Robot, robot speed planning method, device and readable storage medium

Abstract

The application provides a robot, a robot speed planning method, a device and a readable storage medium. The method processes kinematic constraints through a first filter set, processes frequency constraints through a second filter set, and generates a series sliding filter set after time optimization through a third filter set. The frequency constraints are integrated into the kinematic optimal solution by using the rounding matching mechanism in the time optimization algorithm, the time optimality of the speed planning is ensured while all inherent modal frequencies are completely processed, the end vibration problem of the robot caused by incomplete suppression of multi-order inherent modal frequencies is effectively solved, and the precision and stability of the robot work are improved.

Description

Technical Field

[0001] This application relates to the field of robot control technology, and more specifically, to robots, robot speed planning methods, devices, and readable storage media. Background Technology

[0002] In high-speed, high-precision motion control of robots, acceleration and deceleration planning directly affects system performance. Traditional trapezoidal velocity planning is simple to calculate, but the acceleration is discontinuous, which can easily lead to vibration. While S-shaped velocity planning based on trigonometric functions smooths the acceleration, it suffers from computational complexity and neglects the system's frequency domain response. To overcome these shortcomings, existing technologies attempt to introduce frequency domain constraints into the planning process. For example, patent CN121500770A proposes a real-time vibration suppression method based on input shaping and S-shaped velocity planning. By combining input shaping and S-shaped planning, it uses the estimated mean of the system's natural frequencies to suppress vibration in the velocity curve. Patent CN121004600A proposes a robot velocity planning method considering frequency constraints. This method further proposes a robot velocity planning method that considers frequency constraints, introducing frequency domain constraints while optimizing planning time.

[0003] However, the above solutions still have significant shortcomings:

[0004] 1. Incomplete frequency constraints: Real-world robot systems have multiple natural modes. Existing methods only process a single mean frequency, which cannot cover the entire frequency band. When the trajectory excitation component falls into the unprocessed frequency band, it may still cause vibration.

[0005] 2. Unable to guarantee optimal time: When multiple inherent frequency constraints are introduced, the parameter solution space is highly nonlinear, and existing strategies are difficult to converge to the global shortest running time while strictly satisfying multiple frequency domain constraints. Summary of the Invention

[0006] The main objective of this application is to provide a robot, a robot speed planning method, an apparatus, and a readable storage medium to solve the problem of insufficient vibration suppression caused by incomplete frequency constraints in existing speed planning methods, as well as the problem of not being able to achieve globally time-optimal planning under multiple frequency constraints.

[0007] To achieve the above objectives, according to a first aspect of this application, a robot velocity planning method is provided, comprising:

[0008] Obtain the kinematic constraints of the path to be planned and the robot's intrinsic modal frequencies;

[0009] A first time constant sequence of the first filter bank is determined based on the kinematic constraint information. The first filter bank includes a plurality of sliding filters for processing kinematic constraints.

[0010] The second time constant sequence of the second filter bank is determined based on the inherent mode frequency, and the second filter bank includes a plurality of sliding filters for processing frequency constraints;

[0011] Time optimization is performed based on the first time constant sequence and the second time constant sequence to obtain the third time constant sequence of the third filter bank; the third filter bank includes multiple cascaded sliding filters;

[0012] The path length of the path to be planned is constructed as a step signal, and the step signal is input into the third filter group. The third filter group is used to filter the step signal step by step according to the third time constant sequence to obtain the robot's speed planning information.

[0013] Optionally, determining the first time constant sequence of the first filter bank based on the kinematic constraint information includes:

[0014] The first time constant of each first filter in the first filter bank is determined based on the kinematic constraint information and the time-optimal condition; the kinematic constraint information includes the kinematic constraints of kinematic parameters of each order.

[0015] The first time constant is:

[0016] ;

[0017] in, It is the first i The time constant of the first filter represents the time constant of the first filter. The first-order kinematic parameters satisfy the first-order kinematic parameters. Under the condition of first-order kinematic constraints, to the second The shortest time required for the transition of kinematic parameters. Indicates the first The upper limit of the kinematic constraint of order. Indicates the first The upper limit of the kinematic constraint;

[0018] The optimal time condition is:

[0019] 1;

[0020] in, N This indicates the number of the first filters.

[0021] Optionally, determining the second time constant sequence of the second filter bank based on the inherent mode frequencies includes:

[0022] Calculate the second time constant of each second filter in the second filter bank based on the inherent mode frequency:

[0023]

[0024] in, The robot's first j One inherent modal frequency, M This indicates the number of the second filter.

[0025] Optionally, the first time constant sequence is represented as N The second time constant sequence is represented as M Time optimization is performed based on the first time constant sequence and the second time constant sequence, including L rounds of optimization. Each round of the optimization process includes:

[0026] against Each second time constant in Iterate through each first time constant in T Calculate the scaling factor This yields a set of candidate scaling factors. ;

[0027] From the set of candidate scaling factors Select , so that:

[0028] ;

[0029] Will and As a matching pair, Included and delete from T ;

[0030] After performing the optimization process described in round L, The remaining elements and Unmatched elements are included The third time constant sequence is obtained.

[0031] Optionally, the transfer function of each sliding filter in the third filter bank is:

[0032] ;

[0033] in, Indicates the third filter bank k The transfer function of a stage-sliding filter. Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0034] Optionally, the amplitude-frequency response function of each sliding filter in the third filter bank for:

[0035] ;

[0036] in, Indicates the cutoff frequency. , Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0037] Optionally, the step signal is input to the third filter bank, and the third filter bank performs step-by-step filtering on the step signal according to the third time constant sequence to obtain the robot's speed planning information, including:

[0038] Based on the total length of the path to be planned h Constructing a step signal ;

[0039] The step signal is input into the third filter group;

[0040] In the third filter bank, each sliding filter performs a moving average filtering process on the input signal according to the time constant corresponding to the third time constant sequence, and uses the displacement signal output by the last sliding filter as the velocity planning information of the robot; wherein, the input of the next sliding filter is the output of the previous sliding filter.

[0041] According to a second aspect of this application, a robot speed planning device is provided, comprising:

[0042] The data acquisition unit is used to acquire the kinematic constraint information of the path to be planned and the robot's natural modal frequencies;

[0043] The first determining unit is configured to determine a first time constant sequence of a first filter bank based on the kinematic constraint information, and to determine a second time constant sequence of a second filter bank based on the inherent mode frequencies, wherein the first filter bank includes a plurality of sliding filters for processing kinematic constraints, and the second filter bank includes a plurality of sliding filters for processing frequency constraints.

[0044] The second determining unit is used to perform time optimization based on the first time constant sequence and the second time constant sequence to obtain the third time constant sequence of the third filter group, wherein the third filter group includes multiple cascaded sliding filters;

[0045] The speed planning unit is used to construct a step signal from the path length of the path to be planned, input the step signal into the third filter group, and use the third filter group to perform step filtering processing on the step signal according to the third time constant sequence to obtain the speed planning information of the robot.

[0046] According to a third aspect of this application, a robot is provided that performs speed planning using the robot speed planning method described above.

[0047] According to a fourth aspect of this application, a readable storage medium is provided, the readable storage medium storing a computer program that, when executed by a processor, implements the robot speed planning method described above.

[0048] By applying the technical solution of this application, three sets of filters are set up: the first filter set handles kinematic constraints, the second filter set handles frequency constraints, and the third filter set is a series sliding filter set generated after time optimization. The frequency constraints are integrated into the optimal kinematic solution by utilizing the rounding matching mechanism in the time optimization algorithm. This achieves the goal of ensuring the time optimality of velocity planning while fully processing all natural modal frequencies. It effectively solves the problem of end-effector vibration caused by the incomplete suppression of multiple natural modal frequencies, and improves the accuracy and stability of robot operation. Attached Figure Description

[0049] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0050] Figure 1 A hardware structure block diagram of a mobile terminal for executing a robot speed planning method according to an embodiment of this application is shown;

[0051] Figure 2 A flowchart of a robot velocity planning method provided in an embodiment of this application is shown;

[0052] Figure 3 A schematic diagram of the framework structure of three filter banks provided in an embodiment according to this application is shown;

[0053] Figure 4 A waveform diagram of the frequency response function of the amplitude provided in an embodiment according to this application is shown;

[0054] Figure 5 The kinematic curves before employing the robot velocity planning method provided in the embodiments of this application are shown;

[0055] Figure 6 The kinematic curves following the application of a robot velocity planning method are shown in the embodiments provided in this application.

[0056] Figure 7 A schematic diagram of a robot speed planning device provided in an embodiment of this application is shown.

[0057] The above figures include the following reference numerals:

[0058] 102. Processor; 104. Memory; 106. Transmission device; 108. Input / output device; 701. Data acquisition unit; 702. First determination unit; 703. Second determination unit; 704. Speed ​​planning unit. Detailed Implementation

[0059] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0060] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.

