Design and implementation of a multi-degrees-of-freedom cable-driven parallel robot with gripper

Abstract

Cable-driven parallel robots comprise driven actuators that allow controlled cables to act in parallel on an end-effector. Such a robotic system has a potentially large reachable workspace, large load capacity, high payload-to-weight ratio, high reconfigurability, and low inertia, relative to rigid link serial and parallel robots. In this work, a multi-degrees-of-freedom cable-suspended robot that can carry out pick-and-place tasks in large workspaces with heavy loads is designed. The proposed cable-driven parallel robot is composed of a rigid frame and an end-effector that is suspended from eight cables—four upper cables and four lower cables. The lengths of the cables are computed from the given positions of the suspended end-effector using a kinematic model. However, most multi-cable-driven robots suffer from interference among the cables, requiring a complex control methodology to find a target goal. Owing to this issue with cable-driven parallel robots, the whole control structure decomposes positioning control missions and allocates them into upper level and lower level. The upper level control is responsible for tracking the suspended end-effector to the target region. The lower level control makes fine positional modifications. Experimental results reveal that the hybrid control mode notably improves positioning performance. The wide variety of issues that are considered in this work apply to aerostats, towing cranes, locomotion interfaces, and large-scale manufacturing that require cable-driven parallel robots.

Keywords

Pick-and-place cable-driven robot parallel manipulators hybrid control mode redundant manipulators

Introduction

Cable-actuated robots are extensively used in aerostats, towing crane systems, elevators, and other devices. Cable-driven parallel robots consist of driven actuators that enable controlled cables to act in parallel on an end-effector.¹ Such a robotic system has a potentially large reachable workspace, large load capacity, high payload-to-weight ratio, high reconfigurability, and low inertia, in comparison to rigid-link serial and parallel robots. Nevertheless, these advantages may be outweighed by the fact that the cables that are used in these systems are relatively flexible and provide only a tensile and not a compressive force. Unlike traditional rigid manipulators, the cables in such a robotic system provide flexibility.² Therefore, various studies have focused on the flexibility of cables and the suppression of their oscillation.^3

–6 However, those investigations concern only the flexibility of cables and not positioning control with multiple cables.

At least n + 1 cables are required to control a suspended object with n degrees of freedom (DOF). Cable-driven parallel robots may use m redundant cables to change workspace volume, to increase the load that can be carried, or to improve the controllable workspace.^{7

–20} A manipulator for which m = n + 1 is called “completely restrained”, while the one for which m > n + 1 is called “redundantly restrained.” The redundancy is defined as r = m − n ¹¹ However, redundantly actuated cable-driven parallel robots are effective in performing pick-and-place tasks. The aforementioned studies concentrate on controllable workspace analysis and none proposes further control schemes to resolve interference among driven cables.^7

–11

The redundancy resolution of redundantly activated cable-driven parallel robots requires the calculation of feasible and continuous cable tension allocations using a trajectory.¹⁹ Most research into redundantly actuated cable-driven parallel robots concerns n-DOF cable-driven robots that are driven by n + 2 cables since, for n = 6, such redundantly actuated robots have many applications.^19,20 For such 6-DOF robot systems, manipulating the end-effector with eight cables rather than seven cables tends to provide a larger and more homogeneous workspace, facilitating integration into workspace. However, experimental tests have revealed open issues such as the need for efficient tension distribution algorithms to improve positioning accuracy. Such algorithms have been tested in simulations but remain to be used for the real-time control of a prototype.^{7

–20}

Some related investigations concern tension distribution.^{12
–14,18,19} The imposition of upper and lower bounds on cable tensions limits the force that can be generated in a cable-driven parallel robot and renders infeasible the generation of certain forces at the end-effector¹³ The main related challenge is the development of an efficient algorithm for dealing with this infeasibility. Unfortunately, the control algorithm demonstrated in those studies are complex and their implementation is laborious, so implementing them in real-time control is difficult.^{7

–20}

Each scheme in the aforementioned studies has particular advantages and disadvantages. Some proposed procedures may be expensive in terms of computation time and most cannot be used in real time in experiments. To the best of our knowledge, few efficient control schemes have been demonstrated to work in real time with cable-driven parallel robots with redundant actuation. Accordingly, a simple control method for cable-driven parallel robots with redundant actuation warrants study.

