A data-driven switching gain estimation technique for bipedal walking robots

Abstract

This application relates to a data-driven switching gain estimation technique for bipedal walking robots. The technique utilizes the behavioral theory of linear systems to construct a data interpretation system for unknown dynamic hybrid systems. Combined with data-based linear matrix inequalities, a global exponential stability criterion is established, ensuring the global exponential stability of the bipedal robot system under mild conditions. This allows the bipedal walking robot to operate normally without relying on a model. Furthermore, the data-driven hybrid estimation scheme proposed in this application eliminates the system model identification step, reducing resource consumption.

Description

Technical Field

[0001] This application relates to the field of robot control technology, and in particular to a data-driven switching gain estimation technique for a bipedal walking robot. Background Technology

[0002] With the deepening of control science, the innovation of sensor technology, and the rapid development of artificial intelligence and machine learning, robotic systems can now effectively cope with uncertainties and external disturbances during walking by leveraging advanced adaptive algorithms. Bipedal walking robots, as mechanical devices specifically designed for bipedal locomotion, are intended to integrate into human living spaces. These robots stand out for their unique ability to walk in unstructured and complex environments, demonstrating strong environmental adaptability and flexibility. Bipedal walking robots show broad application potential in several key areas, covering disaster relief, service industries, military security, and entertainment and education.

[0003] However, these application scenarios are often accompanied by complex and variable tasks and strong interference characteristics, which places higher demands on bipedal walking robots, including system stability, flexibility, and environmental adaptability. Therefore, ensuring that bipedal walking robots can stably perform their intended tasks under various extreme conditions has become the key to promoting their technological development and practical application. Summary of the Invention

[0004] Therefore, it is necessary to provide a data-driven switching gain estimation technology for bipedal walking robots to address the aforementioned technical problems, enabling bipedal robots to perform well in the face of diverse environments and task requirements.

[0005] Firstly, this application provides a data-driven switching gain estimation technique for bipedal walking robots. This technique includes:

[0006] A model-based state-space model of a bipedal robot system is constructed using a hybrid system framework, and an equivalent system model of the data-based bipedal robot system is constructed based on the state-space model; both the state-space model and the equivalent system model include unknown system matrices.

[0007] Construct prior knowledge of noise in a bipedal walking robot system;

[0008] Based on the equivalent system model and prior knowledge of noise, obtain the set of unknown system matrices; wherein, the expression of the set of unknown system matrices includes the first matrix stripped of the unknown system matrices;

[0009] The dual lemma is used to process the set of matrices of the unknown system to obtain a second matrix related to the first matrix;

[0010] A gain observer is constructed based on a state-space model, and the augmented system is obtained based on the gain observer and the equivalent system model.

[0011] Construct a model-based first stability criterion for bipedal robot systems based on augmented systems;

[0012] The S lemma is used to process the first stability criterion, and then substituted into the second matrix to obtain the data-based second stability criterion;

[0013] Gain estimates are obtained based on the second stability criterion.

[0014] In one embodiment, the state-space model is represented as:

[0015]

[0016] v = Cx,

[0017] Where, x + It is x + The time shift of (k) = x(k+1); The time derivative with respect to state x; x(t, k)∈R n Represent the state of the bipedal robot system; y(t, k)∈R s It is the output of the bipedal robot system; κ(t, k) ∈ [0, κ d Given the constant κ d ∈R ＞0 It represents the periodic switching conditions of the bipedal robot system; A, D, and C are all unknown system matrices.

[0018] In one embodiment, the equivalent system model is represented as:

[0019]

[0020] Y ★ =CX ★ +V ★ ,

[0021] in, and All are Hankel matrices representing data from bipedal robot systems.

[0022] In one embodiment, prior knowledge of noise is represented as:

[0023]

[0024] in, Λ ij Let i, j = 1, 2 be known matrices, and Λ ij satisfy: I is the identity matrix.

