Method and apparatus for determining a continuous trajectory of a vehicle, and its use

Abstract

A method for determining a continuous trajectory of a vehicle, wherein the trajectory connects two points (D1, D2) in space, wherein the trajectory is to pass at least by a location point (D0), wherein a predetermined maximum speed is available for the vehicle and a specific time is available for the vehicle to travel along the continuous trajectory, comprising the steps of: • Obtaining inputs regarding the coordinates of the two points, the location point, as well as the maximum speed and the specified time, • Determining an equivalent mechanical problem with an artificial gravity field, wherein the center of the artificial gravity field (APF) corresponds to the location point, • Varying the starting angle (Δ) and / or amplitude (Q) of the initial vector such that a continuous trajectory is formed, whereby the predetermined maximum speed is not exceeded and the predetermined time is utilized, • whereby the vehicle (UAV) should remain in the vicinity of the location point (D0) for as long as possible.;

Description

BackgroundUnmanned aerial vehicles (UAVs), also known as drones, have already been developed for wireless networks to support network performance as well as new services.The mobility provided by the UAVs in this case makes it possible to develop a multiplicity of trajectories, i.e. trajectories, which are intended to serve specific scenarios in the network. For example, potential overloads in signal forwarding can thus be prevented, see, for example, the articles "Aerial Control System for Spectrum Efficiency in UAV-to-Cellular Communications" by the authors H. Hellaoui, O. Bekkouche, M. Bagaa and T. Taleb, published in IEEE Commun. Mag., vol. 56, no. 10, pp. 108-113, 2018, or "Robust Trajectory and Transmit Power Design for Secure UAV Communications" by the authors M. Cui, G. Zhang, Q. Wu and D. W. K. Ng, published in IEEE Trans. Veh. Technol., vol. 67, no. 9, pp. 9042-9046, 2018, and / or transmission channels of high quality, see, for example, the article "Wireless Communications with Unmanned Aerial Vehicles: Opportunistics and Challenges," by the author Y. Zeng, R. Zhang and T. J. Lim, published in IEEE Commun. Mag., vol. 54, no. 5, pp. 36-42, May 2016.In order to be able to use the advantages, static positions have been developed-similar to classic networks-in order to improve the network performance, i.e. by acting UAVs for (ground-based) users as base stations and / or in order to improve the fault safety by using them as relays.In other networks in which UAVs also perform communication tasks, an attempt is made by a (upstream) design of the trajectory to increase the channel capacity or to improve the energy efficiency or to improve other values.Such UAVs can also be used in other areas. It is only mentioned here for the transport of goods, the monitoring, recovery support, resource investigation, archeology, etc. As examples, reference may be made to "Survey of Important Issues in UAV Communication Networks," authored by L. Gupta, R. Jain and G. Vaszkun, published in IEEE Commun. Surv. & Tuts. vol. 18, no. 2, pp. 1123-1152, second quarter 2016, "Town A Fully Autonomous UAV: Research Platform for Indoor and Outdoor Urban Search and Research", the author T. Tomic, K. Schmid, P. Lutz, and et. al., published in IEEE Rob. & Auto. Mag., vol. 19, no. 3, pp. 46-56, 2012, and "UAV-Based loT Platform: A Grown Surveillance Use Case", the author by N. H. Motlagh, M. Bagaa and T. Taleb, published in IEEE Commun. Mag., vol. 55, no. 2, pp. 128-134, 2017.From Japanese patent application JP 2010-152 684 A a further system is known which provides a route planning from one point to another point. The focus of the method there is the achievement of the target without a collision with obstacles occurring.A movement path in reality generally has to be continuous both in space and time. For a design of such a movement path, therefore, a (infinitely) high number of variables would have to be optimized simultaneously.In previous approaches, discrete models have been used to obtain such trajectories. In each case, two adjacent points can be subject to a boundary condition of a maximum distance from one another. The trajectory can thereby be approximated so that the corresponding grid points are optimized.However, this procedure has the following adverse properties. On the one hand, the resulting movement path is always sub-optimal, and on the other hand, the computational complexity also increases as the point density increases.Another approach is based on a successive-lever-fly (SHF) structural approach. In this, it is assumed that the UAV has both hovering and flight characteristics in which the UAV hovers at certain points for respective times. According to this structure approach of the floating points, a trajectory is developed according to the floating points and floating durations. However, this method cannot be applied to all applications.Although this approach can reduce complexity, it is only possible at the expense of accuracy or at the expense of best target achievement for the trajectory. This is due to the fact that the trajectory between two flying points is generated as a straight line(s). This, on the other hand, does not correspond to real scenarios.As a result, it is found that the trajectories obtained in this way are always sub-optimal. Only by massively increasing the number of points (i.e. smaller grid width) could this problem be reduced, however always at the expense of the calculation time.However, this minimization is purchased with a great increase in the computing power and / or computing time required for creating the movement path.Proceeding from this, it is an object of the invention to provide an improvement.The object is achieved by a method for determining a continuous trajectory of a vehicle, wherein the trajectory connects two points in space, wherein the trajectory is intended to at least pass a location point (D0), wherein a predetermined maximum speed is available for the vehicle and for which a specific time is available for the transfer of the vehicle along the continuous trajectory, comprising the steps:• obtaining inputs relating to the coordinates of the two points, the location point, and the maximum speed and the determined time,• determining an equivalent mechanical problem with an artificial gravity field, wherein the