[0061] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this application described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0062] As described in the background section, the problems of insufficient vibration suppression due to incomplete frequency constraints and the inability to achieve globally optimal time planning under multiple frequency constraints in the prior art have not been effectively solved. To at least partially solve the above technical problems, embodiments of this application provide a robot, a robot speed planning method, an apparatus, and a readable storage medium.

[0063] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0064] The robot speed planning method provided in this application embodiment can be executed on a mobile terminal, computer terminal, or similar computing device. Taking running on a mobile terminal as an example, Figure 1 This is a hardware structure block diagram of a mobile terminal for a robot speed planning method according to an embodiment of the present invention. Figure 1 As shown, a mobile terminal may include one or more ( Figure 1 Only one is shown in the diagram. A processor 102 (which may include, but is not limited to, a microprocessor MCU or a programmable logic device FPGA, etc.) and a memory 104 for storing data are also shown. The mobile terminal may further include a transmission device 106 for communication functions and an input / output device 108. Those skilled in the art will understand that... Figure 1 The structure shown is for illustrative purposes only and does not limit the structure of the mobile terminal described above. For example, the mobile terminal may also include components that are more... Figure 1 The more or fewer components shown, or having the same Figure 1 The different configurations shown.

[0065] The memory 104 can be used to store computer programs, such as application software programs and modules, like the computer program corresponding to the air conditioning control method in this embodiment of the invention. The processor 102 executes various functional applications and data processing by running the computer program stored in the memory 104, thereby realizing the robot speed planning method described above. The memory 104 may include high-speed random access memory and non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory 104 may further include memory remotely located relative to the processor 102, and these remote memories can be connected to the mobile terminal via a network. Examples of the aforementioned networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof. The transmission device 106 is used to receive or send data via a network. Specific examples of the aforementioned networks may include wireless networks provided by the mobile terminal's communication provider. In one instance, the transmission device 106 includes a network interface controller (NIC), which can be connected to other network devices via a base station to communicate with the Internet. In one example, the transmission device 106 may be a radio frequency (RF) module, which is used to communicate with the Internet wirelessly.

[0066] This embodiment provides a robot speed planning method that runs on a mobile terminal, computer terminal, or similar computing device. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Also, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0067] For ease of description, the following explains some of the nouns or terms used in the embodiments of this application:

[0068] Moving average filter: A low-pass filter that smooths the signal by averaging the input signal to remove high-frequency noise and specific frequency components. Its time-domain characteristic is equivalent to performing a rectangular window integral averaging on the input signal.

[0069] Time constant: A parameter of a moving average filter that determines the speed at which the filter responds to the input signal and its frequency selectivity. The smaller the time constant, the faster the filter responds to the input signal; the larger the time constant, the better the smoothing effect of the filter.

[0070] Natural modal frequencies: Specific vibration frequencies that naturally form within a robot's mechanical structure during free vibration. If velocity planning includes components close to the robot's natural modal frequencies, it may cause resonance in parts of the robot's structure.

[0071] Kinematic constraints: A series of restrictions that a robot must follow during motion planning, including upper limits on velocity, acceleration, jerk, and the derivative of jerk.

[0072] The embodiments of this application provide a robot speed planning method. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0073] Figure 2 This is a flowchart of a robot speed planning method according to an embodiment of this application. Figure 2 As shown, the method includes the following steps:

[0074] Step S201: Obtain the kinematic constraint information of the path to be planned and the robot's natural modal frequencies.

[0075] Specifically, the kinematic constraints of the planned path refer to the various physical limitations that the robot must satisfy when executing the path. The robot's motion is described by kinematic parameters of multiple orders, such as displacement, velocity, acceleration, jerk, and jerk derivative. Each order of parameter has its physical upper limit; for example, the upper limit of velocity is determined by the rated speed of the motor, the upper limit of acceleration is determined by the maximum output torque and load inertia of the motor, and the upper limit of jerk is determined by the shock resistance of the mechanical structure. These constraints are usually determined during the robot system design phase and stored in the robot's control system parameters. Natural modal frequencies are inherent properties of the robot's mechanical structure and can be obtained through finite element analysis or measured through frequency sweep experiments. A robot is a multi-degree-of-freedom elastic system with multiple natural modal frequencies. The existence of these frequencies means that if the velocity planning includes frequency components similar to these frequencies, resonance may occur, affecting the accuracy and stability of the robot's operation.

[0076] Step S202: Determine the first time constant sequence of the first filter bank based on the kinematic constraint information. The first filter bank includes multiple sliding filters for processing kinematic constraints. Determine the second time constant sequence of the second filter bank based on the natural mode frequencies. The second filter bank includes multiple sliding filters for processing frequency constraints.

[0077] Specifically, this application uses a sliding filter as the basic tool for speed planning. A sliding filter is a finite impulse response filter, whose time-domain characteristics are equivalent to integral averaging over a rectangular window of the input signal. The time constant is the core parameter of the sliding filter, determining the filter's window length and thus affecting the filter's response speed and frequency selectivity.

[0078] Please refer to Figure 3 , Figure 3 A schematic diagram of the framework structure of the three filter banks in this embodiment is shown. Figure 3 As shown, the first filter bank is used to process kinematic constraints. Its input signals are a step signal and kinematic constraint information. The step amplitude of the step signal represents the total length of the path to be planned. Each sliding filter in the first filter bank corresponds to a kinematic constraint of one order—for example, the first filter corresponds to velocity constraints, the second filter to acceleration constraints, the third filter to jerk constraints, and so on. The time constant of each filter represents the time required for the signal to transition from a certain kinematic state to a higher kinematic state. The time constants of each filter need to meet the time-optimal condition to ensure that the velocity-planned trajectory is completed in the shortest time while satisfying all kinematic constraints.

[0079] The second filter bank handles frequency constraints, with each sliding filter corresponding to a specific intrinsic mode frequency of the robot. Based on the frequency-domain notch characteristic of the sliding filter, when the filter's time constant is an integer multiple of the period of the intrinsic mode frequency, the filter's gain at that frequency is zero, thus accurately suppressing that frequency component. When the robot has multiple intrinsic mode frequencies, by setting multiple second filters corresponding to different frequencies, complete suppression of all intrinsic mode frequencies can be achieved.

[0080] The first and second filter banks are only used to calculate the time constant sequence at this stage, and they do not directly participate in the subsequent speed planning signal processing.

[0081] Step S203: Perform time optimization based on the first time constant sequence and the second time constant sequence to obtain the third time constant sequence of the third filter bank; the third filter bank includes multiple cascaded sliding filters.

[0082] Specifically, the core objective of time optimization is to embed the frequency constraints represented by the second filter bank into the time-optimal solution represented by the first filter bank without significantly increasing the total duration of the trajectory.

[0083] The basic logic of time optimization is as follows: For each second time constant in the second filter bank (representing an intrinsic mode frequency to be suppressed), a first time constant that best matches it is found in the time constant sequence of the first filter bank, based on this time constant. The matching is based on the periodic notch characteristic of the sliding filter—an integer multiple of a filter time constant can also effectively suppress the frequency. Therefore, by using an integer multiple of this second time constant as the time constant of the third filter bank to replace the original first time constant, kinematic constraints and frequency constraints can be satisfied simultaneously with almost no increase in the total duration. For time constants that cannot find a match, they are directly included in the time constant set of the third filter bank to ensure that all frequency constraints are fully addressed.

[0084] Through this "nearest substitution" matching strategy, each time constant in the final third time constant sequence can effectively suppress a certain intrinsic mode frequency while maintaining numerical closeness to the original kinematic optimal solution, thus ensuring the optimality of the total trajectory duration while fully handling all frequency constraints.

[0085] Step S204: The path length of the path to be planned is constructed as a step signal. The step signal is input into the third filter bank. The third filter bank is used to filter the step signal step by step according to the third time constant sequence to obtain the robot's speed planning information.

[0086] Specifically, the total length of the path to be planned is constructed as a step signal and input to the front end of the third filter bank. Please refer to [link / reference needed]. Figure 3 The third filter bank is a cascaded structure consisting of multiple sliding filters connected in series according to a third time constant sequence. In signal processing, the cascading of multiple filters is equivalent to multiple consecutive convolution operations. The signal flows through each stage of the filter in turn, and with each stage, the smoothness of the output signal increases by one order—the displacement curve becomes more continuous, and its higher-order derivatives such as velocity, acceleration, and jerk gradually become continuous without abrupt changes.

[0087] Since each time constant in the third time constant sequence inherits the kinematic constraint characteristics of the first filter bank (ensuring that velocity, acceleration, etc., do not exceed limits) and the frequency constraint characteristics of the second filter bank (forming notches at the natural mode frequencies), the displacement signal ultimately output by the third filter bank naturally satisfies the dual requirements of physical smoothness and resonant frequency suppression. In actual control, the control system can differentiate this displacement signal to obtain feedforward signals such as velocity and acceleration, and then send control commands such as position, velocity, and acceleration to the servo driver to drive the robot to move according to the planned trajectory.

