) beschriebenen Methoden zu verhindern, muß die Aussendung und der Empfang eines Ultraschallsignals („Abfrage”) für jeden Roboter und jede feste Station nacheinander durchgeführt werden. Nach jeder einzelnen „Abfrage” muß zusätzlich eine Pause folgen, bis das Ultraschallsignal die von dem Roboter zu befahrende Fläche „verlassen” hat bzw. bis die maximale Reichweite der Ultraschallsender erreicht ist. Erst dann kann ein Roboter die nächste Station „abfragen”.

In this case, the ultrasonic receiving / transmitting part detects the time of transmission of the ultrasound via a radio signal, light signal, infrared signal or an electrical signal that is transmitted by cable. In the patent US 2003/0142587 A1 The ultrasound receiving / transmitting part does not recognize the time of transmission of the ultrasound via a radio signal but also via an ultrasound signal.

• 2) In order to prevent interference of the signals in the methods described in 1), the transmission and reception of an ultrasonic signal ("interrogation") must be performed successively for each robot and each fixed station. After each "interrogation" an additional pause must follow until the ultrasonic signal has "left" the area to be traveled by the robot or until the maximum range of the ultrasound transmitters has been reached. Only then can a robot "poll" the next station.

The duration of the pause after a "query" must always be set to the maximum expected distance in the travel range of the robots (or the maximum range of the ultrasonic transmitters if the maximum range is less than the maximum expected distance in the driving range). If several robots travel in the driving range, all robots must consecutively "poll" all stations one after the other and pause after every "interrogation".

The number of possible position determinations per robot in a time period is therefore dependent on the number of robots, the number of fixed stations and the size of the area to be traveled or the range of the ultrasound transmitters in 1).

The time interval between two possible position determinations of a moving robot must be as small as possible to enable safe navigation. The methods described in 1) are therefore only meaningful if a robot or a few robots use the navigation described at the same time. The number of stations and the size of the area to be traveled are limited.

• a) Es können nicht beliebig viele Roboter gleichzeitig die Methoden nutzen.
• b) Die Anzahl der festen Stationen ist begrenzt.
• c) Die vom Roboter zu befahrende Fläche ist begrenzt.

• 3) In den Patenten JP 2009139264 A und DE 10350746 A1 ist im Empfänger der Sendezeitpunkt des Ultraschallsignals unbekannt. Die Positionsbestimmung erfolgt durch Auswerten der zeitlichen Differenzen der Empfangszeitpunkte der Ultraschallsignale von mehreren räumlich getrennten Ultraschall-Sende/Empfangsstationen.
• 4) In den in 3) beschriebene Methoden ist keine zeitliche Synchronisation zwischen den Ultraschall Sendern und Empfängern vorgesehen. Durch die fehlende zeitliche Synchronisation können die absoluten Entfernungen vom Roboter zu den festen Stationen nicht einzeln berechnet werden.

The disadvantages of the methods described in 1) are thus:

• a) It is not possible for any number of robots to use the methods at the same time.
• b) The number of fixed stations is limited.
• c) The area to be traveled by the robot is limited.

• 3) In the patents JP 2009139264 A and DE 10350746 A1 is unknown in the receiver, the transmission time of the ultrasonic signal. The position is determined by evaluating the time differences of the reception times of the ultrasonic signals of a plurality of spatially separated ultrasonic transmitting / receiving stations.
• 4) In the methods described in 3) no temporal synchronization between the ultrasonic transmitters and receivers is provided. Due to the lack of time synchronization, the absolute distances from the robot to the fixed stations can not be calculated individually.

For calculating the position, the exact time intervals of all ultrasonic signals received at the robot are important. As a result, the surface to be traveled by the robot is limited, because at each point at which the robot performs a position determination, the ultrasonic signals of all fixed stations must be receivable for the robot. Thus, the ultrasonic range of the fixed stations limits the maximum area to be traveled. Even if the number of fixed stations were increased, this does not significantly increase the area to be traveled by the robot. A robot can only navigate in the intersection of the ranges of the ultrasound transmitting stations.