center of the artificial gravity field corresponds to the location point,• varying the starting angle and / or amplitude of the initial vector so that a continuous trajectory is formed, wherein the predetermined maximum speed is not exceeded and the predetermined time is exploited,• wherein the vehicle (UAV) is intended to remain in the vicinity of the location point (D0) for as long as possible.The object is furthermore achieved by a corresponding device for determining a continuous trajectory of a vehicle, which is characterized in that• means for obtaining inputs relating to the coordinates of the two points, the location point, and the maximum speed and the determined time,• means for determining an equivalent mechanical problem with an artificial gravity field, wherein the centre of the artificial gravity field (APF) corresponds to the location point,• means for varying the starting angle (α) and / or amplitude (Q) of the initial vector so as to form a continuous trajectory, wherein the predetermined maximum speed is not exceeded and the predetermined time is exploited,• wherein the vehicle (UAV) is intended to remain in the vicinity of the location point (D0) for as long as possible,• means for outputting the trajectory thus determinedhas.Further advantageous embodiments and uses are the subject matter of the description, of the figures and of the further claims.The invention is explained in more detail below with reference to the figures. In these, the following shows: Figure 1 The invention will be illustrated in more detail below with reference to the figures. It should be noted that different aspects are described, which can be used individually or in combination. That is, any aspect may be used with various embodiments of the invention unless explicitly shown as a mere alternative.Furthermore, for the sake of simplicity, only one entity will normally be referred to below. If not explicitly stated, however, the invention can also have in each case a plurality of the entities concerned. In this respect, the use of the words "a", "an" and "an" is to be understood only as an indication that at least one entity is used in a simple embodiment.Insofar as methods are described below, the individual steps of a method can be arranged and / or combined in any order, unless the context explicitly reveals some variation. Furthermore, unless expressly stated otherwise, the methods can be combined with one another.Details with numerical values are generally not to be understood as exact values, but also include a tolerance of + / - 1% up to + / - 10%.References to standards or specifications are to be understood as references to standards or specifications that apply / are considered at the time of application and / or-insofar as priority is claimed-at the time of priority application. However, this should not be understood as a general exclusion of applicability to subsequent or replacing standards or specifications.Unlike in previous approaches, a discretized process is not used here to generate the trajectory. Rather, the invention is oriented in the search of an (optimum) trajectory on another approach.In the context of the invention, an artificial potential field (APF) is used for modelling. Based on this, the goal of trajectory creation is re-transformed into an equivalent mechanical problem. In this equivalent mechanical problem, the trajectory can be understood as an extremely soft and thin rope having a variable density representative of the speed of the UAV. The corresponding problem of optimizing the system performance is transformed into a reduction (minimization) in the overall artificial potential energy of the rope.As a result, the rope in the optimal solution remains in a state of equilibrium and the trajectory of the UAV can equivalently be improved (optimized) by shape determination of the rope in the artificial gravity field APF according to the mechanical principles.It follows that the rope remains in the equilibrium state when the potential energy is minimal. Therefore, it also follows that if the cable shape design is shaped according to the mechanical principles, the trajectory / trajectory of the vehicle represented thereby is optimized.It should be noted that although artificial gravity fields have already been used for path determination in other areas (see, for example, CN 111638725 A, CN 108459612 A, CN 104029203 B, CN 111168675 A), these are used only for approximations of the model boundary conditions, such as, for example, obstacles, in order to avoid collisions. In contrast, in the invention, each location of the rope is assigned location information and speed information. The shape of the cable also gives directional information. That is, unlike prior approaches, the artificial severity field has properties that directly affect this information.(UAV) Trajectory CreationEquivalent Mechanical Problem(UAV) TrajectoryDensity Variable Rope(UAV) Path{x̂(s), ŷ(s)}Rope form {x̂'(s), ŷ'(s)}(UAV) Travel Distance SRope length S'(UAV) Speed v(s)Reciprocal of the rope line density(UAV) Speed Limit / Maximum Speed VReciprocal of the minimum rope line densityAllocated time duration TRope mass mMaximum transmission rate R(x,y)Negative artificial gravity field -R" (x,y)Total throughput Û({x̂(s ), ŷ(s)}, v(s))Negative potential energy of the artificial gravity fieldObviously, the maximum transmission rate or the total throughput is dependent on the application.Further details, backgrounds and mathematical evidence can be found in the article "Novel Optimal Trajectory Design in UAV-Assisted Networks: A Mechanical Equilibrium-Based Strategy" by the authors Xiaopeng Yuan, Yulin Hu, Deshi Li and Anke Schmeink in the journal IEEE Journal on Selected Areas in Communications, accepted for publication, from the subject matter of which this patent application was made, and which is cited as explicit reference.In the invention, a method for determining a continuous trajectory of a vehicle is provided. The trajectory here generally connects two points D 1, D 2 in space. These are hereinafter assumed to be on a plane, this not being a necessary boundary condition, but serving only for simplified representation.Let us assume the case that a vehicle starts at the location D1 and has the destination D2. The vehicle UAV is to provide network power for the point D 0, for example. It has a finite maximum speed and a dedicated time duration (flight duration, e.g. maximum