[0088] Through the steps described above in this embodiment, the technical solution of this application achieves at least the following beneficial effects:

[0089] First, it achieves complete suppression of all intrinsic modal frequencies of the robot. By setting up a second filter bank, each second filter corresponds to one intrinsic modal frequency of the robot, and the corresponding time constant is incorporated into the time optimization process, ensuring that each intrinsic modal frequency is suppressed in the final velocity planning trajectory. Compared with existing technologies that only process a single mean frequency or a subset of frequencies, this embodiment can completely cover the robot's multi-order intrinsic modal frequencies, fundamentally avoiding end-effector vibration problems caused by the excitation of unprocessed frequency components, and significantly improving the smoothness of robot operation and machining accuracy.

[0090] Second, while fully addressing all frequency constraints, the time-optimal nature of velocity planning is ensured. Through the "nearest replacement" matching strategy in the time optimization algorithm—using the second time constant as a benchmark, finding the closest integer multiple of it in the first time constant sequence for replacement—each time constant in the third time constant sequence satisfies kinematic constraints while effectively suppressing intrinsic mode frequencies, and minimizing the increase in total duration compared to the original kinematically optimal solution. Compared to existing technologies that rigidly accumulate duration due to multiple frequency filters in series, this embodiment integrates frequency constraints into the time-optimal solution with extremely low time cost, balancing vibration suppression and operational efficiency.

[0091] Third, the collaborative architecture of the three filter groups enhances the flexibility and adaptability of velocity planning. The first filter group is responsible for extracting the time-optimal baseline under kinematic constraints, the second filter group is responsible for extracting frequency constraints, and the third filter group is responsible for executing the fused velocity planning. This "computation-execution" separation architecture means that when the robot's kinematic parameters or intrinsic modal frequencies change, only the time constant sequence of the corresponding filter group needs to be recalculated, without changing the overall framework of velocity planning, thus exhibiting good scalability and adaptability.

[0092] Fourth, a high-order smoothness of the velocity planning trajectory is achieved through a step-by-step filtering mechanism using cascaded sliding filters. With each sliding filter pass, the order of the trajectory's derivative increases in continuity, resulting in a smooth and continuous output displacement signal and its derivatives. This avoids the shocks and vibrations caused by sudden acceleration changes in traditional trapezoidal programming, while also circumventing the complex trigonometric function calculations required in S-shaped programming. This ensures trajectory smoothness while reducing computational complexity.

[0093] In some embodiments, determining the first time constant sequence of the first filter bank based on kinematic constraint information includes: determining the first time constant of each first filter in the first filter bank based on kinematic constraint information and time-optimal conditions; the kinematic constraint information includes kinematic constraints of kinematic parameters of each order; the first time constant is:

[0094] ;

[0095] in, It is the first i The time constant of the first filter represents the time constant of the first filter. The first-order kinematic parameters satisfy the first-order kinematic parameters. Under the condition of first-order kinematic constraints, to the second The shortest time required for the transition of kinematic parameters. Indicates the first The upper limit of the kinematic constraint of order. Indicates the first The upper limit of the kinematic constraint;

[0096] The optimal time condition is:

[0097] 1;

[0098] in, N This indicates the number of the first filters.

[0099] In this embodiment, the formula for calculating the first time constant represents the shortest duration required for a signal to transition from a certain order state to a higher order state under given kinematic constraints. The time-optimal condition ensures that the time constants of each filter stage satisfy the cumulative constraint relationship from back to front, minimizing the response time (i.e., total duration) of the entire filter bank to a step signal. If this condition is not met, it indicates a possible "mismatch" between the initially set kinematic constraints, requiring the time optimization process to adjust the time constants to meet the optimality requirements.

[0100] For example, suppose the path length is 10 (in meters), and the maximum speed is... =3, upper limit of acceleration =0.4, upper limit of accelerometer =0.4, upper limit of the derivative of jerk =5. (Using the formula) Calculated =10 / 3=3.333 (unit: seconds). =3 / 0.4=7.5 (unit, seconds) =0.4 / 0.4=1 (unit, seconds). =0.4 / 5=0.08 (unit, seconds), at this time, If the time-optimal conditions are not met, the time optimization process needs to be initiated for adjustment.

[0101] In some embodiments, determining the second time constant sequence of the second filter bank based on the inherent mode frequencies includes: calculating the second time constant of each second filter in the second filter bank based on the inherent mode frequencies.

[0102]

[0103] in, The robot's first j One inherent modal frequency, M This indicates the number of second filters.

[0104] In this embodiment, the formula for calculating the second time constant is derived from the amplitude-frequency response characteristics of the sliding filter. Setting the filter's time constant to the period corresponding to the intrinsic mode frequency enables the formation of a precise notch filter at the intrinsic mode frequency, effectively suppressing that frequency component. When the robot has multiple intrinsic mode frequencies, by setting multiple second filters corresponding to different frequencies, complete suppression of multiple frequencies can be achieved.

[0105] For example, if the robot's natural modal frequency is 33Hz, that is... = ≈207.35 rad / s, then the corresponding second time constant is ≈0.0303 seconds. When the filter processes the signal, the gain of the 33Hz frequency component is zero, and the vibrational energy at this frequency is completely blocked.

[0106] In some embodiments, the first time constant sequence is represented as N The second time constant sequence is represented as M Time optimization is performed based on the first and second time constant sequences, including L rounds of optimization. Each round of optimization includes:

[0107] against Each second time constant in Iterate through each first time constant in T Calculate the scaling factor This yields a set of candidate scaling factors. ;

[0108] From the set of candidate scaling factors Select , so that:

[0109] ;

[0110] Will and As a matching pair, Included and delete from T ;

[0111] After L rounds of optimization, The remaining elements and Unmatched elements are included The third time constant sequence is obtained.

[0112] In this embodiment, the core idea of ​​the time optimization algorithm is to utilize the frequency domain characteristic of a sliding filter where "integer multiples of the period are still notch points." Specifically, if the time constant of a sliding filter is... Then the sliding filter at frequency A notch is formed at the location; simultaneously, the time constant is... Integer multiples ( , The sliding filter is also in The frequency exhibits notch filtering capability. Therefore, multiplying the frequency time constant by a positive integer still effectively suppresses that frequency. Utilizing this property, the time optimization method searches for the numerically closest value in the first time constant sequence. of and use As Substitute values ​​included Since the values ​​of the two are close, the total duration remains almost unchanged after the replacement. For time constants that cannot be found to match, they are directly incorporated into the third time constant sequence, ensuring the integrity of the frequency constraints.

[0113] For example, continuing from the previous example, the kinematic time constant is , =0.0303. In the first round of optimization, traversal is based on 0.0303. Calculate 3.333 The product is 110 × 0.0303 = 3.333, with an error of 0; Calculate for 7.5. The product is 7.4841, with an error of 0.0159; Calculate for 1 The product is 0.9999, with an error of 0.0001; calculate for 0.08. The product is 0.0606, and the error is 0.0194. The match with the smallest error is 3.333, so 3.333 is replaced with 110 × 0.0303 = 3.333 and incorporated into the third time constant sequence. Delete 3.333. Proceed to the next round of optimization. Continue matching based on the next value in the second time constant sequence. After the loop ends, Unmatched residual elements and All tail elements that did not participate in the matching were included. .

[0114] In some embodiments, the transfer functions of the sliding filters at each stage in the third filter bank are:

[0115] ;

[0116] in, Indicates the third filter bank k The transfer function of a stage-sliding filter. Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0117] In this embodiment, the transfer function is a mathematical tool used in control system analysis to describe the input-output relationship of a system.

[0118] For example, for a time constant of A sliding filter whose impulse response is width ,high A rectangular pulse. When a step signal is input, the output signal rises linearly from 0, and... The input amplitude is reached at each step, forming a ramp. When multiple sliding filters are connected in series, the smoothness of the output increases by one order with each stage.

[0119] In some embodiments, the amplitude-frequency response function of each stage of the sliding filter in the third filter bank for:

[0120] ;

[0121] in, Indicates the cutoff frequency. , Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0122] like Figure 4As shown, the amplitude-frequency response function describes the gain or attenuation of the filter for input signals of different frequencies. The amplitude-frequency response function forms a notch at the cutoff frequency, meaning that the sliding filter can form a notch at its fundamental frequency and all its integer multiples (harmonics). This property is the mathematical basis for the use of integer multiples of the frequency-time constant for rounding matching in this application—integer multiples of the time constant correspond to harmonic notch points of the same natural frequency, thus effectively suppressing that natural mode frequency.

