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VisGeo-PipeTrack: A Visual Geometric Servo Control Framework with MPC-RCAPID Control for UAV-Based Dynamic Pipes Tracking

Zhenyang Gao, Jianlin Chen, Yang Yu, Honghao Shan, Jiale Gao, Ziyan Jia

arXiv:2610.35342v1cs.RO

TL;DR

Many UAV pipe-inspection methods assume static pipes, leaving real-time tracking of moving pipes such as those vibrating or translating as the problem addressed. VisGeo-PipeTrack uses YOLOv5-detected pipe labels and visual geometric constraints for localization, paired with MPC-RCAPID adaptive control. MPC-RCAPID’s average tracking error is reduced by 55.52%, 26.72%, and 26.52% versus standard PID in DPIS, DPEF, and SPIS; under lateral pipeline motion, shortest adjustment time is 3.26 s.

  • Problem

    Many UAV pipe-inspection methods assume static pipes, leaving real-time tracking of moving pipes such as those vibrating or translating as the problem addressed.

    Source: A. Problem Statement and Dynamic Pipes… · p. 2

  • Method

    VisGeo-PipeTrack uses YOLOv5-detected pipe labels and visual geometric constraints for localization, paired with MPC-RCAPID adaptive control.

    Source: §I · p. 2

  • Results

    MPC-RCAPID’s average tracking error is reduced by 55.52%, 26.72%, and 26.52% versus standard PID in DPIS, DPEF, and SPIS; under lateral pipeline motion, shortest adjustment time is 3.26 s.

    Source: B. Simulation Results Based on Airsim · p. 7, C. Experimental Results Based on Tello · p. 8

  • Takeaways & Limitations

    The framework's effectiveness is validated in AirSim simulations and Tello UAV experiments for dynamic-pipe tracking.

    Source: §VI · p. 8

Abstract

from arXiv · show

While unmanned aerial vehicles (UAVs) are increasingly deployed for pipeline inspection, prevailing research predominantly assumes static pipes. In real-world industrial environments, pipes often exhibit dynamic movements, such as vibrations. This imposes more stringent requirements on UAVs' adaptive control and computational efficiency than in static scenarios. Therefore, this paper proposes a servo control framework named VisGeo-PipeTrack, which utilizes geometric constraints to enable UAV tracking of dynamic pipes. To achieve efficient UAV positioning, YOLOv5 is employed to detect labels on the pipe. The positions are derived from visual geometric constraints based on these detected labels to enable precise localization. To address tracking control challenges, a model predictive control based real-time corrected adaptive PID (MPC-RCAPID) controller is proposed. This controller employs the Recursive Least Squares method for real-time model estimation and integrates rolling horizon optimization to dynamically adjust PID parameters. Experiments conducted on both the AirSim simulator and the Tello UAV platform validate the effectiveness of the proposed framework. Simulation comparisons with standard PID, fractional-order PID, adaptive PID, and fuzzy PID demonstrate that MPC-RCAPID achieves the shortest settling time (3.26 s) and the lowest average tracking error (3.52%). In physical experiments on the Tello platform, compared with standard PID control, MPC-RCAPID reduces the average tracking error by 55.52%, 26.72%, and 26.52% across the three test dimensions. These results demonstrate that VisGeo-PipeTrack facilitates efficient autonomous tracking in dynamic pipe environments.

I. INTRODUCTION

Existing UAV inspection methods assume static pipes, while pipe motion raises positioning and collision-avoidance challenges. VisGeo-PipeTrack combines YOLOv5-based visual positioning with MPC-RCAPID control for dynamic-pipe tracking.

I. INTRODUCTION

  • Dynamic pipe motion challenges UAV positioning and control, while existing approaches assume static environments and do not update references or targets in real time.The paper identifies accumulating estimation errors, lagging control responses, and increased collision risk as consequences of this gap.Source: §I · pp. 1–2
  • VisGeo-PipeTrack combines YOLOv5 label detection with geometric constraints to estimate tracking targets while reducing computational overhead.The detected labels define geometric intersections used as target points for UAV tracking.Source: §I · p. 2
  • MPC-RCAPID integrates error prediction, recursive least-squares model estimation, and rolling-horizon PID parameter optimization.The design addresses fixed-parameter PID controllers' limited adaptability.Source: §I · p. 2

A. Problem Statement and Dynamic Pipes Movement

The paper targets UAV tracking in moving pipes, where static-pipe methods cannot update relative position or control targets in real time. It introduces YOLOv5 detection and describes the PID controller components used in the study.