[0025] In one embodiment, the set of unknown system matrices is represented as:

[0026]

[0027] in, Δ is the first matrix.

[0028] In one embodiment, the set of unknown system matrices processed by the duality lemma is represented as:

[0029]

[0030] in, Θ is the second matrix.

[0031] In one embodiment, the gain observer is represented as:

[0032]

[0033] in, It is an estimate of x(t, k), L z ∈R n×s It is the gain matrix, where z represents the index of the gain observer;

[0034] The augmented system is represented as:

[0035]

[0036] Among them, error

[0037] In one embodiment, the first stability criterion is expressed as:

[0038]

[0039] P1≥(1-μ2) τ P2, P2≥(1-μ1) τ P1

[0040] Using the S-lemma to process the first stability criterion, we obtain the second stability criterion, which is expressed as:

[0041]

[0042] P1≥(1-μ2) τ P2, P2≥(1-μ1) τ P1

[0043] Among them, κ d >0, τ>0, γ, μ1, μ2, λ≥0, δ≥0, ρ>0, θ>0 are all unknown constants, R n×n matrix and R n×p Matrix F1 and F2 are both unknown matrices;

[0044] Solve the second stability criterion to obtain the unknown matrices P1, P2, F1, and F2;

[0045] The gain estimate is expressed as:

[0046] L z =P z -1 F z , z∈[1,2].

[0047] Secondly, this application also provides a data-driven switching gain estimation system for a bipedal walking robot. The system includes:

[0048] The model building module is used to construct a model-based state-space model of a bipedal robot system using a hybrid system framework, and to construct an equivalent system model of the data-based bipedal robot system based on the state-space model; wherein, both the state-space model and the equivalent system model include unknown system matrices;

[0049] The noise constraint module is used to construct prior knowledge of noise in the bipedal walking robot system;

[0050] The first calculation module is used to obtain the set of unknown system matrices based on the prior knowledge of the equivalent system model and noise; wherein the expression of the set of unknown system matrices includes the first matrix stripped of the unknown system matrices;

[0051] The second calculation module is used to process the set of unknown system matrices using the dual lemma to obtain a second matrix related to the first matrix;

[0052] The observer construction module is used to build a gain observer based on the state-space model, and obtain the augmented system based on the gain observer and the equivalent system model.

[0053] The stability design module is used to construct a model-based first stability criterion for the bipedal robot system based on the augmented system.

[0054] The third calculation module is used to process the first stability criterion using the S lemma and substitute it into the second matrix to obtain the second stability criterion based on the data.

[0055] The gain estimation module is used to obtain a gain estimate based on the second stability criterion.

[0056] Thirdly, this application also provides a bipedal walking robot. The bipedal walking robot includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the aforementioned data-driven switching gain estimation technique for a bipedal walking robot.

[0057] Fourthly, this application also provides a computer-readable storage medium. This computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the steps in the aforementioned data-driven switching gain estimation technique for a bipedal walking robot.

[0058] Fifthly, this application also provides a computer program product. The computer program product includes a computer program that, when executed by a processor, implements the steps in the aforementioned data-driven switching gain estimation technique for a bipedal walking robot.

[0059] The aforementioned data-driven switching gain estimation technique for bipedal walking robots models the bipedal robot system as an unknown hybrid system and then transforms it into a data-driven switching gain estimation method. This eliminates the need for a pre-defined physical model, making the data-driven approach highly effective for highly complex and nonlinear systems. Furthermore, the data-driven hybrid estimation scheme eliminates the system model identification step, reducing resource consumption. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating a data-driven switching gain estimation technique for a bipedal walking robot in one embodiment.

