An unmanned bicycle asymmetric load inertia parameter online identification method

Abstract

The application discloses an unmanned bicycle asymmetric load inertia parameter online identification method; the method adopts 25 model parameters obtained based on the central axis surface symmetry assumption under the nominal state as the nominal parameter vector; the 10-dimensional inertia parameter correction amount of the reference point of the later frame empty load nominal center of mass is defined. According to the nominal dynamics model, the generalized force residual is calculated, the regression matrix corresponding to the inertia parameter correction amount of the later frame is derived by using the d'Alembert principle and the spatial inertia force expression, and the parameter identification equation is constructed. According to the stability margin and the parameter observability, the constrained micro-amplitude identification excitation is generated, and the recursive estimation method is used to identify the inertia parameter change of the later frame caused by the asymmetric load; the application can identify the influence of the asymmetric load on the dynamics model of the unmanned bicycle without stopping and weighing, without relying on a special calibration platform and without damaging the stable driving of the unmanned bicycle, and ensure that the estimation result meets the physical feasibility constraint of the rigid body inertia parameter.

Description

Technical Field

[0001] This invention belongs to the field of robotics and intelligent equipment technology, specifically relating to the dynamic modeling, parameter identification and stability control technology of unmanned bicycle robots, and particularly to an online identification method for asymmetric load inertial parameters of unmanned bicycles. Background Technology

[0002] Autonomous bicycles are a typical type of nonholonomic, underactuated, multi-rigid-body coupled system. To achieve autonomous balance, trajectory tracking, and speed control, an accurate bicycle dynamics model is typically required. Existing four-rigid-body bicycle models are usually established under the assumption that the mass distribution is symmetric about the central axis, thus the model parameters can be described by 25 structural and inertial parameters. Under this assumption, the lateral center-of-mass coordinates of the rear and front frames are zero, and some inertia products are also zero, for example... , , .

[0003] However, in actual operation of autonomous bicycles, the load may be mounted on a shelf, cargo box, or rear frame platform. The mass, mounting position, and lateral offset of the load will change the equivalent mass distribution of the rear frame and may disrupt the original symmetry of the central axis. In this case, if a 25-parameter symmetric model is still used, the influence of the lateral first-order mass moment and the asymmetric inertia product on the roll-steering coupled dynamics will be ignored, leading to increased model error and consequently affecting stability control, velocity planning, and state estimation.

[0004] On the other hand, asymmetric load inertial parameters cannot always be reliably identified from natural driving data. When the autonomous bicycle is in a straight-line constant-speed or smooth path tracking state, the roll, steering, and yaw responses change relatively little, and the regression matrix may have insufficient rank or an excessively large condition number. Directly applying a large identification excitation may disrupt the balance state of the autonomous bicycle. Therefore, a method is needed to dynamically generate micro-amplitude identification excitations based on the vehicle's stability margin and parameter observability under the protection of a basic stability controller, and to estimate the asymmetric load inertial parameters online.

[0005] While existing methods for identifying robot inertial parameters can express rigid body inertial parameters in a linear regression form, they typically target individual rigid bodies such as robotic arms or mobile robots, and do not directly address the wheel-ground nonholonomic constraints, roll balance stability, and steering-drive coupling input conditions of unmanned bicycles. Existing bicycle dynamics modeling methods, although capable of obtaining a 25-parameter nominal model, usually rely on the assumption of axial symmetry and lack online correction mechanisms for the lateral first-order mass moment and asymmetric inertia product after load lateral offset. Existing continuous excitation or excitation identification methods, while improving the amount of parameter identification information, typically do not integrate safety margins such as the unmanned bicycle's tilt angle, steering angle, actuator margin, path error, and obstacle distance with parameter observability evaluations for excitation amplitude and channel selection.

[0006] Therefore, simply applying the existing technologies mentioned above is insufficient to simultaneously address the issues of asymmetric load model correction, balance safety constraints, and inadequate parameter observability for unmanned bicycles. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing technologies by providing an online identification method for asymmetric load inertial parameters of unmanned bicycles.

[0008] The technical solution adopted in this invention is as follows: This invention provides an online identification method for asymmetric load inertial parameters of unmanned bicycles, the method comprising the following steps: Step 1: Establish the nominal four-rigid-body structure and parameter model of the unmanned bicycle. The parameter model uses 25 model parameters obtained under the assumption of central axis symmetry in the unloaded or nominal state as the nominal parameter vector. ; Step 2: Define generalized coordinates and independent coordinates; Step 3: Determine the nominal center of gravity of the vehicle frame under no-load conditions. Define the 10-dimensional inertial parameter correction for the rear frame at the reference point. ; Step 4: Based on the nominal four-rigid-body structure of the unmanned bicycle, generate a 10-dimensional inertial parameter correction quantity including the rear frame for residual construction and parameter identification. The nonholonomic dynamic equations after loading; Step 5: Based on the nominal parameter vector The nominal model generalized force residual is calculated using the state variables at the current sampling time. ; Step Six: Based on d'Alembert's principle, map the spatial inertial force of the rear frame into a generalized force on independent generalized coordinates, and construct the regression matrix corresponding to the 10-dimensional inertial parameter correction of the rear frame. This forms the parameter identification equation; Step 7: Generate basic stability control variables based on the current state of the unmanned bicycle, and calculate the comprehensive stability margin based on tilt angle, tilt rate, steering angle, steering rate, actuator margin, path error, and obstacle distance. ; Step 8: Based on the regression matrix Constructing an information matrix within a sliding window And based on the information matrix The rank, condition number, minimum eigenvalue, or parameter covariance are used to evaluate the observability of the 10-dimensional rear frame inertial parameter correction. Step Nine: When Meets safety requirements and When observability is insufficient, a small-amplitude identification excitation constrained by the stability margin is superimposed on the basic stability control quantity; when Safety conditions are not met, or When the observability requirement is met, the micro-amplitude identification stimulus is not actively superimposed, and the recursive parameter update is continued using natural driving data; Step 10: Use recursive estimation to obtain the correction amount of the 10-dimensional inertial parameters of the rear frame. Estimated values ​​of the correction amount of the rear frame inertial parameters at each sampling time; Step 11: Apply physical constraints to the estimated value of the rear frame inertia parameter correction, which are positive in mass, have bounded relative displacement of the equivalent center of mass, positive definite central inertia matrix, and realizable principal inertia, and output the dynamic model parameters of the unmanned bicycle after physical constraint projection correction.