A. Problem Statement and Dynamic Pipes Movement

  • Moving pipes can prevent existing UAV methods designed for static pipes from updating relative position or control targets in real time.The paper links motion-related error accumulation with increased collision risk.Source: A. Problem Statement and Dynamic Pipes… · p. 2

B. YOLOv5 Target Detection Algorithm

  • YOLOv5 is selected to detect pipe labels, with the paper citing its accuracy-speed trade-off on embedded platforms.The cited rationale is that YOLOv5 is considered a stable version for this application.Source: B. YOLOv5 Target Detection Algorithm · p. 2

C. PID Controller

  • The PID controller combines proportional, integral, and derivative terms to correct control error and support stable system operation.The passage also identifies the associated gains and integral and derivative time constants.Source: C. PID Controller · p. 2

III. DYNAMIC PIPES TRACKING BASED ON VISUAL GEOMETRIC CONSTRAINTS

The visual servo system estimates the UAV's relative position within a pipe using geometric constraints. YOLOv5 detects four pipe labels, whose configured geometry defines the tracking position.

III. DYNAMIC PIPES TRACKING BASED ON VISUAL GEOMETRIC CONSTRAINTS

  • The visual servo system uses geometric constraints to estimate pipe position and the UAV's relative position from image error.The system is designed as a lightweight tracking servo for pipe positioning.Source: §III · p. 2

A. Label Visual Localization

  • Four YOLOv5-detected labels form two lines whose intersection defines the UAV's relative tracking position inside the pipe.The intersection need not coincide with the pipe's geometric center; pre-attached labels configure the desired relative position.Source: A. Label Visual Localization · p. 3
  • Label recognition confidence remains above 90% across varying lighting, flight attitudes, and label distances, while video streaming exceeds 25 frames per second.The four detected image coordinates are inputs to the subsequent localization algorithm.Source: A. Label Visual Localization · p. 3

B. Geometric Location Solution of Pipes

The UAV estimates its position inside the pipe by intersecting two lines formed from four detected labels. Comparing that intersection with the camera’s visual center yields a position error for flight-attitude adjustment.

B. Geometric Location Solution of Pipes

IV. MPC BASED REAL-TIME CORRECTED ADAPTIVE PID

MPC-RCAPID combines corrected multi-step error prediction with rolling optimization of adaptive PID parameters. It is proposed for dynamic pipe tracking, where fixed-parameter PID can struggle with speed variation and noise.

IV. MPC BASED REAL-TIME CORRECTED ADAPTIVE PID

  • Under vibration or nonuniform motion, fixed-parameter PID may mishandle sudden speed variations and noise, causing tracking-error overshoot or target loss.Source: §IV · p. 4
  • The position error between current and target locations is used for subsequent UAV flight-attitude adjustments.Source: Figure 7 · p. 4
  • MPC-RCAPID senses visual data, predicts corrected future error sequences, and uses rolling optimization to derive PID parameters and UAV control quantities.Source: §IV · p. 4
  • The strategy integrates MPC forward prediction, real-time feedback correction, and adaptive PID tuning for time-varying UAV pipe tracking.Source: §IV · p. 4

A. Modification of the MPC Forward Prediction Model

The forward model predicts future position error with a quadratic form, then corrects its remaining predictions using observed error. RLS updates the model from historical data so it can adapt to changing error dynamics.

A. Modification of the MPC Forward Prediction Model

B. PID Tuning Based on MPC Rolling Optimization

The controller uses rolling-horizon MPC to tune adaptive PID parameters by minimizing predicted tracking error while balancing control smoothness. RLS model updates and real-time error correction support adaptation to changing pipe motion.

B. PID Tuning Based on MPC Rolling Optimization

  • MPC tunes the PID gains by minimizing cumulative squared tracking error over the next N steps, with a penalty that trades tracking accuracy against control smoothness.The cost uses predicted future tracking errors and changes in the control quantity.Source: B. PID Tuning Based on MPC Rolling… · p. 5
  • Finite-difference gradient descent adjusts the optimized PID parameters in the negative cost-gradient direction.The parameter set is θ = {K_P, K_I, K_D}.Source: B. PID Tuning Based on MPC Rolling… · p. 6
  • The learning rate η controls the magnitude of gradient-based parameter updates, and the authors state that MPC-RCAPID enables quick, accurate dynamic-pipe tracking.Source: B. PID Tuning Based on MPC Rolling… · p. 6
  • RLS updates the predictive model in real time, while real-time error corrects prediction errors as pipe motion changes.The controller combines these updates with MPC rolling optimization and adaptive PID control.Source: B. PID Tuning Based on MPC Rolling… · p. 6

A. Tello UAV Platform

The paper validates VisGeo-PipeTrack on a compact Tello platform and in AirSim simulations of pipe motion. In lateral-motion simulation, MPC-RCAPID records the shortest adjustment time and lowest maximum and average errors among five controllers.

