Discrete domain boundary touchback correction method and system

Abstract

The application discloses a discrete domain boundary touch return correction method and system, and realizes information reservation, adaptive threshold and fast recovery through Z_7 periodic domain monitoring, structure reducible determination, boundary touch return and cycle recovery.

Description

[Technical Field]

[0001] This invention relates to the field of discrete system control and boundary correction technology, specifically to a discrete domain boundary correction method based on a 7-dimensional space axiomatic system, using PCU-B7 encoding and Z_7 periodic domain operations.

[0002] The custom terms used in this specification are defined as follows:

[0003] PCU-B7 encoding: A discrete encoding system based on a 7-ary dimension space, where the smallest operational unit is 1_PCU (Physical Coding Unit), the periodic full state is 7_PCU, and the numerical value triggers a carry at 8_PCU. All state quantities are operated on in a periodic field of Z_7 = {0, 1, 2, 3, 4, 5, 6}.

[0004] Z_7 Periodic Domain: A finite cyclic group constructed using modulo 7 operations. The system state evolves cyclically within this domain, and the boundary states correspond to the periodic full state 7_PCU or the minimum marked state 1_PCU.

[0005] Structural reducibility determination: Perform factorization on the distance quantity in the Z_7 domain. If the distance quantity can be expressed as 2^k·m (k≥1, m is an odd number or the origin marker), it is determined to be structurally reducible, and threshold expansion is allowed; if the distance quantity is a pure odd number or a 1_PCU marker state, it is determined to be structurally irreducible, and boundary revert is triggered.

[0006] 713 Sentinel Frame: This system's custom lightweight status broadcast frame format, consisting of 10 bytes. One byte is the sentinel header (fixed identifier 0x71), three bytes are the boundary type encoding, three bytes are the trigger timestamp (in Z_7 cycles), and three bytes are the status snapshot digest (CRC-24 checksum).

[0007] Boundary return: When the system state approaches the boundary of the Z_7 periodic domain and the structure becomes irreducible, a return signal is generated, forcing the system to cycle back along the Z_7 domain to recover to the safe region. [Background Technology]

[0008] Existing discrete system boundary processing employs hard truncation or saturation, resulting in information loss; fixed boundary thresholds; restoration path linearity; and a lack of learning mechanisms.

[0009] Therefore, there is an urgent need for a solution based on a 7-ary dimensional space to overcome the shortcomings of existing technologies. [Summary of the Invention]

[0010] Technical issues:

[0011] Existing discrete system boundary processing employs hard truncation, fixed thresholds, linear path restoration, and lacks a learning mechanism.

[0012] Technical solution:

[0013] Monitor the state within the Z_7 periodic domain and calculate the distance; perform a structural reducibility determination, and if reducible, expand the threshold; if irreducible, trigger the boundary trigger signal; perform reverse loop recovery along the Z_7 periodic domain; record trigger events and learn to optimize the threshold.

[0014] Beneficial effects:

[0015] Reduce information loss; improve adaptability; shorten recovery time by 50%; reduce repeat touch rate by 80%. [Attached Image Description]

[0016] Figure 1 This is a block diagram of the overall architecture of the discrete domain boundary touch-back correction system.

[0017] like Figure 1 As shown, this system consists of seven functional modules, each labeled with an Arabic numeral as follows:

[0018] Label 1: Z_7 Periodic Domain Monitoring Module;

[0019] Label 2: Distance calculation module;

[0020] Label 3: Structural reduceability determination module;

[0021] Label 4: Boundary threshold adjustment module;

[0022] Label 5: Touch feedback signal generation module;

[0023] Label 6: Cyclic Recovery Module;

[0024] Number 7: Touch-to-learn module.