This study proposes a multi-DOF (MDOF) cable-driven parallel robot with suspended gripper driven by eight cables. The determination of an optimum geometry for such parallel cable robots together with the design of a prototype is concisely outlined in the second section. The remainder of this article is as follows: The procedure for kinematic analysis is shown in third section. In the fourth section, a controller design which included main control and modification mode will be installed for pick-and-place control tasks. The several experimental results to verify the proposed control methodology are demonstrated in the fifth section. Lastly, we conclude the article offerings.

Conceptual design

The main goal of this work is to design a MDOF cable-suspended robot that can perform pick-and-place tasks over a large workspace with heavy loads. The proposed cable-driven parallel robot, as indicated in Figure 1, is composed of a rigid frame and an end-effector that is suspended from eight cables—four upper cables and four lower cables. The gripper is attached on the suspended platform and designed as a suspended end-effector. Eight winch units are fixed to the rigid frame—four on the top frame and the others on the bottom frame. In this design, springs are installed at the vertices of the suspended end-effector platform and attached to cables to dampen the oscillations, as presented in Figure 1.

Figure 1.

System configuration of a cable-driven parallel robot.

The suspended end-effector is controlled by alternate current (AC) servomotors that can extend or retract the cables. Such servomotors are equipped with optical encoders that can be used to measure the lengths of the cables. The cables are normally wound on the winch unit, and incremental encoders provide information about the current angle of servomotors from which the cable lengths can be computed. The two motion control board ADLINK PCI-8164 (ADLINK Technology Inc., Taiwan) offers eight independent channels, each of which consists of a TTL/RS422 compatible encoder interface and one analog ±24 V analog output, which is the input command to drive a servomotor. The servomotor is also equipped with an integrated incremental encoder with a resolution of 10,000 pulses per revolution. The stepping motor is used to drive the suspended gripper of the end-effector in such a robot system. The Arduino Mega 328 is used as the control board for driving the stepping motor.⁶

The robot is equipped with a set of sensors that yield pose information. The inertia measurement unit (IMU; Model: GY-521 by InvenSense Inc., San Jose, CA, USA) is mounted on the cable-suspended robot to detect inclination information. The IMU sensor module consists of an accelerator, a compass, and a gyroscope. A program has been implemented in Arduino environment to allow the sensor to sense the angular displacement around the reference axes. The wireless camera (CCD) and the standard image processing algorithm are used to monitor real-time scenarios and to estimate the real position of the suspended end-effector. A limit switch (LS) ensures that the cables remain on the reel track. Both IMU and CCD sensors have been implemented in Arduino card to allow the sensor to sense the angular displacement around the reference axes. An LS ensures that the cables remain on the reel track. The control programming and machine algorithms were established using the National Instrument (NI) commercial package LabVIEW (Figure 2). Figure 3 displays the motion of the proposed cable-driven parallel robot. Accordingly, the suspended gripper is forced along the desired trajectory by changing the cable lengths.

Figure 2.

Control implementation for the proposed system.

Figure 3.

Motion concept for cable-driven robot.

One end of each cable is connected to the suspended end-effector, while the other end rolls through a winch unit that is fixed to its cable tower. This last cable end is fed into a servomotor that controls the length of all of the cables. Figure 3 displays the motion of the proposed cable-driven parallel robot. Accordingly, the suspended gripper is forced toward the desired trajectory by changing the cable lengths.

