1. Introduction
Cables in cable-driven parallel mechanism (CDPM) are capable of pulling the end-effector but not pushing it, resulting in inherent limitations for these systems. The unique feature of using cables instead of rigid links to move loads has made CDPM popular choices in various fields. Despite their advantages, such as high rigidity, low weight, high load capacity, less error compared to serial mechanisms, and less energy consumption, CDPMs still face challenges in improving their performance. The Sharing Production Activities in Dynamic Environment project proposes a human–robot collaboration strategy for moving or lifting industrial objects. This project aims to enhance the performance of CDPMs in industrial applications. The development of geometry reconfiguration changes the workspace size and geometry and improves the system quality compared to other parallel robots. For such mechanisms, the development of cable tension distribution techniques, motion modeling, and control methods presents significant challenges. Caro and Merlet, 2020 [Reference Caro and Merlet1] investigated potential physical failures that may occur during human–robot collaboration in CDPMs, as follows:
1. Cable breaking or deformation of cables due to their mass (the cables are considered as a straight line in several papers);
2. A mechanical failure in the reel;
3. An encoder, motor, or control module failure;
4. Cables stuck in the reel/pulleys to ensure operator safety;
5. Collision avoidance in all forms (between cables, between cables, and obstacles/end effector) and
6. Lower accuracy in position of end effector due to error in measurement length of cables.
This study highlights the impact of physical parameters (including cable properties, shape and size of the end effector and base, location of attachment points, pulleys, and actuator choice and design) on the performance of CDPMs. These parameters become more important for analysis, while reconfiguration of the geometry is applied online on a CDPM because the geometry of the workspace is modified, and the motion of the attachment points has some impact on the model error. Moreover, the physical constraints in cables, collision avoidance, and singularity can affect the performance of the system. In addition, reconfiguration can address these constraints by moving the attachment points, wrench generation capability, and transparency, which are essential for human–robot collaboration. Furthermore, the motion of cables in CDPMs can present several challenges, which can be addressed using the following approaches:
1) Adjust the cables’ length using a motorized reel and pulley system.
2) Modifying the position of attachment points on the base or end effector using reconfiguration of the geometry [Reference Youssef and Otis2].
This review paper focuses on the physical constraints in the geometry of the CDPM, allowing a better reconfiguration of the CDPM geometry, including cable constraints, collision avoidance, and singularity. The contribution of this paper is to suggest a design process and steps to allow the reconfiguration and control architecture of the CDPM while considering safety issues, modelization accuracy, and constraints. To the best of the authors’ knowledge, a design strategy is not fully detailed in previous literature reviews related to the CDPM reconfiguration of the geometry. Therefore, section 2 outlines our methodology for identifying relevant papers to be included in the review to define a design strategy for the CDPM to add the reconfiguration of the geometry, including a control strategy. In section 3, the results of the review are presented by analyzing the contribution of each study in tables divided by the main characteristics of each study. The design strategy with the control architecture is presented in the final section of this paper.
2. Methodology
This paper presents a comprehensive systematic review of the physical models and constraints that must be considered to achieve high-performance (R)CDPMsFootnote 1 for use in human–robot collaboration tasks. By analyzing the relevant literature, this paper aims to identify the key factors that influence the performance of (R)CDPMs and provides insights into future directions for improving their effectiveness in human–robot interaction scenarios. According to the contributions of this paper, the main research questions are as follows.
How is the reconfigurable CDPM applicable in the human–robot collaboration process by considering physical constraints? Therefore, the following research questions are introduced as the main objectives of this review:
1- How (R)CDPM can be applicable in the industry?
2- What are the challenges, advantages, disadvantages, and limitations of (R)CDPM?
3- Which physical constraints can affect the performance of (R)CDPM?
4- How reconfiguration can affect the performance of CDPM?
5- How accuracy and precision could be improved in (R)CDPM?
To answer these questions and suggest a design strategy and control architecture, a search strategy is presented in the following section, using specific keywords to identify the papers that meet our review criteria. By analyzing the selected papers, we aimed to provide acceptable answers to the research questions that motivated this study.
2.1. Search strategy
To our knowledge, there has been little research on modeling reconfigurable CDPM for human–robot collaboration tasks while considering physical constraints such as collision avoidance, payload, cable wrapping, and cable sagging. Therefore, to analyze the latest information available over the past nine years, we conducted a comprehensive systematic literature review of papers published between 2015 and 2023.
The review methodology is primarily based on the guidelines provided by Boolean [Reference Phillips and Barker3]. A comprehensive search for relevant papers on Scopus and Google Scholar using the search terms in the publication titles, abstracts, and keywords is conducted in this paper. Subsequently, an initial selection to eliminate irrelevant research and duplicate papers is performed. This paper aimed to investigate the impact of physical constraints on (R)CDPM, with a primary focus on human–robot collaboration, to improve the performance of (R)CDPM. Accordingly, the keywords are selected as follows.
( TITLE-ABS-KEY ( cable AND driven AND parallel AND robot ) OR TITLE-ABS-KEY ( cable AND driven AND parallel AND mechanism ) OR TITLE-ABS-KEY ( cdpr ) OR TITLE-ABS- KEY ( cdpm ) OR TITLE-ABS KEY (wire AND driven AND parallel AND mechanism ) AND TITLE ( collabora* ) AND ABS ( collaborate* ) )
Despite conducting an extensive search using the selected keywords, a limited number of relevant papers that met the inclusion criteria are encountered. Therefore, to provide a comprehensive review, this review paper is divided into three sections.
a. Impact of physical constraints on (R)CDPM: In addition to considering physical constraints, CDPM components to design CDPM are discussed, such as pulleys, motors, and cable models, which can significantly impact the modeling of the system. A precise mechanism model can improve the performance and stability of (R)CDPM.
b. Papers on (R)CDPM:
This section discusses the relevant literature on the reconfiguration of the CDPM, which is a critical aspect of enhancing the system’s flexibility and adaptability.
c. Papers on (R)CDPM in Human–Robot Collaboration: The papers in this section focus on the utilization of (R)CDPM in the human–robot collaboration process, which requires a high degree of accuracy, safety, and user-friendliness.
By analyzing the relevant literature, the key challenges, opportunities, and future directions for enhancing the performance of (R)CDPM in the human–robot collaboration process are discussed in this paper.