[0009] Furthermore, in step one, the 25 model parameters are: in, For the nominal parameter vector, the superscript Indicates no-load or nominal status; The nominal wheelbase, The nominal front wheel trail, This refers to the nominal fork pivot angle. These are the nominal rear wheel radius, rear wheel mass, and rear wheel circumference. shaft and The moment of inertia of the shaft, and the moment of inertia of the rear wheel are all represented in the rear wheel fixed coordinate system with the rear wheel center of mass as the reference point; These are the nominal rear frame mass and the nominal rear frame center of gravity relative to the rear wheel contact point in the bicycle's upright configuration. coordinates and The coordinates, and the rear frame's orbital distance, represented in the rear frame fixed coordinate system with the nominal center of gravity of the rear frame as the reference point. moment of inertia of the shaft and directional product of inertia; These are the nominal front frame mass and the nominal front frame center of gravity relative to the rear wheel contact point in the upright position of the bicycle. coordinates and Coordinates, and the front frame's orbital plane, represented in the front frame fixed coordinate system with the front frame's center of mass as the reference point. moment of inertia of the shaft and directional product of inertia; These are the nominal front wheel radius, front wheel mass, and front wheel twist rate, respectively. shaft and The moment of inertia of the axle, the moment of inertia of the front wheel are all represented in the front wheel fixed coordinate system with the front wheel center of mass as the reference point; the 25 model parameters are obtained under the assumption that the mass distribution of the bicycle is symmetrical about the axle plane; In step two, generalized coordinates for: in, The angle of rotation of the rear wheel relative to the rear frame. The angle of rotation of the front wheel relative to the front frame. The angle of rotation between the front frame and the rear frame. Yaw angle The angle of inclination, The pitch angle, The coordinates of the origin of the local coordinate system of the rear frame in the world coordinate system; Independent coordinates for: The method employs a velocity mapping relationship determined by wheel-to-ground slip-free contact constraints when constructing the rear frame spatial velocity Jacobian matrix and dynamic residuals. in, For generalized speed, This is a velocity mapping matrix used to map independent generalized velocities. Mapping to complete generalized velocity The velocity mapping relationship serves as the basis for kinematic constraints in the parameter identification calculation of this invention. The generalized coordinates Independent generalized velocity and independent generalized acceleration The position coordinates are obtained from sensor data and state estimation results of the unmanned bicycle; wherein, the position coordinates in the generalized coordinate system are... It is not required to be measured directly by a single sensor; the independent generalized acceleration is obtained through state estimation from at least one of the following: wheel speedometer, inertial measurement unit, angle encoder, positioning module, visual odometry, or laser odometry. Obtained by filtering differentiation, smoothing estimation, or state observer.

[0010] Furthermore, in step three, the 10-dimensional inertial parameter correction amount of the rear frame... for: in, This is the correction amount for the equivalent mass of the rear frame. These are the nominal center of gravity of the vehicle frame under no-load conditions. The equivalent first-order mass moment of the rear frame, with reference point , is The amount of directional correction. These are the nominal center of gravity of the vehicle frame under no-load conditions. The rear frame is used as a reference point. Shaft inertia correction amount These are the nominal center of gravity of the vehicle frame under no-load conditions. Rear frame as reference point Correction for directional inertia product; Nominal rear frame 10-dimensional inertial parameters From the nominal parameter vector The rear frame parameters in the data are expanded to obtain: The origin of the fixed coordinate system of the rear frame is taken as the nominal centroid of the rear frame under no-load conditions. Therefore, under the nominal condition, all three first-order mass moments are zero; the two zero-inertia products correspond to the nominal axial symmetry assumption. and The Used to describe the nominal center of gravity of the rear frame under no-load conditions. The position of the bicycle relative to the contact point of the rear wheel in an upright configuration is not considered as... The first-order mass moment is used in the process; Equivalent inertial parameters of the rear frame after loading for: .

[0011] Furthermore, in step four, the nonholonomic dynamics equations of the loaded unmanned bicycle are used as the basis for residual construction. These dynamics equations are expressed as follows: in, To constrain the quality matrix in the form of embedding, To constrain the Coriolis force, gravity, and velocity-related terms in the embedded form, Let be the constant mapping matrix from input torque to generalized force in independent generalized coordinates, and For the input torque vector, For handlebar steering torque, This is the torque for rear-wheel drive; and It is derived from the nominal four-rigid-body structure of an unmanned bicycle; When the and exist At that time, a nominal model is established, and the corresponding matrix is ​​denoted as follows. ; In step five, the generalized force residual for: in, For the first The input torque vector at each sampling time.

[0012] Furthermore, in step six, The parameter identification equation is: in, For the first The nominal dynamic generalized force residual at each sampling time, For the first The input torque vector at each sampling time, This is the regression matrix corresponding to the 10-dimensional inertial parameter correction of the rear frame. For measuring noise, unmodeled disturbances, and external disturbances; The regression matrix is ​​the first Listed as: in, For the regression matrix The List, ; The Jacobian matrix of the rear frame space velocity with respect to the independent generalized velocities satisfies... ; For rear frame space speed, To increase the space for the rear frame, This refers to the acceleration of the rear frame space after deducting gravity. Let be the spatial gravitational acceleration expressed in the rear frame coordinate system. For the first The spatial inertia basis matrix corresponding to each rear frame inertia parameter. For spatial force cross multiplication operator; The regression matrix for: .

[0013] Further, in step seven, the stability margin is composed of multiple dimensionless safety margin indices, including tilt angle margin, tilt rate margin, steering angle margin, steering rate margin, actuator margin, path error margin, and obstacle distance margin. Each dimensionless safety margin indices are calculated based on their corresponding physical quantities and thresholds, and then the multiple dimensionless safety margin indices determine whether a safe and observable excitation is allowed. Specifically, the safe and observable excitation is a micro-amplitude identification excitation constrained by the stability margin and used to improve parameter observability. The specific meaning of whether to allow the application of safe and observable incentives is: to consider the comprehensive stability margin. With minimum integrated stability margin Compare the results to obtain the safety clearance indicator; like: The security permission flag is defined as not applying an identification stimulus, wherein... The minimum overall stability margin required to allow the application of identification stimuli; like: The safety permission flag is then used to determine the observability of the parameters.

[0014] Furthermore, in step eight, the information matrix : in, , The length of the sliding window; If any of the following conditions are met, the current data is deemed insufficiently observable for the correction of the 10-dimensional rear frame inertial parameters: in, The smallest eigenvalue of the information matrix. The minimum feature value threshold, Let be the rank of the information matrix. The condition number of the information matrix. The condition number threshold; When the information matrix within multiple consecutive sliding windows still fails to meet the full rank or condition number requirements after applying a safe and observable excitation, the identifiable parameter subspace is determined based on the singular value decomposition of the information matrix, and the identifiable parameter combination is output, or the set of parameters to be identified is reduced to a subset of parameters that can be reliably estimated under the current motion state.

[0015] Furthermore, in step nine, a small-amplitude identification excitation constrained by the stability margin is superimposed on the basic stability control quantity to obtain the actual input torque at time k: in, For micro-amplitude recognition incentives; The micro-amplitude identification excitation includes the superposition of the handlebar steering torque channel. Steering recognition excitation, superimposed on the rear wheel drive torque channel The driving identification excitation or a combination of the two, and the upper limit of the total amplitude of the micro-amplitude identification excitation is constrained by the comprehensive stability margin; when steering identification excitation and driving identification excitation are used simultaneously, the upper limit of the total amplitude is allocated as steering identification excitation amplitude and driving identification excitation amplitude according to the preset allocation coefficient or the observability gap of the parameter to be identified.

[0016] Furthermore, in step ten, the recursive estimation is specifically a recursive least squares method with a forgetting factor, to obtain the first... Estimated values ​​of the correction amount of the rear frame inertial parameters at each sampling time; When the unmanned bicycle load remains fixed during a single identification process, the convergence of parameter estimation is determined based on the parameter increment norm, root mean square of residuals, trace of parameter covariance matrix, and observability index of information matrix. When multiple consecutive sliding windows meet the convergence condition, the active application of micro-amplitude identification excitation is stopped and the estimated value of the current rear frame inertial parameter correction is output. When the unmanned bicycle load changes during operation, online tracking continues using recursive estimation with forgetting factor.

[0017] Further, in step eleven, the physical constraint projection correction includes: performing positive projection on the mass parameters, performing interval projection on the relative displacement of the equivalent center of mass, performing positive definite projection on the central inertia matrix, and performing rigid body inertia realizability constraints on the principal inertia; the positive definite projection of the central inertia matrix transforms the inertia matrix with the nominal center of mass of the vehicle frame under no-load as the reference point to the equivalent center of mass after loading through the parallel axis theorem, performs eigenvalue decomposition on the transformed central inertia matrix, corrects the eigenvalues ​​less than the preset positive threshold to the positive threshold, reconstructs the central inertia matrix, and transforms it back to the inertia matrix with the nominal center of mass of the vehicle frame under no-load as the reference point through the parallel axis theorem.