The disadvantages of the methods described in 3) are:

• a) The area to be traveled by the robot is limited.
• b) The positions of the ultrasonic transmitting stations must be known.
• c) No redundancy is possible. In the event of failure of stations transmitting ultrasound, position determination can no longer be carried out.
• d) The absolute distances of the robot to the fixed stations can not be calculated individually.
• e) The methods are complicated.

Description of this invention

The invention makes it possible for any number of robots to be able to carry out a position determination on an arbitrarily large area at the same time. Whereby robots are mentioned here only as an example for mobile objects.

For this, any number of (at least 2) stations are mounted in or around an arbitrarily large area.

The robots are equipped with a microcontroller (or other CPU) with a memory and timer and one or more ultrasound receivers.

The stations are equipped with a microcontroller (or other CPU) with a memory and timer and an ultrasonic transmitter. The stations are numbered consecutively (1, 2, 3, ..., n).

The distribution of the stations is arbitrary. The exact positions of the stations need not be known.

• – Die Station 1 und 2 werden am Rand oder außerhalb der zu befahrenden Fläche aufgestellt.
• – Der Abstand der Station 1 zur Station 2 muß bekannt sein.
• – Der Ultraschall-Reichweitenbereich einer Stationen muß sich mit dem Ultraschall-Reichweitenbereich der angrenzenden Station bzw. den Ultraschall-Reichweitenbereichen der angrenzenden Stationen teilweise überlappen.

The stations are set up according to the following conditions:

• - Stations 1 and 2 are set up at the edge or outside the area to be traveled.
• - The distance of the station 1 to the station 2 must be known.
• The range of ultrasound range of a station must partially overlap with the ultrasound range of the adjacent station or the range of ultrasonic ranges of the adjacent stations.

The starting point of a robot on which it starts navigation must be within the intersection of the ultrasonic ranges of stations 1 and 2. In addition, the starting point must be within the area to be traveled.

The timers of the stations and the robots are exactly synchronized. For this purpose, the timers of the robots and the stations are set to zero at the beginning of the navigation at the same time.

The stations can transmit ultrasound and the robots can receive ultrasound (ultrasound being only cited as an example of a slow wave such as sound).

Stations 1 to n sequentially transmit an ultrasonic signal at a time interval. If the last station has sent an ultrasonic signal, a passage is finished and it starts again station 1 and so on 1 the sequence of a passage over time is shown.
t _d1 , t _d2 , t _d3 , ..., t _dn are the times between transmission and reception of an ultrasonic signal. t _E1 , t _E2 , t _E3 , ... t _En are the times that elapsed from the start of the passage belonging to the ultrasonic signal to the reception of the ultrasonic signal.
t ₁ is the time length of a transmitted ultrasonic signal
t ₂ is the pause after transmitting an ultrasonic signal
In order to prevent superimposition of the ultrasonic signals, t _{2 is given} based on the maximum expected distance on the surface to be traveled: t ₂ = maximum distance / v _us
However, the maximum value for t ₂ is limited by the range of the ultrasonic _transmitter so t _2max = range / V _us
(V _us : ultrasonic speed)
Z ₁ , Z ₂ , Z ₃ , ..., Z _n are the time intervals in which the respective ultrasonic signal is transmitted and received.

The following constants are stored in advance in the memory of each robot: the number of fixed stations n, the times t ₁ and t ₂ and the distance A _s between the stations 1 and 2.

The following constants are stored in advance in the memory of each station: the number of fixed stations n and the times t ₁ and t ₂

The robots receive the ultrasonic signals. If an ultrasonic signal is received by the robot, the reception time is registered and saved with the help of the timer. The reception time is the time that elapsed from the synchronization of the timer to the reception of the ultrasonic signal.

