阅读说明：本技术 用于规划机动车辆的路径和/或轨迹的设备 (Device for planning a path and/or trajectory of a motor vehicle ) 是由 S·奥伯特 J-P·贾卡洛内 P·温格特纳 于 2019-09-27 设计创作，主要内容包括：本发明涉及一种用于规划机动车辆(4)的路径和/或轨迹的设备(2),该设备包括用于接收输入变量序列的模块(6)、以及用于根据所接收的输入变量序列确定与该路径和/或该轨迹相对应的控制律的硬件和软件装置。该设备(2)包括呈紧凑表示集合的形式的时间分类装置(8)。(The invention relates to a device (2) for planning a path and/or a trajectory of a motor vehicle (4), comprising a module (6) for receiving a sequence of input variables, and hardware and software means for determining a control law corresponding to the path and/or the trajectory from the received sequence of input variables. The device (2) comprises time classification means (8) in the form of a compact set of representations.)

1. A device (2) for planning a path and/or trajectory of a motor vehicle (4), comprising a module (6) for receiving a sequence of input variables, and hardware and software means for determining, on the basis of the received sequence of input variables, a control law corresponding to the path and/or trajectory, characterized in that it comprises temporal classification means in the form of a set of compact representations.

2. The device (2) as claimed in claim 1, wherein the time classification means are configured for defining a flood of input sets consisting of different sequences of input variables of variable length to output sets consisting of different sequences of output variables of variable length.

3. The device (2) as claimed in claim 2, wherein the input set comprises a sequence of time input variables and/or a sequence of metric input variables.

4. The device (2) of claim 2 or 3, wherein the set of inputs comprises at least one sequence of input variables selected from: a sequence of raw variables obtained from sensors, a sequence of variables for incorporating a representation of the external environment of the vehicle, a sequence of variables for representing internal parameters of the vehicle, a sequence of variables for representing the behavior of an agent, and a sequence of variables for representing the intent of an agent.

5. The device (2) of any of claims 2 to 4, wherein the set of outputs comprises a sequence of temporal output variables and/or a sequence of metric output variables.

6. The device (2) of any of claims 2 to 5, wherein the set of outputs comprises at least a sequence of outputs selected from: a coordinate pair sequence of waypoints, an abscissa sequence of waypoints, and an ordinate sequence of waypoints.

7. Device (2) according to any one of claims 1 to 6, wherein the temporal classification means comprise a hidden Markov chain model and/or a recurrent neural network, preferably a long-short term memory recurrent neural network (8).

8. The device (2) of any of claims 1 to 7, wherein the time classification means are configured for using a binding-defined time classification function.

9. A method for planning a path and/or trajectory of a motor vehicle (4), the method comprising receiving (F01) a sequence of input variables and determining, on the basis of the sequence of input variables, a control law corresponding to the path and/or trajectory of the motor vehicle, characterized in that the method comprises using (F02) a temporal classification device in the form of a set of compact representations.

10. The method of claim 9, comprising an off-line training phase (P01) of the temporal classification device, in which sets of output variable sequences, each corresponding to the same manipulation, are grouped into first-level groupings.

11. The method of claim 9 or 10, wherein, during the offline training phase (P01), for each first-level grouping, a set of variable sequences each corresponding to a manipulation having a substantially equal period of implementation and/or a substantially equal distance of implementation is grouped as a second-level grouping.

12. The method of any of claims 9 to 11, comprising: transmitting (F02) the index (ind ) by the time sorting device₅₆) And at least one time modulation factor (lon )₅，lon₆，lat，lat₅₆) Reading (F03) in the look-up table (10) together with the transmitted index (ind )₅₆) Associated path and time modulation factor (lon ) transmitted by the network₅，lon₆，lat，lat₅₆) The read path is time modulated (F04).

13. The method according to any of claims 9 to 12, wherein the time classification means transmits (F02) the time modulation factor (lon ) in the longitudinal direction₅，lon₆) And/or transmitting time modulation factors (lat ) in the lateral direction₅₆)。

14. A computer program comprising code configured to implement the method of any one of claims 9 to 13 when executed by a processor or electronic control unit.

Technical Field

The present application relates to the field of devices and methods for planning a path and/or trajectory of a motor vehicle, and computer programs for implementing such methods.