[0018] Compared with the prior art, the beneficial effects of the present invention are: First, this invention does not re-identify all the dynamic parameters of the unmanned bicycle. Instead, based on a nominal four-rigid-body model with 25 parameters, it introduces a 10-dimensional asymmetric inertial parameter correction only for the rear frame, which bears the main load. This approach can describe the lateral first-order mass moment and asymmetric inertia product caused by the left-right offset of the load while retaining the nominal model's structural parameters, wheel parameters, and front frame parameters, thus reducing the dimensionality of online identification and dependence on calibration tests.

[0019] Second, this invention defines the 10-dimensional inertial parameter correction of the rear frame with the nominal center of mass of the rear frame under no-load as the reference point, and constructs an analytical regression matrix of the rear frame inertial parameter correction through the d'Alembert principle and the expression of spatial inertial force, so that a clear linear identification relationship is formed between the nominal dynamic residual and the inertial parameters of asymmetric load, thereby improving the dynamic consistency of parameter identification.

[0020] Third, this invention combines parameter observability evaluation with unmanned bicycle stability margin evaluation. Limited micro-amplitude identification excitation is applied only when natural driving data results in insufficient rank of the information matrix, excessively large condition number, or insufficient minimum eigenvalue, and when safety margins such as tilt angle, steering angle, actuator margin, path error, and obstacle distance meet requirements. This approach improves the information content of the regression matrix at subsequent sampling times without compromising the balance control and path tracking safety of the unmanned bicycle.

[0021] Fourth, this invention imposes mass, equivalent centroid relative displacement, positive definiteness of the central inertia matrix, and principal inertia realizability constraints on the recursive estimation results, and outputs identifiable parameter combinations or dimensionality-reduced parameter subsets when information is insufficient for a long period of time, thereby avoiding the erroneous updating of noise or unobservable directions with inertial parameters that do not conform to the physical laws of rigid bodies, and improving the engineering usability and stability of the online identification results.

[0022] Fifth, this invention is applicable to unmanned bicycle robots, two-wheeled self-balancing mobile robots, and intelligent mobile equipment with asymmetric loads. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0024] Figure 1 This is a schematic diagram of the overall process of the method of the present invention; Figure 2 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0026] It should be noted that, unless otherwise specified, the features in the following embodiments and implementation methods can be combined with each other.

[0027] This invention provides an online identification method for the inertial parameters of an unmanned bicycle under asymmetric loads. Based on a nominal 25-parameter four-rigid-body dynamics model, the method extends the rear frame into a general three-dimensional rigid body when the load disrupts the axial symmetry, and identifies the 10-dimensional inertial parameter correction of the rear frame online.

[0028] Unlike directly re-identifying all dynamic parameters of an unmanned bicycle, this invention retains the 25-parameter four-rigid-body model already established under unloaded or nominal conditions, and only introduces 10-dimensional inertial parameter corrections for the rear frame, which is easily affected by loads and may disrupt the symmetry of the central axis. These 10-dimensional inertial parameter corrections use the nominal center of mass of the rear frame under unloaded conditions as a reference point and include mass corrections, three first-order mass moment corrections, and six inertia parameter corrections. This preserves both the structural and wheel parameters under the nominal model's central axis symmetry condition and the ability to describe the lateral mass moment and asymmetric inertia product caused by the left-right offset of the load.

[0029] This invention further integrates the nominal dynamic residual, the linear parameterization of the rear frame spatial inertial force, the observable excitation under safety margin constraints, and the recursive estimation with physical feasibility projection into a closed-loop online identification process. This process does not simply apply external perturbations to the residual equations; instead, under the influence of basic stability control quantities, it determines whether the natural driving data is sufficient for identification based on the rank, condition number, and minimum eigenvalue of the current information matrix. Only when the natural data is insufficient and the stability margin meets the safety conditions is a restricted steering or drive micro-excitation superimposed, causing changes in the motion state at subsequent sampling times and improving the information content of the subsequent regression matrix.

[0030] Unlike existing methods that independently apply rigid body inertial parameter identification, conventional continuous excitation, and bicycle stability control to robot systems, this invention utilizes 10-dimensional rear frame asymmetric parameters and regression matrices. Stability margin Information matrix There is a synergistic relationship between the physical projection constraints and the 10-dimensional rear frame asymmetric parameters: these parameters are used to characterize the lateral load bias that cannot be expressed by a 25-parameter symmetric model; the regression matrix explicitly linearizes the influence of these asymmetric parameters on independent generalized dynamics; and Together, they determine whether, when, and through which input channel to apply a micro-excitation; the physical projection constraint ensures that the recursive result still corresponds to the achievable rigid body inertial parameters. This forms a closed-loop technical approach of "detecting insufficient information - excitation within the safety boundary - changing the subsequent regression matrix - recursion and physical constraint output," which can simultaneously solve three mutually restrictive problems: asymmetric load modeling, safe driving, and insufficient online identifiability.

[0031] For ease of explanation, in this invention, Represents the 9-dimensional generalized coordinates of the unmanned bicycle. This represents a 3D independent coordinate system selected by the wheel-to-ground no-slip constraint. , and These represent generalized velocity, independent generalized velocity, and independent generalized acceleration, respectively. This represents the velocity mapping matrix determined by the wheel-ground no-slip nonholonomic constraint, used to satisfy... This means mapping independent generalized velocities to complete generalized velocities; and These represent the mass matrix after constraint embedding, as well as the Coriolis force, gravity, and velocity-related terms, respectively. Represents 25 model parameters under no-load or nominal conditions; This represents the 10-dimensional inertial parameter correction of the rear frame caused by asymmetric loads. Indicates the rear frame relative to the independent generalized speed. The spatial velocity Jacobian matrix can be derived from the kinematic relationship between the rear frame coordinate system pose and the generalized coordinates, as well as the velocity mapping matrix. Calculated; Indicates the first The spatial inertia basis matrix corresponding to each rear frame inertia parameter; This represents the spatial force cross-multiplication operator. This invention is not limited to... and The specific analytical form.

[0032] Specifically, such as Figure 1 As shown, the method includes the following steps: Step 1: Establish the nominal four-rigid-body structure and parameter model of the unmanned bicycle.

[0033] A classic four-rigid-body bicycle model is adopted, meaning the nominal four-rigid-body structure of the unmanned bicycle consists of a rear wheel, a rear frame, a front frame, and a front wheel. The parameter model specifically assumes that the bicycle's mass distribution is symmetrical about the central axis under unloaded or nominal conditions, and uses 25 model parameters obtained based on this assumption as a nominal parameter vector. : in, For the nominal parameter vector, the superscript Indicates no-load or nominal status; The nominal wheelbase, The nominal front wheel trail, This refers to the nominal fork pivot angle. These are the nominal rear wheel radius, rear wheel mass, and rear wheel circumference. shaft and The moment of inertia of the shaft, the rear wheel around shaft and The moment of inertia of the shaft is expressed in the rear wheel fixed coordinate system with the rear wheel center of mass as the reference point. These are the nominal rear frame mass and the nominal rear frame center of gravity relative to the rear wheel contact point in the bicycle's upright configuration. coordinates and The coordinates, and the rear frame's orbital distance, represented in the rear frame fixed coordinate system with the nominal center of gravity of the rear frame as the reference point. moment of inertia of the shaft and directional product of inertia; These are the nominal front frame mass and the nominal front frame center of gravity relative to the rear wheel contact point in the upright position of the bicycle. coordinates and Coordinates, and the front frame's orbital plane, represented in the front frame fixed coordinate system with the front frame's center of mass as the reference point. moment of inertia of the shaft and directional product of inertia; These are the nominal front wheel radius, front wheel mass, and front wheel twist rate, respectively. shaft and The moment of inertia of the shaft, the front wheel around shaft and The rotational inertia of the shaft is represented in the front wheel center of mass coordinate system with the front wheel fixed in the reference point.

