Differential measurement method and system based on repeatable state revisit

Abstract

The application discloses a differential measurement method and system based on repeatable state revisiting, and belongs to the field of precision measurement. In view of the problem that systematic pointing errors of a motion mechanism vary with gear positions and are difficult to eliminate in time-sharing pointing measurement, thereby leading to low measurement accuracy, gear position sequences of the motion mechanism are planned, and mechanism state quantities are recorded. Reference observations are collected in a reference period, and revisiting observations are collected by revisiting the same gear position sequences in a measurement period. The stopping of each gear position is guaranteed by the repeatability of the motion mechanism itself. State change quantities are calculated by the difference between the reference observations and the revisiting observations. Systematic pointing errors are determined functions of the mechanism state quantities, and are mutually offset in the difference between the two-period observations of the same state. The upper limit of the revisiting period is determined according to a preset error budget, and the reference gear positions are periodically revisited to truncate time-varying drift. The above errors can be eliminated without improving the hardware precision, and the application is suitable for cross-period measurement scenes such as structure deformation monitoring and rotating mechanical deflection measurement.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology, and specifically to a differential measurement method and system based on repeatable state revisiting. Background Technology

[0002] Structural deformation monitoring of large infrastructure projects (such as bridges, tunnels, dams, and stadiums) typically requires millimeter-level, long-term, automated observation of dozens to hundreds of measuring points. Fixed-field-of-view cameras are constrained by the interplay between field of view and resolution: if the field of view covers the entire structure, the actual size corresponding to a single pixel is too large to meet millimeter-level measurement requirements; if resolution is guaranteed, a single camera can only cover a few measuring points. Therefore, a time-division pointing measurement method using motion mechanisms is commonly adopted in engineering: the camera is driven by a pan-tilt head or turntable, or the ranging or angle measuring unit is driven by a scanning mechanism, pointing to each measuring point in turn according to a predetermined sequence, thus balancing coverage and measurement resolution. In this measurement method, the main bottleneck of measurement accuracy shifts from the camera to the pointing accuracy of the motion mechanism.

[0003] To improve the pointing accuracy of motion mechanisms, existing technologies mainly include the following approaches.

[0004] The first approach is the high-precision shaft system approach. Measurement robots (IATS), scanning total stations, and precision turntables employ high-precision shaft systems and direct-reading solutions using photoelectric encoders. Precision bearings and ground shafts ensure rotational accuracy, while high-bit photoelectric encoders achieve sub-arcsecond angle measurement. This approach has the following drawbacks: First, the cost of high-end encoders and precision shaft systems is more than an order of magnitude higher than that of ordinary electric pan-tilt heads. Second, the size, weight, and power consumption of the device increase significantly with increasing accuracy, making it unsuitable for multi-point deployment and long-term outdoor power supply. Third, measurement accuracy is constrained by the limits of machining, limiting further improvement. Taking a pan-tilt camera scanning multiple targets as an example, the pan-tilt head pointing uncertainty, magnified by the line-of-sight length, becomes the lateral error at the target location (1″ is approximately 0.36mm at a distance of 75m). Millimeter-level measurements require pointing accuracy better than approximately 3″, while the absolute pointing error of ordinary electric pan-tilt heads reaches the angular level, a difference of two orders of magnitude—if selection is based on absolute accuracy, only the aforementioned high-cost solution can be adopted.

[0005] The second approach is the shaft system error modeling and compensation approach. Traditional surveying instruments such as theodolites or total stations typically compensate for shaft system defects using error models: parametric models (e.g., harmonic series models, tilt correction models) are established for errors such as line-of-sight axis error, horizontal axis error, vertical axis tilt, dial eccentricity, encoder scale harmonics, and worm gear transmission periodic errors. These models are then corrected during the solution process after double-sided observation or multi-objective adjustment calibration. This approach has the following drawbacks: First, the error model has truncation errors, and the actual error family includes unmodeled higher-order terms and non-parametric components; second, model parameters drift over time with environmental and operating conditions such as temperature, lubrication status, and wear, requiring periodic recalibration, which is a huge workload for each instrument; third, model mismatch directly translates into systematic measurement deviations that are difficult to self-check. For example, patent document CN103207023B discloses a phase recovery multi-position absolute calibration method, which removes systematic error terms through multi-position measurement and polynomial fitting, but it still belongs to the calibration modeling route, which requires the establishment and fitting of an error model and serves the single-phase absolute measurement accuracy.

[0006] The third approach involves symmetrical and multi-state averaging. Double-sided observations (left and right sides of the instrument) using a theodolite or total station average the results by taking the mean value of the symmetrical axis system, thus eliminating the line-of-sight and transverse axis errors. The repetition method averages the results by rotating the dial across multiple positions, thus eliminating dial scale errors. Optical testing also employs calibration methods that use multi-position measurement fitting to remove systematic terms. The common essence of these techniques is variable-state averaging or symmetrical cancellation. Their shortcomings are: first, they can only cover specific error terms with symmetry or averaging properties (such as line-of-sight, transverse axis, and dial scale errors), and are ineffective for error families of general forms; second, their purpose is to improve the absolute measurement accuracy of a single period, without providing a measurement framework for inter-period state changes; third, averaging only reduces the error amplitude, without utilizing the repeatability of the mechanism's state, and without providing a mechanism for the overall cancellation of any type of systematic error family through same-state revisits and inter-period differences.