[0123] In some embodiments, a step signal is input to a third filter bank, and the step signal is filtered stepwise according to a third time constant sequence using the third filter bank to obtain the robot's velocity planning information, including:

[0124] Based on the total length of the path to be planned h Constructing a step signal ;

[0125] The step signal is fed into the third filter group;

[0126] In the third filter bank, each sliding filter performs a moving average filtering process on the input signal according to the time constant corresponding to the third time constant sequence. The displacement signal output by the last sliding filter is used as the robot's velocity planning information. The input of the next sliding filter is the output of the previous sliding filter.

[0127] For example, the first time constant of the step signal input is The third filter outputs the first displacement signal. The characteristics of this signal are: speed It is a constant value, but the acceleration There is a step jump. The first displacement signal... Input the second time constant as The third filter outputs the second displacement signal. The characteristics of this signal are: acceleration It becomes smooth, but accelerates. A step change still exists. The second displacement signal... Input the third time constant as The third filter outputs the third displacement signal. The characteristics of this signal are: jerk. It becomes smooth, but the derivative of the jerk is increased. A step jump still exists. Similarly, the final output displacement signal of the third filter bank... It is a smooth position trajectory curve that meets all kinematic limits (velocity and acceleration do not exceed limits) and does not contain any first-order intrinsic mode frequency components of the robot.

[0128] Please refer to Figure 5 and Figure 6 , Figure 5 The kinematic curves before employing the robot velocity planning method described in this embodiment are shown. Figure 6 The kinematic curves after employing the robot velocity planning method described in this embodiment are shown. Figure 5 and Figure 6 As can be seen, the total duration was significantly shortened after optimization, verifying the effectiveness of the time optimization.

[0129] This embodiment also provides a robot speed planning device, such as Figure 7 As shown, the device includes:

[0130] The data acquisition unit 701 is used to acquire the kinematic constraint information of the path to be planned and the robot's natural modal frequencies;

[0131] The first determining unit 702 is used to determine the first time constant sequence of the first filter bank according to kinematic constraint information, and to determine the second time constant sequence of the second filter bank according to the natural mode frequency, wherein the first filter bank includes a plurality of sliding filters for processing kinematic constraints, and the second filter bank includes a plurality of sliding filters for processing frequency constraints.

[0132] The second determining unit 703 is used to perform time optimization based on the first time constant sequence and the second time constant sequence to obtain the third time constant sequence of the third filter bank, wherein the third filter bank includes multiple cascaded sliding filters.

[0133] The speed planning unit 704 is used to construct the path length of the path to be planned as a step signal, input the step signal into the third filter bank, and use the third filter bank to perform step filtering processing on the step signal according to the third time constant sequence to obtain the robot's speed planning information.

[0134] Optionally, the first determining unit 702 is specifically used to determine the first time constant of each first filter in the first filter bank based on kinematic constraint information and time-optimal conditions; the kinematic constraint information includes the kinematic constraints of kinematic parameters of each order;

[0135] The first time constant is:

[0136] ;

[0137] in, It is the first i The time constant of the first filter represents the time constant of the first filter. The first-order kinematic parameters satisfy the first-order kinematic parameters. Under the condition of first-order kinematic constraints, to the second The shortest time required for the transition of kinematic parameters. Indicates the first The upper limit of the kinematic constraint of order. Indicates the first The upper limit of the kinematic constraint;

[0138] The optimal time condition is:

[0139] 1;

[0140] in, N This indicates the number of the first filters.

[0141] Optionally, the first determining unit 702 is further configured to calculate the second time constant of each second filter in the second filter bank based on the inherent mode frequency:

[0142]

[0143] in, The robot's first j One inherent modal frequency, M This indicates the number of second filters.

[0144] Optionally, the first time constant sequence is represented as N The second time constant sequence is represented as M The second determining unit 703 is specifically used to perform time optimization based on the first time constant sequence and the second time constant sequence, including an L-round optimization process. Each round of optimization includes:

[0145] against Each second time constant in Iterate through each first time constant in T Calculate the scaling factor This yields a set of candidate scaling factors. ;

[0146] From the set of candidate scaling factors Select , so that:

[0147] ;

[0148] Will and As a matching pair, Included and delete from T ;

[0149] After L rounds of optimization, The remaining elements and Unmatched elements are included The third time constant sequence is obtained.

[0150] Specifically, the transfer functions of each sliding filter in the third filter bank are:

[0151] ;

[0152] in, Indicates the third filter bank k The transfer function of a stage-sliding filter. Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0153] Specifically, the amplitude-frequency response functions of each stage of the sliding filter in the third filter bank. for:

[0154] ;

[0155] in, Indicates the cutoff frequency. , Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0156] Optionally, the speed planning unit 704 is specifically used to plan the speed based on the total length of the path to be planned. h Constructing a step signal ;

[0157] The step signal is input into the third filter group;

[0158] In the third filter bank, each sliding filter performs a moving average filtering process on the input signal according to the time constant corresponding to the third time constant sequence. The displacement signal output by the last sliding filter is used as the robot's velocity planning information. The input of the next sliding filter is the output of the previous sliding filter.

[0159] This embodiment also provides a robot, including one or more processors, a memory, and one or more programs, the one or more programs being stored in the memory and configured to be executed by the one or more processors, wherein the one or more programs, when executed, perform at least the following steps:

[0160] Step S201: Obtain the kinematic constraint information of the path to be planned and the robot's natural modal frequencies.

[0161] Specifically, the kinematic constraints of the planned path refer to the various physical limitations that the robot must satisfy when executing the path. The robot's motion is described by kinematic parameters of multiple orders, such as displacement, velocity, acceleration, jerk, and jerk derivative. Each order of parameter has its physical upper limit; for example, the upper limit of velocity is determined by the rated speed of the motor, the upper limit of acceleration is determined by the maximum output torque and load inertia of the motor, and the upper limit of jerk is determined by the shock resistance of the mechanical structure. These constraints are usually determined during the robot system design phase and stored in the robot's control system parameters. Natural modal frequencies are inherent properties of the robot's mechanical structure and can be obtained through finite element analysis or measured through frequency sweep experiments. A robot is a multi-degree-of-freedom elastic system with multiple natural modal frequencies. The existence of these frequencies means that if the velocity planning includes frequency components similar to these frequencies, resonance may occur, affecting the accuracy and stability of the robot's operation.

[0162] Step S202: Determine the first time constant sequence of the first filter bank based on the kinematic constraint information. The first filter bank includes multiple sliding filters for processing kinematic constraints. Determine the second time constant sequence of the second filter bank based on the natural mode frequencies. The second filter bank includes multiple sliding filters for processing frequency constraints.

[0163] Specifically, this application uses a sliding filter as the basic tool for speed planning. A sliding filter is a finite impulse response filter, whose time-domain characteristics are equivalent to integral averaging over a rectangular window of the input signal. The time constant is the core parameter of the sliding filter, determining the filter's window length and thus affecting the filter's response speed and frequency selectivity.

[0164] Please refer to Figure 3 , Figure 3 A schematic diagram of the framework structure of the three filter banks in this embodiment is shown. Figure 3 As shown, the first filter bank is used to process kinematic constraints. Its input signals are a step signal and kinematic constraint information. The step amplitude of the step signal represents the total length of the path to be planned. Each sliding filter in the first filter bank corresponds to a kinematic constraint of one order—for example, the first filter corresponds to velocity constraints, the second filter to acceleration constraints, the third filter to jerk constraints, and so on. The time constant of each filter represents the time required for the signal to transition from a certain kinematic state to a higher kinematic state. The time constants of each filter need to meet the time-optimal condition to ensure that the velocity-planned trajectory is completed in the shortest time while satisfying all kinematic constraints.

[0165] The second filter bank handles frequency constraints, with each sliding filter corresponding to a specific intrinsic mode frequency of the robot. Based on the frequency-domain notch characteristic of the sliding filter, when the filter's time constant is an integer multiple of the period of the intrinsic mode frequency, the filter's gain at that frequency is zero, thus accurately suppressing that frequency component. When the robot has multiple intrinsic mode frequencies, by setting multiple second filters corresponding to different frequencies, complete suppression of all intrinsic mode frequencies can be achieved.

[0166] The first and second filter banks are only used to calculate the time constant sequence at this stage, and they do not directly participate in the subsequent speed planning signal processing.

[0167] Step S203: Perform time optimization based on the first time constant sequence and the second time constant sequence to obtain the third time constant sequence of the third filter bank; the third filter bank includes multiple cascaded sliding filters.

[0168] Specifically, the core objective of time optimization is to embed the frequency constraints represented by the second filter bank into the time-optimal solution represented by the first filter bank without significantly increasing the total duration of the trajectory.