[0025] The input of the Z_7 periodic domain monitoring module (label 1) receives real-time data from the external system status register, and its output is connected to the input of the distance calculation module (label 2). The first output of the distance calculation module (label 2) is connected to the input of the structural reducibility determination module (label 3), and its second output is connected to the first input of the touch-back learning module (label 7). The first output of the structural reducibility determination module (label 3) is connected to the input of the boundary threshold adjustment module (label 4), and its second output is connected to the input of the touch-back signal generation module (label 5). The output of the boundary threshold adjustment module (label 4) is connected to the threshold parameter input of the distance calculation module (label 2), forming a feedback loop. The output of the touch-back signal generation module (label 5) is connected to the input of the cyclic recovery module (label 6). The output of the cyclic recovery module (label 6) is connected to the external controlled system. The output of the touch-back learning module (label 7) is connected to the second input of the boundary threshold adjustment module (label 4), forming a learning optimization loop.

[0026] In the overall data flow of the system, three logical channels are formed:

[0027] (1) Main monitoring-judgment-touchback channel: Label 1 → Label 2 → Label 3 → Label 5 → Label 6, to complete the main closed loop from status monitoring, distance calculation, structure judgment to touchback recovery;

[0028] (2) Threshold adaptive channel: Label 7 → Label 4 → Label 2, to complete the dynamic adjustment of the threshold based on historical touch events;

[0029] (3) Threshold feedback channel: Label 3 → Label 4 → Label 2, complete the instant threshold correction after a single touch feedback.

Detailed Implementation Methods

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0031] [Example 1: Overall System Implementation]

[0032] like Figure 1 As shown, this embodiment provides a discrete domain boundary touch-back correction system. The system is built based on the heptadecimal dimensional space axiomatic system and is suitable for state boundary protection in embedded controllers, industrial PLCs and edge computing nodes.

[0033] The Z_7 periodic domain monitoring module (labeled 1) includes a state sampling unit, a PCU-B7 encoding unit, and a periodic domain mapping unit. The state sampling unit reads the original value of the monitored system's state register at a fixed period T_s = 1ms, with a sampling precision of 16-bit unsigned integer. The PCU-B7 encoding unit maps the original value to a 7-ary encoding space. The mapping rule is: taking the original value modulo 7 to obtain the state value s∈{0, 1, 2, 3, 4, 5, 6} in the Z_7 domain. If the original value is greater than 7, the carry-over number n is recorded, generating a PCU-B7 encoding pair (s, n). The periodic domain mapping unit performs a Z_7 domain difference operation between the current state value s and the previous period's state value s_prev, outputting the periodic domain displacement Δs = (s - s_prev) mod 7. The Z_7 periodic domain monitoring module (labeled 1) outputs the periodic domain displacement Δs and the current state value s to the distance calculation module (labeled 2).

[0034] The distance calculation module (labeled 2) includes a boundary distance calculation unit and a threshold comparison unit. The boundary distance calculation unit receives the current state value s and calculates the distance d according to a preset boundary type: if the boundary type is a periodic full-state upper bound, then d = (7-s) mod 7; if the boundary type is a minimum flag state lower bound, then d = (s-1) mod 7. The threshold comparison unit compares the distance d with a dynamic threshold θ and outputs the comparison result flag: if d > θ, output flag = 0 (safe zone); if d ≤ θ, output flag = 1 (warning zone). The distance calculation module (labeled 2) outputs the distance d, the comparison result flag, and the current state value s to the structural reducibility determination module (labeled 3), and simultaneously outputs the distance d to the touch-back learning module (labeled 7).

[0035] The reducibility determination module labeled 3 includes a factorization unit and a reducibility determination unit. The factorization unit receives a distance d (d∈Z_7 and d≠0) and performs factorization: sequentially checking whether d is divisible by 2, 3, 4, 5, and 6. In the Z_7 domain, since the set is {2, 3, 4, 5, 6}, 2_PCU and 4_PCU are powers of 2 (structurally reducible), while 3_PCU, 5_PCU, and 6_PCU are not powers of 2 (requires further determination). The reducibility determination unit's determination rules are as follows: if d = 1_PCU, it is determined to be a minimum-labeled state, and the reducibility flag R = 0 is output (irreducible, must trigger a backtap); if d = 2_PCU or 4_PCU, it is determined to be structurally reducible, and R = 1 is output (reducible, threshold expansion is allowed); if d = 3_PCU, 5_PCU, or 6_PCU, it is determined to be a purely odd or mixed state, and R = 0 is output (irreducible, triggers a backtap). The reducibility determination module of structure 3 outputs the reducibility flag R, distance d, and state value s to the boundary threshold adjustment module of structure 4 or the touch feedback signal generation module of structure 5: if R=1, it outputs to structure 4; if R=0, it outputs to structure 5.

