Control Method and Simulation of Reconfigurable Façade Cable-Driven Parallel Robots Based on Heuristic Local Rules

Abstract

Traditional control strategies for Cable-Driven Parallel Robots (CDPRs) rely heavily on global kinematic modeling and precise calibration, severely limiting their adaptability in unstructured or dynamic environments. This study addresses the challenge of rapid deployment without geometric priors by proposing a reconfigurable CDPR system composed of modular units. A novel heuristic control strategy based on “4+2+1” local rules is introduced, comprising translational, attitude correction, and tension maintenance logic. By utilizing local feedback—including cable tension, attitude, and anchor orientation—this method generates control commands without requiring boundary condition calibration, thereby supporting real-time reconfiguration. Numerical simulations of a façade cleaning scenario demonstrate that the system maintains stability across varying topologies, including anchor position changes and unit failures. Compared to a benchmark kinematic method, the proposed strategy reduces trajectory tracking error by approximately 50.5% and suppresses the pitch Root Mean Square Error (RMSE) from a divergent 42.75° (traditional) to 1.52°, effectively preventing the attitude failure typical of uncalibrated model-based control. These findings confirm that the proposed rule-based approach significantly enhances robustness and adaptability, offering a practical solution for deploying CDPRs in complex environments without pre-existing maps.

1. Introduction

Cable-Driven Parallel Robots (CDPRs) have demonstrated their unique value in large-scale applications such as radio telescopes (e.g., FAST) [1,2], automated stages [1], large-scale curtain wall installation [3], and warehousing logistics [2], owing to their vast workspace, high payload-to-weight ratio, and lightweight structure. However, as application scenarios extend to dynamic and unstructured environments like building façade cleaning [4,5,6,7,8], rehabilitation training [9], and post-disaster search and rescue [10], traditional CDPR control paradigms have increasingly revealed limitations regarding deployment flexibility and adaptability to environmental changes.

Current mainstream control strategies—whether traditional methods using p-norm (e.g., 2-norm) optimization to solve for redundant cable Positive Tension Distribution (PTD) [2], non-iterative tension generation schemes proposed to alleviate computational burdens (e.g., the approach by Ameri et al. [7], which uses saturation functions and nonlinear disturbance observers to explicitly generate positive tension), or Nonlinear Model Predictive Control (NMPC) incorporating tension distribution into the feedback structure [11]—essentially adhere to a “map–navigation” paradigm. This paradigm first relies on external measurement devices (such as laser trackers or vision systems [12]) to perform high-precision calibration of geometric parameters like absolute anchor coordinates, constructing a precise, static global “map” (i.e., inverse kinematics and Jacobian models). Subsequently, controllers (such as PID, sliding mode control [2], or adaptive control [13]) perform trajectory tracking and attitude regulation based on this map. This paradigm is tightly coupled with a fixed hardware topology. Consequently, once anchor positions change (e.g., re-deploying CDUs to avoid collisions [14]), the original map becomes invalid, necessitating system suspension and recalibration. This issue is particularly pronounced in scenarios where deploying precision measurement equipment is difficult, such as on space stations [15] or structurally complex building façades [5].

To reduce dependence on precise models, existing research has proposed various improvements. For instance, the Adaptive Synchronization Control (ASC) proposed by Ji et al. [16] can maintain trajectory synchronization amidst kinematic and dynamic parameter uncertainties, yet the construction of synchronization errors still relies on a preset nominal model. The “Assist-As-Needed” (AAN) controller by Asl and Yoon [9] enhances the flexibility of rehabilitation training through an error-driven auxiliary mechanism, but its control strategy, based on a single-degree-of-freedom model, is difficult to generalize directly to topology reconfiguration scenarios involving multiple cables and synergistic units. Bouaouda et al. [17] and Lu et al. [18] have attempted to introduce Deep Reinforcement Learning (DRL) and AI control to address complex dynamics and cable flexibility, but these approaches typically still require a certain degree of geometric priors or offline training data.

At the hardware level, existing research often struggles to decouple physical reconfiguration from control complexity. For instance, Gagliardini et al. [14] designed a movable-anchor structure for large-scale operations; however, this approach essentially adopts an “offline” strategy, requiring system suspension to relocate anchors to pre-calculated positions. An et al. [19] advanced this by enabling “online” reconfiguration for obstacle avoidance, yet their control logic still adheres to a model-based paradigm, necessitating real-time anchor position measurements to continuously update the global Jacobian matrix. While other modular designs like the reconfigurable robot by Zhou et al. [20] and the high-rise cleaning modules by Fang et al. [21] (and similar integrated mechanisms [3,22]) have improved hardware flexibility, they typically do not address the control adaptation issue under zero-knowledge conditions. To reduce dependence on geometric priors, advanced data-driven approaches have emerged. For example, Raman et al. [23] utilized Deep Reinforcement Learning (DRL) for reconfigurable CDPRs, and Fazeli et al. [24] proposed a dynamic model-free framework. However, these methods often suffer from high computational costs or require extensive offline training [23,24], which can be prohibitive for rapid on-site deployment.