[0007] The fourth approach is the static channel differential approach. Methods such as DIC reference area compensation, GNSS double-difference, and InSAR permanent scatterers eliminate common system errors through common-mode differential analysis. However, these methods are all for static observation channels: two observations pass through the same fixed channel, and the system errors naturally share the same mode, allowing for direct subtraction to cancel them out. For example, patent document CN106091946A discloses a bridge self-calibration measurement device and method, which compensates for the system error of the same imaging unit using a fixed reference target, belonging to static channel reference compensation; patent document CN116009042A discloses a method for differential detection of relative deformation between single-station carrier epochs, belonging to epoch differential analysis of static antenna channels. The fundamental difference in time-division pointing scenarios for moving mechanisms lies in the fact that each gear corresponds to a different value of the system error family. If two measurements stop at different gears (or different approach directions at the same gear), the system errors do not share the same mode, and simple subtraction cannot cancel them out. Existing differential methods do not provide a mechanism for making the system errors of moving mechanisms share the same mode.

[0008] The fifth approach is the synchronous averaging approach for rotating machinery. This approach averages multi-cycle signals after aligning them with the rotational phase, suppressing random noise but offering no protection against deterministic shaft or installation system errors. It also fails to provide a measurement framework for state changes across different time periods (between two measurement periods).

[0009] In summary, the existing technology has the following core defects: On the one hand, the existing technology regards the systematic pointing error of the motion mechanism (i.e., the systematic pointing error that changes with the state of the motion mechanism, hereinafter referred to as systematic pointing error) as a quantity that must be eliminated by means of hardware precision suppression (such as the first route) or error model calibration correction (such as the second route). It does not recognize the station repeatability of the motion mechanism that can be utilized in time-sharing pointing measurement, nor does it provide a mechanism to make the systematic pointing error that changes with gear position common mode in the time-sharing pointing scenario of the motion mechanism and cancel it out as a whole in the inter-period differential measurement. On the other hand, the existing technology also does not consider the impact of the time-varying drift of the device and the accumulation of environmental terms over time on the differential results in inter-period measurement and its control methods. Summary of the Invention

[0010] To address the shortcomings of existing technologies, this invention provides a differential measurement method and system based on repeatable state revisiting, aiming to solve the problem that the systematic pointing error that varies with gear position in the time-sharing pointing measurement of motion mechanisms cannot be eliminated in the inter-period differential measurement, resulting in low accuracy of inter-period measurement results.

[0011] To achieve the above objectives, the present invention adopts the following technical solution: A differential measurement method based on repeatable state revisiting includes the following steps: Plan the gear sequence for the motion mechanism and record the mechanism state variables for each gear, where each gear corresponds to one or a group of measured targets; During the baseline period, the motion mechanism is stopped sequentially according to the gear sequence, and a baseline observation of the target being measured at each gear is collected. During the measurement period, the motion mechanism is made to revisit each gear in the gear sequence. The stopping position of the motion mechanism at each gear is guaranteed by the repeatability of the motion mechanism itself, and revisit observations are collected at each gear corresponding to the target being measured at that gear. For each gear position, the difference between the baseline observation and the follow-up observation is used as input to calculate the state change of the corresponding target. The systematic pointing error of the motion mechanism is a function for determining the state of the mechanism. The systematic pointing error cancels out each other in the difference between the two observations of the same state and does not enter the calculation result. The upper limit of the follow-up period is determined based on the preset error budget, and the baseline level is periodically followed up to check and cut off time-varying drift.

[0012] The difference between the actual stopping position of the motion mechanism at the same gear during the reference period and the measurement period is used as the stopping position difference for that gear, and the stopping position difference is used for compensation when calculating the change in state.

[0013] Furthermore, the stopping difference of each gear position is treated as an unknown and solved together with the state change quantity; wherein, the stopping difference is the difference between the actual stopping position of the motion mechanism in the same gear position during the reference period and the measurement period.

[0014] Furthermore, the mechanism state quantity is a periodic phase, the revisit is a co-phase sampling of the periodic phase, and the reference observation and the revisit observation are co-phase sampling observations.

[0015] Furthermore, determining the upper limit of the follow-up visit cycle based on a preset error budget includes: The upper limit of the first return visit cycle is determined based on the preset time-drift budget, and the upper limit of the second return visit cycle is determined based on the linear growth law of the environmental item differential residue with the return visit interval. The smaller value between the first upper limit of the return visit period and the second upper limit of the return visit period shall be used as the upper limit of the return visit period.

[0016] Furthermore, it also includes: When calculating the state change, the difference of the same level is combined with the difference of the spatial reference point to simultaneously cancel the systematic pointing error of the motion mechanism and the motion error of the carrier carrying the motion mechanism.

[0017] Furthermore, the lighting conditions for the target at each level are kept consistent during the reference period and the measurement period.

[0018] Furthermore, when the change in the state of the target exceeds the field of view or linearization range corresponding to the current gear, a new reference period is established for the new gear aligned with the target, and the displacement time sequence of the old and new reference periods is linked by overlapping observations or control points.

[0019] Furthermore, when revisiting each gear position during the measurement period, the motion mechanism approaches and stops in the same rotational direction as when the observations of each gear position were collected during the baseline period.