[0034] The 25 model parameters were obtained under the assumption that the bicycle mass distribution is symmetrical about the central axis.

[0035] Step 2: Define generalized coordinates and independent coordinates.

[0036] Using the generalized coordinates from the nominal four-rigid-body structure of the unmanned bicycle: in, For 9-dimensional generalized coordinates, The angle of rotation of the rear wheel relative to the rear frame. The angle of rotation of the front wheel relative to the front frame. The angle of rotation between the front frame and the rear frame. Yaw angle The angle of inclination, The pitch angle, The coordinates of the origin of the local coordinate system of the rear frame in the world coordinate system.

[0037] Define independent coordinates based on the wheel-ground no-slip contact constraint: in, 3D independent coordinates selected by wheel-ground no-slip constraint When constructing the rear frame spatial velocity Jacobian matrix and dynamic residuals, the velocity mapping relationship determined by the wheel-to-ground no-slip contact constraint is adopted: in, The velocity mapping matrix is ​​determined by the wheel-ground no-slip nonholonomic constraint, used to satisfy... , will independent generalized velocity Mapping to complete generalized velocity ; For independent generalized velocity, The velocity is a 9-dimensional generalized velocity; the velocity mapping matrix serves as the basis for kinematic constraints in the parameter identification calculation of this invention, and this invention is not limited to... The specific analytical form.

[0038] It should be noted that the parameter identification method of this invention uses 9-dimensional generalized coordinates. Independent generalized velocity and independent generalized acceleration It can be obtained from the sensor data and state estimation results of the autonomous bicycle, and does not require that every component in the 9-dimensional generalized coordinates be directly measured by a single sensor. For example, tilt angle. angular velocity The steering angle can be estimated by the inertial measurement unit. Or its speed can be measured by a steering angle encoder, rear wheel steering angle Or its speed can be measured by a wheel speed encoder; position coordinates Independent generalized acceleration can be obtained through state estimation from wheel speed odometer, inertial measurement unit, satellite positioning, visual odometer, laser odometer, or a combination thereof; It can be obtained directly from the filtered derivative of independent generalized velocities, sliding window smoothing estimation, state observers, or filter state variables. For example, in a sampling period of... In this case, the difference form can be used: In addition, low-pass filtering or smoothing filtering can be used to suppress noise; alternatively, a state observer can be used to directly output the signal. and .

[0039] The state estimation method described above can employ extended Kalman filtering, unscented Kalman filtering, complementary filtering, factor graph optimization, or other mobile robot state estimation methods. This invention does not take the state estimation method itself as its inventive point.

[0040] Step 3: Consider asymmetric loads and expand the rear frame inertia parameters.

[0041] After loading, the load is equivalently incorporated into the rear frame. Since the load may be laterally offset, the rear frame no longer satisfies the assumption of symmetry along the central axis. Therefore, the rear frame is equivalent to a general three-dimensional rigid body, with the nominal center of mass of the rear frame under no-load conditions as... Define the 10-dimensional inertial parameters of the rear frame as a reference point and represented in the fixed coordinate system of the rear frame. : in, For the equivalent mass of the rear frame, The equivalent first-order mass moment of the rear frame satisfies: in, The equivalent center of gravity of the rear frame after loading is relative to the nominal center of gravity of the rear frame under no-load conditions. The coordinate displacement; under the upright configuration of the bicycle, the coordinates of the equivalent center of mass of the rear frame after loading relative to the contact point of the rear wheel can be expressed as: .

[0042] For future vehicle frame no-load nominal center of gravity The inertia parameter is the reference point. Under nominal conditions: Furthermore, since the origin of the coordinate system of the rear frame is fixed, it is taken as... In its nominal state, there is still , .

[0043] After loading: in, The nominal 10-dimensional inertial parameters of the rear frame The equivalent inertial parameters of the rear frame after loading. Correction values ​​for the 10-dimensional inertial parameters of the rear frame to be identified: in, This is the correction amount for the equivalent mass of the rear frame. These are the nominal center of gravity of the vehicle frame under no-load conditions. The equivalent first-order mass moment of the rear frame, with reference point , is The amount of directional correction. These are the nominal center of gravity of the vehicle frame under no-load conditions. The rear frame is used as a reference point. Shaft inertia correction amount These are the nominal center of gravity of the vehicle frame under no-load conditions. Rear frame as reference point Correction for directional inertia product.

[0044] Nominal rear frame 10-dimensional inertial parameters From the nominal parameter vector The rear frame parameters in the data are expanded to obtain: Among them, the origin of the fixed coordinate system of the rear frame is the nominal centroid of the rear frame under no-load conditions. Therefore, under the nominal condition, all three first-order mass moments are zero; the two zero-inertia products correspond to the nominal axial symmetry assumption. and The aforementioned Used to describe the nominal center of gravity of the rear frame under no-load conditions. The position of the bicycle relative to the contact point of the rear wheel in an upright configuration is not considered as... The first-order mass moment is used in [the context].

[0045] Step 4: Formulate the nonholonomic dynamic equations after loading for identification.

[0046] Based on the nominal four-rigid-body structure of the unmanned bicycle, a 10-dimensional inertial parameter correction quantity, including the rear frame, is formed for residual construction and parameter identification. The nonholonomic dynamic equations after loading: in, For the nominal parameter vector, The correction amount for the 10-dimensional inertial parameters of the rear frame to be identified. To constrain the quality matrix in the form of embedding, To constrain the Coriolis force, gravity, and velocity-related terms in the embedded form, The constant mapping matrix from input torque to generalized force in independent generalized coordinates is taken as: For the input torque vector, where For handlebar steering torque, This is the torque for rear-wheel drive.

[0047] When the and exist At that time, a nominal model is established.

[0048] and The nominal four-rigid-body structure of the unmanned bicycle is used as the model basis for constructing the nominal dynamic residuals and parameter regression matrices in this invention. This invention does not rely on... and The specific solution method is used as a limitation.

[0049] In this invention, the mass matrix in the form of constraint embedding Terms related to Coriolis force, gravity, and velocity The specific solution can be obtained using existing four-rigid-body nonholonomic dynamics modeling methods, and the present invention will not repeat its recursive derivation process.

[0050] Step 5: Calculate the nominal dynamic residual.

[0051] Based on the nominal parameter vector The nominal model generalized force residual is calculated using the state variables at the current sampling time. .

[0052] In the At each sampling time, the following calculations are performed using the nominal model: in, This is the generalized force vector predicted by the nominal model.

[0053] The actual generalized force vector is: in, This is the actual generalized force vector after the input torque is mapped to independent generalized coordinates. For the first The input torque vector at each sampling time.

[0054] Define the generalized force residual of the nominal model. : Right now: The residual is mainly caused by changes in the rear frame inertial parameters due to asymmetrical loads, external disturbances, and measurement noise.

[0055] Step 6: Construct the parametric regression matrix using the d'Alembert principle.

[0056] The rear frame space velocity is expressed as: in, The spatial velocity of the rear frame consists of the angular velocity of the rear frame and the linear velocity of the origin of the coordinate system fixed to the rear frame. For the rear frame relative to independent generalized speed The spatial velocity Jacobian matrix can be derived from the kinematic relationship between the rear frame coordinate system pose and the generalized coordinates, as well as the velocity mapping matrix. Calculations show that this invention is not limited. The specific analytical form.