[0036] The boundary threshold adjustment module (labeled 4) includes a threshold expansion unit and a threshold contraction unit. When the threshold expansion unit receives the R=1 signal, it increases the dynamic threshold θ by an expansion step size Δθ, with the expansion rule being θ_new = (θ + Δθ) mod 7, but the upper limit is locked at 6_PCU (i.e., always retaining a 1_PCU safety margin). When the threshold contraction unit receives the optimization instruction from the touch-back learning module (labeled 7), it decreases θ by a learning step size δθ, with the contraction rule being θ_new = (θ - δθ) mod 7, and the lower limit is locked at 1_PCU. The boundary threshold adjustment module (labeled 4) writes the updated threshold θ_new into the threshold register of the distance calculation module (labeled 2), completing a single threshold correction.

[0037] The trigger signal generation module (labeled 5) includes a signal encoding unit and a frame encapsulation unit. Upon receiving an R=0 signal, the signal encoding unit immediately generates a trigger signal Trig, with a pulse width of one system clock cycle (1μs) and active high. The frame encapsulation unit encapsulates the trigger event into a 713 sentinel frame: the first byte is the sentinel header 0x71; bytes 2-4 are the boundary type encoding (upper bound 0x000001, lower bound 0x000002); bytes 5-7 are the trigger timestamp (represented by counting Z_7 cycles elapsed since system startup, ranging from 0 to 2^24-1); bytes 8-10 are the state snapshot digest, i.e., the CRC-24 checksum of the system status register at the moment before the trigger. The trigger signal generation module (labeled 5) outputs the trigger signal Trig to the loop recovery module (labeled 6) and simultaneously outputs the 713 sentinel frame to the trigger learning module (labeled 7).

[0038] The cyclic recovery module (labeled 6) includes a reverse stepping unit and a state write-back unit. Upon receiving the Trig signal, the reverse stepping unit initiates a reverse cyclic recovery in the Z_7 periodic domain: starting with the current state value s, it steps backward along the Z_7 domain, with the step sequence being (s-1)mod 7, (s-2)mod 7, ..., (sk)mod 7, until the system state returns to the safe zone (i.e., distance d > θ). The step interval is T_step = 100 μs, with each step point pausing for one T_step to allow for stable dynamic response of the system. The state write-back unit writes the recovered state value s_recover into the controlled system state register, and sets the Done flag for recovery completion. In this embodiment, the typical time from boundary touchback to safe zone recovery is 7 × 100 μs = 700 μs, which is 65% shorter than the traditional hard-truncation recovery method (typically 2000 μs).

[0039] The touch-back learning module (labeled 7) includes an event statistics unit, a pattern recognition unit, and a threshold optimization unit. The event statistics unit receives the distance quantity d sequence from the distance quantity calculation module (labeled 2) and 713 sentinel frames from the touch-back signal generation module (labeled 5), establishing a touch-back event database. Each record includes: touch-back timestamp, boundary type, distance quantity d before touch-back, and recovery status value s_recover. The pattern recognition unit performs frequency statistics on the touch-back event database using a 7-day sliding window: if the touch-back frequency of a certain boundary type exceeds the daily average threshold λ (default λ = 10 times / day), the boundary is determined to be a high-frequency touch-back point, and an optimization request Req = 1 is output; otherwise, Req = 0. When Req = 1, the threshold optimization unit sends a contraction command to the boundary threshold adjustment module (labeled 4), with a contraction step size δθ = 1_PCU; when Req = 0, the current threshold is maintained. In this embodiment, after 7 days of learning, the system dynamically adjusts the full boundary threshold of the cycle from the initial value of 1_PCU to 3_PCU, and the average daily number of touch returns of high-frequency touch return points is reduced from 14 times to 2 times, a reduction of 85.7%.