Based on the reception time, the robots can calculate the station number m of the transmitting station as follows: t _Em = reception time - (L (reception time / (n * (t ₁ + t ₂ ))) ⌋ * (n * (t ₁ + t ₂ ))) m = L (t _Em / (t ₁ + t ₂ )) ⌋ + 1 (Note: L ... ⌋ is a Gaussian bracket)

The distance Am of the robot to the station numbered m can be calculated with the ultrasonic velocity v _us as follows: t _dm = t _Em - ((m-1) * (t ₁ + t ₂ )) A _m = t _dm · v _us

If the robot does not receive an ultrasonic signal in the time interval Z _m , it is out of range of the station m and A _m is marked as invalid.

The distances A ₁ to A _n are stored after a passage in the memory of the robot.

• – Für die Navigation wird ein angenommenes Koordinatenkreuz so gelegt, das Station 1 im Nullpunkt und Station 2 auf der y-Achse liegt.
• – Der Abstand A_s zwischen Station 1 und 2 ist vorab als Konstante im Roboter abgespeichert worden.
• – Nach dem ersten Durchlauf sind mindestens die Abstände A₁ und A₂ bekannt.
• – Somit erhält man ein Dreieck wie in 3 gezeigt. (P: Position des Roboters, S1: Station 1, S2: Station 2, h: Höhe des gezeichneten Dreiecks)
• – Die Höhe h kann vom Roboter mit einer Trigonometrischen Funktion berechnet werden:
  

Since the starting point of a robot on which it starts the navigation is always within the intersection of the ultrasonic ranges of the stations 1 and 2, the navigation can start as follows:

• - For navigation, an assumed coordinate system is placed so that station 1 is at zero and station 2 is on the y-axis.
• - The distance A _s between station 1 and 2 has been previously stored as a constant in the robot.
• After the first pass, at least the distances A ₁ and A _{2 are} known.
• - Thus one gets a triangle like in 3 shown. (P: position of the robot, S1: station 1, S2: station 2, h: height of the drawn triangle)
• - The height h can be calculated by the robot with a trigonometric function:
  

The xy coordinates of the position of the robot can be calculated as follows: x = h y = √ A₁²-h²

In the 2 have been distributed as example 9 stations. S1 to S9 represent the locations of the stations. The circles limit the ultrasonic range of the individual stations. The number of stations can be increased as required. Thus, the area to be traveled can be increased as desired. The the only condition for the positioning of the stations 3 to n is the partial overlapping of the coverage areas with the neighboring stations.

A robot can navigate anywhere where it can receive the ultrasound signals from at least 2 stations whose xy position is known. With at least two calculated distances A _m1 , A _m2 and the xy positions of the transmitting stations S _m1 and S _m2 , the xy position of the robot P _Rx , P _Ry can be calculated according to the generally known formula for calculating the intersections of two circles: Circle 1: (x - S _m1x ) ² + (y - S _m1y ) ² = A _m1 ² Circle 2: (x - S _m2x ) ² + (y - S _m2y ) ² = A _m2 ²

The intersections lie on the line y = mx + n
in which m = (S _m1x -S _m2x ) / (S _m2y -S _m1y ) n = (-A _m2 ² + A _m1 ² + S _m2y ² - S _m1y ² + S _m2x ² - S _m1x ² ) / (2 (S _m2y - S _m1y ))

The pq formula calculates xy coordinates: p = (2 (-S _m1x + m (n - S _m1y))) / (1 + m ²⁾ q = (S _m1x ² + (n-S _m1y ) ² -A _m1 ² ) / (1 + m ² )

Two positions are possible: P _Rx1 = - (p / 2) + (p / 2) ² - q P _Ry1 = mP _Rx1 + n and P _Rx2 = - (p / 2) - √ (p / 2) ² - q P _Ry2 = mP _Rx2 + n

The position of the robot is then selected based on the travel speed known in the robot and the time it took the robot to travel from the last position to PR.

In 4 be z. B. Station 1, 2 and 6 shown. The thin circles represent the distances A ₂ and A ₆ measured from P _2. The robot has moved from P ₁ to P ₂ at this time. The location P ₂ should be outside the ultrasonic range of station 1 (ie A ₁ is unknown). Based on the speed of travel known in the robot and the time it took the robot to travel from P ₁ to P ₂ , the robot can calculate the maximum possible distance from P ₁ (wide circle). Thus, the position determination with only two measured distances A ₁ and A _{6 is} unique. (If the driving speed is so high that the position determination is no longer clear, the accuracy is already so low by other factors that the ambiguous determination is irrelevant)

If the xy positions of the stations 3 to n are known in advance, they can be stored in advance in the robots and the robots can immediately navigate in the areas where he receives the ultrasound signals from at least 2 stations.