[0020] A differential measurement system for implementing the above-described differential measurement method based on repeatable state revisiting includes: The motion mechanism is used to point to multiple targets in a time-division manner according to the gear sequence and record the mechanism state variables of each gear, wherein each gear corresponds to one or a group of targets. The acquisition unit is used to acquire baseline observations at each gear according to the gear sequence during the baseline period, and to acquire follow-up observations at each gear corresponding to the target being measured at each gear when the motion mechanism revisits the gear sequence during the measurement period. The differential calculation unit is used to calculate the state change of the target under test for each gear position, taking the difference between the benchmark observation and the follow-up observation as input. The systematic pointing error of the motion mechanism is a function for determining the state quantity of the mechanism. The systematic pointing error cancels each other out in the difference between the two observations of the same state and does not enter the calculation result. The feedback control unit is used to control the motion mechanism to feedback the gear sequence, so that the stopping position of the motion mechanism in each gear is guaranteed by the repeatability of the motion mechanism itself, and to determine the upper limit of the feedback cycle according to the preset error budget, and to periodically feedback the reference gear to check and cut off the time-varying drift of the differential measurement system.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: Because this invention requires the motion mechanism to revisit the same gear sequence during the measurement period, and the stopping position of each gear is guaranteed only by the repeatability of the motion mechanism itself, without requiring absolute pointing accuracy, the dependence of measurement accuracy on the hardware accuracy of the motion mechanism changes from absolute pointing accuracy to stopping repeatability. Since the stopping repeatability of ordinary motion mechanisms is usually far superior to their absolute pointing accuracy, this invention does not require high-precision shaft systems and high-bit photoelectric encoders; ordinary electric pan-tilt units can meet the measurement requirements. The hardware cost is far lower than that of high-precision shaft system solutions, and the device size, weight, and power consumption are also significantly reduced, which is beneficial for multi-point deployment and long-term outdoor power supply.

[0022] Because this invention treats the systematic pointing error of the motion mechanism as a deterministic function of the mechanism's state variables, and calculates the difference between two observations under the same mechanism state, the systematic pointing error cancels out in the difference and does not enter the solution result. Therefore, the overall cancellation of the systematic pointing error is achieved at the observation level, without the need to establish a shaft system error model, or to calibrate and periodically recalibrate. Furthermore, since the cancellation process does not depend on any error model parameters, this invention is naturally robust to error model mismatch and slow temperature variations during the revisit period. It achieves equivalent measurement accuracy comparable to high-precision shaft system schemes without relying on high-precision shaft systems, effectively breaking through the technical path where measurement accuracy must depend on the absolute pointing accuracy of the mechanism. Its technical effect cannot be expected through the simple superposition of known technical means; it is an unexpected technical effect.

[0023] Since this invention uses the difference between baseline observation and follow-up observation as input to calculate the change in the target state, the output is the change in the state of the measured target (displacement or rotation angle); and the movement of the target during the baseline observation and follow-up observation is the measured object itself rather than the source of error, which does not violate the premise of the method, this invention is naturally adapted to cross-period measurement scenarios such as structural deformation monitoring and long-term evolution measurement.

[0024] Because this invention determines the upper limit of the return visit cycle based on a preset error budget, and periodically returns to the benchmark level to check and cut off time-varying drift, the differential residuals of device time-varying drift and environmental items accumulated over time can be controlled and managed. Through the closed-loop design criterion of the upper limit of the return visit cycle and the periodic check of the benchmark level, the time effectiveness of long-term automated monitoring can be guaranteed, and there is no need for manual maintenance of periodic recalibration of each device.

[0025] Because this invention plans a sequence of gears for the motion mechanism and makes each gear correspond to one or a group of measured targets, a single motion mechanism can cover multiple measurement points by time-division pointing, taking into account both the field of view coverage and single-point measurement resolution, and adapting to the long-term monitoring needs of multiple measurement points of large infrastructure.

[0026] More importantly, retrospective observation and differential cancellation are interdependent and synergistic in this invention: only by retrospective observation and retrospective observation being in the same structural state, and by ensuring that the systematic pointing error has the same value in both periods, can inter-period differential cancellation cancel out any family of systematic errors of any form. Conversely, without retrospective observation, the errors in the two periods do not share a common modulus, and simple subtraction cannot cancel them out; without differential cancellation, the error will still enter the single-period measurement result. It is evident that retrospective observation provides the premise for error common modulus in differential cancellation. The combination of the two ensures that the magnitude of the absolute pointing error does not enter the measurement result at all. This effect cannot be obtained by implementing either feature alone, demonstrating the synergistic relationship between technical features. This also distinguishes this invention from existing technical routes that eliminate errors through hardware suppression, error modeling, or symmetrical averaging.

[0027] Furthermore, the return visit cycle management ensures the continued validity of the cancellation premise in the time dimension: since the present invention determines the upper limit of the return visit cycle according to the preset error budget and periodically returns to the benchmark level, it promptly cuts off the time-varying drift of the device and the accumulation of environmental terms, avoiding the systematic pointing error from drifting over time and destroying the deterministic function property of its mechanism state quantity, thereby making the same state difference cancellation continuously effective in long-term, automated monitoring, and ensuring that the measurement results remain stable and reliable over a long period. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating a differential measurement method based on repeatable state revisiting according to the present invention. Figure 2 This is a schematic diagram illustrating the systematic pointing error cancellation principle of the present invention; Figure 3 This is a schematic diagram of a dual-gimbal camera station revisiting scanning intersection measurement scenario according to Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the dual criteria for the return visit cycle in this invention; Figure 5 This is a schematic diagram of the in-phase differential measurement of rotating machinery according to Embodiment 3 of the present invention; Figure 6 This is a schematic diagram of the same-direction approach strategy of the present invention. Detailed Implementation

[0029] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0030] like Figure 1 As shown, this embodiment provides a differential measurement method based on repeatable state revisiting, including the following steps.