Background

At present, motor vehicles are equipped with advanced driving assistance devices with ever increasing performance levels. Advanced driving assistance devices are intended to allow autonomous driving of a motor vehicle, i.e. driving without intervention of the driver. In particular, advanced driving assistance devices may be used for planning a path and/or trajectory of a motor vehicle. In the present application, the term "planning" and its derivatives will be interpreted according to their usual definition in the field of advanced driving assistance devices, i.e. meaning that the planning of a path or trajectory means that a future series of states (position, speed, acceleration) of the motor vehicle corresponds to a path or trajectory from one state to another desired state. In this application, the path of the vehicle is to be understood as a geometric shape corresponding to the travel of the vehicle between the departure point and the arrival point. The trajectory of the vehicle is to be understood as the change in the position of the vehicle between the departure point and the arrival point over time.

Known examples of methods for planning the path and/or trajectory of a motor vehicle include in particular methods for planning by solving an optimal control problem based on a first-order lagrangian mechanical equation modeling. Methods for generating paths and/or trajectories are generally aimed at finding a good compromise between comfort and safety of the vehicle occupants.

An example of a method for generating a trajectory (hereinafter "the method of Werling") can be found in the paper "Optimal trajectory generation for dynamic street scenes in the free t coordinate system, IEEE Robotics and Automation International Conference ]" m.werling, j.ziegler, s.kammel and s.thru "(the" Optimal trajectory generation for dynamic street scenes "), IEEE Robotics and Automation International Conference" [1 "). The Werling method involves an indirect method for solving an optimal control problem. According to this method, some input parameters are selected, the optimal control problem is partially solved by considering only the selected input parameters, and the solution is a posteriori verified using the unselected input parameters and the selected input parameters. However, using indirect methods lacks robustness due to the large number of input parameters to be considered. Moreover, the fact that collision avoidance constraints are a posteriori verification may result in the eventual rejection of planning a large number of paths and/or trajectories due to collision risk, such that many resources are used for a large number of rejected calculations.

Another example of a trajectory planning method (hereinafter referred to as "the Mercy method") is described in the paper "Time-optimal movement planning in the presence of moving obstacles" of the present times optimal movement plans "of t.mercy, w.van Loock, g.piplers and j.swevers [2 ]. This example uses a direct approach to solving the optimal control problem. According to the direct method, all constraints are considered when solving the problem. Thus, the present invention is closer to the Mercy method than the Werling method. However, the complexity of the algorithms associated with the Mercy method makes it impossible to incorporate them into the onboard equipment of a motor vehicle.

Other examples of path and/or trajectory planning methods include the potential field method in which each obstacle generates a counter-gravity field that tends to prevent the vehicle from approaching it. However, this approach risks getting stuck in local minima and may therefore not generate an optimal solution to the path and/or trajectory planning problem.

Disclosure of Invention

In view of the above, it is an object of the present invention to enable planning of a path and/or trajectory of a motor vehicle, while overcoming the above-mentioned drawbacks.

More specifically, the invention proposes to enable sufficiently robust path and/or trajectory generation while reducing computational complexity.

For this purpose, a device for planning a path and/or a trajectory of a motor vehicle is proposed, comprising a module for receiving a series of input variables, and hardware and software means for determining, from the received series of input variables, a control law corresponding to the path and/or the trajectory.

According to one of its general characteristics, the device comprises temporal classification means in the form of a compact set of representations.

By using a time classification means, a path and/or trajectory can be planned based on the history. Like the Mercy method, this method enables all input parameters to be considered, while having a relatively low complexity. In fact, the use of time classification means requires a lot of work to design and adjust the algorithm, but a little work for the inference phase of the planning. Thus, computing resource requirements are shifted from the online inference case to the offline training phase.

In the present application, the expression "control law" will be explained in the following sense: the control laws corresponding to a path or trajectory include the set of commands required to operate the actuators to cause the vehicle to follow the path or trajectory while modeling the physical constraints of the chassis.

The expression "temporal classification" denotes an action of classifying a plurality of input sequences as a function of time.

The expression "compact representation set" denotes a set formed by input sequences that have undergone an operation to become a compact state (i.e. for example dropping time concepts in the input sequence, or deleting certain points in the input sequence with the aim of reducing their memory footprint).

According to one embodiment, the time classification means is configured for defining a flood of input sets consisting of different sequences of input variables of variable length to output sets consisting of different sequences of output variables of variable length.