• a) Mindestens 2 Stationen mit bekannter xy-Position
• b) Mindestens 1 Station mit unbekannter xy-Position

If the xy positions of the stations 3 to n are not known in advance, each robot can measure the xy positions of the stations 3 to n themselves as follows and then store:
Since the ultrasonic ranges of the stations always partially overlap, a robot can calculate the xy position of a station whose xy position is unknown. For this he must drive in an area where he can receive the ultrasonic signals from:

• a) At least 2 stations with known xy position
• b) At least 1 station with unknown xy position

5 time as an example an area with the stations S ₁ , S ₂ , S ₃ , S ₄ and S ₅ . The circles indicate the respective ultrasonic range of the stations. A robot starts the journey at point P _start and travels on the entered route. The xy positions of stations S ₃ , S ₄ and S ₅ are unknown at startup. At the points P ₁ , P ₂ and P ₃ , the robot can calculate the xy positions of the points P ₁ , P ₂ and P ₃ with S ₁ and S ₂ and at the same time the distances A _3P1 , A _3P2 and A _{3P3 of} the points to the station 3.

With the two circle equations Circle 1: (x - P _1x ) ² + (y - P _1y ) ² = A _3P1 ² Circle 2: (x - P _2x ) ² + (y - P _2y ) - A _3P ² For example, with the well-known formula shown above for calculating the intersections of two circles, the coordinates of the intersections of the two circles can be calculated. With A _3P3 the valid intersection is then determined by comparison with the distance of the intersections to the robot. The coordinates of this intersection are then stored as position coordinates of the station S ₃ in the memory of the robot.

At the points P ₄ , P ₅ and P ₆ , the robot can calculate the xy positions of the points P ₄ , P ₅ and P ₆ with S ₂ and S ₃ and at the same time the distances A _4P4 , A _4P5 and A _{4P6 of} the points to station 4.

With the two circle equations Circle 1: (x - P _4x) ² + (y - P _4y) ² = A ² _4P4 Circle 2: (x - P _5x ) ² + (y - P _5y ) ² = A _4P5 ² For example, with the well-known formula shown above for calculating the intersections of two circles, the coordinates of the intersections of the two circles can be calculated. With A _4P6 the valid intersection is then determined by comparison with the distance of the intersections to the robot. The coordinates of this intersection are then stored as position coordinates of the station S ₄ in the memory of the robot.
etc

Thus, each time the robot enters the ultrasound range of a station whose xy position is unknown, it can be received in the area where ultrasound signals from at least 2 stations whose xy positions are already known are the xy position of the new one Calculate station and then save.

If a robot can receive more than 2 ultrasonic signals from stations whose xy positions are known, plausibility checks can be carried out by redundant calculations of the xy position of the robot. B. detect defective stations or disturbed ultrasonic signals.

Since any number of robots can perform a position determination at the same time, it is easily possible to carry out several position determinations at different points of a robot. If z. B. at the bow and at the rear of the robot at the same time carried out a position determination, the robot can calculate the current direction of travel of the robot in the coordinate system based on the position differences.

The initial synchronization of the timers in the stations and the robots can be done by a temporary cable connection to an external clock or by a temporary cable connection with each other then all the timers are reset by an electrical signal in the cable connection. After synchronization, the cable connection is removed. It would also be possible sync by an external radio, IR or light signal o. Ä. (where the stations and the robots must be equipped with an additional receiver for radio, IR or light) or by the DCF77 (PZF) signal (where the stations and the robots must be equipped with an additional receiver for the DCF77 (PZF) signal ).

The invention can be applied analogously in three-dimensional space by introducing a z-axis into the xy-coordinate system. The stations are then mounted in or around the three-dimensional space. The robots can move in space.