[0057] The acceleration of the rear frame space is expressed as: in, To increase the space for the rear frame, for The derivative with respect to time.

[0058] Rear frame space acceleration after deducting gravity for: in, Let be the spatial gravitational acceleration expressed in the rear frame coordinate system.

[0059] Rear frame spatial inertia matrix increment Regarding the linearity of 10-dimensional inertial parameters: in, The increment in the rear frame spatial inertia matrix caused by parameter correction. for The One element, For the first The spatial inertia basis matrix corresponding to each inertial parameter.

[0060] According to d'Alembert's principle, the virtual work done by the rear frame inertial force system on the virtual displacement can be equivalent to the virtual work done by the spatial inertial force on the spatial virtual velocity. The spatial inertial force of the rear frame is: in, The spatial inertial force of the rear frame caused by the inertial parameter correction amount. This is the spatial force cross multiplication operator. Its generalized force vector mapped onto independent generalized coordinates is: in, This is the generalized force vector generated by the rear frame inertial parameter correction in independent generalized coordinates. Because... about The generalized force residual caused by the linear rear frame inertia parameter correction can be written as a parameter identification equation: This is the regression matrix corresponding to the 10-dimensional inertial parameter correction of the rear frame. This is for measuring noise, unmodeled disturbances, and external disturbances.

[0061] Among them, the regression matrix is ​​the Listed as: in, For the regression matrix The List, ; The Jacobian matrix of the rear frame space velocity with respect to the independent generalized velocities satisfies... ; For rear frame space speed, To increase the space for the rear frame, This refers to the acceleration of the rear frame space after deducting gravity. Let be the spatial gravitational acceleration expressed in the rear frame coordinate system. For the first The spatial inertia basis matrix corresponding to each rear frame inertia parameter. It is a spatial force cross multiplication operator.

[0062] then: Step 7: Calculate the stability margin.

[0063] The basic stability controller generates basic stability control quantities based on the current state of the unmanned bicycle. : in, Based on the shift to stable control quantity, It is the basic drive or braking control quantity.

[0064] Then, the overall stability margin is calculated based on the tilt angle, tilt rate, steering angle, steering rate, actuator margin, path error, and obstacle distance. Since tilt angle, tilt rate, steering angle, steering rate, actuator output, path error, and obstacle distance have different physical dimensions and numerical ranges, this invention calculates the dimensionless safety margin index corresponding to each safety constraint: in, For the tilt margin, For the tilt velocity margin, For steering angle margin, For steering angular velocity margin, For actuator margin, For path error margin, This refers to the obstacle distance margin. The tilt angle threshold, The tilt velocity threshold, The steering angle threshold. The steering angular velocity threshold, The actuator output threshold, This refers to the lateral error of the path. This is the lateral error threshold for the path. Distance to the obstacle For minimum safe distance, To allow for the desired safe distance for applying identification stimuli, and .

[0065] Based on the aforementioned dimensionless safety margin indices, calculate the overall stability margin. : in, For the first The overall stability margin at each sampling time.

[0066] If any dimensionless safety margin index is less than 0, it indicates that the corresponding safety constraint has been breached.

[0067] The overall stability margin With minimum integrated stability margin By comparing the results, a safety permission mark is obtained.

[0068] like: The safety-permitted flag is defined as not applying a safety-observable stimulus, wherein... This refers to the minimum overall stability margin required to allow the application of a safe and observable stimulus. Specifically, the safe and observable stimulus is a small-amplitude identification stimulus constrained by the stability margin and used to improve parameter observability.

[0069] like: The safety permission flag is then used to proceed to step eight to determine the observability of the parameters.

[0070] Step 8: Evaluate the observability of parameters.

[0071] According to the regression matrix Constructing an information matrix within a sliding window : in, , This represents the length of the sliding window.

[0072] If any of the following conditions are met, the current data is deemed insufficient to observable the correction amount for the 10-dimensional rear frame inertial parameters.

[0073] in, The smallest eigenvalue of the information matrix. The minimum feature value threshold, Let be the rank of the information matrix. The condition number of the information matrix. This is the condition number threshold.

[0074] If the information matrix is ​​obtained after safe and observable excitation within multiple consecutive sliding windows... If the full rank or condition number requirement cannot be met for an extended period, then according to... The singular value decomposition determines the identifiable parameter subspace and outputs identifiable parameter combinations, or reduces the dimensionality of the set of parameters to be identified to a subset of parameters that can be reliably estimated under the current motion state. The dimensionality reduction does not change the definition of the 10-dimensional inertial parameter model of the rear frame, and is only used to avoid over-updating unreliably identifiable parameters under conditions of insufficient information.

[0075] Step 9: Generate secure and observable stimuli.

[0076] when: Furthermore, when parameter observability is insufficient, safe and observable stimuli are generated.

[0077] The secure observable excitation is specifically a small-amplitude identification excitation constrained by stability margin and used to improve parameter observability: in, For micro-amplitude recognition incentives, To be superimposed on the handlebar steering torque channel Steering recognition incentives To be superimposed on the rear wheel drive torque channel The driving force for identification and stimulation.

[0078] The micro-amplitude identification stimulus Superimposed on the basic stability control quantity, the actual input torque at time k is: The purpose of generating micro-amplitude identification stimuli only when parameter observability is insufficient is to avoid unnecessary additional disturbances when natural driving data can meet the parameter identification requirements, and to reduce the impact of micro-amplitude identification stimuli on the balance control, path tracking and energy consumption of unmanned bicycles. Only when natural driving data leads to insufficient information matrix rank, excessive condition number or excessive parameter covariance, will micro-amplitude identification stimuli be used to actively increase the amount of information in the roll-steering-drive response.

[0079] It should be noted that the micro-amplitude identification excitation is not achieved by directly changing the generalized force residual on the right-hand side of the current parameter identification equation. Instead of improving parameter observability, it changes the controlled motion state of the unmanned bicycle at subsequent sampling times, thus altering the generalized coordinates at those times. Independent generalized velocity and independent generalized acceleration Measurable changes occur; due to the regression matrix Depend on , and Therefore, the micro-amplitude identification excitation can change the regression matrix at subsequent sampling times. This improves the information matrix within the sliding window. The rank, minimum eigenvalue, and condition number of .

[0080] No. Upper limit of the total amplitude of the micro-amplitude identification excitation allowed at each sampling time. Based on the aforementioned comprehensive stability margin constraint: in, This is the amplitude scaling factor. To incentivize the upper limit of the total amplitude, This is the amplitude limiting function.

[0081] When only steering identification stimulus is used, let: When both steering identification stimuli and drive identification stimuli are used simultaneously, the allocation coefficient will be applied. Assigned to two channels: in, To identify the excitation amplitude for steering, To drive the identification of the excitation amplitude, and The allocation coefficients for steering excitation and driving excitation are respectively, satisfying... , and The allocation coefficient can be determined based on the observability gap of the parameter to be identified; when the observability of the transverse first-order mass moment and the product of inertia is insufficient, it is increased. When the observability of mass, first-order longitudinal mass moment, or pitch-related inertia is insufficient, increase .

[0082] Steering recognition incentives can be: in, To identify the excitation amplitude for steering, For the excitation frequency, For the first Each sampling time, The initial phase is used. The driving identification excitation can be a pseudo-random binary sequence, a swept frequency signal, or a finite-duration pulse signal.

[0083] Among them, the steering identification excitation is used to enhance the lateral first-order mass moment. Inertia product , Observability of asymmetric parameters.

[0084] Step 10: Recursively estimate the inertial parameters of the asymmetric load.

