WO2022198995A1 - Procédé et appareil de planification de trajectoire de marche, support de stockage lisible par ordinateur, et robot - Google Patents

Procédé et appareil de planification de trajectoire de marche, support de stockage lisible par ordinateur, et robot Download PDF

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Publication number
WO2022198995A1
WO2022198995A1 PCT/CN2021/124621 CN2021124621W WO2022198995A1 WO 2022198995 A1 WO2022198995 A1 WO 2022198995A1 CN 2021124621 W CN2021124621 W CN 2021124621W WO 2022198995 A1 WO2022198995 A1 WO 2022198995A1
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trajectory
gait
gait trajectory
standard
fitting
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PCT/CN2021/124621
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English (en)
Chinese (zh)
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郭宜劼
赵明国
熊友军
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深圳市优必选科技股份有限公司
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0214—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with safety or protection criteria, e.g. avoiding hazardous areas
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Definitions

  • the present application belongs to the field of robotics, and in particular, relates to a gait trajectory planning method, device, computer-readable storage medium, and robot.
  • Humanoid robots are complex systems with multiple degrees of freedom.
  • the full dynamic model of the robot combined with model predictive control and other optimization methods can be used to comprehensively consider the multiple degrees of freedom and constraints of the robot.
  • this is a perfect solution for gait trajectory planning, which can not only consider all the dynamics of the robot, but also provide real-time feedback and re-planning for future information.
  • the optimization problems generated by this method are often highly nonlinear and cannot guarantee convexity, a feasible solution may not be found in real-time calculation.
  • the current computer computing power has developed rapidly, it still cannot meet the high real-time requirements of such methods. sexual needs.
  • the embodiments of the present application provide a gait trajectory planning method, device, computer-readable storage medium, and robot to solve the problem that high real-time gait trajectory planning cannot be performed in the prior art.
  • a first aspect of the embodiments of the present application provides a gait trajectory planning method, which may include:
  • the standard gait trajectory library includes several standard gait trajectories, and each standard gait trajectory corresponds to a preset standard traveling speed;
  • an interpolation calculation is performed in the standard gait track of the standard gait track library to obtain a target gait track corresponding to the current traveling speed.
  • performing interpolation calculation in the standard gait trajectory of the standard gait trajectory library according to the current travel speed to obtain a target gait trajectory corresponding to the current travel speed may include:
  • the interpolation calculation is performed in the standard gait trajectory of the standard gait trajectory library according to the following formula:
  • n is the serial number of the standard travel speed, 1 ⁇ n ⁇ N, N is the number of standard travel speeds, vn is the nth standard travel speed, and v n ⁇ v n+1 , is the standard gait trajectory corresponding to vn in the standard gait trajectory library, is the current traveling speed, and gait(t) is the target gait trajectory corresponding to the current traveling speed.
  • the gait trajectory planning method may further include:
  • performing trajectory fitting according to the current gait trajectory and the target gait trajectory may include:
  • constructing a fitting trajectory expression with undetermined coefficients corresponding to the fitting gait trajectory may include:
  • t is the time variable
  • a i is an undetermined coefficient, 0 ⁇ i ⁇ 5.
  • determining the boundary constraints of the fitting trajectory expression according to the current gait trajectory and the target gait trajectory may include:
  • t m is the mth specified time point, 0 ⁇ m ⁇ M, and M is the number of specified time points.
  • a second aspect of the embodiments of the present application provides a gait trajectory planning device, which may include:
  • the gait trajectory library acquisition module is used to acquire the standard gait trajectory library of the robot;
  • the standard gait trajectory library includes several standard gait trajectories, and each standard gait trajectory corresponds to a preset standard travel speed;
  • the speed determination module is used to determine the current travel speed of the robot
  • An interpolation calculation module configured to perform interpolation calculation in the standard gait trajectory of the standard gait trajectory library according to the current travel speed to obtain a target gait trajectory corresponding to the current travel speed.
  • interpolation calculation module is specifically used to perform interpolation calculation in the standard gait trajectory of the standard gait trajectory library according to the following formula:
  • n is the serial number of the standard travel speed, 1 ⁇ n ⁇ N, N is the number of standard travel speeds, vn is the nth standard travel speed, and v n ⁇ v n+1 , is the standard gait trajectory corresponding to vn in the standard gait trajectory library, is the current traveling speed, and gait(t) is the target gait trajectory corresponding to the current traveling speed.