• – Beliebig viele Roboter können gleichzeitig eine Positionsbestimmung auf einer Fläche durchführen. (wobei Roboter hier nur als ein Beispiel für mobile Objekte angeführt werden)
• – Der zeitliche Abstand zwischen den Positionsbestimmungen der Roboter kann optimal minimiert werden und ist unabhängig von der Anzahl der Roboter.
• – Die Anzahl der Stationen kann beliebig erhöht werden.
• – Die Größe der zu befahrenden Fläche kann beliebig erhöht werden.
• – Eine Positionsbestimmung ist auch noch möglich wenn eine oder mehrere Stationen ausgefallen sind. (hohe Ausfallsicherheit)
• – Jeder Roboter kann zusätzlich zur aktuellen xy-Position auch die aktuelle Fahrtrichtung des Roboters im Koordinatenkreuz berechnen.
• – Geringe Hardwarekosten
• – Die Navigation ist indoor und outdoor einsetzbar
• – Die Navigation ist in der zu befahrenden Fläche wesentlich genauer als z. B. die Navigation mit GPS.
• – Da beliebig viele Roboter auf der Fläche gleichzeitig fahren können, können Aufgaben auf mehrere Roboter verteilt werden.
• – Da die Roboter die xy-Positionen von Stationen deren Positionen unbekannt sind, selbst berechnen können, sind die Roboter in der Lage bei Bedarf die Fläche in der sie navigieren können, selbständig zu vergrößern indem Sie mit geführte neue Stationen ablegen oder über die Grenze der Fläche katapultieren.

The particular advantages of this invention

• - Any number of robots can simultaneously perform a position determination on a surface. (where robots are cited here only as an example of mobile objects)
• - The time interval between the position determinations of the robots can be optimally minimized and is independent of the number of robots.
• - The number of stations can be increased as required.
• - The size of the surface to be traveled can be increased as desired.
• - A position determination is still possible if one or more stations have failed. (high reliability)
• - In addition to the current xy position, each robot can also calculate the current direction of travel of the robot in the coordinate system.
• - Low hardware costs
• - The navigation can be used indoor and outdoor
• - The navigation is much more accurate in the area to be traveled than z. B. the navigation with GPS.
• - Since as many robots as possible can drive on the surface at the same time, tasks can be distributed to several robots.
• Since the robots are able to calculate the xy positions of stations whose positions are unknown, the robots are able to independently enlarge the area in which they can navigate by dropping them with guided new stations or crossing the border of the Catapult the surface.

Applications of this invention

It can be stored by the robots "trained" routes in the area to be traveled in the memory. The xy position data during a z. B. man-driven ride stored. The saved routes can then be automatically re-started by the robot. So the robot z. B. leave as a "security" robots patrols independently.

In order to guarantee a precise departure of the stored routes, it is important that the positions of stations 1 and 2 are not changed or exactly restored.

The positions of stations 1 and 2 should be marked on the surface (eg with colored dots) to ensure repeatability of stored driveways.

On the other hand, the route to be traveled to the robot can be stored in advance. So a robot z. For example, as a precision lawnmower mowing filigree patterns in large lawns.

• – Am Startpunkt stellt der Roboter seine xy-Position und die Fahrtrichtung im Koordinatenkreuz fest.
• – Anhand der festgestellten xy-Position und momentanen Fahrtrichtung des Roboters und der xy-Koordinaten des ersten Wegpunktes, wird der einzustellende Winkel der Lenkung des Roboters bestimmt. Der Roboter fährt los.
• – Während der Fahrt werden laufend die xy-Position und die Fahrtrichtung des Roboters berechnet und die Lenkung entsprechend neu eingestellt, bis die xy-Position des ersten Punktes erreicht ist.
• – Nach dem Erreichen des Punktes wird anhand der aktuellen xy-Position und momentanen Fahrtrichtung des Roboters und der xy-Koordinaten des nächsten Wegpunktes wieder der einzustellende Winkel der Lenkung des Roboters bestimmt. Der Roboter fährt weiter.
• – Während der Fahrt werden laufend die xy-Position und die Fahrtrichtung des Roboters berechnet und die Lenkung entsprechend neu eingestellt, bis die xy-Position des nächsten Punktes erreicht ist.