[0085] A recursive estimation is performed, specifically using a recursive least squares method with a forgetting factor: in, For recursive gain, Let covariance be the parameter. Forgetting factor, It is the identity matrix. For the first The estimated value of the correction amount of the rear frame inertial parameters at each sampling time. The forgetting factor. satisfy ;when At that time, all historical sampling data have the same weight; when In this approach, data closer to the current time has a higher weight, while data farther away from the current time has a weight that decays exponentially. Therefore, this approach is suitable for scenarios where the load of an unmanned bicycle changes during operation.

[0086] For fixed load scenarios, the recursive estimation updates the estimated value of the rear frame inertial parameter correction in each sampling period, and determines whether to output a stable identification result based on the convergence criterion.

[0087] The convergence criterion includes at least one of the following: The changes in parameter estimates between two consecutive intervals satisfy And continue Each sampling period; the parameter covariance matrix satisfies or; The residual mean square value satisfies in, For parameter change threshold, The number of sampling periods that continuously satisfy the convergence condition. This is the covariance convergence threshold. This is the residual convergence threshold.

[0088] After the convergence criterion is met, the system outputs the estimated value of the current rear frame inertial parameter correction that meets the convergence criterion as the fixed load identification result. In subsequent operation, if the residual mean square value, parameter covariance or load change detection index exceeds the preset threshold, the system will re-enter the recursive update state.

[0089] For varying load scenarios, the recursive estimation runs continuously online, with the parameter update frequency matching the sensor state estimation frequency or controller frequency, and not less than twice the load variation characteristic frequency. In one embodiment, the parameter update frequency is taken as an integer division of the basic stability control frequency of the unmanned bicycle, and each update uses the most recent... Valid data within each sampling period. If the current sampling time does not meet safety conditions, sensor data is abnormal, or the number of conditions in the regression matrix exceeds the upper limit, parameter updates for that sampling time are paused, and only the estimated value from the previous time is retained. In each parameter update period, the estimated value of the rear frame inertial parameter correction for the current time is output as the result of the variable load identification.

[0090] Step 11: Apply physical constraints and output parameters.

[0091] Physical constraints are applied to the estimated value of the rear frame inertial parameter correction; wherein, for a fixed load scenario, the estimated value of the rear frame inertial parameter correction is specifically the estimated value of the rear frame inertial parameter correction that satisfies the convergence criterion; for a variable load scenario, the estimated value of the rear frame inertial parameter correction is specifically the estimated value of the rear frame inertial parameter correction at the current moment.

[0092] The physical constraints are used to define the set of physically feasible parameters. These include mass constraints, equivalent centroid relative displacement range constraints, positive definite central inertia matrix constraints, and principal inertia realizability constraints.

[0093] The quality constraint is: in, and These are the lower and upper limits of the equivalent mass of the rear frame, respectively.

[0094] The relative displacement range constraint of the equivalent centroid is: in, The equivalent center of gravity of the rear frame after loading is relative to the nominal center of gravity of the rear frame under no-load conditions. The allowable range of coordinate displacement. If absolute geometric coordinates relative to the rear wheel contact point are required, then in the upright configuration of the bicycle, the equivalent center of mass coordinates of the loaded rear frame are: .

[0095] The positive definite constraint of the central inertia matrix is ​​applied to the equivalent central inertia matrix of the rear frame after loading, in order to ensure that the obtained central inertia matrix corresponds to the positive inertia of the real rigid body.

[0096] It should be noted that, It is not used as a direct identification parameter, but is obtained from the first-order mass moment and mass recovery obtained from the identification, that is, the equivalent centroid after loading relative to... The coordinate displacement satisfies because The inertia parameter in the subsequent vehicle frame nominal center of gravity under no-load conditions Using the reference point, first construct a structure relative to... Inertia matrix: Then, based on the parallel axis theorem, the equivalent centroid relative to the loaded area is obtained. Central inertia matrix: in, , It is a third-order identity matrix.

[0097] The positive definite constraint of the central inertia matrix specifically refers to: the central inertia matrix It satisfies positive definiteness, and its minimum eigenvalue is not less than the positive definiteness threshold of inertia. .

[0098] The specific subjectivity feasibility constraint is as follows: The three principal inertia Satisfy the rigid body inertia realizability constraint: The subjectivity realizability constraint is used to ensure that the estimation result can be realized by a certain real quality distribution.

[0099] In another implementation, the physical realizability of the rigid body inertia parameters can also be described by an equivalent pseudo-inertia matrix positive definite constraint.

[0100] If the parameter estimation results exceed the set of physically feasible parameters Then, projection correction is performed: in, For the set of physically feasible parameters, To set The projection operator.

[0101] The projection correction includes the following steps: First, based on the estimated... Calculate the equivalent inertial parameters of the rear frame after loading. : And by After restoration, the equivalent center of gravity of the frame is relative to Coordinate displacement: Then, the relative displacement of the mass and the equivalent centroid is truncated within a range: And recalculate the first-order mass moment after trimming: Subsequently, constructing relative to inertia matrix And according to the parallel axis theorem, it is transformed into the central inertia matrix relative to the equivalent centroid after loading: in, .

[0102] right Perform symmetry processing: And perform eigenvalue decomposition on it: in, The matrix of orthogonal eigenvectors It is a diagonal matrix of eigenvalues.

[0103] If there exists an eigenvalue less than the positive definite inertia threshold Then cut it into : And reconstruct the positive definite central inertia matrix: If the reconstructed principal inertia still does not satisfy the rigid body inertia realizability constraint, then the principal inertia is projected again to satisfy it: in, The central principal inertia after projection; the reprojection can be achieved by trimming the principal inertia that violates the triangle inequality to a feasible interval that satisfies the preset margin, or by positive definite projection of the pseudo-inertia matrix.

[0104] Then, applying the parallel axis theorem back to the nominal center of gravity of the vehicle frame under no-load conditions... Inertia matrix for reference point: Finally, the trimmed mass, first-order mass moment, and rotation... The inertia matrix is ​​then recombined to form physically feasible equivalent inertial parameters for the rear frame. : in, for The corresponding element in. And let: This yields the rear frame inertial parameter correction amount that satisfies the constraints of positive mass, bounded relative displacement of equivalent centroid, positive definite central inertia matrix, and realizability of principal inertia.

[0105] Final output: And the corrected rear frame inertia parameters: Example In this embodiment, the unmanned bicycle is equipped with an inertial measurement unit, a steering angle encoder, a rear wheel speed encoder, a steering motor current sensor, a drive motor current sensor, and a positioning or sensing module.

[0106] This embodiment follows Figure 1 The process shown is executed, wherein S1 to S11 correspond to steps one to eleven in the content of this invention.

[0107] First, a nominal four-rigid-body structure and parameter model of the unmanned bicycle is established. The parameter model uses 25 model parameters obtained under no-load or nominal conditions based on the assumption of central axis symmetry as the nominal parameter vector. And define generalized coordinates and independent coordinates; Secondly, the loaded rear frame is treated as a general three-dimensional rigid body, and a 10-dimensional parameter correction is defined. The system utilizes an inertial measurement unit, steering angle encoder, wheel speed encoder, positioning or odometer module, and state estimation module to obtain... Calculate the nominal dynamic residual Among them, position coordinates This can be provided by the state estimation module and does not require direct measurement; independent generalized acceleration. It can be obtained by filtering differentiation, smoothing estimation or state observer.

[0108] Secondly, based on the rear frame space speed Jacobi Space velocity Space acceleration and spatial inertia basis matrix Construct the regression matrix .

[0109] Then, the system calculates the stability margin. and information matrix When the vehicle stability margin is insufficient, no excitation is applied; when the stability margin is sufficient but observability is insufficient, a small steering or drive identification excitation is superimposed on the basic stability control quantity.