In particular, this characteristic is made possible by the use of time sorting means. Thus, the time classification apparatus does not select a sequence of input variables of a predefined length, but continues to receive input variables until it has sufficient data to determine a satisfactory solution, thereby increasing the length of the sequence. The fill-shoot between the input set and the output set is a fill-shoot application of the input trace set to the output trace set corresponding to different classes of stored traces. For example, the application may belong to a group in which the system used is also able to interpolate or extrapolate trajectories not seen during learning. In the present application, the length of a sequence may be temporal, i.e. corresponding to the sampling period of the sequence, or metric, i.e. corresponding to the sampling distance of the sequence. Similarly, the time classification means generates a variable sequence that can take any length at its output.

Preferably, the input set comprises a sequence of time input variables and/or a sequence of metric input variables.

According to this variant, the trajectories of the various classes are stored in the input set in the memory by temporal classification, but with different lengths, in order to better represent the possible cases.

Advantageously, the input set comprises at least one sequence of input variables selected from: a sequence of raw variables obtained from sensors, a sequence of variables for incorporating a representation of the external environment of the vehicle, a sequence of variables for representing internal parameters of the vehicle, a sequence of variables for representing the behavior of an agent, and a sequence of variables for representing the intent of an agent.

In this application, the term "representing" is used to refer to a set of data representing an event, parameter, state, etc. "merged means" is a data set obtained by merging data obtained from different sensors and/or estimators.

In one embodiment, the output set includes a sequence of temporal output variables and/or a sequence of metric output variables.

Preferably, the set of outputs comprises at least a sequence of outputs selected from: a coordinate pair sequence of waypoints, an abscissa sequence of waypoints, and an ordinate sequence of waypoints.

In another embodiment, the time classification means is configured to use a binding-induced time classification function.

The temporal classification function may be of various types, such as: hidden Markov field, RNN-LSTM-CTC (associative meaning). By using such a function, efficient training of the time classification apparatus can be implemented.

According to yet another embodiment, the temporal classification means comprises a hidden markov chain model and/or a recurrent neural network, preferably a recurrent neural network with long and short term memory.

Such examples are particularly suitable for forming temporal classification devices, as these devices can be easily trained during an off-line training phase.

According to another aspect, a method for planning a path and/or trajectory of a motor vehicle is presented, the method comprising receiving a sequence of input variables, and determining a control law corresponding to the path and/or trajectory of the motor vehicle based on the sequence of input variables.

According to one of its general characteristics, the method comprises the use of temporal classification means in the form of a compact set of representations.

According to one embodiment, the method comprises an offline training phase of the temporal classification device, in which a set of output variable sequences, each corresponding to the same manipulation, is grouped into a first level grouping.

Such grouping is particularly suitable for preparing the time sorting device for its correct operation during the inference phase.

In the present application, the expression "off-line" is used to mean that the off-line phase occurs outside the time period in which the vehicle is controlled by the control law, for example when the vehicle is not moving.

According to one embodiment, during the offline training phase, for each first-level packet, a set of variable sequences each corresponding to a manipulation having a substantially equal period of implementation and/or a substantially equal distance of implementation is grouped as a second-level packet.

Thus, the time classification means is more finely tuned, thereby increasing the robustness of the planning without thereby increasing the computational complexity.

In one embodiment, the method comprises: the method comprises transmitting an index and at least one time modulation factor by the time classification device, reading a path associated with the transmitted index in a look-up table, and time modulating the path read by the transmitted time modulation factor.

The method according to the invention therefore consists in particular in storing a plurality of path patterns having a certain degree of freedom with respect to time, which degree of freedom becomes a parameter. This makes the computational complexity even more limited.

Advantageously, the time classification means transmit the time modulation factor in the longitudinal direction and/or transmit the time modulation factor in the transverse direction.

According to yet another aspect, a computer program is proposed, which comprises code configured for implementing the method as defined above when executed by a processor or an electronic control unit.

Drawings

Other objects, characteristics and advantages of the present invention will become apparent from the following description, provided purely by way of non-limiting example and given with reference to the accompanying drawings, in which:

figure 1 is a schematic representation of a planning apparatus according to an embodiment of the invention,

figure 2 is a schematic representation of a planning method according to an embodiment of the invention,

figure 3 shows a first stage of the method of figure 2,

figure 4 shows a second stage of the method of figure 2, an

Fig. 5 and 6 schematically show the routing of the vehicle in two respective operating situations.