[0169] The basic logic of time optimization is as follows: For each second time constant in the second filter bank (representing an intrinsic mode frequency to be suppressed), a first time constant that best matches it is found in the time constant sequence of the first filter bank, based on this time constant. The matching is based on the periodic notch characteristic of the sliding filter—an integer multiple of a filter time constant can also effectively suppress the frequency. Therefore, by using an integer multiple of this second time constant as the time constant of the third filter bank to replace the original first time constant, kinematic constraints and frequency constraints can be satisfied simultaneously with almost no increase in the total duration. For time constants that cannot find a match, they are directly included in the time constant set of the third filter bank to ensure that all frequency constraints are fully addressed.

[0170] Through this "nearest substitution" matching strategy, each time constant in the final third time constant sequence can effectively suppress a certain intrinsic mode frequency while maintaining numerical closeness to the original kinematic optimal solution, thus ensuring the optimality of the total trajectory duration while fully handling all frequency constraints.

[0171] Step S204: The path length of the path to be planned is constructed as a step signal. The step signal is input into the third filter bank. The third filter bank is used to filter the step signal step by step according to the third time constant sequence to obtain the robot's speed planning information.

[0172] Specifically, the total length of the path to be planned is constructed as a step signal and input to the front end of the third filter bank. Please refer to [link / reference needed]. Figure 3 The third filter bank is a cascaded structure consisting of multiple sliding filters connected in series according to a third time constant sequence. In signal processing, the cascading of multiple filters is equivalent to multiple consecutive convolution operations. The signal flows through each stage of the filter in turn, and with each stage, the smoothness of the output signal increases by one order—the displacement curve becomes more continuous, and its higher-order derivatives such as velocity, acceleration, and jerk gradually become continuous without abrupt changes.

[0173] Since each time constant in the third time constant sequence inherits the kinematic constraint characteristics of the first filter bank (ensuring that velocity, acceleration, etc., do not exceed limits) and the frequency constraint characteristics of the second filter bank (forming notches at the natural mode frequencies), the displacement signal ultimately output by the third filter bank naturally satisfies the dual requirements of physical smoothness and resonant frequency suppression. In actual control, the control system can differentiate this displacement signal to obtain feedforward signals such as velocity and acceleration, and then send control commands such as position, velocity, and acceleration to the servo driver to drive the robot to move according to the planned trajectory.

[0174] Through the steps described above in this embodiment, the technical solution of this application achieves at least the following beneficial effects:

[0175] First, it achieves complete suppression of all intrinsic modal frequencies of the robot. By setting up a second filter bank, each second filter corresponds to one intrinsic modal frequency of the robot, and the corresponding time constant is incorporated into the time optimization process, ensuring that each intrinsic modal frequency is suppressed in the final velocity planning trajectory. Compared with existing technologies that only process a single mean frequency or a subset of frequencies, this embodiment can completely cover the robot's multi-order intrinsic modal frequencies, fundamentally avoiding end-effector vibration problems caused by the excitation of unprocessed frequency components, and significantly improving the smoothness of robot operation and machining accuracy.

[0176] Second, while fully addressing all frequency constraints, the time-optimal nature of velocity planning is ensured. Through the "nearest replacement" matching strategy in the time optimization algorithm—using the second time constant as a benchmark, finding the closest integer multiple of it in the first time constant sequence for replacement—each time constant in the third time constant sequence satisfies kinematic constraints while effectively suppressing intrinsic mode frequencies, and minimizing the increase in total duration compared to the original kinematically optimal solution. Compared to existing technologies that rigidly accumulate duration due to multiple frequency filters in series, this embodiment integrates frequency constraints into the time-optimal solution with extremely low time cost, balancing vibration suppression and operational efficiency.

[0177] Third, the collaborative architecture of the three filter groups enhances the flexibility and adaptability of velocity planning. The first filter group is responsible for extracting the time-optimal baseline under kinematic constraints, the second filter group is responsible for extracting frequency constraints, and the third filter group is responsible for executing the fused velocity planning. This "computation-execution" separation architecture means that when the robot's kinematic parameters or intrinsic modal frequencies change, only the time constant sequence of the corresponding filter group needs to be recalculated, without changing the overall framework of velocity planning, thus exhibiting good scalability and adaptability.

[0178] Fourth, a high-order smoothness of the velocity planning trajectory is achieved through a step-by-step filtering mechanism using cascaded sliding filters. With each sliding filter pass, the order of the trajectory's derivative increases in continuity, resulting in a smooth and continuous output displacement signal and its derivatives. This avoids the shocks and vibrations caused by sudden acceleration changes in traditional trapezoidal programming, while also circumventing the complex trigonometric function calculations required in S-shaped programming. This ensures trajectory smoothness while reducing computational complexity.

[0179] In some embodiments, determining the first time constant sequence of the first filter bank based on kinematic constraint information includes: determining the first time constant of each first filter in the first filter bank based on kinematic constraint information and time-optimal conditions; the kinematic constraint information includes kinematic constraints of kinematic parameters of each order; the first time constant is:

[0180] ;

[0181] in, It is the first i The time constant of the first filter represents the time constant of the first filter. The first-order kinematic parameters satisfy the first-order kinematic parameters. Under the condition of first-order kinematic constraints, to the second The shortest time required for the transition of kinematic parameters. Indicates the first The upper limit of the kinematic constraint of order. Indicates the first The upper limit of the kinematic constraint;

[0182] The optimal time condition is:

[0183] 1;

[0184] in, N This indicates the number of the first filters.

[0185] In this embodiment, the formula for calculating the first time constant represents the shortest duration required for a signal to transition from a certain order state to a higher order state under given kinematic constraints. The time-optimal condition ensures that the time constants of each filter stage satisfy the cumulative constraint relationship from back to front, minimizing the response time (i.e., total duration) of the entire filter bank to a step signal. If this condition is not met, it indicates a possible "mismatch" between the initially set kinematic constraints, requiring the time optimization process to adjust the time constants to meet the optimality requirements.

[0186] For example, suppose the path length is 10 (in meters), and the maximum speed is... =3, upper limit of acceleration =0.4, upper limit of accelerometer =0.4, upper limit of the derivative of jerk =5. (Using the formula) Calculated =10 / 3=3.333 (unit: seconds). =3 / 0.4=7.5 (unit, seconds) =0.4 / 0.4=1 (unit, seconds). =0.4 / 5=0.08 (unit, seconds), at this time, If the time-optimal conditions are not met, the time optimization process needs to be initiated for adjustment.

[0187] In some embodiments, determining the second time constant sequence of the second filter bank based on the inherent mode frequencies includes: calculating the second time constant of each second filter in the second filter bank based on the inherent mode frequencies.

[0188]

[0189] in, The robot's first j One inherent modal frequency, M This indicates the number of second filters.

[0190] In this embodiment, the formula for calculating the second time constant is derived from the amplitude-frequency response characteristics of the sliding filter. Setting the filter's time constant to the period corresponding to the intrinsic mode frequency enables the formation of a precise notch filter at the intrinsic mode frequency, effectively suppressing that frequency component. When the robot has multiple intrinsic mode frequencies, by setting multiple second filters corresponding to different frequencies, complete suppression of multiple frequencies can be achieved.

[0191] For example, if the robot's natural modal frequency is 33Hz, that is... = ≈207.35 rad / s, then the corresponding second time constant is ≈0.0303 seconds. When the filter processes the signal, the gain of the 33Hz frequency component is zero, and the vibrational energy at this frequency is completely blocked.

[0192] In some embodiments, the first time constant sequence is represented as N The second time constant sequence is represented as M Time optimization is performed based on the first and second time constant sequences, including L rounds of optimization. Each round of optimization includes:

[0193] against Each second time constant in Iterate through each first time constant in T Calculate the scaling factor This yields a set of candidate scaling factors. ;

[0194] From the set of candidate scaling factors Select , so that:

[0195] ;

[0196] Will and As a matching pair, Included and delete from T ;

[0197] After L rounds of optimization, The remaining elements and Unmatched elements are included The third time constant sequence is obtained.

[0198] In this embodiment, the core idea of ​​the time optimization algorithm is to utilize the frequency domain characteristic of a sliding filter where "integer multiples of the period are still notch points." Specifically, if the time constant of a sliding filter is... Then the sliding filter at frequency A notch is formed at the location; simultaneously, the time constant is... Integer multiples ( , The sliding filter is also in The frequency exhibits notch filtering capability. Therefore, multiplying the frequency time constant by a positive integer still effectively suppresses that frequency. Utilizing this property, the time optimization method searches for the numerically closest value in the first time constant sequence. of and use As Substitute values ​​included Since the values ​​of the two are close, the total duration remains almost unchanged after the replacement. For time constants that cannot be found to match, they are directly incorporated into the third time constant sequence, ensuring the integrity of the frequency constraints.