Keywords for physical constraints of CDPM:
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1. Sagging
( TITLE-ABS-KEY ( cable AND driven AND parallel AND robot ) OR TITLE-ABS-KEY ( cable AND driven AND parallel AND mechanism ) OR TITLE-ABS-KEY ( cdpr ) OR TITLE-ABS- KET ( cdpm ) AND TITLE ( sag* ) AND ABS ( sag* ) )
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2. Wrapping
( TITLE-ABS-KEY ( cable AND driven AND parallel AND robot ) OR TITLE-ABS-KEY (cable AND driven AND parallel AND mechanism ) KEY ( cable AND driven AND parallel AND mechanism ) OR TITLE-ABS- KEY ( cdpr ) OR TITLE-ABS- KEY ( cdpm ) AND TITLE ( wrap* ) AND ABS ( wrap* ) )
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3. Creep
(TITLE-ABS-KEY(cable AND driven AND parallel AND robot ) OR TITLE-ABS-KEY ( cable AND driven AND parallel AND mechanism ) OR TITLE-ABS-KEY ( cdpr ) OR TITLE-ABS- KEY ( cdpm ) AND TITLE ( creep ) AND ABS ( creep ) )
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4. Unstable payload
( TITLE-ABS-KEY ( cable AND driven AND parallel AND robot ) OR TITLE-ABS-KEY (cable AND driven AND parallel AND mechanism) OR TITLE-ABS-KEY ( cdpr ) OR TITLE-ABS- KEY ( cdpm ) AND TITLE-ABS-KEY ( unstable AND payload )
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5. Singularity
( TITLE-ABS-KEY ( cable AND driven AND parallel AND robot ) OR TITLE-ABS-KEY ( cable AND driven AND parallel AND mechanism ) OR TITLE-ABS- KEY ( cdpr ) OR TITLE-ABS- KEY ( cdpm ) AND TITLE ( singular* ) AND ABS ( singular) )
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6. Collision avoidance
( TITLE-ABS-KEY ( cable AND driven AND parallel AND robot ) OR TITLE KEY (cable AND driven AND parallel And mechanism) OR TITLE-ABS-KEY ( cdpr ) OR TITLE-ABS- KEY (cdpm) AND TITLE (collision) OR TITLE (interference) AND ABS(collision) OR ABS (collision))
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7. Reconfiguration
( TITLE-ABS-KEY ( cable AND driven AND parallel AND robot ) OR TITLE-ABS-KEY (cable AND driven AND parallel AND mechanism) OR TITLE-ABS- KEY ( cdpr ) OR TITLE-ABS- KEY ( cdpm ) AND TITLE (reconfigure*))
By analyzing the selected papers using specific keywords, this review will aggregate recent studies on the advantages, drawbacks, and challenges of (R)CDPMs, suggest new research approaches for future projects, and identify areas that require further investigation.
2.2. Data extraction
The data extraction process primarily involves the selection of physical constraints and reconfiguration approaches that directly impact the performance of the CDPM. The results of a thorough search conducted using Scopus and Google Scholar are presented in Table I.
Table I. Parameters that impact the performance of reconfiguration for a cable-driven parallel mechanism related to its workspace.
2.3. Physical constraints with PRISMA method
Figure 1 presents the components of (R)CDPM. The PRISMA method, as illustrated in Figure 2, is utilized to identify and analyze the relevant literature on the physical constraints of the CDPM. Initially, 114 papers are identified and screened and 88 remained after the screening process. Eligible papers included both journal articles and conference papers. The results of the analysis are discussed in detail in the following section.
Figure 1. Components of the (R)CDPM.
Figure 2. PRISMA research method.
3. Results
The focus of this review is the utilization of (R)CDPM in industrial applications, where the use of lightweight components is critical for the ease of relocation and installation. A cable system is an appropriate choice for (R)CDPM due to its lightweight nature. The design of each component must consider different approaches in order to accommodate a large workspace. This section illustrates the five-step process of mechanical design, as shown in Figure 3.
Figure 3. RCDPM incremental V-cycle (V-Model XT) with virtual prototyping (1 and 2) and iterations based on component implementation (3) and component integration (4).
Step1. problem definition: In this step, the identification of CDPM’s application in various fields, such as industry, rehabilitation, and medicine, is accomplished based on the fulfillment of specific requirements.
Step 2: Mechanical design and software simulation: Subsequently, the mathematical formulation of the mechanical design is identified in two distinct parts.
Step 2.1. Topology design: This step involved the type and topology design of the mechanical structure of the CDPM. This includes identifying the number of degrees of freedom, shape of the end effector and base frame, type of transmission system, and the degree of redundancy. Six types of DOFs for CDPM are presented by Verhoeven [Reference Verhoeven90]: pure translational motion of 1, 2, and 3 DOFs (1T, 2T, and 3T) with the point end effector, and the 2T1R, 3T2R, and 3T3R (T denotes translation and R denotes rotation) DOFs based on the nonpoint end effector.
Step 2.2. Size and dimension design: The dimensions of the end effector and base frame are determined in this step. This is a critical aspect of design as it involves determining the optimal dimensions for the CDPM. Kelaiaia et al. 2012 [Reference Kelaiaia, Company and Zaatri91] proposed an Atlas approach and a cost function approach for dimensional synthesis. The cost function in this paper is proposed to optimize the system while considering several constraints.
Step 3. Hardware implementation: This step involves the hardware of the CDPM structure components, such as the motor drive and controller.
Step 4. Validation, Test, and Experimentation: The validation is a functional and experimental validation. This is the final step to prove that the CDPM meets all required standards. Figure 3 shows the details of all four steps.
This review primarily focuses on steps 2 and 3, as well as several challenges that enhance the (R)CDPM performance. Section A discusses the impact of physical design parameters, such as the type and dimensions of the components (i.e., cables, end effector, base frame, sensors, and actuators), on the (R)CDPM performance. Section A.1 discusses the physical parameters, which consist of the mechanical parameters of the cables, and section A.2 discusses the geometrical parameters of the transmission system, end effector, and base frame. Section B introduces some of the constraints faced by (R)CDPMs and their impact on performance, such as physical constraints in cables, collision avoidance, instability, and payload, which impact the workspace and performance of the CDPM. Figure 4 indicates sections A and B and shows how reconfiguration in section C is used to avoid collisions between humans and cables. The next section of this paper is divided into three sections.
Figure 4. Physical constraints impact on the reconfiguration.
3.1. Physical design parameters
Mechanical design is important in describing a (R)CDPM. Improving the mechanical behavior of the mechanism can significantly improve the performance of the (R)CDPM. Schmidt, V. L. 2017 [Reference Schmidt92] discusses several components of the (R)CDPM, which are available in Figure 5.
Figure 5. Concepts of the (R)CDPM design (physical constraints).
Some of the most important parameters include:
1. Cable parameters such as cable length, cable mass, cable diameter, number of cables, and material of cables
2. Geometrical parameters of CDPM including the size and shapes of the base and end effector, actuators, and pulleys
3. Payload
To improve the performance of (R)CDPM, each component requires a mathematical model in the control scheme to improve the performance of the R-CDPM. In some research papers, these models are considered in the dynamic or kinematic aspects of the control scheme [Reference Piao, Jin, Jung, Choi, Park and Kim40]; however, in many studies, these models have been ignored [Reference Khoshbin, Youssef, Meziane and Otis47].
To improve the accuracy of CDPR kinematic and dynamic models [Reference Peng, Xiao, Chen, Wei, Lin and Zhuo93] and enhance CDPM performance, one approach is to use a kinematic model that considers pulleys and a model of a continuous-mass elastic cable.