[0031] Step S1: File creation. Plan the gear sequence s1, s2, ..., s for the motion mechanism. k Each gear position corresponds to one or a group of measured targets, and the mechanism state variables of each gear position are recorded. The gear position sequence can be planned according to the distribution of the measured targets and the field of view size. The field of view of each gear position can cover one or more measured targets. The mechanism state variables are recordable quantities used to characterize the state of the motion mechanism, including but not limited to encoder readings, gear index, and rotation phase.

[0032] Step S2: Initial Data Acquisition. During the baseline period t0, the motion mechanism is brought to a stop sequentially according to the gear sequence, and baseline observations are acquired for the target object at each gear. These observations can be images, angle readings, or other forms of measurement data; the baseline observations can be averaged over multiple frames and archived to suppress random noise.

[0033] Step S3: Follow-up Data Acquisition. During the measurement period t1, the motion mechanism is made to follow up on each gear in the gear sequence, and follow-up observations are collected at each gear corresponding to the target being measured. The stopping position at each gear is guaranteed by the repeatability of the motion mechanism itself, without requiring absolute pointing accuracy; preferably, each gear approaches and stops in the same rotational direction as the reference period (i.e., approaching in the same direction, see...). Figure 6 ), to eliminate the bifurcations of backlash lag.

[0034] Step S4: Differential Calculation for Each Range. For each range, using the difference between the baseline observation and the follow-up observation as input, calculate the corresponding state change of the measured target.

[0035] like Figure 2 As shown, the cancellation principle of this invention lies in the fact that the systematic pointing error family b(s) of the motion mechanism (including encoder calibration error, repeatable shaft wobble, dial or mounting eccentricity, stable components of backlash, etc.) is a deterministic function of the mechanism state s (gear position, phase, or position). Let the two measurements be in the same state s. k Follow-up visit, that is, a follow-up visit during the measurement period to the same position in the baseline period (the difference between the actual position in period t1 and the position in the baseline period is the position difference δ). s For ease of explanation, let the base period stop position be the nominal gear s. k Then the difference between the two observations is: Δy k =y(t1;s k )-y(t0;s k ) =J x ·Δx+[b(s k )-b(s k )]+b′(s k )·δ s +Δε k =J x ·Δx+b′(s k )·δ s +Δε k (Equation 1); Where, Δy k The difference between two observations (specifically, the image point difference Δu in visual observation) is the difference between two observations. k j, see equation 1a); Δx is the change in the target state (the measured quantity), J x For the observation of Jacobi, δ s The difference between the two periods' stop positions, Δε k For non-repeatable terms (random stop jitter and time-varying drift). In the second row of Equation 1, [b(s k )-b(s k b′(s) represents the cancellation term for systematic pointing errors under the same conditions, and its value is zero.k )·δ s The actual stopping position difference δ between the two periods s The resulting first-order residual originates from the actual stop position s in period t1. k +δ s Error value b(s) k +δ s ) relative to b(s) k The first-order Taylor expansion of b(s) is: k +δ s )-b(s k )≈b′(s k )·δ s The residue after cancellation is only the scale error slope b′(s) k ) and the difference between the positions δ s The product (second-order small quantity) and the non-repeating term Δε k —The magnitude of the absolute pointing error is not included in the measurement result at all.

[0036] It should be noted that the cancellation in Equation 1 applies only to the mechanism-side error family b(s); the change in the state of the measured target (displacement or rotation) is the unknown quantity to be determined in the observation equation, and the difference between the two observation periods caused by it is the output signal of the differential calculation. Therefore, the movement of the target during the two periods does not violate the premise of this method, as it is itself the measured quantity; what needs to remain unchanged are the mechanism error family and the parameters of the observation device.

[0037] The physical composition and repeatability basis of the systematic pointing error family b(s) include: ① Encoder scale error—the deterministic deviation of the code disk markings, which can be expanded into the harmonic series of the gear angle, constant for each gear; ② Worm gear or gear transmission periodic error—periodic with the transmission ratio, with the same value for the same gear; ③ Repeatable component of shaft wobble—caused by the bearing raceway morphology, determined by the shaft angle position; ④ Dial or mounting eccentricity—first harmonic, a deterministic function; ⑤ Backlash hysteresis—with a direction-dependent bi-branch structure (different values ​​for forward and reverse approach, see [reference]). Figure 6 After adopting the same-direction approach strategy, it degenerates into a single-branch deterministic function. All of the above are deterministic functions of the mechanism state, constituting b(s) that can be canceled in Equation 1; the only non-repeatable ones are random stop jitter and slow time-varying drift, which are controlled by multi-frame averaging and revisit cycle management (step S5).

[0038] Taking visual observation as an example, gear S k The difference Δu between two image points of target j k j and the change in the target state Δx j The relationship is: Δu k j=(f / λ k j)·B k j·Δx j +b′(sk )·δ s +Δε k (Equation 1a); Where f is the focal length, λ k j is the line-of-sight length of the target, B k j is the projection direction matrix, i.e., the observation Jacobian J in Equation 1. x The specific form under visual observation; the subject (f / λ) k j)·B k j·Δx j b′(s) represents the difference between two image points caused by the change in the state of the measured target; k )·δ s With Δε k As defined in Equation 1, these are the residual stop difference and the non-repeatable term, respectively, which can be suppressed through stop difference reading compensation or augmented solution. A single station provides two-dimensional constraints in the vertical plane of the line of sight; three-dimensional displacement can be obtained by differential intersection of two stations at the same level (see Example 1). This solution is linear least squares, requiring no iteration; multiple objectives are solved independently at each level, without coupling.