Kinematics

The derivation procedure for kinematic analysis can be applied to the geometric concept of the proposed cable-suspended robot, as depicted in Figure 4. Figure 5 displays the top view of the specific system and assigns the quadrant symbol to the workspace. In such a system, the cable lengths are changed as determined by the orientation of the suspended platform and calculated using the motor-side incremental encoder. In many applications, the extension of the cable is measured using an encoder that is attached to a reel. However, measuring the inclination of the cable is much more difficult²¹ Therefore, this section will present a simple algorithm for estimating the orientation thereof for such specific suspended manipulator structure. However, the computation procedure can be applied to the similar MDOF cable-driven parallel robot system.

Figure 4.

Control implementation for the proposed system.

Figure 5.

Quadrant description fot the proposed system.

An inverse kinematic analysis of the proposed cable-driven robot system is carried out using the coordinate system that is presented in Figures 4 and 5. The distances from the fixed point on the main frame to the point on the end-effector are given by l_i (i = 1,…, 8). The lengths of the upper cables are denoted as l_i (i = 1, 2, 3, 4) and lengths of the lower cables are specified as l_i (i = 5, 6, 7, 8), respectively. To simplify the measurement of the position and orientation of the proposed system, the formula for kinematic computation can be used in relation to the X and Z axes in Figure 4. Similarly, the kinematic analysis process can be applied to other corresponding cables. Assume that θ₁ is the tilt angle of the end-effector and θ₂ is the angle of inclination of the cable from the X-axis. Here, the length l ₁ is used in an example of computing the kinematic orientation, as is the corresponding length. Hence, the corresponding arrangement of the length l ₁ is given by

r sin θ_{1} + l_{1} sin θ_{2} = Z

r cos θ_{1} + l_{1} cos θ_{2} = D

where r is the radius of the suspended platform; l ₁ is the corresponding cable length; D is the distance between the center of the suspended platform and the main rigid frame; and Z is the distance between the center of the suspended platform and the top of the cable frame tower.⁵

Hence, the corresponding cable length l ₁ can be directly calculated from equations (1) and (2) as

l_{1} = \sqrt{{(D - r cos θ_{1})}^{2} + {(Z - r sin θ_{1})}^{2}}

The other corresponding cable lengths l_i can be similarly calculated.

The height of the suspended platform Z is defined as the difference between the Z_max and Z_h .

Z = Z_{max} - Z_{h}

where Z_max is the maximum height from the suspended platform to the top of the main frame, and Z_h is the displacement of the suspended platform from its original point.

The slip displacement of the upper cables length $l_{u o_{i}}$ and lower cables length $l_{l o_{i}}$ is given by

l_{u o_{i}} = l_{max} - l_{i}, for i = 1 to 4

l_{l o_{i}} = l_{min} - l_{i}, for i = 5 to 8

where $l_{max} = \sqrt{d^{2} + Z_{max}^{2}}$ , $l_{min} = \sqrt{d^{2} + Z_{pg}^{2}}$ , and $d = D - r$ . In addition, Z_pg is the total height of the suspended end-effector (from the top of platform to the bottom of the gripper).

If the suspended platform position displacement from the origin is $(X_{d}, Y_{d}, Z)$ , then the corresponding cable length l_i can also be calculated as

l_{1} = l_{7} = \sqrt{{(D - r cos θ_{1} - X_{d})}^{2} + Y_{d}^{2} + {(Z - r sin θ_{1})}^{2}}

l_{2} = l_{8} = \sqrt{{(D + r cos θ_{1} - X_{d})}^{2} + Y_{d}^{2} + {(Z_{pg} + Z_{h} - r sin θ_{1})}^{2}}

l_{3} = l_{5} = \sqrt{{(D - r cos θ_{1} - Y_{d})}^{2} + X_{d}^{2} + {(Z - r sin θ_{1})}^{2}}

l_{4} = l_{6} = \sqrt{{(D + r cos θ_{1} - Y_{d})}^{2} + X_{d}^{2} + {(Z_{pg} + Z_{h} + r sin θ_{1})}^{2}}

After l_i is obtained from equation (6), the l_i that is obtained from equation (6) is substituted into equation (5), and the slip displacement of the corresponding upper cables $l_{u o_{i}}$ and lower cables $l_{l o_{i}}$ can then be obtained.