For instance, motorized reels are used to coil cables, whereas some studies utilize pulleys to direct cables from winches to cable attachment points. The pulleys in the geometric model can enhance the estimation of the payload center of mass [Reference Picard, Caro, Claveau and Plestan94]. By selecting the optimal values for these physical parameters, it is feasible to design a CDPM that satisfies the specific performance requirements for a given application. In subsection (A.1), the cable’s physical parameters, which affect the high performance of the CDPM, are discussed. Due to nonlinear friction and model error, sensorless methods that rely on motor current for wrench estimation are less accurate than sensor-based approaches. Exteroceptive sensors are recommended to ensure accurate end-effector pose measurements despite system perturbations and modeling errors.
3.1.1 Mechanical properties of cables
The cables are used as the connection elements of the CDPR end effector to a fixed base frame, and significantly influence the performance of the robot. Generally, cables are good at transmission and weak at constraints. Cables can produce only positive tension, which has nonlinear features such as rigidity (with a linear or hysteresis model [Reference Baklouti, Courteille, Caro and Dkhil95, Reference Choi and Park96], damping [Reference Baklouti, Courteille, Caro and Dkhil95], operating preload, creep [Reference Piao, Jin, Jung, Choi, Park and Kim40], sagging due to heavy weight cables, deformation of cables, wrapping, lifetime (preload and sagging are not intrinsic cable properties), and stiffness. These mechanical properties of cables can influence the CDPR performance, add complexity to the dynamic model of the CDPM, and may cause unexpected vibration at the end effector. In addition, neglecting these nonlinear features in a dynamic model of the CDPM to design a controller increases the tracking errors. The physical parameters of the cables are as follows:
Cable mass: The gravitational force acting on heavier cables may experience greater vibration, elasticity, and wrapping. Particularly, in the context of large workspace applications with heavy cables, the sagging of cables can add complexity to their modeling [Reference Nguyen, Gouttefarde, Company and Pierrot97]. Active cable tension control systems can also be used to maintain optimal tension in cables regardless of their mass.
Cable length: The cable length can be changed using winches actuated by motors fixed on the base frame.
The gravitational force acting on the cables induces tensile stress that causes elongation in their length, leading to sagging. Longer cables pose a higher risk of entanglement with other cables, which can impede robot performance. Cables that exceed the optimal length may exhibit heightened vibration and slackness, which can compromise the stability of the system and increase the risk of collision or other operational hazards, thereby undermining the safety, reliability, and efficiency of robotic systems.
Meanwhile, the controller is required to track the desired trajectory, but cable deformation can increase the cable length and cause deviations in the position and orientation of the end-effector. However, this deformation cannot be easily measured in practice. Piao et al. 2017 [Reference Piao, Jin, Jung, Choi, Park and Kim40] proposed an elongation compensator (precise cable deformation). His model is a serial combination of a linear spring and two Voigt models and is a function of the payload and cable length. This paper consists of two parts. The first part is inverse kinematics to compute the desired length of the cables. Inverse kinematic is used for massless inextensible cables in the CDPM. However, it becomes a nonlinear kineto-static problem by considering the mass and elasticity of the cables. It is important to note that cable length can also affect the robot’s workspace and performance, as longer cables can limit the robot’s speed and motion range.
Cable diameter: An increase in cable diameter results in a decrease in sag due to the increased moment of inertia. Larger diameter cables exhibited greater vibration resistance. Cables with smaller diameters may increase the risk of collision due to increased bending and deformation. Although the internal configuration of cables can lead to variations in their diameters, these changes are typically negligible, and the diameter of the cable is considered constant [Reference Choi and Park96].
Cable stiffness: A parameter that can affect the stiffness of the (R)CDPM is cable stiffness. The cable stiffness can be considered as linear [Reference Mottola, Gosselin and Carricato98]. By considering the cable model and its stiffness in the design of the controller (to track the desired pose of the end effector), the system can be made more accurate and better able to evaluate the stability in the presence of mechanical uncertainties and disturbances. Stiffer cables are less likely to sag and wrap, which improves the accuracy and precision of the CDPRs. They are also better equipped to resist deformation and bending because of their high-frequency vibrations. The cable stiffness is related to the Young’s modulus, which is a measure of the material’s resistance to deformation under stress. Active cable tension control systems can be highly beneficial for managing cable stiffness and reducing any potential vibrations. With these types of systems, the tension in the cables is adjusted to optimize the stiffness and limit any sagging or vibration. This is especially crucial for CDPMs that have considerable movement and require precise control.
Cable material: Mechanical phenomena can vary depending on the cable material used. Different materials, such as steel [Reference Yuan, Courteille, Gouttefarde and Hervé26], ultrahigh-molecular-weight polyethylene (Dyneema®), Spectra®, and aramid (also named Kevlar®), are used for cable construction. To compare the effects of different cable materials and structures on the CDPM behavior, static and dynamic models of a CDPM are established and parameterized with cable properties. The mechanical properties of the cables, including the stiffness, damping, hysteresis, and creep, are compared in Table II using an evaluation ranging from 1 (low) to 5 (high). As can be seen in Table I, the steel cable has a higher value than the Dyneema and Kelvar cables. However, this evaluation can be adapted by considering the requirements of the final application. For CDPM, if weight and flexibility are critical factors, Dyneema might be the best option because of its high strength-to-weight ratio and flexibility, whereas the creep in Dyneema is higher than that in steel and Kelvar. Steel may be more suitable for applications requiring high strength and durability. Kevlar can be a good middle ground with a balance between strength, weight, and durability.
Table II. Comparison between cables.
It is important to note that the elastic modulus for Dyneema is not constant and the viscous effect must be considered. Conversely, with steel cables, there is no need for a preliminary loading cycle and the creep effect must not be considered. For example, Gueners et al. 2021 [Reference Gueners, Bouzgarrou and Chanal99] compared aramid, Dyneema, and steel cables. Materials with higher Young’s moduli are less elastic and tend to be less prone to sagging and wrapping. The IPAnema cable robot presented by Miermeister et al. 2015 [Reference Miermeister, Kraus, Lan and Pott100] used Dyneema cables that have a lower weight but a more complex elastic behavior in the most relevant force transition element. The findings of this study indicate that Dyneema polyethylene cables exhibit time-varying elastic behavior and are susceptible to overload-induced changes. Moreover, hysteresis effects have been observed in these cables.
Viscoelasticity of cables: Polymer cables improve the performance dynamics in high-payload CDPM systems due to their low inertia effect and low friction between moving parts. However, their viscoelastic behavior and elasticity can lead to imprecise position control, resulting in errors in tracking set points and feedback loop outputs. To improve the performance of the CDPM, the viscosity of the cable is considered in the controller design [Reference Korayem, Yousefzadeh and Tourajizadeh101]. The elongation of polymer cables can cause errors in the position of the end-effector, particularly for heavy payloads.