[0199] For example, continuing from the previous example, the kinematic time constant is , =0.0303. In the first round of optimization, traversal is based on 0.0303. Calculate 3.333 The product is 110 × 0.0303 = 3.333, with an error of 0; Calculate for 7.5. The product is 7.4841, with an error of 0.0159; Calculate for 1 The product is 0.9999, with an error of 0.0001; calculate for 0.08. The product is 0.0606, and the error is 0.0194. The match with the smallest error is 3.333, so 3.333 is replaced with 110 × 0.0303 = 3.333 and incorporated into the third time constant sequence. Delete 3.333. Proceed to the next round of optimization. Continue matching based on the next value in the second time constant sequence. After the loop ends, Unmatched residual elements and All tail elements that did not participate in the matching were included. .

[0200] In some embodiments, the transfer functions of the sliding filters at each stage in the third filter bank are:

[0201] ;

[0202] in, Indicates the third filter bank k The transfer function of a stage-sliding filter. Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0203] In this embodiment, the transfer function is a mathematical tool used in control system analysis to describe the input-output relationship of a system.

[0204] For example, for a time constant of A sliding filter whose impulse response is width ,high A rectangular pulse. When a step signal is input, the output signal rises linearly from 0, and... The input amplitude is reached at each step, forming a ramp. When multiple sliding filters are connected in series, the smoothness of the output increases by one order with each stage.

[0205] In some embodiments, the amplitude-frequency response function of each stage of the sliding filter in the third filter bank for:

[0206] ;

[0207] in, Indicates the cutoff frequency. , Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0208] like Figure 4 As shown, the amplitude-frequency response function describes the gain or attenuation of the filter for input signals of different frequencies. The amplitude-frequency response function forms a notch at the cutoff frequency, meaning that the sliding filter can form a notch at its fundamental frequency and all its integer multiples (harmonics). This property is the mathematical basis for the use of integer multiples of the frequency-time constant for rounding matching in this application—integer multiples of the time constant correspond to harmonic notch points of the same natural frequency, thus effectively suppressing that natural mode frequency.

[0209] In some embodiments, a step signal is input to a third filter bank, and the step signal is filtered stepwise according to a third time constant sequence using the third filter bank to obtain the robot's velocity planning information, including:

[0210] Based on the total length of the path to be planned h Constructing a step signal ;

[0211] The step signal is fed into the third filter group;

[0212] In the third filter bank, each sliding filter performs a moving average filtering process on the input signal according to the time constant corresponding to the third time constant sequence. The displacement signal output by the last sliding filter is used as the robot's velocity planning information. The input of the next sliding filter is the output of the previous sliding filter.

[0213] For example, the first time constant of the step signal input is The third filter outputs the first displacement signal. The characteristics of this signal are: speed It is a constant value, but the acceleration There is a step jump. The first displacement signal... Input the second time constant as The third filter outputs the second displacement signal. The characteristics of this signal are: acceleration It becomes smooth, but accelerates. A step change still exists. The second displacement signal... Input the third time constant as The third filter outputs the third displacement signal. The characteristics of this signal are: jerk. It becomes smooth, but the derivative of the jerk is increased. A step jump still exists. Similarly, the final output displacement signal of the third filter bank... It is a smooth position trajectory curve that meets all kinematic limits (velocity and acceleration do not exceed limits) and does not contain any first-order intrinsic mode frequency components of the robot.

[0214] Please refer to Figure 5 and Figure 6 , Figure 5 The kinematic curves before employing the robot velocity planning method described in this embodiment are shown. Figure 6 The kinematic curves after employing the robot velocity planning method described in this embodiment are shown. Figure 5 and Figure 6 As can be seen, the total duration was significantly shortened after optimization, verifying the effectiveness of the time optimization.

[0215] This embodiment also provides a readable storage medium, which includes a stored program, wherein the program controls the device where the readable storage medium is located to execute any of the robot speed planning methods described above during runtime.

[0216] Specifically, the robot speed planning methods mentioned above include:

[0217] Step S201: Obtain the kinematic constraint information of the path to be planned and the robot's natural modal frequencies.

[0218] Specifically, the kinematic constraints of the planned path refer to the various physical limitations that the robot must satisfy when executing the path. The robot's motion is described by kinematic parameters of multiple orders, such as displacement, velocity, acceleration, jerk, and jerk derivative. Each order of parameter has its physical upper limit; for example, the upper limit of velocity is determined by the rated speed of the motor, the upper limit of acceleration is determined by the maximum output torque and load inertia of the motor, and the upper limit of jerk is determined by the shock resistance of the mechanical structure. These constraints are usually determined during the robot system design phase and stored in the robot's control system parameters. Natural modal frequencies are inherent properties of the robot's mechanical structure and can be obtained through finite element analysis or measured through frequency sweep experiments. A robot is a multi-degree-of-freedom elastic system with multiple natural modal frequencies. The existence of these frequencies means that if the velocity planning includes frequency components similar to these frequencies, resonance may occur, affecting the accuracy and stability of the robot's operation.

[0219] Step S202: Determine the first time constant sequence of the first filter bank based on the kinematic constraint information. The first filter bank includes multiple sliding filters for processing kinematic constraints. Determine the second time constant sequence of the second filter bank based on the natural mode frequencies. The second filter bank includes multiple sliding filters for processing frequency constraints.

[0220] Specifically, this application uses a sliding filter as the basic tool for speed planning. A sliding filter is a finite impulse response filter, whose time-domain characteristics are equivalent to integral averaging over a rectangular window of the input signal. The time constant is the core parameter of the sliding filter, determining the filter's window length and thus affecting the filter's response speed and frequency selectivity.

[0221] Please refer to Figure 3 , Figure 3 A schematic diagram of the framework structure of the three filter banks in this embodiment is shown. Figure 3 As shown, the first filter bank is used to process kinematic constraints. Its input signals are a step signal and kinematic constraint information. The step amplitude of the step signal represents the total length of the path to be planned. Each sliding filter in the first filter bank corresponds to a kinematic constraint of one order—for example, the first filter corresponds to velocity constraints, the second filter to acceleration constraints, the third filter to jerk constraints, and so on. The time constant of each filter represents the time required for the signal to transition from a certain kinematic state to a higher kinematic state. The time constants of each filter need to meet the time-optimal condition to ensure that the velocity-planned trajectory is completed in the shortest time while satisfying all kinematic constraints.

[0222] The second filter bank handles frequency constraints, with each sliding filter corresponding to a specific intrinsic mode frequency of the robot. Based on the frequency-domain notch characteristic of the sliding filter, when the filter's time constant is an integer multiple of the period of the intrinsic mode frequency, the filter's gain at that frequency is zero, thus accurately suppressing that frequency component. When the robot has multiple intrinsic mode frequencies, by setting multiple second filters corresponding to different frequencies, complete suppression of all intrinsic mode frequencies can be achieved.

[0223] The first and second filter banks are only used to calculate the time constant sequence at this stage, and they do not directly participate in the subsequent speed planning signal processing.

[0224] Step S203: Perform time optimization based on the first time constant sequence and the second time constant sequence to obtain the third time constant sequence of the third filter bank; the third filter bank includes multiple cascaded sliding filters.

[0225] Specifically, the core objective of time optimization is to embed the frequency constraints represented by the second filter bank into the time-optimal solution represented by the first filter bank without significantly increasing the total duration of the trajectory.

[0226] The basic logic of time optimization is as follows: For each second time constant in the second filter bank (representing an intrinsic mode frequency to be suppressed), a first time constant that best matches it is found in the time constant sequence of the first filter bank, based on this time constant. The matching is based on the periodic notch characteristic of the sliding filter—an integer multiple of a filter time constant can also effectively suppress the frequency. Therefore, by using an integer multiple of this second time constant as the time constant of the third filter bank to replace the original first time constant, kinematic constraints and frequency constraints can be satisfied simultaneously with almost no increase in the total duration. For time constants that cannot find a match, they are directly included in the time constant set of the third filter bank to ensure that all frequency constraints are fully addressed.

[0227] Through this "nearest substitution" matching strategy, each time constant in the final third time constant sequence can effectively suppress a certain intrinsic mode frequency while maintaining numerical closeness to the original kinematic optimal solution, thus ensuring the optimality of the total trajectory duration while fully handling all frequency constraints.

[0228] Step S204: The path length of the path to be planned is constructed as a step signal. The step signal is input into the third filter bank. The third filter bank is used to filter the step signal step by step according to the third time constant sequence to obtain the robot's speed planning information.

[0229] Specifically, the total length of the path to be planned is constructed as a step signal and input to the front end of the third filter bank. Please refer to [link / reference needed]. Figure 3 The third filter bank is a cascaded structure consisting of multiple sliding filters connected in series according to a third time constant sequence. In signal processing, the cascading of multiple filters is equivalent to multiple consecutive convolution operations. The signal flows through each stage of the filter in turn, and with each stage, the smoothness of the output signal increases by one order—the displacement curve becomes more continuous, and its higher-order derivatives such as velocity, acceleration, and jerk gradually become continuous without abrupt changes.