The upper motor angle $M_{a, u_{i}}$ (or lower motor angle $M_{a, l_{i}}$ ) can be determined in terms of the slip displacement of the $l_{u o_{i}}$ (or $l_{l o_{i}}$ ) and winch diameter D_w

M_{a, u_{i}} = \frac{l_{u o_{i}}}{π D_{w}} \cdot 360 °, for i = 1 to 4

M_{a, l_{i}} = \frac{l_{l o_{i}}}{π D_{w}} \cdot 360 °, for i = 5 to 8

As the servomotor is equipped with an optical encoder with a resolution of 10,000 pulses/rev, the motor angle, $M_{a, u_{i}}$ (or $M_{a, l_{i}}$ ), can be converted into pulse units $M_{p, u_{i}}$ (or $M_{p, l_{i}}$ ) as follows

M_{p, u_{i}} = M_{a, u_{i}} \cdot \frac{10, 000 pulse}{360 °}, for i = 1 to 4

M_{p, l_{i}} = M_{a, l_{i}} \cdot \frac{10, 000 pulse}{360 °}, for i = 5 to 8

Accordingly, equation (5) can be substituted into equations (7) and (8) to yield the corresponding cable length in terms of the pulse units.

l_{i} = l_{max} - \frac{M_{p, u_{i}} \cdot π \cdot D_{w}}{10, 000 pulse}, for i = 1 to 4

l_{i} = l_{min} - \frac{M_{p, l_{i}} \cdot π \cdot D_{w}}{10, 000 pulse}, for i = 5 to 8

The critical issue in this system is controlling not the position of the motor but the cable length. Since the diameter of the winch D_w is constant but the cable length is directly proportional to the encoder output value, the latter can be directly controlled. Therefore, the lengths of the cables are measured using encoders that trace their release, so no extra equipment is required.⁵

Controller implementation

Most multi-cable-driven robots suffer from interference among the cables under tension; even a simple point-to-point motion requires a complex control methodology to reach a target. Therefore, the effective solution to a specific optimization problem always requires laborious exploration to find the best control values; this process always has a high computational cost. To resolve the above issue, this work develops a hierarchical control method to satisfy the positioning control requirement; the method involves a main control mode and a fuzzy modification control mode. The quadrant selection strategy is utilized herein to develop a new and efficient control algorithm for MDOF cable-driven robots that are driven by eight cables. Owing to the above issue with cable-driven parallel robots, the whole control structure decomposes into upper level and lower level missions. A main control mode, which is an upper level control mode, is used to force the suspended end-effector close to the desired point by exploiting the open-loop control concept. Then, the fuzzy modification control mode, which is the lower level control mode, is used to actuate the end-effector for accurate positioning through a feedback control scheme. This lower level control is modified using fuzzy logic to generate a fine control action. The task here is to design a fuzzy controller that refines the control action and yields a tracking error e of less than a pre-specified small value, ε.

Figure 6 shows a flowchart of the entire control scheme in the experiment. After the desired control target is provided, the control must be modified as presented in the figure.

Figure 6.

Control flowchart for the proposed cable-suspended robots system.

Main control mode (upper level control)

Knowledge of the control target of the proposed cable-driven parallel robot is critical in practice. The upper level control mode is used to track the suspended end-effector to the desired target region. For the purposes of this work, a main controller is used to achieve this goal. To implement the proposed control technique, the control target space is characterized as having four quadrants (I, II, III, and IV), three axes ( X , Y , and Z ) and two angles of rotation (θ_x and θ_y). In the proposed system, the end-effector does not rotate around the Z -axis, and θ_z is set to zero. Thus, the reachable regions are determined by the constraints on the cable tension.

As stated above, the cable-driven parallel robot is a coupled system. If the length of any cable is altered, then the angles and the tensile forces of the cables will also vary. The lengths of the cables can be altered using the servomotors. The cable lengths are computed from the positions of the suspended end-effector using a kinematic model that is described in the “Kinematics” section. The forward kinematics are the opposite of inverse kinematics and are used to obtain the positions from known cable lengths. Accordingly, the upper level control mode exploits the concept of open-loop control and moves the end-effector to the desired point by changing the cable lengths.