  • the gait trajectory planning device may also include:
  • the current gait trajectory determination module is used to determine the current gait trajectory of the robot
  • a trajectory fitting module configured to perform trajectory fitting according to the current gait trajectory and the target gait trajectory, to obtain a fitted gait trajectory that smoothly transitions from the current gait trajectory to the target gait trajectory.
  • trajectory fitting module may include:
  • a fitted trajectory expression construction unit used for constructing a fitted trajectory expression with undetermined coefficients corresponding to the fitted gait trajectory
  • a boundary constraint condition determining unit configured to determine the boundary constraint condition of the fitting trajectory expression according to the current gait trajectory and the target gait trajectory;
  • a designated time point selection unit used to select several designated time points within a preset trajectory fitting period, and calculate the value of the target gait trajectory at each designated time point;
  • An optimization target construction unit for constructing an optimization target corresponding to the fitting trajectory expression according to the value of the target gait trajectory at each specified time point;
  • An undetermined coefficient solving unit configured to determine each undetermined coefficient of the fitting trajectory expression according to the optimization objective and the boundary constraints, so as to obtain the fitting gait trajectory.
  • fitting trajectory expression building unit is specifically used to construct the fitting trajectory expression shown in the following formula:
  • t is the time variable
  • a i is an undetermined coefficient, 0 ⁇ i ⁇ 5.
  • boundary constraint determination unit is specifically used to determine the boundary constraint shown in the following formula:
  • optimization target construction unit is specifically used to construct the optimization target shown in the following formula:
  • t is the time variable, is the target gait trajectory, t m is the mth specified time point, 0 ⁇ m ⁇ M, and M is the number of specified time points.
  • a third aspect of the embodiments of the present application provides a computer-readable storage medium, where the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, implements any of the above-mentioned gait trajectory planning methods step.
  • a fourth aspect of the embodiments of the present application provides a robot, including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the computer program when the processor executes the computer program.
  • the steps of any of the above gait trajectory planning methods are provided.
  • a fifth aspect of the embodiments of the present application provides a computer program product, which, when the computer program product runs on a robot, causes the robot to execute the steps of any of the above gait trajectory planning methods.
  • the embodiments of the present application acquire a standard gait trajectory library of the robot; the standard gait trajectory library includes several standard gait trajectories, and each standard gait trajectory The gait trajectories all correspond to a preset standard travel speed; determine the current travel speed of the robot; perform interpolation calculation in the standard gait trajectory of the standard gait trajectory library according to the current travel speed, and obtain a The target gait trajectory corresponding to the travel speed.
  • the target gait trajectory corresponding to the current traveling speed can be obtained only by the interpolation calculation of the standard gait trajectory, which effectively ensures the high real-time performance of the gait trajectory planning.
  • FIG. 1 is a flowchart of an embodiment of a gait trajectory planning method in an embodiment of the present application
  • Fig. 2 is the schematic diagram of the state trajectory of the robot workspace
  • Fig. 3 is a schematic diagram of the mutation of gait trajectory
  • Fig. 5 is the schematic diagram of fitting gait trajectory
  • FIG. 6 is a structural diagram of an embodiment of a gait trajectory planning device in an embodiment of the present application.
  • FIG. 7 is a schematic block diagram of a robot in an embodiment of the present application.
  • the term “if” may be contextually interpreted as “when” or “once” or “in response to determining” or “in response to detecting” .
  • the phrases “if it is determined” or “if the [described condition or event] is detected” may be interpreted, depending on the context, to mean “once it is determined” or “in response to the determination” or “once the [described condition or event] is detected. ]” or “in response to detection of the [described condition or event]”.
  • an embodiment of a gait trajectory planning method in the embodiment of the present application may include:
  • Step S101 obtaining a standard gait trajectory library of the robot.
  • the standard gait trajectory library includes several standard gait trajectories, and each standard gait trajectory corresponds to a preset standard traveling speed.
  • the gait trajectory in this embodiment of the present application may refer to a certain single state trajectory, or may refer to a combination of multiple state trajectories.