Addressing the aforementioned issues, this paper attempts to explore a “Local Perception—Synergistic Control” approach, distinct from the traditional “map–navigation” paradigm. The core idea is to no longer explicitly construct a global geometric model but instead utilize simple heuristic local rules and distributed feedback to achieve synergistic stability of trajectory and attitude in the absence of global geometric priors. To reduce conceptual ambiguity, the term “reconfigurable” in this paper primarily emphasizes that the Cable Driving Unit (CDU) serves as an independent physical module capable of asymmetric deployment in unstructured environments, allowing for the online addition, removal, or repositioning of nodes during operation, while the control strategy adapts to these configuration changes without recalibration. To avoid conceptual ambiguity, the term “calibration-free” in this paper is strictly defined as the elimination of the need to calibrate global geometric parameters, such as the absolute coordinates of anchors relative to the global frame. This stands in contrast to the traditional “map-based” control, which fails without a precise geometric map. However, it is important to distinguish this from “sensor calibration”. Local onboard sensors (e.g., the zero-bias of the IMU or the sensitivity of tension sensors) still require routine standardization to ensure measurement accuracy. The proposed strategy removes the dependency on the environmental geometry map, not the instrumental accuracy.

Under these definitions, this paper seeks to combine the philosophy of “Local Rules—Distributed Feedback—Global Stability” with a reconfigurable modular hardware architecture to enhance the deployment efficiency and topological adaptability of CDPRs in typical unstructured scenarios such as building curtain wall cleaning. Centering on this objective, the main contributions of this paper include:

1. Proposing a calibration-free control principle based on Relative-Azimuth aware Coordination (RAC), which generates control commands relying solely on anchor relative quadrant information and end-effector attitude and tension feedback;

2. Constructing a hierarchical–distributed hybrid control framework composed of “4+2+1” local rules, achieving the synergy of trajectory command decomposition, attitude stabilization, and tension maintenance;

3. Designing a modular reconfigurable CDPR system architecture and validating the effectiveness and robustness of the control method under static configuration changes and dynamic topology reconfiguration (including unit failure) in a high-rise curtain wall cleaning simulation scenario.

The structure of the full paper is arranged as follows: Section 2 introduces the control strategy based on local rules; Section 3 elaborates on the reconfigurable system design; Section 4 presents the simulation modeling, parameter settings, and result analysis; and Section 5 summarizes the paper and discusses future work.

2. Local Rule-Based Control Strategy

The control system presented in this paper adopts a “4+2+1” architecture driven by local rules to adapt to the topological changes and parameter uncertainties resulting from the reconfigurable hardware. The “4” corresponds to four quadrant-based translational walking rules, the “2” corresponds to attitude correction rules targeting positive and negative inclinations, and the “1” corresponds to a distributed cable tension maintenance rule. These three categories of rules are executed in parallel in the time domain and superimposed at the command level to achieve comprehensive control over trajectory, attitude, and tension.

2.1. Kinematic Principles of Rule Design

Traditional CDPR control universally adopts the “Global Geometric Mapping” (GGM) paradigm, which constructs inverse kinematic relations and the Jacobian matrix based on the absolute coordinates of anchors to solve for cable length (or velocity) commands. To avoid dependence on precise geometry, this paper adopts a control approach based on Local Relative-Azimuth Awareness: the system no longer uses specific coordinate values of anchors but relies solely on the quadrant information of anchors relative to the moving platform, as well as local feedback quantities such as attitude and tension.

In the two-dimensional plane, let the velocity of the moving platform’s centroid in the global coordinate system be denoted as

$$\begin{array}{c}v=\left[\begin{array}{c}{\nu }_x\\ {\nu }_y\end{array}\right],\end{array}$$

(1)

let the length of the $i$-th cable be $L_i$, and the unit direction vector pointing from the moving platform centroid to the $i$-th anchor be

$$\begin{array}{c}{u}_i=\left[\begin{array}{c}{u}_{ix}\\ u_{iy}\end{array}\right],\end{array}$$

(2)

neglecting cable elasticity and platform rotation, the differential kinematic relationship can be written as

$$\begin{array}{c}\dot{L_i}=-u_i^{T}v=-\left(u_{ix}{v}_x+u_{iy}{v}_y\right),\end{array}$$

(3)

when further considering the influence of the pitch angular velocity $\dot{\theta }$ of the platform about its centroid on cable length, the above equation generalizes to

$$\begin{array}{c}\dot{L_i}=-u_i^{T}v-r_i\dot{\theta },\end{array}$$

(4)

where $r_i$ represents the equivalent lever arm of the $i$-th cable acting on the moving platform. The above relationship indicates that as long as the signs of the components of $u_i$ on each coordinate axis are known, it is possible to determine whether the cable should execute a winding or releasing operation under a given platform velocity command, without requiring the precise coordinates of the anchors.

This paper classifies the anchor quadrants based on the signs of the projection components of $u_i$ in the Cartesian coordinate system, categorizing anchor orientations into four types: Left-Upper (LU), Left-Lower (LD), Right-Upper (RU), and Right-Lower (RD). This classification not only facilitates rule construction but also corresponds to the basic requirements of 2D force closure: as long as there is cable distribution in each quadrant, omnidirectional control of the moving platform can be achieved through the resultant force and moment.

In the presence of multiple redundant cables, this paper treats multiple cables within the same quadrant as a single “Virtual Cable”. For the set of cables ${\mathcal{C}}_{\mathcal{q}}$ belonging to the same quadrant $q$, the length rate-of-change command is defined as

$$\begin{array}{c}\dot{L_i}=w_i\dot{L_q^{\ast }}, i\in {\mathcal{C}}_{\mathcal{q}}, {\displaystyle \sum _{i\in {\mathcal{C}}_{\mathcal{q}}}}{w}_i=1,\hspace{0.17em}{w}_i>0,\end{array}$$

(5)

where $\dot{L_q^{\ast }}$ is the target cable velocity for quadrant $q$, and $w_i$ is a distribution weight determined based on factors such as cable-rated load or current tension. Through this dimensionality reduction mapping, the complex redundant cable system is equivalent to four quadrant drive channels, facilitating the design of unified local rules.