Piao et al. 2017 [Reference Piao, Jin, Jung, Choi, Park and Kim40] developed a mathematical model of polymer cable deformation using a five-element cable model with a series combination of a linear spring and two Voigt models for pick-and-place applications. The viscoelastic cable model is defined using a brute force method, and the errors in cable length due to viscoelastic effects through position control under a heavy payload, based on the identified viscoelastic cable model, are compensated. The goal is to improve the accuracy of the pick-and-place operations, particularly for high-payload applications.
Korayem, M. H., 2020 [Reference Korayem, Yousefzadeh and Tourajizadeh101] used the Gibbs–Appell formulation to obtain a dynamic equation by considering the viscoelasticity of cables. Subsequently, a feedback linearization controller, along with two other controllers (optimal controller and finite horizon model predictive controller), is proposed to track the payload tracking task in a wide workspace.
Korayem et al. 2017 [Reference Korayem, Yousefzadeh and Beyranvand102] developed a dynamic model of the CDPM that considers the viscoelastic properties of the cables. The feedback linearization gains are obtained using the LQR method to balance the control input and tracking error. The system states are estimated using the LQG method in the presence of noise, which is assumed to be the result of the end-effector vibrations caused by cable elasticity.
Cable lifetime: Cable lifetime is a crucial factor in CDPM design. Real cables can achieve a reasonable lifetime only if the minimum bending radius is exceeded. Furthermore, the friction on the attachment points can reduce the lifetime of the cables.
Temperature: Temperature variations can exert a substantial influence on cable material properties, such as the Young’s modulus and thermal expansion coefficient, thereby leading to modifications in cable stiffness and length. Thermal expansion of cables can cause sagging and wrapping, which can result in unwanted vibrations. Increased temperatures can also reduce cable stiffness, rendering them more elastic. To mitigate the effects of temperature variations on cables, active tension control and temperature compensation techniques can be employed, which can effectively counteract the negative impact on cables and alleviate sagging in the (R)CDPM. More details on these challenges are discussed in the following sections.
3.1.2. Geometrical parameters of the transmission system, end effector, and base frame
CDPMs comprise a base frame, an end effector, pulleys, winches, and actuators. The point-to-point straight-line model neglects pulley and cable shapes. The CDPM can be designed by considering geometrical constraints. Cables are wound on winches, guided by pulleys, and connected to the end effector on the opposite side. There is a correlation between the dimensions of these components and the performance of the CDPM in terms of the static and kinematic equilibria of the end effector. Moreover, the mass, shape, and size of the end effector can significantly affect several physical constraints of a CDPM, including sagging, wrapping, collision, vibration, elasticity, workspace, and singularity.
Mass of end effector and base frame: The mass of the end effector and base frame is crucial in the CDPM design. The mass of the end effector influences cable sagging, wrapping around pulleys, vibration, and singularity issues. To improve the performance of the CDPM, the end-effector mass must be increased to have a larger gravitational force or springs can be added [Reference Duan, Vashista and Agrawal103]. Picard et al., 2018 [Reference Picard, Caro, Plestan and Claveau104] design a PD controller with real-time mass estimation and compensation in feedforward terms for a suspended CDPM. This mechanism is used to select and place objects of different shapes, sizes, and masses. Dynamometers quantify the force exerted by individual cables on a moving platform and are used to evaluate the payload mass in real time. Increasing the payload mass improves the performance of the controller compared to its two counterparts.
Shape and size of the end effector and base frame: The size and shape of the end effector and base frame exert a substantial impact on the center of gravity, which in turn increases the tension and sagging in the cables. The shape and size of the base frame can affect the singularity of the robot by constraining its motion in specific directions. Asymmetrical or irregularly shaped end effectors and base frames heighten vibrations, leading to cables wrapping tightly around the pulleys and constraining the robot’s range of motion and accuracy. Additionally, larger end effectors hinder the robot’s ability to navigate around obstacles and increase the risk of collisions with nearby objects. There are two geometric models of the end effectors: Init X and Optim. Init X has a shape similar to a parallelepiped, with attachment points located on both the upper and lower planes. It also has vertical plane symmetry, and its cables are crossed as in the IPanema robot family [Reference Pott105]. In Optim geometry, the attachment points are determined through estimation to maximize the stiffness of the end effector within the workspace. In addition, this design aims to prevent collisions between cables connected to the same plane.
Attachment points: Attachment points are fixed to the base and end effector with single holes [Reference Barnett and Gosselin106] or ceramic guidance [Reference Hiller, Fang, Mielczarek, Verhoeven and Franitza107] used to minimize cable friction. Deflection pulleys are commonly used in CDPMs with one or two pulleys fitted with plain or ball bearings. Multidegree-of-freedom pulleys are used for lifting, with 2DOF pulleys having a rotation axis aligned with the cable direction [Reference Rognant and Courteille108]. One pulley attachment point is constant on the fixed base frame. Additionally, attachment points can include additional guides.
Hay and Snyman 2005 [Reference Hay and Snyman109] utilized a dynamic optimization algorithm to estimate the optimal attachment point on the base of a planar CDPM, taking into account the maximum workspace. The connection between the attachment points on the base and end effector is symmetrically distributed and consists of four modes: non-cross, horizontal-cross, vertical-cross, and double-cross connections. A cable with a small diameter is attached to the end effector with a knot or crimped through a hole [Reference Barnett and Gosselin106]. Additional guidance elements are used in large-scale applications.
Pulley: Simplifying pulleys as ideal points and ignoring cable elasticity is a common approach for researching the connection between the cable and base frame. However, this point-to-point assumption oversimplifies the robot model and can cause errors in the trajectory of the end-effector. This approach is accurate only when the cable radius is small or the CDPM span is large. Calculating the tangent points and wrap angles of the cables in the pulleys is essential for this approach. Wang et al, 2019 [Reference Wang, Kinugawa and Kosuge86] presented four categories for cable outlet mechanisms on the base: eyelet, single-pulley, double-pulley, and multipulley types. In scenarios where the cable outlet point is fixed, the eyelet type is ideal. However, the relative motion between the cable and eyelet can cause friction, cable breakage, and reduced accuracy. To address this issue, the pulley can be presented as an RRP kinematic (spatial) or an RP kinematic (planar). To address these errors, Gonzalez-Rodriguez et al. [Reference Gonzalez-Rodriguez, Castillo-Garcia, Ottaviano, Rea and Gonzalez-Rodriguez110] proposed a method for mounting compensation pulleys at the cable attachment point on the end effector. However, although this method is suitable for planar CDPRs, it is not appropriate for low-speed spatial CDPRs.
Paty, Thibaut, et al. 2021 [Reference Paty, Binaud, Caro and Segonds111] modeled two types of pulleys: a single revolute joint pulley and a new double revolute joint pulley. They then compared the accuracy of the end-effector pose with those of the new pulleys and conventional pulleys. For cables of short lengths, it may be possible to replace the winch with a linear actuator. The combination of a linear actuator and a hoist system can increase the cable length. Pott, A. 2012 [Reference Pott105] introduced a kinematic model of the pulley mechanism used in winches for CDPMs. It also proposes a pulley friction compensation method for winch-integrated cable force measurement in CDPMs.