Detailed Description

Referring to fig. 1, a planning apparatus 2 is schematically shown. The device 2 is intended to plan a path for a motor vehicle 4 incorporating it. Obviously, the configuration of the apparatus 2 for planning the trajectory of the vehicle 4 can be envisaged without departing from the scope of the invention. In the illustrated example, the vehicle 4 is driven autonomously. Without departing from the scope of the invention, it is possible to envisage that the vehicle incorporating the device 2 is not autonomously driven; that is, the vehicle is driven by the driver. In this case, the device 2 is only intended to provide assistance to the driver (for example in a dangerous situation).

In the illustrated example, the device 2 forms part of an autonomous driving architecture (not shown). More specifically, the device 2 is data-linked with a prediction module (not shown), a sensor consolidation module (not shown) and a positioning module (not shown) belonging to an autonomous driving architecture.

The device 2 comprises a receiving module 6 for data link with other modules of the autonomous driving architecture and with the vehicle's onboard computer. More precisely, the module 6 is able to receive a plurality of sequences of input variables. A sequence is a collection of values that a variable takes. A time series is a collection of values that a variable takes at a number of different times. A metric sequence is a set of values that a variable takes at a number of different positions. In the illustrated example, the sequence is temporal and consists of variable values taken at a plurality of times separated by intervals of 40 ms.

In the illustrated example, module 6 receives a sequence of input vectors whose scalars are input variables that may be internal constraints and external constraints. The internal constraints relate in particular to the comfort and safety of the passengers in the vehicle 4 and include the intention of the driver, the prediction of future manoeuvres, the speed of the vehicle 4, or the input of the driving pattern of the vehicle 4 by the passengers. The external constraints relate in particular to environmental conditions and to traffic and comprise the position, speed and acceleration of other vehicles, the curvature of the road, meteorological conditions, road surface type, conditions of day or night, or information relating to visibility.

The device 2 comprises a Recurrent Neural Network 8, generally referred to by the english term "Recurrent Neural Network" or by the corresponding acronym "RNN". Reference may be made to the document "object Generation Using RNN with Context Information for Mobile Robots [ generating trajectories of Mobile Robots Using RNN and background Information ]" in the journal of Robot Intelligence Technology and Applications [ Robot Intelligence and Applications ] by y. The recurrent neural network 8 is data-linked with the receiving module 6.

In the illustrated example, the recurrent neural network 8 is of the long-short term memory type. This property is commonly referred to by the english Term "Long Short Term Memory" or the corresponding acronym "LSTM".

The recurrent neural network 8 is configured to use a join-sense time classification function. Such a function is generally referred to by the english term "Connectionist Temporal Classification" or the corresponding acronym "CTC". The recurrent neural network 8 thus forms a temporal classification means of the device 2. Furthermore, the use of a recurrent neural network makes it possible to generate variable-length output variable sequences by collecting variable-length input variable sequences.

The recurrent neural network 8 is configured for determining and transmitting the index ind, the longitudinal modulation factor lon and the transversal modulation factor lat based on the input variables received by the receiving module 6. More specifically, the variables ind, lon, and lat are determined so that the sum of the lateral jerks experienced by the vehicle 4 during a maneuver is minimized while ensuring the degree of safety, avoiding any obstacles, and observing the maximum maneuver length.

It is clear that the invention is not limited to the use of a recurrent neural network 8. In particular, a Hidden Markov Model (also known by the english term "Hidden Markov Model" or the corresponding acronym "HMM") may be used.

The device 2 has a look-up table 10. Table 10 may be referred to by the english name "Look-Up Table" or the corresponding acronym "LUT". Table 10 is data linked to the recurrent neural network 8. Table 10 contains a plurality of path shapes based on index ind. The path shapes stored in the table 10 correspond to possible paths of the vehicle 4.

The device 2 comprises a time modulator 12. The modulator 12 is data-linked to the recurrent neural network 8 and the table 10. More specifically, the modulator 12 is capable of modulating the longitudinal position and the lateral position of the points forming the path conveyed by the table 10, respectively, with respect to time, based on the longitudinal modulation factor and the lateral modulation factor conveyed by the recurrent neural network 8. In other words, modulator 12 is capable of expanding or contracting the paths conveyed by table 10. The path expanded or contracted by modulator 12 is associated with a velocity profile that determines a time series of waypoints. The time series is supplied to a control law device (not shown) of the vehicle 4.

With reference to fig. 2, the main phases of a method for planning the path of a motor vehicle 4 that can be implemented by the apparatus 2 are shown.