[0061] Figure 2 This is a schematic diagram of the switching gain observation of a bipedal robot system in one embodiment;

[0062] Figure 3 This is a data-driven schematic diagram of a bipedal robot system in one embodiment;

[0063] Figure 4 This is a block diagram of a data-driven switching gain estimation system for a bipedal walking robot in one embodiment. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0065] To facilitate understanding, the technical terms used in this invention will be explained. A hybrid system is a unique dynamic system that integrates continuous and discrete dynamic systems and addresses the interaction between them. This system model has demonstrated wide application value in various academic and industrial fields, such as robotics, industrial automation, flight control, power system management, traffic network optimization, and bioengineering. The concept of hybrid systems is particularly important in the operation of bipedal walking robots. The robot's walking process involves not only continuous limb movements but also a series of key discrete state transition events, especially at the moments when the feet contact and disengage from the ground. These state changes significantly influence the robot's dynamic behavior. The gait cycle of bipedal walking consists of multiple alternating continuous motion phases (such as single-leg support, double-leg support, and leg swing), while the transitions between these phases exhibit significant discreteness. It is precisely this interweaving of continuous motion and discrete events that makes hybrid systems an ideal framework for describing the dynamic behavior of bipedal robots. It allows researchers to finely control the robot's continuous motion trajectory while accurately capturing and processing key discrete state transition points within the same model, thus achieving a comprehensive characterization of the complex motion characteristics of bipedal walking robots. Therefore, hybrid systems theory occupies a central position in the modeling of bipedal walking robots, providing strong theoretical support for achieving efficient and stable walking control.

[0066] In the precision control system of bipedal walking robots, noise suppression and state observers are two indispensable elements, directly affecting the robot's stability, accuracy, and robustness in complex and changing environments. Noise, as a major form of external disturbance, poses a challenge to the robot's ability to maintain balance, plan gait, and perform precise movements. To address this challenge, bipedal robot systems rely on efficient observers to accurately estimate the system's internal state. As an observation tool, the core value of an observer lies in using noisy or erroneous sensor data, through complex dynamic models and feedback mechanisms, to indirectly deduce key state variables (such as precise center of mass position and joint angles) that are difficult to measure directly. This capability is particularly crucial for bipedal walking robots, as directly and comprehensively measuring all state variables in complex execution environments is both impractical and costly. Furthermore, observers also play a vital role in system fault diagnosis and response. They can quickly identify the source of a fault, quantify its severity, and provide maintenance personnel with immediate and accurate fault information, significantly shortening troubleshooting and repair time and ensuring the robot system quickly returns to stable operation. Therefore, by optimizing the design and application of the observer, the bipedal walking robot can exhibit superior control performance and adaptability when facing noise interference and complex environments.

[0067] In robot learning, particularly in the research of bipedal walking robots, two distinct strategic frameworks exist: model-driven and data-driven. Model-driven methods are rooted in a deep understanding of the system's physical mechanisms, using precise mathematical models to characterize the robot's dynamic changes during walking. This process emphasizes the rigor of theoretical derivation and system analysis. However, constructing comprehensive and accurate models is challenging when dealing with complex physical phenomena in real-world environments (such as variable friction, unpredictable collisions, and flexible contact). In contrast, data-driven methods exhibit unique advantages. They utilize advanced data science techniques such as machine learning and deep learning to directly extract patterns and laws of robot behavior from massive amounts of data, without requiring a pre-defined physical model. This characteristic makes data-driven methods highly effective for highly complex and nonlinear systems, especially when models are difficult to build precisely or involve significant uncertainties. Through continuous practice and feedback learning, data-driven models can autonomously optimize control strategies, enabling robots to adapt to diverse environments and task requirements. Given these advantages, data-driven methods have become a research hotspot in the field of robot learning and are widely applied in key tasks such as stability control and intelligent walking. It has not only advanced bipedal walking robot technology but also provided strong support for realizing more intelligent, flexible, and adaptable robotic systems. Therefore, data-driven methods are expected to play a more central and crucial role in future robotics research.

[0068] This application provides a data-driven switching gain estimation technique for bipedal walking robots, such as... Figure 1 As shown, it includes the following steps:

[0069] Step 101: Construct a model-based state space model of the bipedal robot system using a hybrid system framework, and construct an equivalent system model of the data-based bipedal robot system based on the state space model; wherein, both the state space model and the equivalent system model include an unknown system matrix.