Actuator: When designing a CDPM, the designer must consider factors such as motor power and actuator capacity. The capacity of an actuator is a crucial parameter that affects the size of the workspace.
Gagliardini et al. 2015 [Reference Gagliardini, Caro and Gouttefarde112] presented an optimization problem that focuses on the design procedure, specifically the sizing of the actuators such as motors, winches, and gearboxes (which connect the winches to the motors) to enhance the Twist Feasible Workspace).
Banadaki, S.M.D., 2007 [Reference Banadaki113] presented the mechanical design of CDPMs comprising motor selection, speed reduction mechanism, cable-winding mechanism, end-effector design, and base design. In a specific study, four Aerotech DC1017 servomotors are utilized with an encoder fixed at the end of each motor to read the angular position. The cable winding unit in this investigation consists of a motor, speed reduction mechanism, and threaded drum with shafts and bearings.
Motor: The tension in the cables can be estimated by utilizing the current measurements and estimating the motor torques. However, this method may not be effective in cases of high friction stemming from the transmission systems. Therefore, a force sensor can be attached to the attachment points on the end-effector to mitigate this issue [Reference Yang Ho, Kraus, Mangold and Pott114]. Furthermore, it is possible to attach a force sensor to an intermediate pulley. Ottaviano, E. 2007 [Reference Ottaviano115] demonstrated that an error greater than 1 N is observed between the theoretical estimation and the force sensor, due to the presence of vibrations and the friction of the pulleys.
Winch: Inclusion of the winch geometry can enhance the positional accuracy. The winch, where the cable is wound, is one of the most intricate mechanical components of a CDPM. Inaccuracies in this component can result in high geometric errors and adversely affect the performance of the CDPM. As a solution, many CDPMs utilize electric motors to regulate the cable length. However, the cable is wound freely, making it difficult to control the wind on the winch. A thread on the winch to constrain the lateral winding of the cable is proposed to avoid cable winding on the winch and improve the cable winding precision [Reference Pott, Mütherich, Kraus, Schmidt, Miermeister and Verl116].
Nevertheless, the primary drawback of this approach is the lack of a fixed attachment point, which necessitates integration of the cable position on the winch into the geometric model of the CDPM. Another method is discussed in [Reference Rognant and Courteille108] to move the winch in both translation and rotation. To address these issues, the attachment points can be stabilized by selecting an appropriate reduction ratio between the pitch of the drive screw and diameter of the winch. However, this method may result in a reduced dynamic performance due to both translational and rotational inertia. Alternatively, a rotating threaded winch and fixed attachment point can be utilized, such as a simple hole or pulley with two degrees of freedom in rotation, as demonstrated in IPAnema 3 [Reference Pott, Mütherich, Kraus, Schmidt, Miermeister and Verl116]). The Skycam winch does not employ a thread but instead utilizes cable winding guidance through the use of pulleys, translational guides, and a drive screw. Heap et al 2022 [Reference Heap, Keeley, Yao, Naclerio and Hawkes117] presented lightweight and small winches with high force capabilities.
3.2. Physical constraints
Therefore, careful consideration of CDPM constraints, such as cable physical constraints (cable sagging, wrapping, collision avoidance, creep, and sagging), and implementation of appropriate techniques can significantly enhance the overall performance and accuracy of the CDPM.
There are the following challenges which need to be considered.
1) CDPMs are susceptible to cable wear and breakage during operation, which presents a challenge in ensuring their reliability and longevity. The lack of research and standards related to the durability of CDPMs, including guidelines for detecting and replacing worn cables, makes it difficult to ensure their sustainability and dependability.
2) Ensuring the precise maintenance of CDPMs is challenging because of various factors, such as cable reconfiguration, nonlinear cable deformation, long-term tension, and induced cable creep. This decline in accuracy significantly affects the effectiveness of the CDPMs, particularly in industrial settings. One possible solution is the implementation of rapid self-calibration techniques.
3) In certain applications where high bandwidth or system stiffness is required [Reference Diao and Ma118], uncontrollable vibrations can pose a significant challenge.
Controlling vibrations in CDPMs is challenging due to the flexibility and low rigidity of cables. Existing vibration suppression methods lack versatility and often require expensive high-performance controllers. To address these issues, a unified framework for hardware and software control is required. Increasing the natural frequency is one way to reduce the vibration of the mechanism. The relationship between the natural frequencies of CDPMs is affected by the relationship between the shape of the end effector and the shape of the frame. A linear equation of motion is proposed using the Lagrange approach. Different end-effector shapes can result in varying natural frequencies [Reference Piao, Jung, Seon, Park, Park and Ko119].
4) The rapid development cycle of CDPMs is impeded by insufficient industrial infrastructure, including the absence of high-performance cables, drive modules, and control systems. In addition, the lack of mature software for efficient analysis and development presents a significant challenge.
5) The rapid development cycle of CDPMs is impeded by insufficient industrial infrastructure such as high-performance cables, drive modules, and control systems. Furthermore, the absence of mature software for efficient analysis and development is a significant challenge.
6) In CDPMs, workspace analysis is a critical challenge that is more significant than rigid mechanisms due to the complexity of the design parameter constraints, which may be coupled with cable tension. The workspace is an essential parameter for designing, controlling, and implementing CDPMs because it defines the space in which the end-effector can operate under varying position and orientation constraints. CDPM workspaces are sets of end-effector poses that satisfy geometric constraints, force balancing, and structural stiffness with boundary conditions such as force, impact moment, and noise.
Several methods are proposed to determine the workspace.
a) The first method involves continuing with common algorithms for interval analysis. Lamine et al. 2016 [Reference Lamine, Bennour and Romdhane120] established a workspace for a planar three-degree-of-freedom (3DOF) CDPM with four cables and a six-degree-of-freedom (6DOF) spatial CDPM with eight cables, utilizing interval analysis techniques. Additionally, the minimum size of CDPM required to achieve a given workspace is analyzed.
b) The second method employed in this study is the point-wise approach, which involves utilizing a finite set of discrete points to ensure compliance with workspace constraints.
Pusey et al. [Reference Pusey, Fattah, Agrawal and Messina121] introduced a pointwise method and performance index to assess the impact of a robot’s structure, including the size of the fixed and end effectors, on the workspace size.
c) A third approach is the analytical method, which relies on the workspace boundary and geometric relationships between the end effector and cable lengths. This method uses kinematic equations to define the hull of the workspace and offers improved accuracy compared to point-wise methods. It is commonly employed for straightforward mechanism geometry and is relatively easy to implement.
d) Another method for calculating the workspace is the hybrid method, which combines both the analytical and numerical methods. With this approach, analytical methods are used to determine the workspace boundaries, whereas numerical methods are used to calculate the workspace points within those boundaries. Hybrid methods offer a more accurate and efficient calculation of the workspace than analytical or numerical methods alone.