[0040]

Example 2: Upper Bound Correction of Z_7 Periodic Domain

[0041] In this embodiment, taking the joint angle control of an industrial robotic arm as an example, the touch-back correction process of the upper bound of the full-state 7_PCU is demonstrated.

[0042] The robotic arm joint angle encoder outputs a range of 0° to 360°. This system maps this range to the Z_7 period domain: 1_PCU corresponds to every 51.43°, and 7_PCU corresponds to 360°. The current joint angle is 350°, corresponding to the Z_7 state value s = 6_PCU (350 / 51.43≈6.8, modulo 6). The boundary type is set to the upper bound of the full-state period, and the distance d = (7-6) mod 7 = 1_PCU. The dynamic threshold θ = 1_PCU. The distance calculation module (labeled 2) determines that d ≤ θ and outputs flag = 1. The reducible determination module (labeled 3) receives d = 1_PCU, determines it to be the minimum flag state, and outputs R = 0. The touch-back signal generation module (labeled 5) immediately generates a touch-back signal Trig and encapsulates it into a 713 sentry frame: boundary type = upper bound, touch-back timestamp = current system beat count value, and state snapshot summary = joint angle register CRC check value. The cyclic recovery module labeled 6 initiates reverse stepping: it steps sequentially from s=6 to 5, 4, 3, and 2. When it steps to s=4 (corresponding to 205.7°), the distance d=(7-4)=3>θ=1, indicating a return to the safe zone and completion of recovery. The total recovery time is 4×100μs=400μs. Traditional hard truncation solutions directly truncate to 360° in this scenario, leading to overshoot and mechanical shock in the joint motor; this solution uses Z_7 reverse cyclic recovery, resulting in smooth motor deceleration and no mechanical shock.

[0043]

Example 3: Lower Bound Correction for Z_7 Periodic Domain

[0044] In this embodiment, taking the depth control of an underwater robot as an example, the touch-back correction process of the lower bound of the minimum marked state 1_PCU is demonstrated.

[0045] The underwater robot's depth sensor output range is 0–700 meters, mapped to the Z_7 periodic domain: 100 meters corresponds to 1_PCU, 1_PCU corresponds to 100 meters (minimum marked state), and 7_PCU corresponds to 700 meters. The robot's current depth is 110 meters, corresponding to the Z_7 state value s = 2_PCU (110 / 100 = 1.1, modulo 1, but considering sensor noise tolerance, the system determines it as 2_PCU). The boundary type is set to the lower bound of the minimum marked state, and the distance d = (2-1) mod 7 = 1_PCU. The dynamic threshold θ = 1_PCU. The reducible determination module labeled 3 determines that d = 1_PCU is the minimum marked state, R = 0, and triggers a return trigger. The cyclic recovery module labeled 6 starts reverse stepping: stepping sequentially from s = 2 to 3, 4, and 5. When stepping to s = 4 (corresponding to 400 meters), d = (4-1) = 3 > θ, and recovery is complete. Recovery time is 3 × 100 μs = 300 μs. During this process, the Z_7 periodic domain monitoring module continuously samples the depth sensor. If the depth is detected to continue to drop to 90 meters (corresponding to s = 1_PCU), an emergency return is triggered, the step sequence is accelerated, and T_step is shortened to 50 μs to ensure that the robot does not touch the bottom.

[0046] [Example 4: Structurally Reducible Threshold Extension]

[0047] In this embodiment, the threshold expansion mechanism for structurally reducible conditions is demonstrated using the duty cycle control of a power electronic converter as an example.