[0230] Since each time constant in the third time constant sequence inherits the kinematic constraint characteristics of the first filter bank (ensuring that velocity, acceleration, etc., do not exceed limits) and the frequency constraint characteristics of the second filter bank (forming notches at the natural mode frequencies), the displacement signal ultimately output by the third filter bank naturally satisfies the dual requirements of physical smoothness and resonant frequency suppression. In actual control, the control system can differentiate this displacement signal to obtain feedforward signals such as velocity and acceleration, and then send control commands such as position, velocity, and acceleration to the servo driver to drive the robot to move according to the planned trajectory.

[0231] Through the steps described above in this embodiment, the technical solution of this application achieves at least the following beneficial effects:

[0232] First, it achieves complete suppression of all intrinsic modal frequencies of the robot. By setting up a second filter bank, each second filter corresponds to one intrinsic modal frequency of the robot, and the corresponding time constant is incorporated into the time optimization process, ensuring that each intrinsic modal frequency is suppressed in the final velocity planning trajectory. Compared with existing technologies that only process a single mean frequency or a subset of frequencies, this embodiment can completely cover the robot's multi-order intrinsic modal frequencies, fundamentally avoiding end-effector vibration problems caused by the excitation of unprocessed frequency components, and significantly improving the smoothness of robot operation and machining accuracy.

[0233] Second, while fully addressing all frequency constraints, the time-optimal nature of velocity planning is ensured. Through the "nearest replacement" matching strategy in the time optimization algorithm—using the second time constant as a benchmark, finding the closest integer multiple of it in the first time constant sequence for replacement—each time constant in the third time constant sequence satisfies kinematic constraints while effectively suppressing intrinsic mode frequencies, and minimizing the increase in total duration compared to the original kinematically optimal solution. Compared to existing technologies that rigidly accumulate duration due to multiple frequency filters in series, this embodiment integrates frequency constraints into the time-optimal solution with extremely low time cost, balancing vibration suppression and operational efficiency.

[0234] Third, the collaborative architecture of the three filter groups enhances the flexibility and adaptability of velocity planning. The first filter group is responsible for extracting the time-optimal baseline under kinematic constraints, the second filter group is responsible for extracting frequency constraints, and the third filter group is responsible for executing the fused velocity planning. This "computation-execution" separation architecture means that when the robot's kinematic parameters or intrinsic modal frequencies change, only the time constant sequence of the corresponding filter group needs to be recalculated, without changing the overall framework of velocity planning, thus exhibiting good scalability and adaptability.

[0235] Fourth, a high-order smoothness of the velocity planning trajectory is achieved through a step-by-step filtering mechanism using cascaded sliding filters. With each sliding filter pass, the order of the trajectory's derivative increases in continuity, resulting in a smooth and continuous output displacement signal and its derivatives. This avoids the shocks and vibrations caused by sudden acceleration changes in traditional trapezoidal programming, while also circumventing the complex trigonometric function calculations required in S-shaped programming. This ensures trajectory smoothness while reducing computational complexity.

[0236] In some embodiments, determining the first time constant sequence of the first filter bank based on kinematic constraint information includes: determining the first time constant of each first filter in the first filter bank based on kinematic constraint information and time-optimal conditions; the kinematic constraint information includes kinematic constraints of kinematic parameters of each order; the first time constant is:

[0237] ;

[0238] in, It is the first i The time constant of the first filter represents the time constant of the first filter. The first-order kinematic parameters satisfy the first-order kinematic parameters. Under the condition of first-order kinematic constraints, to the second The shortest time required for the transition of kinematic parameters. Indicates the first The upper limit of the kinematic constraint of order. Indicates the first The upper limit of the kinematic constraint;

[0239] The optimal time condition is:

[0240] 1;

[0241] in, N This indicates the number of the first filters.

[0242] In this embodiment, the formula for calculating the first time constant represents the shortest duration required for a signal to transition from a certain order state to a higher order state under given kinematic constraints. The time-optimal condition ensures that the time constants of each filter stage satisfy the cumulative constraint relationship from back to front, minimizing the response time (i.e., total duration) of the entire filter bank to a step signal. If this condition is not met, it indicates a possible "mismatch" between the initially set kinematic constraints, requiring the time optimization process to adjust the time constants to meet the optimality requirements.

[0243] For example, suppose the path length is 10 (in meters), and the maximum speed is... =3, upper limit of acceleration =0.4, upper limit of accelerometer =0.4, upper limit of the derivative of jerk =5. (Using the formula) Calculated =10 / 3=3.333 (unit: seconds). =3 / 0.4=7.5 (unit, seconds) =0.4 / 0.4=1 (unit, seconds). =0.4 / 5=0.08 (unit, seconds), at this time, If the time-optimal conditions are not met, the time optimization process needs to be initiated for adjustment.

[0244] In some embodiments, determining the second time constant sequence of the second filter bank based on the inherent mode frequencies includes: calculating the second time constant of each second filter in the second filter bank based on the inherent mode frequencies.

[0245]

[0246] in, The robot's first j One inherent modal frequency, M This indicates the number of second filters.

[0247] In this embodiment, the formula for calculating the second time constant is derived from the amplitude-frequency response characteristics of the sliding filter. Setting the filter's time constant to the period corresponding to the intrinsic mode frequency enables the formation of a precise notch filter at the intrinsic mode frequency, effectively suppressing that frequency component. When the robot has multiple intrinsic mode frequencies, by setting multiple second filters corresponding to different frequencies, complete suppression of multiple frequencies can be achieved.

[0248] For example, if the robot's natural modal frequency is 33Hz, that is... = ≈207.35 rad / s, then the corresponding second time constant is ≈0.0303 seconds. When the filter processes the signal, the gain of the 33Hz frequency component is zero, and the vibrational energy at this frequency is completely blocked.

[0249] In some embodiments, the first time constant sequence is represented as N The second time constant sequence is represented as M Time optimization is performed based on the first and second time constant sequences, including L rounds of optimization. Each round of optimization includes:

[0250] against Each second time constant in Iterate through each first time constant in T Calculate the scaling factor This yields a set of candidate scaling factors. ;

[0251] From the set of candidate scaling factors Select , so that:

[0252] ;

[0253] Will and As a matching pair, Included and delete from T ;

[0254] After L rounds of optimization, The remaining elements and Unmatched elements are included The third time constant sequence is obtained.

[0255] In this embodiment, the core idea of ​​the time optimization algorithm is to utilize the frequency domain characteristic of a sliding filter where "integer multiples of the period are still notch points." Specifically, if the time constant of a sliding filter is... Then the sliding filter at frequency A notch is formed at the location; simultaneously, the time constant is... Integer multiples ( , The sliding filter is also in The frequency exhibits notch filtering capability. Therefore, multiplying the frequency time constant by a positive integer still effectively suppresses that frequency. Utilizing this property, the time optimization method searches for the numerically closest value in the first time constant sequence. of and use As Substitute values ​​included Since the values ​​of the two are close, the total duration remains almost unchanged after the replacement. For time constants that cannot be found to match, they are directly incorporated into the third time constant sequence, ensuring the integrity of the frequency constraints.

[0256] For example, continuing from the previous example, the kinematic time constant is , =0.0303. In the first round of optimization, traversal is based on 0.0303. Calculate 3.333 The product is 110 × 0.0303 = 3.333, with an error of 0; Calculate for 7.5. The product is 7.4841, with an error of 0.0159; Calculate for 1 The product is 0.9999, with an error of 0.0001; calculate for 0.08. The product is 0.0606, and the error is 0.0194. The match with the smallest error is 3.333, so 3.333 is replaced with 110 × 0.0303 = 3.333 and incorporated into the third time constant sequence. Delete 3.333. Proceed to the next round of optimization. Continue matching based on the next value in the second time constant sequence. After the loop ends, Unmatched residual elements and All tail elements that did not participate in the matching were included. .

[0257] In some embodiments, the transfer functions of the sliding filters at each stage in the third filter bank are:

[0258] ;

[0259] in, Indicates the third filter bank k The transfer function of a stage-sliding filter. Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0260] In this embodiment, the transfer function is a mathematical tool used in control system analysis to describe the input-output relationship of a system.

[0261] For example, for a time constant of A sliding filter whose impulse response is width ,high A rectangular pulse. When a step signal is input, the output signal rises linearly from 0, and... The input amplitude is reached at each step, forming a ramp. When multiple sliding filters are connected in series, the smoothness of the output increases by one order with each stage.

[0262] In some embodiments, the amplitude-frequency response function of each stage of the sliding filter in the third filter bank for:

[0263] ;

[0264] in, Indicates the cutoff frequency. , Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

[0265] like Figure 4 As shown, the amplitude-frequency response function describes the gain or attenuation of the filter for input signals of different frequencies. The amplitude-frequency response function forms a notch at the cutoff frequency, meaning that the sliding filter can form a notch at its fundamental frequency and all its integer multiples (harmonics). This property is the mathematical basis for the use of integer multiples of the frequency-time constant for rounding matching in this application—integer multiples of the time constant correspond to harmonic notch points of the same natural frequency, thus effectively suppressing that natural mode frequency.