flight duration due to battery power... ). Obviously, network performance is also limited. The total throughput in terms of the network power which the vehicle UAV can then make available is dependent on the location of the vehicle UAV. In short, the vehicle UAV should stay in the vicinity of the point D 0 for as long as possible.In the simplest case, i.e. if the cable is long enough-or if the available time (associated time duration) is long enough, the trajectory can not only pass by the location point D 0 as shown in FIG. 1, but the vehicle UAV can even dwell at the location D 0 for a time, see FIGS. 1 and 3.That is, in this case, the vehicle UAV would move from the point D 1 to the point D 0, stay at the point D 0, and then move to the point D 2, for example. In this case, the direct connection would be the best.In contrast, the case is different if the time duration is not sufficient. This is illustrated in FIG. 4 in comparison with FIG. 3. In this case, the rope would no longer be long enough to allow dwell at location point D0. That is, the rope passes in the vicinity of the location point D0.In this case, the problem can be reformulated into an equivalent problem (as indicated above by the correspondences).For this purpose, in a first step, inputs must be obtained with respect to the coordinates of the two points, the location point, and the maximum speed and the determined time.Subsequently, a mechanical problem equivalent thereto can be determined with an artificial gravity field, wherein the center of the artificial gravity field (APF) corresponds to the location point D0 (or its projection in the plane).It can now be shown mathematically that a solution excites which satisfies all boundary conditions.FIGS. 5, 6 and 7 now show how it is possible to arrive at the optimum solution by varying the starting angle α and / or amplitude Q of the initial vector. It should be noted that the variation of start angle α and / or amplitude Q of the initial vector is not fixed in a specific manner / order.In FIG. 6, for example, the amplitude Q is first varied for the starting point D 1 at the same starting angle α. That is, depending on the value of the amplitude, the rope has a different initial tension at location D1.In this case, in the example, the amplitude increases in terms of amount, i.e. |Q1|<|Q2|<|Q3|. In this case, the amplitude Q2represents a first solution in which the rope / trajectory also passes through the point D2.In FIG. 7, the starting angle α is now changed with an already optimized amplitude. The cable length S also changes with the starting angle α, i.e. for starting angles α1<α2<α3that increase in the example, the cable length increases, i.e. S1<S2<S3.It applies here in each case that a continuous trajectory is formed, wherein the predetermined maximum speed is not exceeded and the predetermined time is utilized.This relationship is also evident once again from FIGS. 8-10. FIG. 8 shows ropes generated respectively with a fixed starting angle α and variation of the amplitude Q0, while FIG. 9 shows ropes generated with fixed amplitude and different starting angles α. In both cases, it is apparent that there is a case where the rope passes through the location point D 2, respectively. Furthermore, it is also immediately apparent that the variations each have a monotone influence. In FIG. 10, produced ropes with different starting angles but optimized amplitude are shown.The optimum solution for the initial tension Q (amplitude and starting angle) is achieved when point D2 is reached starting from point D1 and is the total cable length.It should be noted that the rope is continuous and thus the trajectory is continuous. Since each point can be mathematically calculated, the speed and direction can also be calculated at each point of the rope. In this case, the rope in the artificial gravity field only has to be produced once at the beginning according to the method.In one embodiment of the invention, the device for determining a continuous trajectory of a vehicle according to the presented methods comprises means for obtaining inputs with respect to the coordinates of the two points, the location point, as well as the maximum speed and the determined time, means for determining an equivalent mechanical problem with an artificial gravity field, wherein the center of the artificial gravity field (APF) corresponds to the location point, means for varying the starting angle (α) and / or amplitude (Q) of the initial vector, such that a continuous trajectory is formed, wherein the predetermined maximum speed is not exceeded and the predetermined time is exploited, and means for outputting the trajectory thus determined.Exemplary means can be provided by a (program-based) PC, in particular a microprocessor / microcontroller, an ASIC or an FPGA, together with typical input / output devices, memories, etc.In particular, the invention allows the use of a method according to the invention for providing a continuous trajectory for a land-based vehicle, e.g. a self-steering vehicle, an exploratory vehicle, a working machine, etc. However, the invention also easily allows the use of a method according to the invention for providing a continuous trajectory for an airborne vehicle, such as a transport drone. The invention also allows the use of a method according to the invention for providing a continuous trajectory for UAV-based telecommunication equipment.Within the scope of the invention, a new approach is provided to create a trajectory under predefinable boundary conditions. In this case, the complete creation approach is initially converted into an equivalent physical problem with the aid of an artificial gravity field APF. This allows the problem to be analyzed and an optimal solution (not just an approximately optimal solution) can be characterized or determined according to the physical principles.As shown in the presented example of a single-user network (see counterparts), an optimal solution can be found. This approach can also be extended to other problems.Furthermore, a closed shape of the trajectory solution can be provided by the invention. This allows the computing requirements to be significantly reduced, and therefore an optimum solution of a trajectory can be created even on low-power devices. This is advantageous in particular when the creation of a trajectory has to take place quickly, for example in applications requiring low latency.