2.2. Trajectory Control Rules

Based on the aforementioned kinematic relationships, this paper constructs trajectory control rules for four directions, as shown in Figure 1a. The core logic is to decompose complex omnidirectional motion into simple quadrant actions. Taking rightward translation as an example, let the desired velocity of the moving platform be $v_{cmd}={\left[v_0,0\right]}^T$ (where $v_0>0$). According to the differential kinematics equation, if the anchor pointed to by u_i is located in the RU or RD quadrant (i.e., the two cables on the right in Figure 1a), the cable should execute a winding operation; if the anchor is located in the LU or LD quadrant (i.e., the two cables on the left), the cable should execute a releasing operation. Similarly, the four sub-figures at the bottom of Figure 1a respectively illustrate the winding/releasing logic of the CDUs in each quadrant during right, left, up, and down movements. The following “Quadrant–Action” mapping is obtained through induction:

1. Rightward Translation: CDUs in RU and RD quadrants wind; CDUs in LU and LD quadrants release.

2. Leftward Translation: CDUs in LU and LD quadrants wind; CDUs in RU and RD quadrants release.

3. Upward Translation: CDUs in LU and RU quadrants wind; CDUs in LD and RD quadrants release.

4. Downward Translation: CDUs in LD and RD quadrants wind; CDUs in LU and RU quadrants release.

The above rules embody a qualitative control philosophy based on the sign characteristics of the Jacobian matrix: as long as the quadrant relationship of the anchors relative to the moving platform remains unchanged, even if their specific coordinates drift, the sign allocation for winding/releasing remains compatible with geometric constraints, thereby ensuring kinematic feasibility.

It should be noted that this basic rule set primarily generates open-loop translational velocity commands and does not explicitly control the platform attitude. In actual asymmetric deployment conditions, relying solely on walking rules would lead to gradual drifting of the platform attitude; therefore, it is necessary to superimpose attitude control rules (see Section 2.3) on this basis for compensation.

2.3. Attitude Control Rules

Attitude stability is one of the core constraints of the entire control system. To maintain the platform approximately horizontal under asymmetric anchor layouts and external disturbances, this paper superimposes a layer of attitude closed-loop control on top of the basic walking rules, the mechanism of which is shown in Figure 1b.

Let the pitch angle of the moving platform about the horizontal axis be $\theta$, the desired attitude be ${\theta }_{ref}=0$, and the attitude error be defined as $e_{\theta }=\theta -{\theta }_{ref}$. This paper adopts a Proportional-Derivative (PD) attitude control law and distributes the control action by quadrant. Let the quadrant weight corresponding to the $i$-th cable be $s_i\in \{+1,-1\}$, whose value is determined by the rule that “when $\theta >0$, CDUs in RU/LD wind and LU/RD release; when $\theta <0$, the opposite applies”. The cable length rate-of-change component generated by attitude control can be written as:

$$\begin{array}{c}{\dot{L_i}}^{\left(\theta \right)}=-s_i\left(K_{\mathrm{p},\theta }{e}_{\theta }+K_{\mathrm{d},\theta }{\dot{e}}_{\theta }\right),\end{array}$$

(6)

where $K_{p,\theta }$ and $K_{d,\theta }$ are the proportional and derivative gains for attitude control, corresponding to the simulation parameter settings given in Section 4.2.2.

When $\theta >0$ (i.e., the “left side high” state shown in the bottom right of Figure 1b), cables in the RU and LD quadrants (where $s_i>0$) execute winding, while cables in the LU and RD quadrants (where $s_i<0$) execute releasing; when $\theta <0$ (shown in the bottom left of Figure 1b), the quadrant action directions are reversed. After superimposing this attitude regulation component with the basic walking component, the comprehensive cable length rate-of-change command for the $i$-th cable is formed:

$$\begin{array}{c}\dot{L_i}={\dot{L_i}}^{\left(move\right)}+{\dot{L_i}}^{\left(\theta \right)}+{\dot{L_i}}^{\left(T\right)},\end{array}$$

(7)

where ${\dot{L_i}}^{\left(move\right)}$ is given by the quadrant walking rules in Section 2.2, and ${\dot{L_i}}^{\left(T\right)}$ is produced by the tension maintenance rule (see Section 2.4). In the simulation, the attitude feedback frequency is set to a value higher than the position control frequency to ensure that the attitude closed loop possesses sufficient bandwidth.

It is worth noting that the aforementioned quadrant attitude rules imply the physical premise that “the moving platform is always located within the convex hull of the anchors, and the quadrant attribution of each anchor does not change abruptly during motion”. In typical applications, such as building curtain wall cleaning, following the convention of “boundary deployment, internal operation” naturally satisfies this condition, thereby ensuring the consistency of the attitude control moment direction and the validity of the rules.

2.4. Cable Tension Maintenance Rule

To ensure the effective execution of the control strategy, all cables must be maintained in a tensioned state. As illustrated in Figure 1c, a fully distributed local tension closed-loop is implemented within each CDU in this paper. This rule operates independently of motion commands: when the sensor detects that the real-time tension $T_i$ falls below the preset minimum safety threshold $T_{min}$ (i.e., ${\mathrm{e}}_{\mathrm{T}\mathrm{i}}>0$), the local controller automatically triggers the winch to execute additional winding compensation (as indicated by the arrow in the figure) without altering the global direction of motion, continuing until the tension is restored to the safe range. This mechanism provides a fundamental guarantee of mechanical stability for the system during large-span operations and under external disturbances.