[0039] Step S5: Drift Control. Determine the upper limit of the revisit period based on the preset error budget, and periodically revisit the baseline position to check and cut off time-varying drift.

[0040] To eliminate the residual term b′(s) caused by the two-period stop difference δs k )·δ s Auxiliary reading devices can be installed at each gear position to measure the difference between the actual stopping position of the motion mechanism at the same gear position during the reference period and the measurement period (i.e., the stopping position difference at that gear position). The auxiliary reading device can be a near-field camera combined with coded markers: coded markers are fixed at the rotating parts of the motion mechanism, and the near-field camera reads the marker pose and converts it into the actual stopping position of the mechanism; alternatively, a differential encoder reading method can be used: a photoelectric encoder reads the actual stopping positions for two periods and calculates the difference. After measuring the stopping position difference, it is substituted into Equation 1 for compensation when calculating the change in state, for example, using -b′(s k )·δ s The difference between the two observations can be corrected, or the position difference can be substituted into the observation equation as a known quantity to reduce the residual to the reading noise level. For example, the arrangement of the near-field camera and the coded marker should ensure that the marker is within the camera's field of view and that the measurement range covers all positions of the mechanism.

[0041] When the position difference is large (such as when inspection vehicles or drones hover and revisit at the centimeter or even angle level) and difficult to measure accurately with a reading device, the position difference at each level can be treated as an unknown and solved jointly with the state change in the difference observation equation (i.e., augmented solution). Specifically, the position difference δ sk By incorporating the unknown vector, an augmented observation equation system is established: Δy k =J x ·Δx+J s ·δ sk +Δε k (Equation 2); Among them, J s δ is the Jacobian of the stop difference with respect to the observed value. sk Let be the stop difference at the k-th gear (as an unknown), and Δx be the state change (as an unknown). Using global least squares, we compare Δx with δ... sk Joint solution; the solution residuals of this method are not sensitive to the magnitude of the stop difference, that is, large changes in the stop difference have little impact on the solution results. Its observability is guaranteed by redundant observations provided by multiple ranges, multiple stations, and a small number of control points.

[0042] When the object being measured is a periodically moving body such as rotating machinery, the mechanism's state variables can be expressed using periodic phases (such as the rotational phase φ). k (or track phase). At this point, a phase-in-phase trigger (such as a key phase sensor, photoelectric pulse generator, or encoder zero-position pulse) can be installed on the rotating component. When the rotating component reaches the same rotational phase φ as the reference period... k The camera is triggered to capture images, making the two observations in the same phase. By differentiating the in-phase sampling observations across periods, changes in state such as dynamic deflection can be measured. In-phase sampling ensures that each observation corresponds to a fixed angular position on the rotating component, meaning that each observation is in the same mechanical state, which is consistent with the principle of equal-angle sampling in rotating machinery.

[0043] See Figure 4 The results show that the environmental item residuals increase approximately linearly with the revisit interval, and the upper limit of the revisit period T is obtained by taking the smaller of the device drift budget limit. max The time effectiveness of this method is ensured by the follow-up cycle management. On one hand, the residual first term after cancellation in Equation 1 is the product of the scale error slope and the stop position difference, and its upper bound satisfies: |r1| ≤ |b′(s k )|·|δ s | (Equation 3); That is, the value of the residual first term is jointly limited by the scale error slope and the stop difference, constituting the small-quantity premise criterion for Equation 1 to hold: the stop repeatability of a normal gimbal (arcsecond to angular grade) multiplied by the scale error slope (dimensionless small quantity) is usually a second-order small quantity, and the residual first term can be ignored; when |b′(s k )|·|δ s When the error exceeds the preset error budget (i.e., a small portion of the premise is breached), the augmented solution method described above (Equation 2) is adopted. On the other hand, the difference residual of the environmental terms (temperature gradient, atmospheric refraction) increases approximately linearly with the revisit interval, and its slope is equal to the time-varying rate v of the environmental terms. env The drift rate of the device when it cannot be repeated is v.drift The upper limit of the follow-up visit cycle can be determined by two criteria: based on the device's time-drift rate v. drift Budget B for time drift error drift Determine the upper limit of the first return visit period based on the time-varying rate v of the environmental item. env Error budget B for environmental items env Determine the upper limit of the second follow-up visit cycle, and use the smaller of the two values ​​as the upper limit of the follow-up visit cycle: T max =min(B env / v env B drift / v drift (Equation 4) The time-drift rate and the time-varying rate of environmental terms can be estimated by regression analysis of historical back-visit data, or by environmental monitoring sensors (such as temperature and air pressure sensors) and device status monitoring data; the error budget is pre-allocated according to the measurement accuracy requirements. In addition, random stop jitter decreases by an average of 1 / √n after multiple frames or multiple back-visits; non-repeatable shaft clearance is the bottom line that this method cannot eliminate, and the repeatability index of the mechanism rather than the absolute accuracy index should be used as the basis for procurement when selecting a model.

[0044] For example, the residual terms of this method and their suppression methods can be summarized in Table 1 below. The example magnitudes of each residual term in the table are only used to illustrate the relative magnitude relationship and suppression logic of each residual term, and do not constitute a limitation on the measurement accuracy of this invention.