[0266] In some embodiments, a step signal is input to a third filter bank, and the step signal is filtered stepwise according to a third time constant sequence using the third filter bank to obtain the robot's velocity planning information, including:

[0267] Based on the total length of the path to be planned h Constructing a step signal ;

[0268] The step signal is fed into the third filter group;

[0269] In the third filter bank, each sliding filter performs a moving average filtering process on the input signal according to the time constant corresponding to the third time constant sequence. The displacement signal output by the last sliding filter is used as the robot's velocity planning information. The input of the next sliding filter is the output of the previous sliding filter.

[0270] For example, the first time constant of the step signal input is The third filter outputs the first displacement signal. The characteristics of this signal are: speed It is a constant value, but the acceleration There is a step jump. The first displacement signal... Input the second time constant as The third filter outputs the second displacement signal. The characteristics of this signal are: acceleration It becomes smooth, but accelerates. A step change still exists. The second displacement signal... Input the third time constant as The third filter outputs the third displacement signal. The characteristics of this signal are: jerk. It becomes smooth, but the derivative of the jerk is increased. A step jump still exists. Similarly, the final output displacement signal of the third filter bank... It is a smooth position trajectory curve that meets all kinematic limits (velocity and acceleration do not exceed limits) and does not contain any first-order intrinsic mode frequency components of the robot.

[0271] Please refer to Figure 5 and Figure 6 , Figure 5 The kinematic curves before employing the robot velocity planning method described in this embodiment are shown. Figure 6 The kinematic curves after employing the robot velocity planning method described in this embodiment are shown. Figure 5 and Figure 6 As can be seen, the total duration was significantly shortened after optimization, verifying the effectiveness of the time optimization.

[0272] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. They can be implemented using computer-executable program code, and thus can be stored in a storage device for execution by a computing device. In some cases, the steps shown or described can be performed in a different order than those described herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0273] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0274] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0275] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0276] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0277] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0278] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0279] Computer-readable media include both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0280] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0281] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0282] As can be seen from the above description, the embodiments of this application achieve the following technical effects:

[0283] First, it achieves complete suppression of all intrinsic modal frequencies of the robot. By setting up a second filter bank, each second filter corresponds to one intrinsic modal frequency of the robot, and the corresponding time constant is incorporated into the time optimization process, ensuring that each intrinsic modal frequency is suppressed in the final velocity planning trajectory. Compared with existing technologies that only process a single mean frequency or a subset of frequencies, this embodiment can completely cover the robot's multi-order intrinsic modal frequencies, fundamentally avoiding end-effector vibration problems caused by the excitation of unprocessed frequency components, and significantly improving the smoothness of robot operation and machining accuracy.

[0284] Second, while fully addressing all frequency constraints, the time-optimal nature of velocity planning is ensured. Through the "nearest replacement" matching strategy in the time optimization algorithm—using the second time constant as a benchmark, finding the closest integer multiple of it in the first time constant sequence for replacement—each time constant in the third time constant sequence satisfies kinematic constraints while effectively suppressing intrinsic mode frequencies, and minimizing the increase in total duration compared to the original kinematically optimal solution. Compared to existing technologies that rigidly accumulate duration due to multiple frequency filters in series, this embodiment integrates frequency constraints into the time-optimal solution with extremely low time cost, balancing vibration suppression and operational efficiency.

[0285] Third, the collaborative architecture of the three filter groups enhances the flexibility and adaptability of velocity planning. The first filter group is responsible for extracting the time-optimal baseline under kinematic constraints, the second filter group is responsible for extracting frequency constraints, and the third filter group is responsible for executing the fused velocity planning. This "computation-execution" separation architecture means that when the robot's kinematic parameters or intrinsic modal frequencies change, only the time constant sequence of the corresponding filter group needs to be recalculated, without changing the overall framework of velocity planning, thus exhibiting good scalability and adaptability.

[0286] Fourth, a high-order smoothness of the velocity planning trajectory is achieved through a step-by-step filtering mechanism using cascaded sliding filters. With each sliding filter pass, the order of the trajectory's derivative increases in continuity, resulting in a smooth and continuous output displacement signal and its derivatives. This avoids the shocks and vibrations caused by sudden acceleration changes in traditional trapezoidal programming, while also circumventing the complex trigonometric function calculations required in S-shaped programming. This ensures trajectory smoothness while reducing computational complexity.

[0287] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A robot speed planning method, characterized in that, include: Obtain the kinematic constraints of the path to be planned and the robot's intrinsic modal frequencies; A first time constant sequence of the first filter bank is determined based on the kinematic constraint information. The first filter bank includes a plurality of sliding filters for processing kinematic constraints. The second time constant sequence of the second filter bank is determined based on the inherent mode frequency, and the second filter bank includes a plurality of sliding filters for processing frequency constraints; Time optimization is performed based on the first time constant sequence and the second time constant sequence to obtain the third time constant sequence of the third filter bank; the third filter bank includes multiple cascaded sliding filters; The path length of the path to be planned is constructed as a step signal, and the step signal is input into the third filter group. The third filter group is used to filter the step signal step by step according to the third time constant sequence to obtain the robot's speed planning information.

2. The method according to claim 1, characterized in that, Determining the first time constant sequence of the first filter bank based on the kinematic constraint information includes: The first time constant of each first filter in the first filter bank is determined based on the kinematic constraint information and the time-optimal condition; the kinematic constraint information includes the kinematic constraints of kinematic parameters of each order. The first time constant is: ； in, It is the first i The time constant of the first filter represents the time constant of the first filter. The first-order kinematic parameters satisfy the first-order kinematic parameters. Under the condition of first-order kinematic constraints, to the second The shortest time required for the transition of kinematic parameters. Indicates the first The upper limit of the kinematic constraint of order. Indicates the first The upper limit of the kinematic constraint; The optimal time condition is: 1； in, N This indicates the number of the first filters.

3. The method according to claim 2, characterized in that, Determining the second time constant sequence of the second filter bank based on the inherent mode frequencies includes: Calculate the second time constant of each second filter in the second filter bank based on the inherent mode frequency: in, The robot's first j One inherent modal frequency, M This indicates the number of the second filter.

4. The method according to claim 3, characterized in that, The first time constant sequence is represented as N The second time constant sequence is represented as M Time optimization is performed based on the first time constant sequence and the second time constant sequence, including L rounds of optimization. Each round of the optimization process includes: against Each second time constant in Iterate through each first time constant in T Calculate the scaling factor This yields a set of candidate scaling factors. ; From the set of candidate scaling factors Select , so that: ； Will and As a matching pair, Included and delete from T ; After performing the optimization process described in round L, The remaining elements and Unmatched elements are included The third time constant sequence is obtained.

5. The method according to claim 1, characterized in that, The transfer functions of each sliding filter in the third filter bank are: ； in, Indicates the third filter bank k The transfer function of a stage-sliding filter. Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

6. The method according to claim 1, characterized in that, The amplitude-frequency response function of each sliding filter in the third filter bank for: ； in, Indicates the cutoff frequency. , Indicates the third filter bank k The time constant of the stage sliding filter This represents the third time constant sequence.

7. The method according to claim 1, characterized in that, The step signal is input to the third filter bank, and the third filter bank performs step-by-step filtering on the step signal according to the third time constant sequence to obtain the robot's speed planning information, including: Based on the total length of the path to be planned h Constructing a step signal ; The step signal is input into the third filter group; In the third filter bank, each sliding filter performs a moving average filtering process on the input signal according to the time constant corresponding to the third time constant sequence, and uses the displacement signal output by the last sliding filter as the velocity planning information of the robot; wherein, the input of the next sliding filter is the output of the previous sliding filter.

8. A robot speed planning device, characterized in that, include: The data acquisition unit is used to acquire the kinematic constraint information of the path to be planned and the robot's natural modal frequencies; The first determining unit is configured to determine a first time constant sequence of a first filter bank based on the kinematic constraint information, and to determine a second time constant sequence of a second filter bank based on the inherent mode frequencies, wherein the first filter bank includes a plurality of sliding filters for processing kinematic constraints, and the second filter bank includes a plurality of sliding filters for processing frequency constraints. The second determining unit is used to perform time optimization based on the first time constant sequence and the second time constant sequence to obtain the third time constant sequence of the third filter group, wherein the third filter group includes multiple cascaded sliding filters; The speed planning unit is used to construct a step signal from the path length of the path to be planned, input the step signal into the third filter group, and use the third filter group to perform step filtering processing on the step signal according to the third time constant sequence to obtain the speed planning information of the robot.

9. A robot, characterized in that, The robot performs speed planning using the method described in any one of claims 1 to 7.

10. A readable storage medium, characterized in that, The readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 7.

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