To calculate the workspace that satisfies the geometric constraints in a CDPM, it is necessary to have a thorough understanding of the various constraints involved. The workspace of the mechanism is determined by considering these constraints. For instance, the workspace must be constrained within the free workspace to prevent collisions with obstacles in the environment and to avoid singularities, which are configurations in which the robot loses one or more degrees of freedom. Additionally, the physical constraints of the robot structure limit the joint angles. The workspace of the robot could not exceed the maximum length, tension, and joint angles. Furthermore, the workspace of two CDPMs with the same base frame size is dependent on the size and shape of the end effector as well as the positions of the attachment points on the base and end effector. To further enhance the workspace and performance of CDPMs, it is necessary to delve into the details of several constraints, including physical constraints in cables, reconfiguration, collision avoidance, singularity, and an unstable payload.
3.2.1. Physical constraints in cables
Cable tension is a critical issue affecting the vibration, control, and performance of CDPMs. Several constraints, including the energy efficiency, uniformity of cable forces, and stiffness, must be considered when determining a solution for cable forces. The tension of cables must be monitored to ensure reliable operation, and this can be achieved in two ways. First, the current consumption and properties of the motors can help estimate the tensile forces (tension) in the cables. Second, a more accurate approach involves adding a force sensor around the attachment points of cables in the reel. Alternatively, the third approach is to add a force sensor to the end-effector side for each cable. The first approach, which involves measuring the current in the motor, is suitable for mechanisms with extremely low inertia and friction. The second approach reduces the impact of the nonlinear properties of the reel; however, it is important to note that the cable should not exhibit significant sagging.
The third approach is necessary for situations where sagging is a critical concern. In such cases, measuring the tensile force difference between the attachment on the reel and the attachment point on the end effector is necessary to improve the estimation of the current state of the mechanism. A constraint exists in cable tension, with tension limited between the minimum tension to prevent sagging and the maximum tension to avoid excessive friction between mechanical components, which can lead to vibration and potential cable ripping [Reference Cobilean, Oarcea and Stan122]. The stiffness of CDPMs can be limited by the maximum tension in cables [Reference Xiong and Diao123], due to mechanical cable resistance or actuator torque limitation.
In fully constrained CDPMs, there are infinite combinations of cable tensions that can balance a desired Cartesian wrench because the number of cables is higher than the degrees of freedom while satisfying the limitations of lower and upper tension in the cables. As the tensile force increases, the vibration in the end effector is reduced quadratically; however, it cannot be eliminated as the principal frequency harmonics of the vibration increase and could become audible. Furthermore, active cable tension control systems can be utilized to maintain optimal tension and minimize vibrations in the cables. Vibration damping materials can also be employed to reduce cable vibrations and improve the performance of CDPM.
a) Cable sagging: To mitigate cable sagging, the minimum tension bound should be elevated. In many robotic systems, cables are treated as massless and have a negligible impact on dynamic analysis when compared to rigid bodies; however, this assumption is not valid for larger CDPMs [Reference Tho and Thinh8].
In high-payload scenarios, where an encoder is used at the reel, the elongation of the cables can cause an error in the positioning of the end effector. In ref. [Reference Merlet31], the Irvine sagging cable model is utilized to account for the cable elasticity and deformation caused by cable mass in CDPMs. However, a limitation of CDPMs is cable sagging during the end-effector movement. The inclusion of cable mass in workspace analysis presents further challenges, and reducing the cable tension to mitigate sagging could result in decreased end-effector stiffness and increased sagging. Alternatively, increasing tension may not be a reliable solution for addressing cable sagging. The optimal tension distribution algorithm optimizes the lower tension constraint by minimizing energy consumption, friction, vibration, and other factors. The algorithm estimates cable sagging by analyzing the lengths of the cables exceeding a certain threshold and their orientations.
Table III presents the cable sagging in the CDPM.
Table III. Impact of cable sagging due to mass and elasticity on the CDPM/(R)CDPM.
b) Cable Wrapping:
Occasionally, potential interference between the cable and rigid links of the mechanisms is considered. Wrapping the cable around a rigid link can significantly affect the workspace of CDPMs. In addition, cable length errors may arise due to cable wrapping. Table IV discusses the phenomenon of cable wrapping on the CDPM.
Table IV. Impact of cable wrapping due to mass and elasticity on the CDPM/(R)CDPM.
c) Creep: Continuous and slow deformation of a material under long-term constant mechanical stress is known as creep. This is a time-dependent parameter, and if left unchecked, can cause mechanical failure well below the yield strength of the material. If cable elongations due to creep are not compensated for, errors in cable lengths can reduce the accuracy of motion tracking. Several factors affect the creep behavior of polymer cables, including cable length, material mechanical properties, and temperature [Reference Piao, Jin, Choi, Park, Kim and Jung39]. The creep behavior of polymer cables can have a negative impact, particularly in pick-and-place applications. Table V discusses the cable creep phenomenon in the CDPM.
Table V. Impact of cable creep on the CDPM/(R)CDPM.
3.2.2. Unstable payload
In situations where the load is unstable, CDPMs may encounter issues, such as falling loads or posing a risk of injury to humans in the workspace. Automated construction or rapid transport of construction materials via mechanisms can be viable solutions to address such critical scenarios and reduce accidents. Some methods have proposed balancing the object on the end-effector as a means of preventing instability. Ali and Aphiratsakun 2015 [Reference Ali and Aphiratsakun124] propose the implementation of PID controllers to balance a ball at the center of the end effector, starting from a random initial position. In addition, a method for recovering the positional control of the ball after applying an external disturbance to the end effector is proposed. The controller is designed to regulate the system for both scenarios with and without external disturbances. The proposed approach entails regulating the disturbance to recover the ball’s position, which requires approximately 30 s to achieve in this application. Table VI presents the phenomenon of an unstable payload on the CDPM.
Table VI. Impact unstable payload on the CDPM/(R)CDPM.
3.2.3. Collision avoidance
CDPMs face distinct challenges when it comes to collision avoidance, including designing a geometry that prevents collisions, implementing real-time collision-detection algorithms, and determining workspace limitations. One solution is to study the geometry reconfiguration, as the shape of the end effector or the number of cables can limit the stability, singularity, and wrench feasible workspace. Reconfiguration or changing the attachment location of the cables can help overcome these limitations. This review presents various methods for collision avoidance in CDPMs, including strategies for preventing collisions between cables, between cables and end effectors, and between cables and obstacles. These methods are presented in Tables VII and VIII. Table VII presents the collision avoidance (between cables and obstacles and between obstacles with end effectors) methods on the (R)CDPM, while Table VIII discusses the impact of collision avoidance between cables [Reference Youssef and Otis2], between cable and human [Reference Khoshbin, Youssef, Meziane and Otis47, Reference Khoshbin, Otis and Meziane125], and between cables and end effectors on the (R)CDPM. In addition, several strategies can be used to detect interference-free constant-orientation workspaces.