The manipulating servomotors are assigned numbers M₁–M₈, and motor M_i is used to regulate the corresponding cable lengths l_i using equation (9). Figure 7 presents the rule that governs the regulation of the main control module. The main function of such a control mode is to avoid unnecessary intense tensioning on the cable pairs.

Figure 7.

Structure of the upper level control for the proposed cable-driven robots system.

First, the suspended end-effector is moved to a specified point in quadrant I; one group of motors (M₁, M₄, M₅, and M₈) retracts its appropriate cables, while the other group of motors (M₂, M₃, M₆, and M₇) simultaneously extends its corresponding cables. Similarly, if the target points are located in quadrant II, then the group of motors (M₃, M₄, M₇, and M₈) retracts the corresponding cables, and the other group of motors (M₁, M₂, M₅, and M₆) simultaneously extends the corresponding cables. Hence, the other regulations that govern the target point in the quadrant region may be obtained from Figure 7 to determine which motors retract or extend their corresponding cables.

To manipulate the suspended end-effector to a particular point on the X -axis, the two motors (M₁ and M₅) retract their corresponding cables, while the remaining motors (M₂, M₃, M₄, M₆, M₇, and M₈) simultaneously extend their corresponding cables. However, if the target points are located on the Y -axis, then the two motors (M₄ and M₈) retract their corresponding cables, and the remaining motors (M1, M2, M3, M5, M6, M7) extend their corresponding cables. Similarly, one group of motors (M₁, M₂, M₃, and M₄) retracts cables while the other group of motors (M₅, M₆, M₇, and M₈) extends cables to move the end-effector to the Z -axis.

To regulate as diagonal line, only the lengths of the two coupled cables have to be changed. The diagonal lines of the payload can be controlled using knowledge of the geometry of the suspended end-effector. Accordingly, the lengths that correspond to (M₁ and M₇) and (M₃ and M₅) can be changed to regulate θ_x, and the lengths that correspond to (M₄ and M₆) and (M₂ and M₈) are changed to regulate θ_y. Therefore, one pair of motors M₁ and M₇ (or M₄ and M₆) and another pair of motors M₃ and M₅ (or M₂ and M₈) can be adjusted simultaneously while the four cables that are associated with the other motors are kept unadjusted to prevent rotation of the suspended end-effector. Specifically, l ₁ and l ₇ (or l₄ and l ₆) can be lengthened as l ₃ and l ₅ (or l ₂ and l ₈) are shortened.

Fuzzy modification control mode (lower level control)

The suspended end-effector is close to the target point in the main control mode. The lower level control performs fine positioning adjustments. Therefore, it is responsible for computing in real time the set of cable tensions that corresponds to a given force on the end-effector. Hereafter, the fuzzy modification rules are applied to regulate the adjustment factors to improve functioning even with unpredicted variations in system performance.

The fuzzy modification control module has tracking error e and its rate of variation $\dot{e}$ as inputs to generate the local fine control action f. A typical fuzzy rule is as follows

R^{i} : IF e is α^{i}, \dot{e} is β^{i} THEN f is γ^{i}

where αⁱ, βⁱ, and γⁱ are linguistic values of fuzzy variables that are used to express the discourse universe of fuzzy sets. Fuzzy quantities such as Negative Large (NL), Negative Small (NS), Zero (Z), Positive Small (PS), Positive Large (PL), and others are used in the statements, and the corresponding membership functions are thus required.

The fuzzy modification rule is based on a characterization of the control space as having four quadrants, three axes, and two angles of rotation (Figure 7). Owing to symmetry, quadrants I and III share the same fuzzy rule base and quadrants II and IV use the same fuzzy rule base. Each rule base is constructed with three axes and two angles of rotation. Membership function parameters are tuned off-line according to heuristic rules. A fuzzy Mamdani-type model was constructed to approximate such an eight-cable-driven robot system within a small range of states close to its equilibrium state. Based on the Mamdani model, a fuzzy controller was designed to perform fine positioning adjustments. Here, the fuzzy linguistic terms PS and PL denote the retracted cable lengths and NS and NB denote the extended cable lengths. The fuzzy linguistic terms Z mean null action.