  • Figure 2 shows a schematic diagram of the state trajectory of some robot workspaces, including but not limited to the pitch angle ⁇ t (t) and roll angle ⁇ t (t) of the upper body posture, the forward position x of the upper body relative to the support feet t (t), lateral position y t (t) and height h t (t), and forward position x f (t), lateral position y f (t) of the swing foot relative to the waist, and the swing foot relative to the ground Height z f (t), where t is a time variable.
  • the gait trajectory in this embodiment of the present application may be a combination of the above state trajectories, namely:
  • gait(t) [ ⁇ t(t), ⁇ t( t ), xt ( t ),yt( t ),ht( t ),xf( t ), yf ( t ),zf (t)]
  • the gait trajectory under a preset gait cycle (marked as T) can be generated in advance through the full dynamic model of the robot, and this gait trajectory can be used as the corresponding standard travel speed. Standard gait trajectory.
  • the number of standard traveling speeds to be set and the specific value of each standard traveling speed can be set according to actual conditions, which are not specifically limited in this embodiment of the present application.
  • Step S102 determining the current traveling speed of the robot.
  • the measured value of the forward speed of the robot's waist at this time can be taken as the current traveling speed, which is recorded as
  • Step S103 Perform interpolation calculation in the standard gait trajectory of the standard gait trajectory library according to the current travel speed to obtain a target gait trajectory corresponding to the current travel speed.
  • interpolation calculation can be performed in the standard gait trajectory of the standard gait trajectory library according to the following formula:
  • n is the serial number of the standard travel speed, 1 ⁇ n ⁇ N, N is the number of standard travel speeds, vn is the nth standard travel speed, and v n ⁇ v n+1 , is the standard gait trajectory corresponding to vn in the standard gait trajectory library, and gait(t) is the target gait trajectory corresponding to the current traveling speed.
  • the interpolation calculation can be performed according to the following formula:
  • the robot can select the gait trajectory most suitable for the current speed in real time even if it is disturbed by the speed during the traveling process, so as to ensure its own stability.
  • FIG. 3 is a schematic diagram of the sudden change of the gait trajectory, in which the forward position x f (t) of the swinging foot relative to the waist is used as an example for illustration.
  • the traveling speed of the robot is 0m/s, that is, the gait of walking on the spot, at the 0.1s moment of the gait cycle, it is suddenly disturbed, resulting in the sudden change of the traveling speed to 0.6m/s, and the gait from 0m/s is required.
  • the trajectory is switched to the gait trajectory of 0.6m/s, which causes the instability of the robot's walking.
  • trajectory fitting can be performed according to the current gait trajectory and the target gait trajectory , to obtain a fitted gait trajectory that smoothly transitions from the current gait trajectory to the target gait trajectory.
  • the process of trajectory fitting may specifically include the following steps:
  • Step S401 constructing a fitting trajectory expression with undetermined coefficients corresponding to the fitting gait trajectory.
  • the specific expression used can be set according to the actual situation, including but not limited to high-order polynomials and Bezier curves.
  • the fitted trajectory expression can be constructed as follows:
  • a i is an undetermined coefficient, 0 ⁇ i ⁇ 5, that is, there are altogether 6 undetermined coefficients a 0 , a 1 , a 2 , a 3 , a 4 , and a 5 .
  • the corresponding velocity expression can be obtained by taking the derivative of it, namely:
  • Step S402 Determine boundary constraints of the fitting trajectory expression according to the current gait trajectory and the target gait trajectory.
  • the time range under one gait cycle is [0, T], and the fitting gait trajectory needs to connect the position of the current gait trajectory at the current time t 0 and the target gait trajectory at the final time T position, and at the same time satisfy the velocity continuity, that is, it is required to determine the boundary constraints shown in the following formula:
  • Step S403 Select several designated time points within a preset trajectory fitting period, and calculate the value of the target gait trajectory at each designated time point.
  • the trajectory fitting period is [t 0 , T], and the number of specified time points can be set according to the actual situation.
  • two specified time points t 1 and t 2 can be selected as follows:
  • the value of the target gait trajectory at each specified time point can be calculated separately, that is, and
  • Step S404 constructing an optimization target corresponding to the fitting trajectory expression according to the values of the target gait trajectory at each specified time point.
  • optimization objective can be constructed as follows:
  • the fitting trajectory is as close as possible to the target gait trajectory, and the deviation between the two is minimized, wherein t m is the mth specified time point, 0 ⁇ m ⁇ M, and M is the specified time point number of.