[0070] The construction of a data-driven state-space model for a bipedal walking robot system describes an unknown hybrid system of the bipedal robot, specifically modeled as follows:

[0071]

[0072] y = Cx,

[0073] Where, x + It is x + (k) = x(k+1) time shift, where k is a positive integer; It is the time derivative with respect to state x, specifically expressed as: x(t, k)∈R n Represent the state of the bipedal robot system; y(t, k)∈Rs It is the output of the bipedal robot system; κ(t, k) ∈ [0, κ d Given the constant κ d ∈R ＞0 This is the periodic switching condition for a bipedal robot system; A∈R n×n D∈R n ×n and C∈R s×n Let A be the state matrix of the unknown system, D be the state matrix of the continuous-time dynamic system, and C be the output matrix of the system.

[0074] Based on the state-space model, a data-driven equivalent system model for the bipedal walking robot system is constructed, which takes the following form:

[0075]

[0076] Y ★ =CX ★ +V★

[0077] in, Where w and v are the process noise and measurement noise, respectively;

[0078]

[0079] and Let be the Hankel matrix representing the data of a bipedal robot system in the continuous time domain or the discrete time domain, where u represents the system output.

[0080] Step 102: Construct prior knowledge of noise in the bipedal walking robot system.

[0081]

[0082] in, Λ ij Let i, j = 1, 2 be known matrices, and Λ ij satisfy: Prior knowledge of noise constrains the maximum value of noise.

[0083] Step 103: Based on the prior knowledge of the equivalent system model and noise, obtain the set of unknown system matrices; wherein, the expression of the set of unknown system matrices includes the first matrix stripped of the unknown system matrices.

[0084] In this embodiment, a set of data-driven system matrices is designed for the bipedal robot system, and its form is as follows:

[0085]

[0086] in, Δ is the first matrix.

[0087] Step 104: Use the dual lemma to process the set of unknown system matrices and obtain the second matrix related to the first matrix.

[0088] In the duality lemma, if Δ is invertible, then the following sets hold:

[0089]

[0090] in, Θ is the second matrix.

[0091] Step 105: Construct a gain observer based on the state-space model, and obtain the augmented system based on the gain observer and the equivalent system model.

[0092] The data-driven gain observer in a bipedal walking robot system takes the following form:

[0093]

[0094] in, It is an estimate of x(t, k), L z ∈R n×s It is the gain matrix. If the error It converges to 0 for all (t, k) ∈ K. Figure 2 The hybrid switching gain observation framework is shown. Let the observer gain designed in region 1 be L1, and the observer gain designed in region 2 be L2, where y s Let ψ be the switching point between region 1 and region 2, and let ψ be the minimum dwell time.

[0095] A data-driven augmented system for a bipedal walking robot system is established based on a gain observer, in the following form:

[0096]

[0097] Step 106: Construct the first stability criterion for the bipedal robot system based on the model according to the augmented system.

[0098] The first stability criterion is the global exponential stability criterion.

[0099] Each solution of the hybrid system in step 101 is defined in the hybrid time domain as:

[0100] K: = {(t, k), t∈[t]} k , t k+1 ],k∈N},

[0101] Among them, t k :=kκ d and t k+1 :=(k+1)κ d Let ζ(t, k, x0) represent the jump period for action switching in the bipedal robot. It is well known that the system solution in step 101 is a locally absolutely continuous function of the mapping (t, k) ∈ K. Let ζ(t, k, x0) be the solution of the system of equations in step 101 for (t, k) ∈ K, where x0 is the initial condition.