Table VII. Impact of collision avoidance between cables and obstacle and between obstacle and end effector on the CDPM/(R)CDPM.
Table VIII. Impact of collision avoidance between cables and between cable and end effector on the CDPM/(R)CDPM.
In reference [Reference Wischnitzer, Shvalb and Shoham126], the inverse kinematics problem for the mechanism and numerical solution for colliding wires are computed for a six-degree-of-freedom CDPM with negligible friction between the wires at the connecting points. Furthermore, a wrench-feasible workspace is identified in the upper bound of the colliding cables. The results reveal that the workspace is larger when cable collisions are permitted compared to a collision-free scenario.
To avoid collisions with obstacles and repel a mechanism approaching boundaries, the local artificial potential field (APF) [Reference Ge and Cui127] is utilized. The APF [Reference Ding, Zheng, Liu, Guo and Guo128] approach utilizes attraction and repulsion functions to guide a mechanism toward a target while avoiding obstacles. Stability analysis is conducted using the Lyapunov function. Other approaches including sample-based methods [Reference Zou, Hu, Cao, Xu, Yu, Lu and Xiong49], geometry-based methods [Reference Yang, Alvarez and Bruggemann129], biased rapidly exploring random trees (RRT), and velocity obstacle-based methods [Reference Chakravarthy and Ghose130] are used to update the path planning problem to avoid collision with moving obstacles. Carpio-Aleman et al 2018 [Reference Carpio-Aleman, Saltarén-Pasmino, Rodríguez, Portilla, Cely, González-Álvarez and Castillo-Guerrero53] used a straightforward trigonometric calculation to determine the distance between the cables and end effector segment at regular intervals. Bak et al. 2019 [Reference Bak, Hwang, Yoon, Park and Park52] introduced a revised version of the goal-biased RRT algorithm, along with the Gilbert–Johnson–Keerthi algorithm, to address the issue of cable collisions by determining the distance between the mechanism limbs and fixed objects. Although various studies have proposed optimal designs and reconfigurable CDPM theories that rely on fixed configurations to avoid obstacles, their effectiveness in complex tasks and cluttered environments remains questionable due to the limited geometric configurations of the CDPM. Reconfiguration is achieved by relocating the attachment points on the base (motorized reel location) to enable the desired initial trajectory.
3.2.4. Singularity
Singularity is a point in the robot’s workspace where it loses one DOF and reduces the accuracy of the CDPM. Table IX presents the impact of singularity on CDPM performance.
Table IX. Impact of singularity on the CDPM/(R)CDPM.
3.2.5. Reconfiguration CDPM
Moving the attachment points on the base or altering the cable-pulley rotation, as prescribed by the reconfiguration theory, provides a superior solution compared to maintaining fixed attachment points. This approach involves modifying the geometric configuration of the (R)CDPM to update their constraints; however, it also results in an increased complexity of the process. The (R)CDPM has been proposed for applications in cluttered environments or where multiple end effectors are required. Table X shows several studies on the reconfiguration of CDPM. Kumar, Rajesh, and Sudipto Mukherjee 2021 [Reference Kumar and Mukherjee79] present the optimization of attachment points position based on rigid body dynamics of multiple contact problems to reduce cable slackening and the emergence of singularity poses.
Table X. Impact of cable sagging due to mass and elasticity on the CDPM/(R)CDPM.
3.3. Suggested methodology for (R)CDPM design and control
On the one hand, in the industry and assembly process, the robot must repeat the repetitive process and track the desired trajectory that is introduced to the robot. The physical uncertainties in the mechanism due to the properties of cables, such as sagging, wrapping, creep, and other properties such as unstable payload and singularity, affect the performance of the robot in tracking the trajectory when the robot and human are collaborating. In the pick-and-place processes, there are several control methods for CDPM as follows: cartesian position/velocity control such as 1-cable length control, cartesian position (outer loop) to articular cable length (inner loop), 2-cable tensile control, cartesian position to articular force and cartesian wrench control such as 3-cable length control: cartesian wrench to articular cable length control, 4-cable tensile control: cartesian wrench to articular force control. Articular control with a tensile cable force is proposed by Otis et al. 2009 [Reference Otis, Nguyen-Dang, Laliberté, Ouellet, Laurendeau and Gosselin133] as a set point to adjust the Cartesian pose of the end-effector. Vision-based and model-based controls are used to improve the performance of the tracking trajectory by the end effector. A precise robot model is not required because the pose of the end effector can be estimated directly in Cartesian space. However, in vision-based control, precise measurement of the end-effector pose is achieved using external sensors such as cameras and motion capture systems to mitigate the influence of cable properties such as sagging and stretching. This approach estimates the positions of objects using visual data from a camera mounted on the end effector, rather than relying on a forward kinematics problem [Reference Zake, Chaumette, Pedemonte and Caro134]. Predicting exact uncertainties in a complex CDPM is impractical. Therefore, utilizing visual data is advised, with two configurations: (1) eye-to-hand configuration, achieved by observing the robot with a stationary camera in the environment and (2) eye-in-hand configuration, where the camera on the end effector observes the target object (payload) in the environment. In vision-based control, the effectiveness of CDPM is highly dependent on the quality of the camera. The precision, resolution, and sensitivity of the sensors are essential for improving pose estimation, although this results in higher costs. Transitioning from model-based to vision-based control can improve the accuracy of CDPMs.
By contrast, reconfiguration is used to avoid collisions between cables [Reference Youssef and Otis2] or between humans and cables [Reference Khoshbin, Youssef, Meziane and Otis47]. In addition, designing reconfigurable CPDMs, (R)CDPM, to avoid collisions between cables or between humans and cables and choosing the optimal controller for the mechanism to track the desired pose is a challenge. A controller can improve the performance of the (R)CDPM to track the trajectory; however, constraints such as positive tension in cables may limit the performance of the CDPM. Designing a robust controller in the presence of uncertainty due to the physical properties of the CDPM is recommended.
There are several conventional model-based controllers such as PID [Reference Bayani, Sadeghian, Masouleh and Kalhor135], sliding mode [Reference Lv, Tao and Ji136], and prediction control [Reference Santos, Chemori and Gouttefarde137]. These controllers are developed for both the task and joint spaces to enhance tracking of the desired position of the end effector. Aflakiyan et al. 2015 [Reference Aflakiyan, Bayani and Masouleh138] presented the Ziegler–Nichols method to estimate the parameters of the PD controller, ensuring stability with state feedback and PD, while the dynamic pulley is considered in the equation of the mechanism.