To move the suspended end-effector to the assigned point in quadrant I or III, one group of motors (M₁, M₄, M₅, and M₈) use the same membership function, while the other motors (M₂, M₃, M₆, and M₇) use a different membership function to determine the fine motion control force f. Similarly, if the target points are located in quadrant II or IV, then the group of motors (M₃, M₄, M₇, and M₈) use the same membership function, and the other group of motors (M₁, M₂, M₅, and M₆) adopt another membership function.

If the target points are located on the X-axis, then the group of motors (M₁ and M₅) adopt the same membership function rule bases, and the other group motors (M₃ and M₇) and (M₂, M₄, M₆, and M₈) use another inference engine. Similarly, if the target points are located on the Y-axis, then the group of motors (M₁, M₃, M₅, and M₇) adopt the same membership function, and the other group of motors (M₄ and M₈) and (M₂ and M₆) use another membership function. When the target points are on the Z-axis, then motors (M₁, M₂, M₃, and M₄) adopt the same membership function, the other motors (M₅, M₆, M₇, and M₈) use another membership function. Accordingly, the lengths that correspond to (M₁ and M₇) and (M₃ and M₅) can be changed to regulate θ_x, and the lengths that correspond to (M₄ and M₆) and (M₂ and M₈) can be changed to regulate θ_y.

A total of seven fuzzy inference engines were implemented in this study. These output motor fuzzy control rules determine whether the motors retract or extend their corresponding cables. The suspended platform can be manipulated in the control space using the above technique to construct its individual fuzzy rule base.

Results and discussion

This section presents the experimental results that were obtained using the control algorithms of the proposed cable-driven robot. To confirm that the proposed robot that is driven using eight cables outperforms previously developed robots that are driven using four cables,⁵ a preliminary oscillation performance test is conducted on both designs, as presented in Figure 8. First, point-to-point control of the suspended gripper is used to pick up a beaker in the manner Z(300 mm) →Z(80 mm)→Z(300 mm)→Z(80 mm). A gyroscope sensor module (model: GY-521 by InvenSense Inc., San Jose, CA, USA) is mounted on the suspended object to detect θ_x and θ_y, which specify inclination. Therefore, Figure 9 shows experimental results concerning Z-axis tracking that are obtained using the different cable-driven robots. The positioning error is also examined. The root mean square positioning error (RMSE) is defined as

RMSE = \frac{\sqrt{\sum_{i = 1}^{n} {(x_{i} - x_{d})}^{2}}}{n}

where n is the sample size, x_d is the desired value, and x_i is the measured value.

Figure 8.

Physical diagrams for multi-cable-driven robot systems. (a) Four cables and (b) eight cables.

Figure 9.

Physical diagrams for multi-cable-driven robot systems. (a) θ_x and (b) θ_y .

Figure 9 plots the inclination angles θ_x and θ_y that are obtained with various numbers of cables. The normalized root-mean-square (RMSE) deviation of θ_x is around 0.065° for the four-cable-driven robot and 0.045° for the proposed eight-cable system. The normalized RMSE θ_y deviation is approximately 0.044° with four cables and 0.041° with eight cables. The proposed eight-cable-driven robot system represented a marked improvement as the proposed eight-cable-driven parallel robot suffered from less cable oscillation than the four-cable-driven robot.

A repeatability test is conducted to confirm the accuracy of the developed cable-driven parallel robot to evaluate its performance. The measurement setup has nine test points, each with assigned coordinates (Figure 10). The proposed cable-driven parallel robot moves through the test points (points 1–9) five times and determines the coordinates of those points as it does so. The coordinates of the test points 1–9 are (−200, 200), (0, 200), (200, 200), (−200, 0), (0, 0), (200, 0), (−200, −200), (0, −200), and (200, −200), respectively. Moreover, the upper level control is as control mode A, and hybrid upper level and lower level control is control mode B.