[0110] Finally, the recursive least squares method is used to estimate... The results are then subjected to physical constraint projection and confidence level evaluation. When the confidence level meets the requirements, the correction amount of the asymmetric load inertia parameter of the rear frame and the corrected dynamic model parameters are output.

[0111] In one specific embodiment, the unmanned bicycle uses to Driving at a certain speed, the control cycle is taken The parameter recursive estimation period is taken as Sliding window length Pick to One sampling point. Overall stability margin threshold. Pick to The upper limit of the total amplitude of micro-amplitude recognition excitation Take the rated torque of the actuator to Steering identification excitation frequency Pick to The driving identification stimulus uses finite-duration pulses or pseudo-random binary sequences, the duration of which does not exceed the time corresponding to the current sliding window length. Forgetting factor. Pick to When the change in parameter estimates between two consecutive intervals is less than 100%, the change in parameter estimates between two consecutive intervals is less than 100%. and continuously satisfy Each sampling period, and the mean square value of the residual is less than [number] times. At that time, the convergence of the fixed load parameter estimation is determined. The above values ​​are used to illustrate one embodiment of the present invention, which can be adjusted according to the size of the unmanned bicycle, speed range, and sensor noise level while satisfying safety margins and actuator constraints.

[0112] In another specific embodiment, if the load mounted on the rear frame is relative to the nominal center of gravity of the rear frame under no-load conditions... If lateral offset exists, the steering identification stimulus is preferentially used for enhancement. , and The observability; if the load mainly manifests as an increase in mass or changes in longitudinal or vertical position, then the drive identification excitation is preferentially used to enhance the observability. , , And the observability of pitch-related inertia corrections. When within multiple consecutive sliding windows... If the full rank or condition number requirements are still not met, the system outputs the identifiable parameter combination determined by singular value decomposition and temporarily suspends the update of unreliably identifiable parameter directions.

[0113] In another specific embodiment, after an asymmetric load is installed on the rear frame, the dynamic response and residuals during the same driving process are predicted using both the method with only a 25-parameter nominal model and the method described in this invention. Compared to using only a 25-parameter nominal model, this invention, by estimating the 10-dimensional asymmetric inertia parameter correction of the rear frame online, can reduce the dynamic residuals caused by the lack of modeling of the lateral first-order mass moment and the asymmetric inertia product under asymmetric load conditions, and improve the prediction accuracy of roll-steering coupled dynamics. The comparison process can be verified using real vehicle data, semi-physical test data, or dynamic simulation data.

[0114] like Figure 2 As shown, this application provides an electronic device including a memory 101 for storing one or more programs and a processor 102. When the one or more programs are executed by the processor 102, they implement the method as described in any of the first aspects above.

[0115] The system also includes a communication interface 103. The memory 101, processor 102, and communication interface 103 are electrically connected directly or indirectly to each other to enable data transmission or interaction. For example, these components can be electrically connected to each other via one or more communication buses or signal lines. The memory 101 can be used to store software programs and modules, and the processor 102 executes various functional applications and data processing by executing the software programs and modules stored in the memory 101. The communication interface 103 can be used for signaling or data communication with other node devices.

[0116] The memory 101 may be, but is not limited to, random access memory (RAM), read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.

[0117] The processor 102 can be an integrated circuit chip with signal processing capabilities. The processor 102 can be a general-purpose processor 102, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0118] In the embodiments provided in this application, it should be understood that the disclosed methods and systems can also be implemented in other ways. The method and system embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0119] In addition, the functional modules in the various embodiments of this application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0120] On the other hand, embodiments of this application provide a computer-readable storage medium storing a computer program thereon. When executed by processor 102, the computer program implements the methods described in any of the first aspects above. If the functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0121] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A method for online identification of asymmetric load inertial parameters of an unmanned bicycle, characterized in that, The method includes the following steps: Step 1: Establish the nominal four-rigid-body structure and parameter model of the unmanned bicycle. The parameter model uses 25 model parameters obtained under the assumption of central axis symmetry in the unloaded or nominal state as the nominal parameter vector. ; Step 2: Define generalized coordinates and independent coordinates; Step 3: Determine the nominal center of gravity of the vehicle frame under no-load conditions. Define the 10-dimensional inertial parameter correction for the rear frame at the reference point. ; Step 4: Based on the nominal four-rigid-body structure of the unmanned bicycle, generate a 10-dimensional inertial parameter correction quantity including the rear frame for residual construction and parameter identification. The nonholonomic dynamic equations after loading; Step 5: Based on the nominal parameter vector The nominal model generalized force residual is calculated using the state variables at the current sampling time. ; Step Six: Based on d'Alembert's principle, map the spatial inertial force of the rear frame into a generalized force on independent generalized coordinates, and construct the regression matrix corresponding to the 10-dimensional inertial parameter correction of the rear frame. This forms the parameter identification equation; Step 7: Generate basic stability control variables based on the current state of the unmanned bicycle, and calculate the comprehensive stability margin based on tilt angle, tilt rate, steering angle, steering rate, actuator margin, path error, and obstacle distance. ; Step 8: Based on the regression matrix Constructing an information matrix within a sliding window And based on the information matrix The rank, condition number, minimum eigenvalue, or parameter covariance are used to evaluate the observability of the 10-dimensional rear frame inertial parameter correction. Step Nine: When Meets safety requirements and When observability is insufficient, a small-amplitude identification excitation constrained by the stability margin is superimposed on the basic stability control quantity; when Safety conditions are not met, or When the observability requirement is met, the micro-amplitude identification stimulus is not actively superimposed, and the recursive parameter update is continued using natural driving data; Step 10: Use recursive estimation to obtain the correction amount of the 10-dimensional inertial parameters of the rear frame. Estimated values ​​of the correction amount of the rear frame inertial parameters at each sampling time; Step 11: Apply physical constraints to the estimated value of the rear frame inertia parameter correction, which are positive in mass, have bounded relative displacement of the equivalent center of mass, positive definite central inertia matrix, and realizable principal inertia, and output the dynamic model parameters of the unmanned bicycle after physical constraint projection correction.

2. The method according to claim 1, characterized in that, In step one, the 25 model parameters are: in, For the nominal parameter vector, the superscript Indicates no-load or nominal status; The nominal wheelbase, The nominal front wheel trail, This refers to the nominal fork pivot angle. These are the nominal rear wheel radius, rear wheel mass, and rear wheel circumference. shaft and The moment of inertia of the shaft, and the moment of inertia of the rear wheel are all represented in the rear wheel fixed coordinate system with the rear wheel center of mass as the reference point; These are the nominal rear frame mass and the nominal rear frame center of gravity relative to the rear wheel contact point in the bicycle's upright configuration. coordinates and The coordinates, and the rear frame's orbital distance, represented in the rear frame fixed coordinate system with the nominal center of gravity of the rear frame as the reference point. moment of inertia of the shaft and directional product of inertia; These are the nominal front frame mass and the nominal front frame center of gravity relative to the rear wheel contact point in the upright position of the bicycle. coordinates and Coordinates, and the front frame's orbital plane, represented in the front frame fixed coordinate system with the front frame's center of mass as the reference point. moment of inertia of the shaft and directional product of inertia; These are the nominal front wheel radius, front wheel mass, and front wheel twist rate, respectively. shaft and The moment of inertia of the axle, the moment of inertia of the front wheel are all represented in the front wheel fixed coordinate system with the front wheel center of mass as the reference point; the 25 model parameters are obtained under the assumption that the mass distribution of the bicycle is symmetrical about the axle plane; In step two, generalized coordinates for: in, The angle of rotation of the rear wheel relative to the rear frame. The angle of rotation of the front wheel relative to the front frame. The angle of rotation between the front frame and the rear frame. Yaw angle It is the angle of inclination. The pitch angle, The coordinates of the origin of the local coordinate system of the rear frame in the world coordinate system; Independent coordinates for: The method employs a velocity mapping relationship determined by wheel-to-ground slip-free contact constraints when constructing the rear frame spatial velocity Jacobian matrix and dynamic residuals. in, For generalized speed, This is a velocity mapping matrix used to map independent generalized velocities. Mapping to complete generalized velocity The velocity mapping relationship serves as the basis for kinematic constraints in the parameter identification calculation of this invention. The generalized coordinates Independent generalized velocity and independent generalized acceleration The position coordinates are obtained from sensor data and state estimation results of the unmanned bicycle; wherein, the position coordinates in the generalized coordinate system are... It is not required to be measured directly by a single sensor; the independent generalized acceleration is obtained through state estimation from at least one of the following: wheel speedometer, inertial measurement unit, angle encoder, positioning module, visual odometry, or laser odometry. Obtained by filtering differentiation, smoothing estimation, or state observer.