The wave-based controller can move the position of the end effector in the presence of uncertainty, without requiring precise calibration or installation. It can also effectively dampen the vibrations within the system. The effectiveness of wave-based controllers in vibration rejection stems from their capability to propagate and manipulate waves along a structure to counteract these vibrations [Reference Khalilpour, Khorrambakht, Taghirad and Cardou139]. Khalilpour et al. 2019 [Reference Khalilpour, Khorrambakht, Harandi, Taghirad and Cardou140] introduced models for actuator and power transmission systems by employing cascade control in uncertain conditions. The inner loop regulates the tensile forces in the cables and requires tension sensors. The outer loop uses a robust sliding-mode controller to follow the desired position. A sliding mode controller in Cartesian space for a 6-degree-of-freedom (6 DOF) CDPM is introduced, relying on cable length sensors (motor encoders within the reel) [Reference Lv, Tao and Ji136]. The challenge with this controller is chattering, which is a phenomenon in which the control signal rapidly switches between two values. Several approaches have been proposed to mitigate this issue in sliding mode controllers. To ensure stability, a novel approach is suggested based on the Lyapunov theory proposed by Khalilpour et al. 2018 [Reference Khalilpour, Khorrambakht, Harandi, Taghirad and Cardou141]. The authors proposed a method for controlling CDPMs in Cartesian coordinates without calibration. They considered uncertainties in parameters, such as attachment points, and analyzed the stability of the closed-loop system using the Lyapunov matrix. Sancak et al 2022 [Reference Sancak, Yamac and Itik142] improved the tracking of the desired trajectory of the end effector using the reinforcement learning (RL) method. Tho & Thinh 2021 [Reference Tho and Thinh8] predicted sagging in cables using ANFIS. Kumar et al 2019 [Reference Kumar, Antoine and Abba143] employed input–output feedback linearization using the pole placement technique to achieve the desired end-effector position. This linearization method is designed for a specific type of nonlinear system by altering a suitable coordinate and applying a linearizing state feedback. The effectiveness of the controller is demonstrated in the presence of noise. Kiani et al. 2017 [Reference Kiani and Mashhadi144] present a model reference adaptive controller to reject external disturbances or vibrations in the end effector. The adaptive fuzzy sliding mode control presented by Aghaseyedabdollah et al. 2022 [Reference Aghaseyedabdollah, Abedi and Pourgholi145] is proposed to tune the gain of the PID sliding surface and reduce chattering and payload disturbances. However, there are many papers about design controllers for CDPM; to the best of our knowledge, there is a gap in design controllers for reconfigurable CDPM when the kinematic, dynamic, and Jacobian matrices of the mechanism are changing because of moving attachment points on the base. Designing a robust controller in the presence of uncertainty due to the physical properties of the cable-driven parallel is recommended. The parameters of the controller can be tuned in real time to achieve a higher performance.
Figure 6 presents the steps for designing a Cartesian end-effector controller for the (R)CDPM. Given the physical challenges posed by the mechanism, there are uncertainties in the dynamics of the RCDPM due to changes in the kinematic or attachment-point position on the base. We recommend the use of a robust controller in future work to achieve high stability in human–robot collaboration.
Figure 6. RCDPM controller design steps.
Figure 7 presents the control architecture for the (R)CDPM using human–robot collaboration. In the proposed architecture for 6 DOF CDPM with eight cables, several constraints can be modified by geometrical modification or reconfiguration; however, we focus on reconfiguration theory to avoid collisions between cables or between cables and humans by the relocation of attachment points on the base. The Cartesian control law is proposed to generate the desired velocity as a reference signal for the predictor velocity controller to generate the desired tension for each motor.
An adaptive generalized prediction controller is proposed for several key reasons. The goal of the GPC compensator is to generate a tensile force to minimize the tracking trajectory error and disturbance rejection. First, this controller is capable of modeling the linear CDPM and can estimate the parameters of the linear transfer function of the system, even in the presence of uncertainty in the dynamics of the CDPM and changing attachment points on the base. For the adaptive component, the recursive least squares (RLS) algorithm is employed to estimate the parameters of the transfer function of the CDPM dynamics, which are variable due to the changing dynamics of the mechanism. The estimated CDPM model is utilized to design a predictor and an optimizer, which served as the two components of a predictive controller. From the RLS, an update of the controller parameters is achieved based on these newly estimated parameters. Second, this controller integrates a tension distribution algorithm directly into the controller to compute the cable tensions [Reference Santos, Chemori and Gouttefarde146]. In another type of controller, the desired wrench is computed, and tension is applied to the system using the tension distribution method [Reference Gouttefarde, Lamaury, Reichert and Bruckmann147]. Meanwhile, in the optimization equations, the constraints in the control input (limitation in the positive and maximum cable tensile forces) and output are considered. Subsequently, a cable tension controller is used to reduce the tension error between the desired tension generated by the predictor controller and the current measured tension. Moreover, a reconfiguration controller is proposed to adapt the geometry and move the attachment points on the base to avoid collisions between humans and cables.
Table XI. Functions in closed-loop control block diagrams.
Figure 7. Suggested control architecture for (R)CDPM using human-robot collaboration.
Some control options can be added, namely, a stability observer and safety validation. A stability observer is useful for analyzing the stability of the controller architecture, including human impact.
A safety validation to guarantee safety is presented in ref. [Reference Winter and Ament148]. The functions shown in Figure 7 are presented in Table XI.
4. Conclusion and future work
Several parameters can be introduced as constraints that can affect the performance of the CDPM. In the first part of this paper, the physical parameters of the CDPM are discussed; in the second part, physical constraints such as singularity, cable sagging, unstable payload, cable wrapping, and collision avoidance in the modeling of the CDPM are considered to improve the system performance. Different reconfiguration methods to avoid collisions between cables or between cables and humans are discussed to improve the performance of the CDPM. A total of 88 papers are reviewed to find all the constraints to be considered in the design step suggested in this paper.
In human–robot collaboration applications such as picking, placing, or assembly/disassembly processes, the end effector needs to track the desired trajectory.
In future work, design controllers besides reconfiguration theory can improve the performance of CDPM in human–robot collaboration for the assembly/disassembly process. The reconfiguration guarantees human safety and avoids collisions between cables or cables and humans, whereas the controller aims at the end effector to track the desired trajectory in the assembly process.
A controller is proposed to improve the precision of the end effector in the presence of constraints such as sagging, wrapping, creep, unstable payload, and singularity. This is because the reconfiguration theory changes both the kinematic and dynamic models of the CDPM.
Author contributions
EK, MO, and RM contributed in developing the study concept. EK performed the initial manuscript, while MO and RM provided supervision. All authors participated in reviewing, revising, and approving the final version of the manuscript.
Financial support
This work received financial support from the Fonds de recherche du Quebec – Nature et technologies (FRQNT) under grant numbers 2020-CO-275043 and 2016-PR-188869. This project uses the infrastructure obtained by the Ministere de l’Economie et de l’Innovation (MEI) du Quebec, John R. Evans Leaders Fund of the Canadian Foundation for Innovation (CFI), and the Infrastructure Operating Fund (FEI) under the project number 35,395. Other financial support was also used in this project. Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant number RGPIN-2018-0632.
Competing interests
The authors declare that they have no competing interests.
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