  • Step S405 Determine each undetermined coefficient of the fitting trajectory expression according to the optimization objective and the boundary constraint condition to obtain the fitting gait trajectory.
  • FIG. 5 shows the fitted gait trajectory corresponding to the example in Figure 3. Through this fitted gait trajectory, a smooth and continuous switching from the current trajectory to the new trajectory is realized. The above trajectory fitting process is repeated at each moment, that is, rolling trajectory fitting is performed.
  • the standard gait trajectory library of the robot is obtained; the standard gait trajectory library includes several standard gait trajectories, and each standard gait trajectory corresponds to a preset standard travel speed; determine the current travel speed of the robot; perform interpolation calculation in the standard gait trajectory of the standard gait trajectory library according to the current travel speed to obtain a target gait trajectory corresponding to the current travel speed.
  • the target gait trajectory corresponding to the current traveling speed can be obtained only by the interpolation calculation of the standard gait trajectory, which effectively ensures the high real-time performance of the gait trajectory planning.
  • FIG. 6 shows a structural diagram of an embodiment of a gait trajectory planning apparatus provided by an embodiment of the present application.
  • a gait trajectory planning device may include:
  • the gait trajectory library acquisition module 601 is used to acquire the standard gait trajectory library of the robot;
  • the standard gait trajectory library includes several standard gait trajectories, and each standard gait trajectory corresponds to a preset gait trajectory standard travel speed;
  • a speed determination module 602 used to determine the current travel speed of the robot
  • the interpolation calculation module 603 is configured to perform interpolation calculation in the standard gait trajectory of the standard gait trajectory library according to the current travel speed to obtain a target gait trajectory corresponding to the current travel speed.
  • interpolation calculation module is specifically used to perform interpolation calculation in the standard gait trajectory of the standard gait trajectory library according to the following formula:
  • n is the serial number of the standard travel speed, 1 ⁇ n ⁇ N, N is the number of standard travel speeds, vn is the nth standard travel speed, and v n ⁇ v n+1 , is the standard gait trajectory corresponding to vn in the standard gait trajectory library, is the current traveling speed, and gait(t) is the target gait trajectory corresponding to the current traveling speed.
  • the gait trajectory planning device may also include:
  • the current gait trajectory determination module is used to determine the current gait trajectory of the robot
  • a trajectory fitting module configured to perform trajectory fitting according to the current gait trajectory and the target gait trajectory, to obtain a fitted gait trajectory that smoothly transitions from the current gait trajectory to the target gait trajectory.
  • trajectory fitting module may include:
  • a fitting trajectory expression construction unit used for constructing a fitting trajectory expression with undetermined coefficients corresponding to the fitted gait trajectory
  • a boundary constraint condition determining unit configured to determine the boundary constraint condition of the fitting trajectory expression according to the current gait trajectory and the target gait trajectory;
  • a designated time point selection unit used to select several designated time points within a preset trajectory fitting period, and calculate the value of the target gait trajectory at each designated time point;
  • an optimization target construction unit configured to construct an optimization target corresponding to the fitting trajectory expression according to the values of the target gait trajectory at each specified time point;
  • An undetermined coefficient solving unit configured to determine each undetermined coefficient of the fitting trajectory expression according to the optimization objective and the boundary constraints, so as to obtain the fitting gait trajectory.
  • fitting trajectory expression building unit is specifically used to construct the fitting trajectory expression shown in the following formula:
  • t is the time variable
  • a i is an undetermined coefficient, 0 ⁇ i ⁇ 5.
  • boundary constraint determination unit is specifically used to determine the boundary constraint shown in the following formula:
  • optimization target construction unit is specifically used to construct the optimization target shown in the following formula:
  • t m is the mth specified time point, 0 ⁇ m ⁇ M, and M is the number of specified time points.
  • FIG. 7 shows a schematic block diagram of a robot provided by an embodiment of the present application. For convenience of description, only parts related to the embodiment of the present application are shown.
  • the robot 7 of this embodiment includes a processor 70 , a memory 71 , and a computer program 72 stored in the memory 71 and executable on the processor 70 .
  • the processor 70 executes the computer program 72
  • the steps in each of the above embodiments of the gait trajectory planning method are implemented, for example, steps S101 to S103 shown in FIG. 1 .