3. The method according to claim 1, characterized in that, In step three, the 10-dimensional inertial parameter correction amount of the rear frame for: in, This is the correction amount for the equivalent mass of the rear frame. These are the nominal center of gravity of the vehicle frame under no-load conditions. The equivalent first-order mass moment of the rear frame, with reference point , is The amount of directional correction. These are the nominal center of gravity of the vehicle frame under no-load conditions. The rear frame is used as a reference point. Shaft inertia correction amount These are the nominal center of gravity of the vehicle frame under no-load conditions. Rear frame as reference point Correction for directional inertia product; Nominal rear frame 10-dimensional inertial parameters From the nominal parameter vector The rear frame parameters in the data are expanded to obtain: The origin of the fixed coordinate system of the rear frame is taken as the nominal centroid of the rear frame under no-load conditions. Therefore, under the nominal condition, all three first-order mass moments are zero; the two zero-inertia products correspond to the nominal axial symmetry assumption. and The Used to describe the nominal center of gravity of the rear frame under no-load conditions. The position of the bicycle relative to the contact point of the rear wheel in an upright configuration is not considered as... The first-order mass moment is used in the process; Equivalent inertial parameters of the rear frame after loading for: 。 4. The method according to claim 1, characterized in that, In step four, the nonholonomic dynamics equations of the loaded unmanned bicycle are used as the basis for residual construction. The dynamics equations are expressed as follows: in, To constrain the quality matrix in the form of embedding, To constrain the Coriolis force, gravity, and velocity-related terms in the embedded form, Let be the constant mapping matrix from input torque to generalized force in independent generalized coordinates, and For the input torque vector, For handlebar steering torque, This is the torque for rear-wheel drive; and It is derived from the nominal four-rigid-body structure of an unmanned bicycle; When the and exist At that time, a nominal model is established, and the corresponding matrix is ​​denoted as follows. ; In step five, the generalized force residual for: in, For the first The input torque vector at each sampling time.

5. The method according to claim 1, characterized in that, In step six, The parameter identification equation is: in, For the first The nominal dynamic generalized force residual at each sampling time, For the first The input torque vector at each sampling time, This is the regression matrix corresponding to the 10-dimensional inertial parameter correction of the rear frame. For measuring noise, unmodeled disturbances, and external disturbances; The regression matrix is ​​the first Listed as: in, For the regression matrix The List, ; The Jacobian matrix of the rear frame space velocity with respect to the independent generalized velocities satisfies... ; For rear frame space speed, To increase the space for the rear frame, This refers to the acceleration of the rear frame space after deducting gravity. Let be the spatial gravitational acceleration expressed in the rear frame coordinate system. For the first The spatial inertia basis matrix corresponding to each rear frame inertia parameter. For spatial force cross multiplication operator; The regression matrix for: 。 6. The method according to claim 1, characterized in that, In step seven, the stability margin is composed of multiple dimensionless safety margin indices, including tilt angle margin, tilt rate margin, steering angle margin, steering rate margin, actuator margin, path error margin, and obstacle distance margin. Each dimensionless safety margin indices are calculated based on their corresponding physical quantities and thresholds. The multiple dimensionless safety margin indices then determine whether a safe and observable excitation is permitted. Specifically, the safe and observable excitation is a micro-amplitude identification excitation constrained by the stability margin and used to improve parameter observability. The specific meaning of whether to allow the application of safe and observable incentives is: to consider the comprehensive stability margin. With minimum integrated stability margin Compare the results to obtain the safety clearance indicator; like: The security permission flag is defined as not applying an identification stimulus, wherein... The minimum overall stability margin required to allow the application of identification stimuli; like: The safety permission flag is then used to determine the observability of the parameters.

7. The method according to claim 1, characterized in that, In step eight, the information matrix : in, , The length of the sliding window; If any of the following conditions are met, the current data is deemed insufficiently observable for the correction of the 10-dimensional rear frame inertial parameters: in, The smallest eigenvalue of the information matrix. The minimum feature value threshold, Let be the rank of the information matrix. The condition number of the information matrix. The condition number threshold; When the information matrix within multiple consecutive sliding windows still fails to meet the full rank or condition number requirements after applying a safe and observable excitation, the identifiable parameter subspace is determined based on the singular value decomposition of the information matrix, and the identifiable parameter combination is output, or the set of parameters to be identified is reduced to a subset of parameters that can be reliably estimated under the current motion state.

8. The method according to claim 1, characterized in that, In step nine, a small-amplitude identification excitation constrained by the stability margin is superimposed on the basic stability control quantity to obtain the actual input torque at time k: in, For micro-amplitude recognition incentives; The micro-amplitude identification excitation includes the superposition of the handlebar steering torque channel. Steering recognition excitation, superimposed on the rear wheel drive torque channel The driving identification excitation or a combination of the two, and the upper limit of the total amplitude of the micro-amplitude identification excitation is constrained by the comprehensive stability margin; when steering identification excitation and driving identification excitation are used at the same time, the upper limit of the total amplitude is allocated as steering identification excitation amplitude and driving identification excitation amplitude according to the preset allocation coefficient or the observability gap of the parameter to be identified.

9. The method according to claim 1, characterized in that, In step ten, the recursive estimation is specifically a recursive least squares method with a forgetting factor, to obtain the first... Estimated values ​​of the correction amount of the rear frame inertial parameters at each sampling time; When the unmanned bicycle load remains fixed during a single identification process, the convergence of parameter estimation is determined based on the parameter increment norm, root mean square of residuals, trace of parameter covariance matrix, and observability index of information matrix. When multiple consecutive sliding windows meet the convergence condition, the active application of micro-amplitude identification excitation is stopped and the estimated value of the current rear frame inertial parameter correction is output. When the load on the unmanned bicycle changes during operation, online tracking continues using recursive estimation with a forgetting factor.

10. The method according to claim 1, characterized in that, In step eleven, the physical constraint projection correction includes: performing positive projection on the mass parameters, performing interval projection on the relative displacement of the equivalent center of mass, performing positive definite projection on the central inertia matrix, and performing rigid body inertia realizability constraints on the principal inertia; the positive definite projection of the central inertia matrix transforms the inertia matrix with the nominal center of mass of the vehicle frame under no-load as the reference point to the equivalent center of mass after loading through the parallel axis theorem, performs eigenvalue decomposition on the transformed central inertia matrix, corrects the eigenvalues ​​less than the preset positive threshold to the positive threshold, reconstructs the central inertia matrix, and then transforms it back to the inertia matrix with the nominal center of mass of the vehicle frame under no-load as the reference point through the parallel axis theorem.

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