The method includes a first phase P01 of training the recurrent neural network 8. Phase P01 is implemented when the on-board computer (not shown) of vehicle 4 is off-line, i.e., prior to transportation of vehicle 4, during maintenance of vehicle 4, or during extended periods of vehicle 4 shutdown.

Referring to fig. 3, phase P01 includes a first step E01 of recording the actual driver behavior. For example, the behavior of a test driver on a vehicle of the same model as vehicle 4 may be recorded. The type of maneuver may be identified and recorded at the same time the behavior is identified and recorded. For example, an action of leaving the center of a traffic lane to reach the center of the traffic lane (which may be the same lane or a different lane) may be identified and recorded.

Phase P01 includes a second step E02 of grouping the recorded data by manipulation type. More specifically, in step E02, a plurality of first-level groupings are created, each grouping corresponding to a respective manipulation recorded in step E01. For example, if data has been recorded during step E01 for a lane-changing maneuver, a re-centering maneuver within the same lane, an emergency braking maneuver, and an emergency avoidance maneuver of the vehicle, respectively, then four first-level groupings are associated with the four aforementioned maneuvers, respectively.

The method comprises a third step E03 of grouping the recorded data by manipulation length. In step E03, a plurality of second level packets are created in each first level packet, each second level packet corresponding to a respective manipulation length recorded in step E01. For example, if data has been recorded for an emergency braking maneuver for a distance of 20 meters (+/-10%), an emergency braking maneuver for a distance of 30 meters (+/-10%), and an emergency braking maneuver for a distance of 50 meters (+/-10%), respectively, the first level packets associated with the emergency braking maneuver are subdivided into three second level packets associated with the aforementioned three maneuver lengths, respectively.

Stage P01 includes a fourth step E04 enriching Table 10. In step E04, the tracks stored in Table 10 are refined using the tracks received in step E01.

Phase P01 includes a step E05 of separating the distinctive characteristics associated with the different groupings defined in steps E02 and E03. In particular, in step E05, the distinguishing characteristic may be:

information obtained from the merging module, such as: status information about the vehicle 4; status information about surrounding objects; representing, for each neighboring vehicle, a map of the neighboring vehicle's position, speed, and acceleration, as well as free space or risk-free space around the neighboring vehicle; and the boundary line of the traffic lane,

-information relating to the background, such as road surfaces, weather forecasts, conditions of day or night or visibility information,

information relating to the vehicle 4, such as the selection of a driving mode,

information about the intention, such as actual or simulated operation of the indicator light, sudden changes in the direction angle, sudden braking (so that an intention to brake suddenly is detected).

Phase P01 comprises a step E06 of defining temporal sorting means. In this case, a recurrent neural network 8 of the RNN-LSTM type using the CTC function is defined in step E06.

Phase P01 includes a step E07 of training the recurrent neural network 8. Step E07 is implemented by using as input the set of distinctive characteristics separated in step E05 and by using as output the possible trajectories recorded and grouped in steps E01, E02 and E03.

The invention is not limited to the steps described above with reference to the illustrated examples. In particular, instead of using the grouping technique implemented in steps E02 and E03, a competitive learning strategy may be used. Other variants that may be used are described in the publication "Trajectory clustering for motion prediction, International Conference on Intelligent Robots and Systems [ for Trajectory clustering for motion prediction, Intelligent robotics and Systems ]" [4] by c.sung, d.feldman and d.rus.

Referring to fig. 2, the method includes a second phase P02 of making the inference. Phase P02 is performed online; i.e. this phase is continuously carried out while the vehicle 4 is running. Although phase P01 is represented above and has been described before phase P02, phase P01 may be after and/or before phase P02.

Referring to fig. 4, stage P02 includes a first step F01 of receiving a sequence of input variables. The received sequence of input variables consists of n vectors, each vector being formed by the module 10 at the instant t_iThe different input variables received make up, where i is in the range of 1 to n. The value of the number n is chosen such that the length of the input variable sequence is sufficient to determine the correlation values ind, lon and lat. The input variables are substantially identical to the distinguishing characteristics separated in step E05 of phase P01, typically data obtained from the sensor consolidation module and other information from certain specific sensors (such as road maintenance and visibility conditions) or information about the intent from the action planner. In an example of this embodiment, the received sequence is temporal. Another type of sequence, in particular a metric sequence, can be envisaged without departing from the scope of the invention.

Phase P02 includes a second step F02 of inputting the sequence of input variables into the recurrent neural network 8. In step F02, the index ind, the longitudinal modulation factor lon, and the transverse modulation factor lat delivered by the recurrent neural network 8 are collected.