A. Tello UAV Platform

  • The Tello UAV was selected for experimental validation and system development because of its compact size; visual servo control is considered crucial for autonomous pipeline tracking with precise geometric-center localization.Figure 8 identifies a 720P onboard camera and dimensions of 9.8 cm (length) × 9.25 cm (width).Source: A. Tello UAV Platform · p. 6, Figure 8 · p. 6

B. Simulation Results Based on Airsim

  • AirSim tests used a 0.4 m-diameter, 1 m-long pipe moving horizontally at 30 cm/s for 2 seconds before stopping, with collision avoidance as an objective.The comparison implemented PID and MPC-RCAPID; Fig. 9 and Fig. 10 show the simulation and tracking positions.Source: B. Simulation Results Based on Airsim · p. 6, Figure 9 · p. 6, Figure 10 · p. 7
  • 3.26 s adjustment time, 10.91% maximum error, and 3.52% average error made MPC-RCAPID best among five controllers under lateral pipe motion.Standard PID recorded 5.16 s, 14.19% maximum error, and 6.96% average error; FO-PID, A-PID, and F-PID also had longer adjustment times or larger errors.Source: Table I · p. 7, B. Simulation Results Based on Airsim · p. 7

C. Experimental Results Based on Tello

Physical Tello experiments compare MPC-RCAPID with standard PID across dynamic internal shuttle, dynamic external following, and static internal shuttle scenarios. MPC-RCAPID reduces average tracking error in all three dimensions.

C. Experimental Results Based on Tello

  • The physical platform processes camera images for label detection, geometric positioning, and environmental perception, then returns control instructions to the UAV for closed-loop adjustment.The setup includes a Tello UAV, visual monitoring camera, ground station computer, physical pipes, and a mobile vehicle.Source: C. Experimental Results Based on Tello · p. 7
  • The experiments used N = 5, Δt = 0.05, λβ = 0.9, and λRLS = 0.98, with initial PID gains Kp0, Ki0, Kd0 = 20, 3.5, 6.5.The authors describe these settings as trade-offs among computation, prediction, sampling, and correction, with initial gains tuned in simulation and real-machine testing.Source: C. Experimental Results Based on Tello · p. 8
  • 55.52%, 26.72%, and 26.52% average tracking-error reductions were achieved in DPIS, DPEF, and SPIS, respectively, versus standard PID.Maximum tracking error was reduced by 50.63%, 17.17%, and 17.45% in those same scenarios.Source: C. Experimental Results Based on Tello · p. 8
  • The authors report that smaller tracking errors increase the UAV’s error-tolerance space and reduce inner-wall collision risk during pipe tracking.Source: C. Experimental Results Based on Tello · p. 8

VI. CONCLUSION

VisGeo-PipeTrack combines visual-geometric localization with MPC-RCAPID control for dynamic-pipe UAV tracking, including internal traversal and external tracking. Its effectiveness is validated in AirSim and Tello experiments.

VI. CONCLUSION

  • VisGeo-PipeTrack integrates lightweight visual-geometric localization and MPC-RCAPID control for UAV tracking in dynamic pipes, covering internal traversal and external tracking.The framework is intended to support swift, stable attitude adjustments.Source: §VI · p. 8
  • The experimental process is shown from global and UAV-camera views to monitor the UAV’s flight attitude.Source: Figure 12 · p. 8
  • The framework’s effectiveness is validated through AirSim simulations and Tello UAV experiments.Table III is identified as a comparison of Tello UAV experimental results; the supplied caption does not report its values.Source: §VI · p. 8, Table III · p. 8
  • Future work targets irregular pipes and multiple internal obstacles, improved label placement and geometric positioning, and lighter YOLOv5 and MPC-RCAPID implementations.The stated aim is airborne integration of perception and control, reducing ground-station reliance and enhancing tracking autonomy.Source: §VI · p. 8
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