Claims

Method for determining a continuous trajectory of a vehicle, wherein the trajectory connects two points (D1, D2) in space, wherein the trajectory is intended to at least pass a location point (D0), wherein a predetermined maximum speed is available for the vehicle and for which a specific time is available for the transfer of the vehicle along the continuous trajectory, comprising the steps: • obtaining inputs with respect to the coordinates of the two points, the location point, and the maximum speed and the specific time, • determining an equivalent mechanical problem with an artificial gravity field, wherein the center of the artificial gravity field (APF) corresponds to the location point, • varying the starting angle (α) and / or amplitude (Q) of the initial vector, such that a continuous trajectory is formed, wherein the predetermined maximum speed is not exceeded and the predetermined time is utilized, • wherein the vehicle (UAV) is to stay in the vicinity of the location point (D0) for as long as possible.Device for determining a continuous trajectory of a vehicle according to claim 1, comprising • means for obtaining inputs relating to the coordinates of the two points, the location point, as well as the maximum speed and the determined time, • means for determining an equivalent mechanical problem with an artificial gravity field, wherein the centre of the artificial gravity field (APF) corresponds to the location point, • means for varying the starting angle (α) and / or amplitude (Q) of the initial vector so as to form a continuous trajectory, wherein the predetermined maximum speed is not exceeded and the predetermined time is exploited, • wherein the vehicle (UAV) is to stay in the vicinity of the location point (D0) for as long as possible, • means for outputting the trajectory thus determined.Use of a method according to claim 1 for providing a continuous trajectory for a land-based vehicle.Use of a method according to claim 1 for providing a continuous trajectory for an aerial vehicle.

5. use of a method according to claim 1 for providing a continuous trajectory for UAV-based telecommunications equipment.

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