[0045] Table 1

[0046] When the motion mechanism is mounted on a mobile carrier (such as an inspection vehicle or a drone), a spatial reference point (such as a fixed control sign or a stable background feature) can be set in the measurement scenario, and the differential observation of the same range and the differential observation of the spatial reference point can be combined (i.e., spatiotemporal double difference): the differential observation of the same range cancels the systematic pointing error on the motion mechanism side, and the differential observation of the spatial reference point cancels the motion error of the carrier itself. The combination of the two can cancel both types of errors at the same time.

[0047] To suppress spurious displacement (i.e., illumination bias aliasing) caused by changes in illumination, the illumination conditions for the target at each setting should be kept consistent during the reference period and the measurement period. For example, use a non-frequency flash source for illumination, or control the camera exposure time and gain to be consistent. When the observation environment is natural light and difficult to control, observation can be carried out during periods of stable illumination, or the illumination bias can be offset by differential observation of the spatial reference point.

[0048] When the change in the state of the target exceeds the field of view or linearization range corresponding to the current gear (such as large deformation caused by long-term evolution), a new reference period is established with the new gear aligned with the target, so that the subsequent measurement period revisits the new gear sequence; the old and new reference periods are linked by overlapping observations or control points: if the old and new gear fields of view have a target or area covered by the same area, the reference is transferred by using the difference between the two observations of the common target; otherwise, the coordinate transformation relationship is established by using the known coordinates of a small number of control points, and the displacement time series of the old and new reference periods are spliced ​​into a continuous time series.

[0049] See Figure 6 To eliminate the ambiguity caused by backlash, during the measurement period, when revisiting each gear position, the motion mechanism approaches and stops in the same rotational direction as when the observations of each gear position were collected during the baseline period, and does not reverse after reaching the position. Because the backlash of worm gear or gear transmission causes different stopping values ​​for forward and reverse approaches (forming a double branch), approaching in the same direction can ensure that both periods stop on the same branch, thus reducing the backlash to a single-branch deterministic function of the mechanism state, which is then incorporated into b(s) to participate in the cancellation of Equation 1; this method is also applicable to ordinary worm gear gimbals.

[0050] Example 1: Pan-tilt scanning dual-station intersection (structural displacement monitoring). See also Figure 3 This embodiment uses long-term deformation monitoring of bridge deck measuring points on a large bridge as an example to illustrate the complete implementation process of the present invention.

[0051] (1) Measurement Device Composition. The measurement device in this embodiment includes two pan-tilt camera stations and a data processing unit. Each pan-tilt camera station includes an electric pan-tilt head, a camera mounted on the pan-tilt head, and an encoder; the two pan-tilt camera stations are located on both sides of the structure under test, so that the lines of sight from the two stations form an intersection angle γ at the measurement point. For example, the line of sight is about 75m long, and the intersection angle γ is 60°–90° (in the optimal depth error zone); the pan-tilt head is a common electric pan-tilt head that only requires repeatability of stopping position; each station points to the bridge surface measurement point according to K = 8–16 gears, and each gear corresponds to one or a group of measurement points. The data processing unit is used to perform differential calculation within the same gear and return visit cycle management.

[0052] (2) Deployment and control field. The distance between the two stations is set so that the intersection angle γ∈[60°,90°]; control field markers containing depth distribution are deployed 3–5m behind each station for checking the station's own movement.

[0053] (3) Initial data acquisition. Plan K gear positions, with each position covering 1–3 measurement points. Record the gear position index and encoder readings for each position. At the reference period t0, the gimbal approaches and stops sequentially along the same rotation direction (same-direction approach, see [reference]). Figure 6Once in position, the camera acquires multiple frames at each setting and averages them, archiving them as the baseline observation for that setting. For example, at least 200 frames are acquired at each setting and averaged to suppress random noise.

[0054] (4) Follow-up data collection. During each measurement period t1, the gimbal repeats the same gear sequence and approach direction as the baseline period. The stopping position of each gear is guaranteed by the repeatability of the gimbal itself, and no absolute pointing accuracy is required. Multiple frames of images are collected at each gear and averaged to obtain the follow-up observation of that gear.

[0055] (5) Differential calculation within the same range. The difference between the benchmark observation and the follow-up observation is calculated for each range, and the three-dimensional displacement of each measuring point is calculated by intersection of the two stations according to Equation 1a. Among them, the position difference of each range is measured by the encoder differential reading or the auxiliary reading method of the near-field camera with the coded mark, and is compensated in the calculation according to the above method.

[0056] (6) Drift control. Determine the upper limit of the revisit period according to Formula 4; revisit the baseline at the beginning and end of each measurement period to check and cut off the time-varying drift of the device and the accumulation of environmental items.

[0057] (7) Output. Output the displacement time sequence and uncertainty of each measuring point for bridge deformation assessment.

[0058] Example 2: Inspection Vehicle Follow-up Measurement (Augmented Solution). This example uses a track or utility tunnel inspection scenario to illustrate the implementation of this method on a coarse positioning motion platform.

[0059] (1) Measurement device composition. The inspection vehicle carries a camera and travels along the inspection route to image the structure under test at the set measurement station positions; the inspection vehicle and the camera constitute a motion mechanism observation system mounted on a mobile carrier. Several measurement station positions are set up along the inspection route, and a small number of control points are set up.