[0102] For the state-space model in step 101, the definition of stability is as follows:

[0103] Closed set It is globally exponentially stable if there exist constants a, b > 0 and c such that

[0104] ||ζ(t0, k0, x0)|| H <a,

[0105] ||ζ(t, k, x0)|| H ≤b||ζ(t0, k0, x0)|| H e -c(t+k) ,

[0106] For any initial condition x0, initial time t0 = 0, k0 = 0 and (t, k) ∈ K hold true, then the bipedal robot system is stable.

[0107] Therefore, the first stability criterion based on the model is expressed using a linear matrix inequality as follows:

[0108] If a constant κ exists d >0, τ>0, γ, μ1, μ2, R n×n matrix R n×p Matrices F1 and F2, such that:

[0109]

[0110] P1≥(1-μ2) τ P2, P2≥(1-μ1) r P1 (6)

[0111] The bipedal robot system is stable if it holds true for all times (t, k) ∈ K.

[0112] In another embodiment, since the uncertainty term in conditions (1) and (2) of the first stability criterion is only the unknown system matrix A, a data set containing only A is required. As can be seen from steps 102 to 104, the unknown system matrix A is contained within the noisy data W. ★From this, it is not difficult to conclude that the noise data W ★ The following conditions must be met:

[0113]

[0114] in, Γ ij Let i, j = 1, 2 be known matrices, and Γ be a matrix. ij satisfy: and Using a technique similar to step 103, the noise data W is processed. ★ The unknown system matrix A in the image is stripped to obtain:

[0115]

[0116] in, In this embodiment, Ω is the first matrix. According to the duality lemma, this condition is equivalent to:

[0117]

[0118] in, In this embodiment, Y is the second matrix.

[0119] Step 107: Apply the S lemma to process the first stability criterion and substitute it into the second matrix to obtain the second stability criterion based on the data.

[0120] The S lemma is: Assume R (s+h)×(s+h) matrix and It is symmetric. If there exists R s×h Matrix N such that the Slater condition is:

[0121]

[0122] For all N∈R s×h S 22 ≤0, Q 22 ≤0 and If and only if the following constants exist: σ≥0 and ρ>0, then...

[0123]

[0124] This is true. Furthermore, the observable hypothesis is given as follows:

[0125] If the data (X, Y) ★ ) is observable if and only if Make

[0126]

[0127] By applying the S lemma to the first stability criterion, we can obtain the second stability criterion. Under the above assumptions, if there exist constants λ≥0, δ≥0, ρ>0, θ>0, and κ... d >0, τ>0, γ, μ1, μ2 and R n×n matrix and R n×p Matrices F1 and F2, such that

[0128]

[0129] P1≥(1-μ2) τ P2, P2≥(1-μ1) τ P1 (6)

[0130] If established, the bipedal robot system will be stable.

[0131] In this embodiment, the conditions (1) and (2) in step 106 with the unknown system matrix A are transformed into the conditions (1) and (2) in step 107 with only the second matrix Y, and the conditions (3) and (4) in step 106 with the unknown system matrices C and D are transformed into the conditions (1) and (2) in step 107 with only the second matrix Θ, thereby realizing the transformation of the bipedal robot system from the model-based first stability criterion to the data-based second stability criterion.

[0132] Step 108: Obtain the gain estimate based on the second stability criterion.

[0133] By solving the second stability criterion, the unknown matrices P1, P2, F1, and F2 are calculated and obtained. The data-based switching gain estimate is then:

[0134] L z =P z -1 F z , z∈[1,2].

[0135] To verify the stability of the data-driven switching gain estimation process in the bipedal walking robot system, assuming that the data-driven switching gain estimation given in step 107 is feasible, the verification steps are as follows:

[0136] S1. Using Lemma S, conditions (1) and (2) in step 107 are given:

[0137]

[0138] S2. By multiplying both sides of formula S1 by (I, A) and its transpose, we get:

[0139]

[0140] then,

[0141]

[0142] This means that conditions (1) and (2) in step 107 can ensure that conditions (1) and (2) in step 106 are true.