2.5. System Stability Analysis

To validate the theoretical effectiveness of the proposed “4+2+1” local rule-based control strategy, this section conducts a convergence analysis of the closed-loop system based on Lyapunov stability theory. Considering that the control strategy adopts a hierarchical architecture with decoupled attitude stabilization and trajectory tracking, and incorporates nonlinear threshold characteristics into the attitude control law, we will explicitly prove the Uniformly Ultimately Boundedness (UUB) of the attitude subsystem and the asymptotic stability of the position subsystem, respectively.

Let the state vector of the system be defined as $x={\left[e_p^T,\theta ,\dot{\theta }\right]}^T$, where ${\mathrm{e}}_{\mathrm{p}}$ denotes the position tracking error vector, and $\theta$ and $\dot{\theta }$ represent the pitch angle and pitch angular velocity of the moving platform, respectively.

2.5.1. Bounded Stability Analysis of the Attitude Control System

Consider the attitude dynamics equation of the moving platform $I\ddot{\theta }={\tau }_{net}$, where $I$ is the moment of inertia of the platform about its centroid, and ${\tau }_{net}$ is the resultant external torque acting on the platform. The total mechanical energy of the system is selected as the Lyapunov candidate function $V_{\theta }$:

$$\begin{array}{c}{V}_{\theta }={\displaystyle \frac{1}{2}}{k}_{p,\theta }{\theta }^2+{\displaystyle \frac{1}{2}}I\dot{{\theta }^2},\end{array}$$

(8)

where $K_{p,\theta }>0$ is the equivalent proportional gain for attitude control. Differentiating $V_{\theta }$ with respect to time yields

$$\begin{array}{c}\dot{V_{\theta }}=k_{p,\theta }\theta \dot{\theta }+I\dot{\theta }\ddot{\theta }=\dot{\theta }\left(k_{p,\theta }\theta +{\tau }_{net}\right).\end{array}$$

(9)

According to the attitude control rules described in Section 2.3, when the attitude deviation exceeds the preset safety threshold $ϵ$ (i.e., $\left|\theta \right|>ϵ$), the controller generates a restoring moment by adjusting the winding and releasing of cables in diagonal quadrants. Mathematically, this control law is equivalent to a Proportional-Derivative (PD) feedback with an introduced damping term:

$$\begin{array}{c}{\tau }_{ctrl}=-\left(k_{p,\theta }\theta +k_{d,\theta }\dot{\theta }\right),\end{array}$$

(10)

where $K_{d,\theta }>0$ is the derivative gain. Assuming that the dynamic response of the actuators is rapid and ignoring external random disturbances, the resultant torque of the closed-loop system is primarily composed of the control torque (i.e., ${\tau }_{net}\approx {\tau }_{ctrl}$). This is substituted into the derivative equation

$$\begin{array}{c}\dot{V_{\theta }}=\dot{\theta }\left[k_{p,\theta }\theta -\left(k_{p,\theta }\theta +k_{d,\theta }\dot{\theta }\right)\right]=-k_{d,\theta }\dot{{\theta }^2},\end{array}$$

(11)

From this, it follows that when $\left|\theta \right|>ϵ,\dot{V_{\theta }}\le 0$. Since $\dot{V_{\theta }}$ is negative semi-definite, according to LaSalle’s Invariance Principle, the system state trajectory will converge to the largest invariant set $S=\{\left(\theta ,\dot{\theta }\right)\mid \dot{V_{\theta }}\equiv 0\}$, which implies $\dot{\theta }=0$, and consequently $\theta \to 0$ is derived from the dynamics equation. However, considering the existence of the threshold mechanism in the control strategy, when $\left|\theta \right|\le ϵ$, the control input is zero, and the system is in a state of free floating or subject only to gravitational torque. Combining these two cases, the attitude subsystem satisfies the condition of Uniformly Ultimately Boundedness (UUB) stability. This implies that regardless of the initial state, the system trajectory will eventually enter and remain within a compact set $\Omega =\{\left(\theta ,\dot{\theta }\right)\mid \left|\theta \right|\le ϵ,\dot{\theta }\approx 0\}$ centered at the origin, thereby theoretically guaranteeing that the platform attitude can be stabilized within the safe range permitted by engineering standards.

2.5.2. Asymptotic Stability Analysis of Position Tracking

For the position control subsystem, the position error energy function $V_p$ is defined as

$$\begin{array}{c}{V}_p={\displaystyle \frac{1}{2}}{e}_p^T{e}_p,\end{array}$$

(12)

where $e_p=p_d-p_{actual}$. Taking the derivative of $V_p$ with respect to time yields

$$\begin{array}{c}\dot{V_p}=e_p^T\dot{e_p}.\end{array}$$

(13)

According to the “quadrant-aware” walking rules defined in Section 2.2, the velocity command $v_{cmd}$ generated by the controller is proportional to the position error, i.e., $v_{cmd}=K_{pos}{e}_p$, where $K_{pos}>0$ is the position gain.

Since CDPRs are over-actuated systems, and the quadrant mapping rules designed in this paper ensure that the actual motion vector $v_{actual}$ synthesized by cable tensions maintains directional consistency with the command vector $v_{cmd}$ (i.e., the vector inner product is greater than zero), we can let $\dot{e_p}=-v_{actual}\approx -v_{cmd}$. Substituting this into the above equation yields

$$\begin{array}{c}\dot{V_p}\approx e_p^T\left(-k_{pos}{e}_p\right)=-k_{pos}|e_p{|}^2.\end{array}$$

(14)

Evidently, for any non-zero error $e_p\ne 0$, the condition $\dot{V_p}<0$ holds. This indicates that the position subsystem is asymptotically stable, and the control strategy can drive the system to continuously decrease the potential energy function until the position error converges to zero.