[0060] (2) Initial data collection. During the baseline period, the location of each station is planned and the location information of each station (such as odometer readings, track markings or positioning data) is recorded as the mechanism state variables; the inspection vehicle travels to the location of each station and images the structure under test at each station to obtain the baseline observation.

[0061] (3) Follow-up data collection. During each measurement period, the inspection vehicle travels to the same set of stations again and images the measured structure at each station to obtain follow-up observations. Due to track irregularities and parking position errors, there is a deviation in the actual stopping position when the inspection vehicle passes the same station twice (the difference in stopping position between trips can reach the centimeter level or even the angular level), which exceeds the small amount premise shown in the residual first term of Equation 1.

[0062] (4) Augmented solution. For cases where the position difference exceeds a small threshold, the position difference of each station is treated as an unknown and solved jointly with the displacement of the measuring point in the differential observation equation using the augmented solution method described above. Its observability is guaranteed by the coverage of multiple stations and a small number of control points. This method is robust to the magnitude of the position difference, making it applicable to coarse positioning platforms such as inspection vehicles.

[0063] Example 3: In-phase differential rotation of rotating machinery (periodic state). See also Figure 5 This embodiment uses the intertemporal measurement of the dynamic deflection change of rotating machinery as an example to illustrate the implementation under periodic phase conditions.

[0064] (1) Measuring device configuration. The rotating component is the object being measured; the camera is fixedly mounted on a stationary base near the rotating component for imaging the rotating component; the in-phase trigger is used to generate a trigger signal that is synchronized with the rotation angle phase of the rotating component. For example, the in-phase trigger can be a key phase sensor (outputting a reference pulse per revolution) or an encoder zero-position pulse.

[0065] (2) Trigger phase determination. The trigger phase φ is defined by the reference pulse edge (e.g., rising edge) of the in-phase trigger. k For example, a single trigger phase (e.g., φ1 = 0) can be used, or multiple trigger phases φ1, φ2, ..., φ can be used at equal intervals. M (Corresponding to the M angular positions within one revolution of the rotating component).

[0066] (3) Initial data acquisition. During the baseline period, when the rotating component reaches the trigger phase φ k When the camera is triggered by the same phase trigger, the reference observation at that phase is obtained; the trigger phase is recorded as the mechanism state quantity.

[0067] (4) Follow-up acquisition and in-phase differential. In each measurement period, at the same trigger phase φ k The camera is triggered to capture images, resulting in a follow-up observation. Differential analysis is performed on the in-phase sampling observations across different periods to measure the change in dynamic deflection. Since the systematic pointing error family b(φ) of the shaft system and installation is determined with the rotation phase when the mechanism is in the rotation phase, it is canceled out phase by phase in the in-phase differential analysis.

[0068] (5) Supplementary explanation. This embodiment is equivalent to upgrading the synchronous averaging idea (averaging for random items) to a systematic pointing error cancellation method (for deterministic error families); its revisit period is determined according to Equation 4.

[0069] Example 4: UAV hovering revisit measurement (augmented solution aerial survey mode). This example uses an aerial survey scenario of UAV imaging of a structure to illustrate the implementation of state revisit in the form of nominal waypoints.

[0070] (1) Measurement device configuration. The multi-rotor UAV is equipped with a camera to image the structure under test according to a set of planned nominal hovering positions; a small number of control points are set up on the ground, and the airborne positioning system (such as RTK) provides the position estimate of the UAV.

[0071] (2) Initial data collection. During the baseline period, the nominal hovering positions are planned and their waypoint coordinates are recorded as the state variables of the mechanism; the UAV flies to each nominal hovering position in sequence and images the structure under test at each position to obtain the baseline observation.

[0072] (3) Follow-up data collection. During each measurement period, the UAV flies back to the same set of nominal hovering positions to image, and the follow-up observations are obtained. Due to the positional deviation of the UAV hovering (which can be up to the decimeter level), the actual hovering position deviates from the nominal waypoint, which exceeds the small amount premise shown in the first term of the residual in Equation 1.

[0073] (4) Augmented solution. Using the above-mentioned augmented solution method, the pose deviation of each hovering position is taken as an unknown and solved together with the displacement of the measuring point; its observability is guaranteed by the coverage of multiple hovering positions and a small number of ground control points.

[0074] (5) Supplementary explanation. This embodiment shows that the nominal waypoint is the state s, and the state revisit is not limited to the mechanical gear. This method also covers the revisit measurement scenario of the air platform.

[0075] Example 5: Differential Measurement System. This example provides a differential measurement system for implementing the above method, including a motion mechanism, a data acquisition unit, a differential calculation unit, and a revisit control unit.

[0076] (1) The motion mechanism is used to point to multiple targets in a time-division manner according to the gear sequence and record the mechanism state quantity of each gear, wherein each gear corresponds to one or a group of targets. For example, the motion mechanism can be an electric pan-tilt head, turntable, scanning mirror or inspection vehicle, etc., and is equipped with an encoder to record the mechanism state quantity.

[0077] (2) The acquisition unit is used to acquire benchmark observations at each gear according to the gear sequence during the benchmark period, and to acquire follow-up observations of the target to be measured at each gear when the motion mechanism revisits the gear sequence during the measurement period. For example, the acquisition unit may be a camera, a ranging unit or an angle measuring unit, which is mounted on the motion mechanism and points to the target to be measured as the mechanism rotates.