  • the processor 70 executes the computer program 72
  • the functions of the modules/units in the above device embodiments for example, the functions of the modules 601 to 603 shown in FIG. 6 are implemented.
  • the computer program 72 may be divided into one or more modules/units, and the one or more modules/units are stored in the memory 71 and executed by the processor 70 to complete the this application.
  • the one or more modules/units may be a series of computer program instruction segments capable of performing specific functions, and the instruction segments are used to describe the execution process of the computer program 72 in the robot 7 .
  • FIG. 7 is only an example of the robot 7, and does not constitute a limitation to the robot 7. It may include more or less components than the one shown, or combine some components, or different components, such as
  • the robot 7 may also include input and output devices, network access devices, buses, and the like.
  • the processor 70 may be a central processing unit (Central Processing Unit, CPU), or other general-purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuit (Application Specific Integrated Circuit, ASIC), Field-Programmable Gate Array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.
  • a general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
  • the memory 71 may be an internal storage unit of the robot 7 , such as a hard disk or a memory of the robot 7 .
  • the memory 71 can also be an external storage device of the robot 7, such as a plug-in hard disk equipped on the robot 7, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, Flash card (Flash Card) and so on.
  • the memory 71 may also include both an internal storage unit of the robot 7 and an external storage device.
  • the memory 71 is used to store the computer program and other programs and data required by the robot 7 .
  • the memory 71 may also be used to temporarily store data that has been output or will be output.
  • the disclosed apparatus/robot and method may be implemented in other ways.
  • the device/robot embodiments described above are only illustrative.
  • the division of the modules or units is only a logical function division.
  • the shown or discussed mutual coupling or direct coupling or communication connection may be through some interfaces, indirect coupling or communication connection of devices or units, and may be in electrical, mechanical or other forms.
  • the units described as separate components may or may not be physically separated, and components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution in this embodiment.
  • each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically alone, or two or more units may be integrated into one unit.
  • the above-mentioned integrated units may be implemented in the form of hardware, or may be implemented in the form of software functional units.
  • the integrated modules/units if implemented in the form of software functional units and sold or used as independent products, may be stored in a computer-readable storage medium.
  • the present application can implement all or part of the processes in the methods of the above embodiments, and can also be completed by instructing the relevant hardware through a computer program.
  • the computer program can be stored in a computer-readable storage medium, and the computer When the program is executed by the processor, the steps of the foregoing method embodiments can be implemented.
  • the computer program includes computer program code, and the computer program code may be in the form of source code, object code, executable file or some intermediate form, and the like.
  • the computer-readable storage medium may include: any entity or device capable of carrying the computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM, Read-Only Memory) ), random access memory (RAM, Random Access Memory), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content contained in the computer-readable storage medium may be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction, for example, in some jurisdictions, according to legislation and patent practice, computer-readable Storage media exclude electrical carrier signals and telecommunications signals.

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Abstract

L'invention concerne un procédé et un appareil de planification de trajectoire de marche, un support de stockage lisible par ordinateur, et un robot (7). Le procédé comprend les étapes consistant à : acquérir une bibliothèque de trajectoires de marche standard d'un robot (7) (S101), la bibliothèque de trajectoires de marche standard comprenant une pluralité de trajectoires de marche standard, et chaque trajectoire de marche standard correspondant à une vitesse de déplacement standard prédéfinie ; déterminer la vitesse de déplacement actuelle du robot (7) (S102) ; et effectuer un calcul d'interpolation dans une trajectoire de marche standard dans la bibliothèque de trajectoires de marche standard en fonction de la vitesse de déplacement actuelle pour obtenir une trajectoire de marche cible correspondant à la vitesse de déplacement actuelle (S103). Selon le procédé, une trajectoire de marche cible correspondant à la vitesse de déplacement actuelle peut être obtenue simplement en effectuant un calcul d'interpolation dans une trajectoire de marche standard, garantissant ainsi efficacement une pertinence temporelle élevée de la planification de trajectoire de marche.
PCT/CN2021/124621 2021-03-26 2021-10-19 Procédé et appareil de planification de trajectoire de marche, support de stockage lisible par ordinateur, et robot WO2022198995A1 (fr)

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