In summary, the Lyapunov analysis demonstrates that the hierarchical control strategy proposed in this paper guarantees the stability of the attitude subsystem within a bounded range while achieving the asymptotic convergence of the position subsystem.

It is noteworthy that the proposed “4+2+1” rules essentially constitute a Switched System. As the moving platform moves or the target command changes, the set of CDUs participating in winding or releasing (i.e., the active modes) undergoes discrete switching. However, since all subsystems (i.e., the rules for each quadrant) share the same Lyapunov functions $V_p$ and $V_{\theta }$ (i.e., Common Lyapunov Functions) that render their energy monotonically decreasing, according to the stability theory of switched systems, the system guarantees global asymptotic stability under arbitrary switching sequences. This provides solid theoretical support for the heuristic rules proposed in this paper.

3. Reconfigurable System Design

Following the algorithmic foundation in Section 2, this section details the hardware implementation. Notably, this mechatronic architecture employs industrial-grade components, serving as a concrete blueprint for the physical prototype currently under development. To realize the “4+2+1” strategy, a modular “unit + system” architecture is designed to support distributed computing and reconfiguration, as illustrated in Figure 2.

3.1. Modular Execution Unit (MEU)

The Modular Execution Unit (MEU) is designed as the system’s central core, integrating perception, decision-making, and communication functions; it serves as the “brain” and operation platform of the entire distributed network. As illustrated in Figure 2b, the unit is powered by an independent lithium battery. Its hardware primarily integrates a high-performance main control board (MCU) acting as the network master, along with a LoRa wireless communication module. At the perception level, the MEU is equipped with a high-precision Inclination sensor as a core feedback element, which is utilized to calculate platform attitude errors in real-time to drive the “attitude correction rules”. At the execution level, the unit also integrates operational payloads, such as solenoid valves and nozzles, to execute specific curtain wall cleaning tasks. The MEU is responsible for real-time fusion of attitude data, generating motion decisions based on adaptive control strategies, and broadcasting control commands to all slave CDUs via the wireless communication module.

3.2. Modular Cable Driving Unit (CDU)

The Cable Driving Unit (CDU) is designed as an integrated and standardized mechatronic module. As illustrated in Figure 2c, each unit functions as an independent driving node, with its hardware core comprising a Power Supply, Motor Driver, Motor, Winding Roll, and a Tension Sensor for force feedback. Notably, this Tension Sensor serves as the physical sensing foundation for the aforementioned “distributed tension maintenance rule,” responsible for real-time monitoring of the cable tension state. Furthermore, the CDU internally integrates a local control board (MCU) and a Digital Transmitter, facilitating data interaction with the master control terminal via a LoRa wireless communication module. The selection of LoRa (Long Range) technology over conventional Wi-Fi or ZigBee is justified by its superior signal penetration capabilities in complex building environments. In high-rise façade cleaning scenarios, the line-of-sight between the MEU (on the façade) and CDUs (on the rooftop) is frequently obstructed by concrete parapet walls, glass structures, or metal scaffolding. LoRa’s spread-spectrum modulation technique ensures reliable communication linkage and strong anti-interference performance even under such severe occlusion, which is critical for system safety. This highly integrated modular design enables the system to flexibly scale up or down by adjusting the number of CDUs according to specific task requirements regarding workspace and payload capacity, thereby providing the physical basis for the on-demand reconfiguration of the system topology.

3.3. Distributed Wireless Network Architecture

This system constructs a distributed network architecture based on wireless communication technology, designed to address the difficulty of rapid deployment in traditional cable-driven robots caused by cable tethering. As illustrated in Figure 2a, the overall architecture presents a star topology centered on the MEU and surrounded by multiple CDUs, adopting a design paradigm of “logical centralization and physical decentralization”. At the logical control level, the system establishes a master-slave communication protocol with the MEU acting as the central computing node; it undertakes global task scheduling, command broadcasting, and multi-sensor data fusion to ensure the real-time performance and determinism of multi-unit coordination. At the physical deployment level, by integrating wireless transceiver modules and independent power supply units, complete decoupling between nodes is achieved. Each CDU is transformed into a highly autonomous distributed unit, completely eliminating complex signal and power cable connections. This design of physical discretization ensures that the physical deployment of CDUs is no longer constrained by the global geometric coordinates of anchors or electrical connections, allowing for asymmetric, plug-and-play, rapid installation based on environmental features such as the load-bearing distribution of the building façade. Consequently, by organically fusing the efficiency of centralized control with the flexibility of distributed deployment via wireless ad hoc network technology, this architecture significantly reduces system setup complexity and provides solid underlying link support for realizing task-oriented reconfigurable topologies.

4. Simulation Modeling and Verification

To quantitatively evaluate the effectiveness and robustness of the proposed calibration-free adaptive control strategy under the reconfigurable architecture, this Section constructs a numerical simulation model of the Cable-Driven Parallel Robot (CDPR) based on the MATLAB/Simulink platform(version R2023b). By simulating trajectory tracking tasks under complex operating conditions characterized by asymmetry and disturbances, the core performance of the system is verified.

4.1. Scenario Setup

The simulation experiments adopt high-rise building glass curtain wall cleaning as a typical application scenario. Modern high-rise buildings exhibit vast differences in dimensions and architectural forms; their rooftop structures are often not regular rectangles and are typically obstructed by ventilation ducts, parapet walls, and other obstacles. Consequently, when deploying Cable Driving Units (CDUs) on the rooftop, operators cannot arrange the layout in an ideal symmetrical pattern but must rely on available on-site load-bearing points for rapid, irregular placement. The physical deployment and path planning logic for this typical operational scenario are illustrated in Figure 3.