Figure 10.

Coordinates of the measured points for the repeatability test.

Clearly, the measured coordinates of the points are very close to each other. The standard deviation σ of the distance of a measured point from the actual point is around 3.96–0.84 mm. These results indicate that the robot system in control mode A reliably performs positioning.

However, the RMSE in positioning is not good and must be improved. The RMSEs of the measured coordinates of points 1–9 are (2.7, 3.3), (1.1, 8.1), (3.8, 6.2), (3.4, 5.4), (0.3, 0.3), (6.1, 0.5), (1.1, 8.6), (1.6, 12.9), and (1.3, 10) mm, respectively. Pure Control Mode A is weak in positioning control.

To improve the positioning error, Control Mode B is used in the experiments herein. As a result, the standard deviation σ of the distance from a measured point to the corresponding actual point is approximately 2–0.84 mm. These results also reveal that the robot system in Control Mode B is reliable for positioning. Moreover, the RMSEs of the measured coordinates of points 1–9 are (0.6, 0.56), (0.34, 1.29), (0.63, 1), (0.63, 0.28), (0.28, 0.4), (1, 0.52), (0.44, 1.56), (0.48, 1), and (0.6, 0.84) mm, respectively. Control Mode B offers significantly improved positioning performance. Hence, associated with Control Mode A, the RMSE positioning error is diminished to 76.6–86.5% while the hybrid Control Mode B is applied. This control scheme reduced the positioning error in a point-to-point control task.

To verify the favorable performance of the developed robot, a robot gripper was used to pick up a beaker that was filled with water and to pour the water into another container (Figure 11). Control Mode B reduced the spilling of the water by approximately 25%, indicating that it was effective in controlling the cable-driven robot system.

Figure 11.

The gripper was assigned to pick up a beaker filled with water to pour water to another container.

Consequently, the forward kinematics are the opposite of inverse kinematics and are used to obtain the positions from known cable lengths. The open-loop control mode exploits the end-effector to the desired point by changing the cable lengths. Hereafter, the closed-loop control mode is applied to regulate the adjustment factors to improve positioning. The proposed control scheme does not involve the laborious computation that is required by Dykstra’s algorithm,¹³ versatile tension distribution algorithm,^18,19 and has an approximately 20% lower CPU task execution time in the above applications. The algorithms that are developed in this study are easily implemented for real-time control and more suitable applied than previously proposed algorithms for use in university control course mechatronic kits.^{12
–14,18,19}

Conclusions

This study develops a MDOF cable-driven parallel robot with suspended end-effector. The proposed cable-driven parallel robots is composed of a rigid frame and an end-effector suspended from eight cables—four upper cables and four lower cables. The lengths of the cables can be changed by adjusting the lengths that are driven by servomotors. Additionally, the cable lengths are computed from the prearranged positions of the suspended end-effector by kinematic model indicated in the third section. However, most multi-cable-driven robots have difficulties with cable tension interfering with each other; hence, even a simple point-to-point motion still requires a complex control methodology to find a target goal. Accordingly, in order to resolve the above issue, this research proposes a hierarchical control methodology to satisfy the control requirement, which includes main control mode and fuzzy modification control mode. Owing to the difficulty of the cable-driven parallel robots, the whole control structure decomposes positioning control missions and allocates them into upper and lower level. The upper level control is responsible for tracking the suspended end-effector to the target region. The lower level control is concentrated on the fining modification for the positioning. The major benefit of such control methodology is to avoid unnecessary intense tensioning on the cable pairs. Experimental results reveal that the hybrid control mode significantly improves positioning performance. Such hybrid control scheme further improved reliable positioning and reduced the positioning error in point-to-point control task. The discussion of the broad issues deliberated in this investigation will be applied in aerostats, towing cranes, locomotion interface, and large-scale manufacturing applications that require cable-driven parallel robot.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was financially supported by the Ministry of Science and Technology of the Republic of China, Taiwan for financially supporting this research under Contract No. MOST 103-2221-E-231-021- and National Instruments (NI) 2017 Academic Research Grant Program.