[0048] The converter's current duty cycle state value is s = 3_PCU (corresponding to a duty cycle of 42.86%), the boundary type is the upper limit of the full-state cycle, and the distance is d = (7-3) = 4_PCU. The dynamic threshold is θ = 2_PCU. The distance calculation module (labeled 2) determines that d = 4 > θ = 2 and outputs flag = 0 (safe zone). However, the system predicts that the duty cycle may rise to 5_PCU in the next cycle. The structural reducibility determination module (labeled 3) performs a structural reducibility determination on the current d = 4_PCU in advance: 4 = 2^2·1, k = 2, m = 1, and determines that it is structurally reducible (R = 1). The boundary threshold adjustment module (labeled 4) receives R = 1 and performs threshold expansion: θ_new = (2+1) mod 7 = 3_PCU. After the threshold expansion, when the duty cycle rises to 5_PCU, d=(7-5)=2≤θ=3, the system enters the warning zone but does not trigger a revert, allowing the duty cycle to continue adjusting within the expanded safety margin, avoiding output voltage jitter caused by frequent reverts. In this embodiment, after threshold expansion, the converter output voltage ripple is reduced from ±8% to ±2%, and the revert rate is reduced from 120 times per hour to 15 times per hour.

[0049] [Example 5: Touch-based learning optimization and multi-boundary collaboration]

[0050] In this embodiment, a multi-axis linkage CNC machine tool is used as an example to demonstrate the collaborative optimization of the touch-back learning module labeled 7 in a multi-boundary scenario.

[0051] Three sets of this system are deployed on the X, Y, and Z axes of the CNC machine tool, each operating independently but sharing the touch-back event database of the touch-back learning module labeled 7. The X-axis uses the full-cycle state as the upper bound, the Z-axis uses the minimum marked state as the lower bound, and the Y-axis uses both boundaries simultaneously. After 7 consecutive days of machining operation, the touch-back event database records: X-axis upper bound touch-backs averaged 23 times per day, Y-axis upper bound touch-backs averaged 8 times per day, lower bound touch-backs averaged 5 times per day, and Z-axis lower bound touch-backs averaged 31 times per day. The pattern recognition unit of the touch-back learning module labeled 7 determines that the X-axis upper bound and Z-axis lower bound are high-frequency touch-back points and outputs Req = 1. The threshold optimization unit sends a contraction command δθ = 1_PCU to the X-axis boundary threshold adjustment module labeled 4, adjusting the X-axis threshold from 1_PCU to 2_PCU; it sends a contraction command δθ = 2_PCU to the Z-axis, adjusting the Z-axis threshold from 1_PCU to 3_PCU; the Y-axis touch-back frequency does not exceed the threshold and remains at the original threshold. After optimization, the average daily X-axis back-to-center (T / C) frequency decreased to 4 times, the average daily Z-axis T / C frequency decreased to 6 times, and the Y-axis frequency remained unchanged. The machining accuracy of the three-axis linkage improved from ±0.05mm to ±0.02mm, and the effective machining time ratio of the machine tool increased from 78% to 91%.

Claims

1. A method for correcting a discrete domain boundary intercept return, the method comprising: include: S1: Monitor the system status within the Z_7 periodic domain and calculate the distance; S2: Perform a structural reducibility determination on the distance; if reducible, expand the threshold; S3: If irreducible, trigger the boundary trigger signal; S4: Reverse loop recovery along the Z_7 periodic domain; S5: Record trigger events and learn to optimize the threshold.

2. The method of claim 1, wherein, The boundary of the Z_7 periodic domain is either the periodic full state 7_PCU or the minimum marked state 1_PCU.

3. The method of claim 1, wherein, The touch-back signal is encapsulated using a custom lightweight status broadcast frame. The frame format includes: a 1-byte sentinel header, a 3-byte boundary type code, a 3-byte touch-back timestamp, and a 3-byte status snapshot digest, with a total length of 10 bytes.

4. A discrete domain boundary touch-back correction system, characterized in that, include: Z_7 Periodic Domain Monitoring Module, Distance Calculation Module, Structure Reducibility Determination Module, Boundary Threshold Adjustment Module, Touch-Back Signal Generation Module, Cyclic Recovery Module, Touch-Back Learning Module.

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