As illustrated in Figure 3a, the system is deployed on an unstructured façade; Figure 3b displays the global “boustrophedon” (zigzag) coverage path planned to meet the requirements of full-façade cleaning. To efficiently validate the core performance of the algorithm within numerical simulations, the complex global path is simplified into the closed-loop rectangular trajectory shown in Figure 3c. This trajectory extracts typical characteristics of the operational path—including horizontal traversing, vertical elevation, and right-angle turns—thereby effectively capturing the controller’s response characteristics during various motion stages. Consequently, the randomness and asymmetry of the final CDU layout, combined with the practical necessity of dispensing with precise calibration for each anchor, collectively form an ideal verification model for examining the reconfigurability and control robustness of the proposed design.

It is important to note the simplifying assumptions adopted in this simulation setup. To explicitly isolate and validate the algorithmic logic of the proposed “4+2+1” strategy, the numerical model focuses on the kinematic and static interactions while simplifying certain physical non-linearities. Specifically, the cables are modeled as massless straight lines, neglecting the catenary effects (sagging) that may arise in large-span configurations. Additionally, mechanical constraints such as pulley friction and transmission backlash, as well as potential packet losses or latencies in the LoRa communication network, are not explicitly included in this iteration. While these idealizations are appropriate for the preliminary theoretical verification, the impact of these physical dynamics will be rigorously addressed in future physical prototype experiments.

4.2. Simulation Environment and Parameter Settings

4.2.1. Simulation Environment Setup

The simulation workspace is defined as a 2D vertical plane with dimensions of $40\mathrm{m}\times 80\mathrm{m}$, where the CDUs are deployed near the boundaries. The Modular Execution Unit (MEU) is modeled as a rigid square platform with a side length of $2\mathrm{m}$ and a uniform mass distribution. To reflect real-world constraints, a minimum cable tension threshold is enforced to prevent slackness. The key physical parameters of the simulation environment are detailed in

Table 1. Physical Parameters of the Simulation Environment.

Parameter	Symbol	Value	Unit
Workspace Dimensions	$W\times H$	$40\times 80$	m
MEU Side Length	$L_{meu}$	2.0	m
MEU Mass	$m$	15.0	kg
Moment of Inertia	$I$	3.2	$\mathrm{kg}\cdot {\mathrm{m}}^2$
Gravitational Acceleration	$g$	9.81	$\mathrm{m}/{\mathrm{s}}^2$
Minimum Tension Threshold	$T_{min}$	80	N

Note: MEU, Mobile End-effector Unit.

.

4.2.2. Control and Disturbance Parameters

The control parameters were determined through a combination of theoretical stability analysis and simulation tuning. The attitude control loop employs a Proportional-Derivative (PD) controller, augmented with specific gains for attitude balance ($K_{bal}$) and directional error correction ($K_{dir}$) to enhance robustness. The position control loop utilizes a proportional controller ($K_{pos}$) to govern the translational velocity. To rigorously evaluate the system’s adaptability, stochastic disturbances are introduced, including random angular velocity injections and parametric uncertainties in mass and inertia. The specific control gains, logical thresholds, and disturbance settings are listed in

Table 2. Control System Gains and Disturbance Settings.

Category	Parameter	Symbol	Value
Attitude Loop	Proportional Gain	$K_{p,\mathsf{\theta }}$	3.0
	Derivative Gain	$K_{d,\mathsf{\theta }}$	1.5
	Balance Gain	$K_{bal}$	1.8
	Directional Gain	$K_{dir}$	$0.8$
Position Loop	Proportional Gain	$K_{pos}$	$0.5$
Motion Constraints	Nominal Speed	$v_0$	0.3 m/s
	Max Winch Speed	$v_{max}$	0.8 m/s
Logic Thresholds	Attitude Threshold	${\mathsf{ϵ}}_{\mathsf{\theta }}$	$3°$
	Adjustment	$T_{out}$	5.0 s
	Max Mode Steps	$N_{mode}$	2
Disturbances	Angular Velocity Noise	$\Delta \mathsf{\omega }$	Random
	Parametric Uncertainty	$\Delta m,\Delta I$	$\pm 10\%,\pm 15\%$

.

4.3. Results and Analysis

This section systematically evaluates the performance of the proposed rule-driven control method, focusing on three aspects: “attitude stability, trajectory tracking accuracy, and topological adaptability”. All simulations are based on the curtain wall cleaning scenario presented in Section 4.1 and the unified parameters set in Section 4.2. Key evaluation metrics include Pitch Root Mean Square Error (Pitch RMSE), Trajectory Root Mean Square Error (Trajectory RMSE), maximum deviations in X/Y directions, and the maximum working tension of each cable. By comparing simulation results under different control strategies and topological configurations, the robustness and reconfigurability of the method under calibration-free conditions can be comprehensively characterized.

4.3.1. Verification of Basic Control Performance

To validate the fundamental feasibility of the proposed “4+2+1” local rule-based control strategy, this section establishes a benchmark simulation under a standard symmetric configuration. The simulation utilizes a symmetric four-CDU layout with anchor coordinates located at (20, 40), (20, −40), (−20, 40), and (−20, −40). The comprehensive performance of the system under the full implementation of the proposed “4+2+1” control strategy is evaluated. The simulation results, illustrating the global trajectory, pitch angle variation, trajectory deviation, and cable tensions, are presented in Figure 4.