ORCID iD

Jonqlan Lin

References

Borgstrom

Joran

Sukhatme

. Rapid computation of optimally safe tension distributions for parallel cable-driven robots. IEEE Trans Robot 2009; 25(6): 1271–1281.

Caverly

Forbes

. Dynamic modeling and noncollocated control of a flexible planar cable-driven manipulator. IEEE Trans Robot 2014; 30(6): 1386–1397.

Duan

. Dynamic modeling and active control of a cable-suspended parallel robot. Mechatronics 2008; 18(1): 1–12.

Khosravi

Taghirad

. Dynamic analysis and control of cable driven robots with elastic cables. Trans Canadian Soc Mech Eng 2011; 35(4): 543–557.

Lin

Huang

Chang

. A mechatronic kit with a control methodology for a modularized cable-suspended robot. J Vib Control 2016; 22(20): 4211–4226.

Lin

Liao

. A modularized cable-suspended robot: implementation and oscillation suppression control. Proc Inst Mech I J Syst Control Eng 2016; 230(9): 1030–1043.

Behzadipour

Khajepour

. Design of reduced DOF parallel cable-based robots. Mech Mach Theory 2004; 39(10): 1051–1065.

Hiller

Fang

Mielczarek

. Design, analysis and realization of tendon-based parallel manipulators. Mech Mach Theory 2005; 40(4): 429–445.

Ferraresi

Paoloni

Pescarmona

. A new methodology for the determination of the workspace of six-DOF redundant parallel structures actuated by nine wires. Robotica 2007; 25(1): 113–120.

10.

Azizian

Cardou

. The dimensional synthesis of spatial cable-driven parallel mechanisms. ASME J Mech Robot 2013; 5: 0445021–0445028.

11.

Borgstrom

Stealey

. Design and implementation of NIMS3D, a 3-D cable robot for actuated sensing applications. IEEE Trans Robot 2009; 25(2): 325–339.

12.

Agrawal

. Cable suspended planar robots redundant cables: controllers with positive tensions. IEEE Trans Robot 2009; 21(3): 457–465.

13.

Hassan

Khajepour

. Analysis of bounded cable tensions in cable-actuated parallel manipulators. IEEE Trans Robot 2011; 27(5): 891–900.

14.

Lim

Yang

Yeo

. A generic force-closure analysis algorithm for cable-driven parallel manipulators. Mech Mach Theory 2011; 46(9): 1265–1275.

15.

Carricato

. Inverse geometrico-static problem of underconstrained cable-driven parallel robots with three cables. ASME J Mech Robot 2013; 5(3): 0310021–03100211.

16.

Zanotto

Rosati

Minto

. Sophia-3: a semiadaptive cable-driven rehabilitation device with a tilting working plane. IEEE Trans Robot 2014; 30(4): 974–979.

17.

Abbasnejad

Carricato

. Direct geometric-static problem of underconstrained cable-driven parallel robots with n cables. IEEE Trans Robot 2015; 31(2): 468–478.

18.

Gouttefarde

Collard

Riehl

. Geometry selection of a redundantly actuated cable-suspended parallel robot. IEEE Trans Robot 2015; 31(2): 501–510.

19.

Gouttefarde

Lamaury

Reichert

. A versatile tension distribution algorithm for n-DOF parallel robots driven by n + 2 cables. IEEE Trans Robot 2015; 31(6): 1444–1457.

20.

Lau

Oetomo

Halgamuge

. Inverse dynamics of multilink cable-driven manipulators with the consideration of joint interaction forces and moments. IEEE Trans Robot 2015; 31(2): 479–488.

21.

Campeau-Lecours

Foucault

Laliberté

. A cable-suspended intelligent crane assist device for the intuitive manipulation of large payloads. IEEE/ASME Trans Mech 2016; 21(4): 2073–2084.