[0143] S3. Similarly, applying Lemma S to conditions (3) and (4) in 107, we can obtain:

[0144]

[0145] The data-based switching gain estimation L in step 108 z Substituting into the above equation, we get:

[0146]

[0147] S4, Definition The expression is:

[0148]

[0149] Through the Multiplying both sides of the equation by (I, D, C) and its transpose respectively, we get:

[0150]

[0151] It is not difficult to conclude that conditions (3) and (4) in step 106 are true.

[0152] like Figure 3 The diagram illustrates the data-driven principle of the bipedal robot system in this application. In the diagram, sensors collect input and output state data of the bipedal robot system and transmit them to the unknown hybrid system. The sensors also collect noise data. A data gain observer estimates the switching gain based on the data collected by the sensors using the switching gain estimation technique proposed in this invention. The data gain observer outputs the switching gain estimate and transmits it to the actuator of the bipedal robot system for execution. The execution result is then fed back to the observer. The state changes of the bipedal robot caused by the actuator's execution are also reflected in the unknown hybrid system and the noise data.

[0153] This invention proposes a data-driven estimation technique for bipedal walking robots with periodic jumps and unknown hybrid systems. By designing a state observer and establishing a global exponential stability criterion using linear matrix inequalities, the bipedal walking robot system is kept in a relatively stable state, ensuring that the system can perform its tasks normally without relying on a model.

[0154] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0155] Based on the same inventive concept, this application also provides a bipedal walking robot data-driven switching gain estimation system for implementing the aforementioned data-driven switching gain estimation technique for bipedal walking robots. The solution provided by this system is similar to the implementation described in the above-described technology. Therefore, the specific limitations of one or more embodiments of the bipedal walking robot data-driven switching gain estimation system provided below can be found in the above-described limitations of the data-driven switching gain estimation technique for bipedal walking robots, and will not be repeated here.

[0156] In one embodiment, such as Figure 4 As shown, a data-driven switching gain estimation system for a bipedal walking robot is provided, comprising:

[0157] The model building module 401 is used to construct a state space model of a model-based bipedal robot system using a hybrid system framework, and to construct an equivalent system model of a data-based bipedal robot system based on the state space model; wherein, both the state space model and the equivalent system model include an unknown system matrix;

[0158] Noise constraint module 402 is used to construct prior knowledge of noise in the bipedal walking robot system;

[0159] The first calculation module 403 is used to obtain a set of unknown system matrices based on the prior knowledge of the equivalent system model and noise; wherein, the expression of the set of unknown system matrices includes a first matrix stripped of the unknown system matrices;

[0160] The second calculation module 404 is used to process the set of unknown system matrices using the dual lemma to obtain a second matrix related to the first matrix;

[0161] The observer construction module 405 is used to construct a gain observer based on the state-space model and obtain the augmented system based on the gain observer and the equivalent system model.

[0162] Stability design module 406 is used to construct a model-based first stability criterion for the bipedal robot system based on the augmented system.

[0163] The third calculation module 407 is used to process the first stability criterion using the S lemma and substitute it into the second matrix to obtain the second stability criterion based on the data.

[0164] Gain estimation module 408 is used to obtain gain estimation based on the second stability criterion.

[0165] Each module in the aforementioned data-driven switching gain estimation system for bipedal walking robots can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in the processor of the bipedal walking robot in hardware form or independent of it, or they can be stored in the memory of the bipedal walking robot in software form, so that the processor can call and execute the corresponding operations of each module.

[0166] In one embodiment, a bipedal walking robot is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in all the above-described technical embodiments.

[0167] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of all the above-described technical embodiments.

[0168] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps of all the above-described technical embodiments.

[0169] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data shall comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0170] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0171] 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.