Stage P02 includes a third step F03 of entering the index ind into Table 10. In step F03, the path shapes passed by the table 10 are collected.

Stage P02 includes a fourth step of time modulating the path shape collected in step F03. In step F04, longitudinal expansion or contraction of the path shape collected in step F03 with respect to the factor lon is performed, and lateral expansion or contraction of the path shape collected in step F03 with respect to the factor lat is performed.

Stage P02 includes a step F05 of checking for collision avoidance. In step F05, it is checked whether the modulated path obtained at the end of step F04 does not risk a collision of the vehicle 4 with another object. If there is a risk of collision with another object, an error signal is transmitted, so that the phase P02 is repeated by selecting a different path.

Fig. 5 and 6 show examples of paths that may be planned by the device 2 for the vehicle 4. Fig. 5 shows a first operating situation of the vehicle 4, and fig. 6 shows a second operating situation of the vehicle 4.

Fig. 5 and 6 schematically show a roadway 14 comprising a plurality of traffic lanes laterally delimited by a first boundary line 16, a second boundary line 18 and a third boundary line 20. Also shown schematically is a centerline 22 of the lane between lines 16 and 18 and a centerline 24 of the lane between lines 18 and 20. In both operating situations, a path is planned which enables the vehicle 4 to change lanes. In the initial state and the final state, the lateral velocity is zero. The longitudinal speed is the same in the initial state and the final state.

Referring to fig. 5, the corresponding index ind is transmitted at the recurrent neural network 8₅₆The path 26, represented schematically by a series of circles, is then passed by the table 10. The path 26 corresponds to the path shape collected in step F03 of the method according to the invention. Recurrent neural network 8 transfer factor lon₅The factor is selected to minimize the sum of the lateral jerks throughout the maneuver. In the examples of FIGS. 5 and 6, the recurrent neural network delivers the factor lat₅₆Equal to 1. The path 28, schematically represented by a series of crosses, corresponds to the factor lon transmitted by the modulator 12 in the recurrent neural network 8₅Under the action of (2) a longitudinally extended path. Path 28 corresponds to the modulated path obtained at the end of step F04 of the method according to the invention. Under these conditions, the vehicle 4 will follow the path 28.

Referring to fig. 6, a first obstacle 28 and a second obstacle 30 are located on the roadway 14. Index ind passed by the recurrent neural network 8₅₆As in the case of fig. 5. Thus, reference is again made here to path 26 of fig. 5. However, the recurrent neural network 8 takes into account the presence of the obstacles 28 and 30 and transmits the factor lon₆To enable avoidance of obstacles 28 and 30. Surface schematic by a series of squaresPath 32 is shown corresponding to a factor lon by modulator 12₆A longitudinally constricted path under the action of the force. The path 32 thus corresponds to the modulated path obtained at the end of step F04 and will be the path followed by the vehicle 4 in this operating mode.

In view of the above, the present invention makes it possible to provide optimal paths and/or trajectories while allowing all internal and external constraints to be considered, while using little computational resources in the inference phase. In particular, by using a temporal classification means, the demand for computational resources is shifted to an offline training phase, enabling robust planning to be obtained while limiting its complexity.

List of cited publications:

[1]Moritz Werling、Julius Ziegler、optimal trajectory generation for dynamic street scenes in a family of parameters]. Robotics and Automation (ICRA),2010IEEE International Conference on.ieee [ Robotics and Automation (ICRA),2010IEEE International Conference]Page 987-.

[2] Time-optimal motion planning in the presence of moving obstacles in Time-optimal motion planning by Tim Mercy, Wannes Van lock, Goele pipelers et al, 2015.

[3] You-Min Lee and Jong-Hwan Kim's Trajectory Generation Using RNN with Context Information for Mobile Robots [ generate trajectories of Mobile Robots Using RNN and Context Information ]. Robot Intelligence Technology and Applications 4. Springer, Cham,2017, pages 21-29 (ISBN: 978-3-319-.

[4] Track clustering for motion prediction [ clustering of tracks for motion prediction ] by Cynthia Sung, Dan Feldman, and Daniela Rus. Intelligent Robots and Systems (IROS),2012IEEE/RSJ International Conference on IEEE [ Intelligent robot and System (IROS),2012IEEE/RSJ International Conference IEEE ], 1547 nd 1552 of 2012.