[0078] (3) The differential calculation unit is used to calculate the state change of the corresponding target for each gear, taking the difference between the baseline observation and the follow-up observation as input. The systematic pointing error of the motion mechanism is a function for determining the mechanism's state. This systematic pointing error cancels out each other in the difference between the two observations of the same state and is not included in the calculation result. For example, the differential calculation unit can use a data processing computer or an embedded processor to perform the differential calculation of the same gear as described in Equations 1 and 1a.

[0079] (4) The feedback control unit is used to control the feedback gear sequence of the motion mechanism, so that the stopping position of the motion mechanism in each gear is guaranteed by the repeatability of the motion mechanism itself, and determines the upper limit of the feedback cycle according to the preset error budget, and periodically feedbacks the reference gear to check and cut off time-varying drift. For example, the feedback control unit can be a motion controller or a programmable controller, which is connected to the drive motor and encoder of the motion mechanism.

[0080] The connection relationships of the above units are as follows: the acquisition unit is installed on the motion mechanism and is communicatively connected to the differential calculation unit; the differential calculation unit is communicatively connected to the feedback control unit; and the feedback control unit is controllably connected to the motion mechanism. The measurement system of this embodiment can perform differential measurement according to the above workflow.

[0081] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the technical scope of the present invention. Therefore, any minor modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A differential measurement method based on repeatable state revisiting, characterized in that, Includes the following steps: Plan the gear sequence for the motion mechanism and record the mechanism state variables for each gear, where each gear corresponds to one or a group of measured targets; During the baseline period, the motion mechanism is stopped sequentially according to the gear sequence, and a baseline observation of the target being measured at each gear is collected. During the measurement period, the motion mechanism is made to revisit each gear in the gear sequence. The stopping position of the motion mechanism at each gear is guaranteed by the repeatability of the motion mechanism itself, and revisit observations are collected at each gear corresponding to the target being measured at that gear. For each gear position, the difference between the baseline observation and the follow-up observation is used as input to calculate the state change of the corresponding target. The systematic pointing error of the motion mechanism is a function for determining the state of the mechanism. The systematic pointing error cancels out each other in the difference between the two observations of the same state and does not enter the calculation result. The upper limit of the follow-up period is determined based on the preset error budget, and the baseline level is periodically followed up to check and cut off time-varying drift.

2. The differential measurement method according to claim 1, characterized in that, The difference between the actual stopping position of the motion mechanism at the same gear during the reference period and the measurement period is measured by an auxiliary reading device and used as the stopping difference for that gear. The stopping difference is then used to compensate for the change in state.

3. The differential measurement method according to claim 1, characterized in that, The stopping position difference of each gear is treated as an unknown and solved together with the state change quantity; wherein, the stopping position difference is the difference between the actual stopping position of the motion mechanism in the same gear during the reference period and the measurement period.

4. The differential measurement method according to claim 1, characterized in that, The mechanism state quantity is a periodic phase, the revisit is a co-phase sampling of the periodic phase, and the reference observation and the revisit observation are co-phase sampling observations.

5. The differential measurement method according to claim 1, characterized in that, The step of determining the upper limit of the follow-up visit cycle based on the preset error budget includes: The upper limit of the first return visit cycle is determined based on the preset time-drift budget, and the upper limit of the second return visit cycle is determined based on the linear growth law of the environmental item differential residue with the return visit interval. The smaller value between the first upper limit of the return visit period and the second upper limit of the return visit period shall be used as the upper limit of the return visit period.

6. The differential measurement method according to claim 1, characterized in that, Also includes: When calculating the state change, the difference of the same level is combined with the difference of the spatial reference point to simultaneously cancel the systematic pointing error of the motion mechanism and the motion error of the carrier carrying the motion mechanism.

7. The differential measurement method according to claim 1, characterized in that, The lighting conditions for the target at each level are kept consistent during the reference period and the measurement period.

8. The differential measurement method according to claim 1, characterized in that, When the change in the state of the target exceeds the field of view or linearization range corresponding to the current gear, a new reference period is established with the new gear aligned with the target, and the displacement time sequence of the old and new reference periods is linked by overlapping observations or control points.

9. The differential measurement method according to claim 1, characterized in that, When revisiting each gear position during the measurement period, the motion mechanism approaches and stops in the same rotational direction as when the observations of each gear position were collected during the baseline period.

10. A differential measurement system for implementing the differential measurement method based on repeatable state revisiting as described in any one of claims 1 to 9, characterized in that, include: The motion mechanism is used to point to multiple targets in a time-division manner according to the gear sequence and record the mechanism state variables of each gear, wherein each gear corresponds to one or a group of targets. The acquisition unit is used to acquire baseline observations at each gear according to the gear sequence during the baseline period, and to acquire follow-up observations at each gear corresponding to the target being measured at each gear when the motion mechanism revisits the gear sequence during the measurement period. The differential calculation unit is used to calculate the state change of the target under test for each gear position, taking the difference between the benchmark observation and the follow-up observation as input. The systematic pointing error of the motion mechanism is a function for determining the state quantity of the mechanism. The systematic pointing error cancels each other out in the difference between the two observations of the same state and does not enter the calculation result. The feedback control unit is used to control the motion mechanism to feedback the gear sequence, so that the stopping position of the motion mechanism in each gear is guaranteed by the repeatability of the motion mechanism itself, and to determine the upper limit of the feedback cycle according to the preset error budget, and to periodically feedback the reference gear to check and cut off the time-varying drift of the differential measurement system.

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