[0172] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A data-driven switching gain estimation technique for a bipedal walking robot, characterized in that, The technology includes: A model-based state-space model of a bipedal robot system is constructed using a hybrid system framework, and an equivalent system model of the bipedal robot system based on data is constructed based on the state-space model; wherein, both the state-space model and the equivalent system model include an unknown system matrix; Construct prior knowledge of noise in the bipedal walking robot system; Based on the equivalent system model and the prior knowledge of the noise, a set of unknown system matrices is obtained; wherein, the expression of the set of unknown system matrices includes a first matrix stripped of the unknown system matrices; The set of matrices of the unknown system is processed using the duality lemma to obtain a second matrix related to the first matrix; A gain observer is constructed based on the state-space model, and an augmented system is obtained based on the gain observer and the equivalent system model. Based on the augmented system, a model-based first stability criterion is constructed for the bipedal robot system. The first stability criterion is processed using the S lemma, and then substituted into the second matrix to obtain the second stability criterion based on the data. The gain estimate is obtained based on the second stability criterion.

2. The technology according to claim 1, characterized in that, The state-space model is represented as follows: Where, x + It is x + The time shift of (k) = x(k+1); The time derivative with respect to state x; x(t,k)∈R n Represents the state of the bipedal robot system; y(t,k)∈R s It is the output of the bipedal robot system; κ(t,k)∈[0,κ d Given the constant κ d ∈R ＞0 is the periodic switching condition of the bipedal robot system; A, D, and C are all the unknown system matrices.

3. The technology according to claim 2, characterized in that, The equivalent system model is represented as follows: Y ★ =CX ★ +V ★ , in, and All of these are Hankel matrices representing the data of the bipedal robot system.

4. The technology according to claim 3, characterized in that, The prior knowledge of the noise is represented as follows: in, Λ ij ,i,j=1,2 are known matrices, Λ ij satisfy:

5. The technology according to claim 4, characterized in that, The set of unknown system matrices is represented as follows: in, Δ is the first matrix.

6. The technology according to claim 5, characterized in that, The set of matrices of the unknown system after processing with the duality lemma is represented as: in, Θ is the second matrix.

7. The technology according to claim 6, characterized in that, The gain observer is represented as: in, It is an estimate of x(t,k), L z ∈R n×s It is the gain matrix, where z represents the index of the gain observer; The augmentation system is represented as follows: Among them, error 8. The technology according to claim 7, characterized in that, The first stability criterion is expressed as: By applying the S-lemma to the first stability criterion, the second stability criterion is obtained, which is expressed as: Among them, κ d >0, τ>0, γ, μ1, μ2, λ≥0, δ≥0, ρ>0, θ>0 are all unknown constants, R n×n matrix and R n×p Matrix F1 and F2 are both unknown matrices; Solve the second stability criterion to obtain the unknown matrices P1, P2, F1, and F2; The gain estimate is expressed as:

9. A data-driven switching gain estimation system for a bipedal walking robot, characterized in that, The system includes: The model building module is used to construct a model-based state space model of the bipedal robot system using a hybrid system framework, and to construct a data-based equivalent system model of the bipedal robot system based on the state space model; wherein, both the state space model and the equivalent system model include an unknown system matrix; A noise constraint module is used to construct prior knowledge of noise in the bipedal walking robot system; The first calculation module is used to obtain a set of unknown system matrices based on the equivalent system model and the prior knowledge of the noise; wherein the expression of the set of unknown system matrices includes a first matrix stripped of the unknown system matrices; The second calculation module is used to process the set of matrices of the unknown system using the dual lemma to obtain a second matrix related to the first matrix; An observer construction module is used to construct a gain observer based on the state-space model, and to obtain an augmented system based on the gain observer and the equivalent system model. A stability design module is used to construct a model-based first stability criterion for the bipedal robot system based on the augmented system. The third calculation module is used to process the first stability criterion using the S lemma and substitute it into the second matrix to obtain the second stability criterion based on the data. The gain estimation module is used to obtain a gain estimate based on the second stability criterion.

10. A bipedal walking robot, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the data-driven switching gain estimation technique for bipedal walking robots as described in any one of claims 1 to 8.

Images