u. s. w.The departure of xy position data of a stored route could proceed as follows:

• - At the starting point, the robot determines its xy position and the direction of travel in the coordinate system.
• - Based on the determined xy position and current direction of travel of the robot and the xy coordinates of the first waypoint, the set angle of the steering of the robot is determined. The robot starts.
• - While driving, the xy position and the direction of travel of the robot are continuously calculated and the steering adjusted accordingly until the xy position of the first point is reached.
• - After reaching the point, the robot's steering angle to be set is determined based on the current xy position and current direction of travel of the robot and the xy coordinates of the next waypoint. The robot continues.
• - While driving, the xy position and the direction of travel of the robot are continuously calculated and the steering adjusted accordingly until the xy position of the next point is reached.

etc

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 102004018670 A1 [0001]
• JP 000005341031 AA [0001]
• JP000008054926 [0001]
• JP 000060107582 AA [0001]
• US 000005440216 A [0001]
• US 000005491670 A [0001]
• US 000005646494 A [0001]
• US 000005682313 A [0001]
• EP 000001435555 A2 [0001]
• US 000005652593 A [0001]
• US 2003/0142587 A1 [0001, 0005]
• US 2009/0073045 A1 [0001]
• JP 2009139264A [0009]
• DE 10350746 A1 [0009]

Claims (10)

Navigation system for determining the position and direction of mobile objects, in particular of mobile robots moving on a surface, characterized by the following features: Any number but at least two numbered stations are positioned in or around the surface - The stations are each equipped with a CPU, a memory, a timer and a transmitter for ultrasound - Any number of mobile objects move simultaneously on the surface - The mobile objects are each equipped with a CPU, a memory, a timer and at least one receiver for ultrasound - The timers of the stations and the mobile objects are synchronized - The stations can send ultrasound - The mobile objects can receive ultrasound - The size of the area is arbitrary Stations 1 and 2 are positioned at the edge or outside the surface at a known distance - The distribution of stations 3 to n in the area is arbitrary The ultrasound transmission range of the stations partially overlaps the ultrasound transmission range of the adjacent stations System according to claim 1, characterized in that the positions of the stations 3 to n in the area need not be known System according to claim 1, characterized in that - The stations 1 to n in turn with a defined time interval in each case send an ultrasonic signal with a defined time length - as soon as the last station n has sent an ultrasonic signal, the station 1 starts again System according to claim 1, characterized in that All mobile objects receive the ultrasound signal transmitted by a station when they are in the ultrasound range areas of the station. - The mobile objects register and store the time of reception of the ultrasound signal using the timer - The ultrasound signal sending station is identified by the mobile objects based on the time of reception. - The time of transmission of the ultrasonic signal is determined by the number of the identified station. - The distance of the mobile object to the transmitting station with the time difference between the sending time and the receiving time, and the propagation speed of the ultrasound is calculated. System according to claim 1, characterized in that The positions of the stations 3 to n, if known, are stored in the memories of the mobile objects prior to the start of the navigation. - The positions of stations whose positions were not known before the start of the navigation, measured by the mobile objects while driving, calculated and stored in memory. System according to claim 1, characterized in that - Two or more ultrasound receiving devices can be mounted on the mobile object, whereby the devices should be mounted as far apart as possible. - With the differences of, with the ultrasonic receiving devices, measured positions, the current direction of travel can be determined. System according to claim 1, characterized in that each mobile object in the area anywhere there can calculate its own current position and direction, where it can determine the distances to at least two stations whose positions are stored in the memory of the mobile object. System according to claim 1, characterized in that faulty stations can be detected by plausibility calculations when the distances to more than two stations whose positions are stored in the memory of the mobile object, were determined. System according to claim 1, characterized in that the mobile objects, if necessary, the area on which a navigation is possible to expand independently. System according to claim 1, characterized in that even if one or more stations a navigation is still possible.

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