As demonstrated in the figure, the MEU successfully completes the closed-loop motion under the synergistic action of the local rules. The actual trajectory closely adheres to the reference path, exhibiting clear geometric features without the concave deformation typically associated with the lack of global geometric models. Simultaneously, the attitude control rules effectively suppress the overturning moment induced by the movement; the pitch angle of the platform is tightly locked within a narrow range near $0°$ throughout the entire process, preventing any divergent trends even during the force-intensive turning phases. Quantitatively, the Pitch Root Mean Square Error (RMSE) is maintained at a low level of approximately $1.60°$, which directly contributes to a high trajectory precision with a Trajectory RMSE of $0.553\mathrm{m}$. The maximum instantaneous deviations in the X and Y directions are limited to $0.800\mathrm{m}$ and $1.402\mathrm{m}$, respectively, achieving sub-meter level accuracy within the large $40\mathrm{m}\times 80\mathrm{m}$ workspace. Furthermore, the tension curves confirm the effectiveness of the distributed tension maintenance rule, as the tension values of all four cables continuously adapt to the motion while remaining strictly within the valid working range of $80\mathrm{N}$ to $300\mathrm{N}$.

4.3.2. Verification of Static Reconfigurability

This section validates the static reconfigurability of the proposed control framework, specifically evaluating its capability to maintain consistent performance across varying topological layouts without parameter recalibration or geometric model updates. To simulate typical unstructured deployment scenarios, two complex configurations are evaluated and compared: an asymmetric four-cable topology, which represents irregular anchor deployment necessitated by obstacle avoidance, and a redundant five-cable topology, which represents a system scalability scenario involving an additional actuator.

The comparative simulation results, as presented in Figure 5, demonstrate that the proposed local rule-based strategy exhibits remarkable robustness against geometric variations. As illustrated in the trajectory tracking (Figure 5a,b) and pitch angle (Figure 5c) plots, the system performance under the asymmetric four-cable layout is nearly identical to that under the redundant five-cable layout. In both scenarios, the Modular Execution Unit (MEU) successfully tracks the reference rectangular path with high fidelity, maintaining straight trajectories and sharp corners. Crucially, the pitch angle in both configurations remains tightly locked within a safe, narrow range near $0°$, confirming that the quadrant-based attitude rules can effectively suppress overturning moments induced by geometric asymmetry. Quantitative analysis of the path deviation (Figure 5d) further reinforces this consistency; the maximum deviation curves for both topologies exhibit a high degree of overlap, with peak errors bounded within the same magnitude (approximately 1.5 m to 2.0 m) even during the transient stages at trajectory corners. Furthermore, in the redundant five-cable configuration, the tension curves reveal that the newly added cable seamlessly integrates into the distributed force network, sharing the load with the original cables without causing internal force conflicts or control instability, thereby proving that the “4+2+1” local rules effectively decouple control performance from specific geometric parameters.

4.3.3. Verification of Dynamic Reconfigurability

To rigorously evaluate the controller’s adaptability and robustness, this section introduces dynamic abrupt changes to the system topology during operation, simulating two critical scenarios: the sudden alteration of anchor positions and the failure of a redundant actuator.

Verification of Adaptability to Anchor Reconfiguration

The system initially executes the trajectory tracking task under the symmetric Scheme A. At $t=800\mathrm{s}$, while the MEU is in the downward motion phase (Stage 4), the physical anchor coordinates are instantaneously switched to the asymmetric Scheme B to simulate an abrupt environmental change. As captured in Figure 6, this topological mutation triggers a sharp, instantaneous redistribution of internal forces across all four cables (Figure 6d); however, the local tension feedback loops rapidly stabilize these fluctuations within the working range, preventing sustained oscillations or tension violation. This rapid internal adjustment ensures that the end-effector’s attitude (Figure 6b) experiences only negligible transient disturbances before returning to the safe threshold, thereby maintaining a smooth and continuous global trajectory (Figure 6c) without the deviations or jumps typically associated with model mismatches.

Verification of Fault Tolerance to Actuator Failure

The system’s fault tolerance is examined by simulating the sudden failure of the redundant actuator (LU2) in a five-cable configuration at $t=800\mathrm{s}$. The dynamic response recorded in Figure 7 confirms that while the tension in the failed cable drops immediately to zero (Figure 7d), the remaining four cables autonomously compensate for the load loss through their independent tension maintenance rules without requiring high-level replanning. This distributed “self-healing” mechanism ensures a seamless transition of the force equilibrium, resulting in a virtually unaffected pitch angle (Figure 7b) and consistent trajectory tracking (Figure 7a), effectively demonstrating the system’s resilience to partial hardware failure under zero-prior-knowledge conditions.

4.3.4. Comparative Analysis of Robustness Against Geometric Uncertainty

To quantitatively evaluate the effectiveness and robustness of the presented work compared to related works, this section conducts a comparative experiment against a standard model-based kinematic controller (represented by the approach in [11]). To further elucidate the advantages of the proposed strategy,

Table 3. Qualitative comparison of different control paradigms for reconfigurable CDPRs.

Feature/Metric	Traditional Model-Based [11,19]	Data-Driven (RL/TDE) [23,24]	Proposed Local Rule-Based (Ours)
Geometry Dependency	High	Low	None
Reconfiguration	Offline	Online	Online
Calibration Need	Mandatory	Moderate	None
Computational Cost	Medium	High	Low
Robustness to Error	Poor	Good	Excellent

Note: MEU, Mobile End-effector Unit.

provides a qualitative comparison with existing mainstream control paradigms.

While traditional model-based methods [11,19] offer theoretical precision, they suffer from poor robustness against geometric uncertainties. Advanced data-driven approaches [23,24], although flexible, impose high computational burdens suitable for high-end processors. In contrast, as summarized in Table 3, our local rule-based method achieves a unique balance: it eliminates the need for geometric calibration and complex matrix computations, offering superior robustness and deployment efficiency for unstructured environments.

To intuitively demonstrate this decisive advantage in dealing with installation errors, a comparative simulation is conducted as shown in Figure 8. In this scenario, significant deviations are intentionally introduced between the nominal anchor coordinates (used by the controller) and the actual physical anchor coordinates (represented by the purple triangles and hollow squares in Figure 8a) to simulate a typical rapid deployment site lacking precision calibration.

The simulation results in Figure 8 reveal a distinct divergence in the performance mechanism between the two strategies. The traditional model controller (blue curve) exhibits severe distortion in trajectory tracking (Figure 8a,b), particularly the “corner-cutting” phenomenon at rectangular turns. This degradation stems from the violation of its fundamental premise: model-based controllers strictly assume that the geometric parameters in the controller ($A_{ideal}$) are identical to the physical system ($A_{actual}$). However, in the uncalibrated scenario ($A_{ideal}\ne A_{actual}$), the commands calculated based on the nominal inverse kinematics inevitably conflict with the actual geometric constraints, resulting in systematic deviation. More critically, a catastrophic divergence is observed in attitude stability (Figure 8d). Since the traditional controller operates in an open-loop manner regarding cable lengths, it unknowingly enforces a cable distribution that is theoretically “balanced” for the nominal symmetric model but generates severe unbalanced torques on the actual asymmetric anchor layout. Consequently, the platform under the traditional controller exhibits a massive inclination, with a Pitch RMSE reaching 42.75°, indicating a complete failure in maintaining a horizontal pose. In stark contrast, the proposed local rule-based controller (red curve) operates independently of global coordinate priors. By dynamically adjusting cable lengths based solely on real-time inclination sensor feedback, it actively compensates for the torque induced by geometric asymmetry. As a result, the platform attitude is tightly locked near horizontal, with a Pitch RMSE of only 1.52°. The error statistics in Figure 8c,d quantitatively confirm this superior robustness: compared to the uncalibrated traditional model, the proposed method reduces the Mean Absolute Error (MAE) from 0.92 m to 0.37 m (reduction of 59.8%) and the Trajectory RMSE from 1.11 m to 0.55 m (reduction of 50.5%). Most notably, it reduces the Pitch RMSE from the divergent 42.75° to 1.52° (reduction of 96.4%), compellingly proving that in unstructured environments where high-precision calibration is unavailable, the proposed strategy maintains superior control fidelity despite significant geometric model mismatches.

5. Conclusions

Addressing the limitations of traditional Cable-Driven Parallel Robots (CDPRs), which rely heavily on high-precision calibration and struggle to adapt to unstructured environments, this paper proposes and validates a reconfigurable CDPR scheme based on heuristic local rules. The core contribution of this scheme lies in the successful decoupling of the control logic from the system’s physical topology through the deep coupling of modular hardware and calibration-free control.

The main research findings of this paper are summarized as follows:

1. Achieved deep decoupling of control logic and physical configuration. Through the proposed modular architecture, it is proven that the force closure and motion stability of the system can be maintained relying solely on the perception and feedback of local relative relationships, without the need for prior knowledge of global coordinates or complex calibration. This breaks the inherent cognitive assumption of traditional CDPRs that “high-precision calibration is a prerequisite for control”.

2. Established an adaptive control framework with “fault immunity” characteristics. The proposed multi-level rule strategy (the “4+2+1” rules) not only achieves trajectory tracking but, more importantly, endows the system with adaptive adjustment capabilities in the event of partial execution unit failure or sudden position changes. Quantitative results show that the system’s adjustment time when facing topological abrupt changes is consistently less than 3 s. This immediate response mechanism based on physical feedback demonstrates greater practical robustness than model-based replanning methods.

3. Validated the effectiveness of “distributed local rules” for global behavior control. Quantitative analysis indicates that compared to the uncalibrated benchmark model-based method, the proposed rule-driven strategy reduces the Pitch Root Mean Square Error (Pitch RMSE) from 42.75° to 1.52° (a reduction of 96.4%) and simultaneously decreases the Trajectory RMSE from 1.11 m to 0.55 m (a reduction of 50.5%), successfully stabilizing the platform attitude within the safe threshold permitted by engineering standards throughout the process. This suggests that through low-dimensional local rule constraints, the system can achieve predictable and controllable macro-stable behavior in highly redundant and uncertain unstructured spaces, offering a new theoretical perspective for solving rapid robot deployment problems in complex constrained spaces.

This study presents a robust control paradigm for CDPRs in unstructured scenarios like building automation and post-disaster rescue. Although verified here on a planar configuration, the “local perception–synergistic execution” logic offers a theoretical possibility for extension to spatial 3D (Spatial CDPRs) systems. A promising direction for this expansion involves generalizing the current 2D “Quadrant-based” division to a 3D “Octant-based” division, where monitoring the vector component signs $\left({\mathit{u}}_{\mathit{x}},{\mathit{u}}_{\mathit{y}},{\mathit{u}}_{\mathit{z}}\right)$ could potentially expand the control logic from 4 azimuths to 8 spatial regions. Regarding the adaptability to complex geometric features (e.g., protrusions and depressions on the curtain wall surface), it is important to note that the proposed MEU operates as a non-contact floating platform. By maintaining a preset standoff distance, the system inherently avoids physical interference with surface irregularities that fall within the safety clearance. Consequently, the capability to physically engage with and clean these complex features is intended to be achieved through modular end-effectors. Currently, the physical prototype based on the design in Section 3 is being assembled. Future work will focus on the experimental verification of the proposed control strategy on this physical platform, as well as the integration of adaptive cleaning modules, such as telescopic brushes or compliant manipulators, to specifically address the cleaning requirements of irregular surfaces.