Cable-driven parallel robots (CDPRs) are a subclass of parallel robots. Instead of rigid links, CDPRs consist of cables, which connect a moving mobile platform with the cable robot frame. By changing the cable lengths, the mobile platform can be moved. Advantageous properties of CDPRs are their large workspace, scalability, high payloads and high dynamics.
Most industrial applications, such as 3D-printing, pick and place, or assembly tasks, require a high accuracy of the robot. Meeting the required accuracy for industrial applications can be critical for CDPRs [1
]. Therefore, accuracy improvement is an important field of research of CDPRs [2
]. The accuracy of CDPRs is influenced by various effects:
Cable properties (elasticity, creep, hysteresis, cable wear, ...);
Mechanical components: CDPR-frame, platform, pulleys, drive trains (manufacturing accuracy, mechanical play, motor/encoder resolution, stiffness, friction, ...);
Winch properties (cable flattening, coiling errors, non-linear cable length to drive ratio, ...);
Accuracy of the calibration;
Geometric and kinematic models used in the controller (cable sagging caused by cable mass, pulley kinematic, deflection due to external forces, ...).
A detailed list can also be found in [4
] (p. 26).
Among these effects, cable elasticity is one of the major factors influencing the accuracy of CDPRs, especially of CDPRs with plastic fiber cables [2
]. Furthermore, regarding long-term accuracy, cable creep is an important issue. Cable creep especially appears using synthetic fiber cables, which are often used for CDPRs because of their low inertia and thus good dynamics. Over a longer period of time, the cables elongate because of the constant load of the platform. Thus, the offset of the relation between encoder values and cable length changes, which leads to an accuracy error.
Most CDPR-controllers are based on the assumption that cables are inelastic and straight lines. An inverse kinematic code translates a given pose into cable length and then into encoder values, which are sent to the winches. The encoders measure the rotation of the drum onto which the cable is coiled, as for example on the IPAnema [5
] or CoGiRo [6
]. The main practical problem is the difficulty measuring the actual distance between the platform and the frame as the winch-integrated measurement cannot capture the influence of creep, sagging, elasticity, coiling errors, flattening, or non-linear cable length to drive ratios on the cable length. This eventually leads to pose errors.
One method used to compensate for errors caused by cable creep is a frequent recalibration of the home pose to correct the offset of the relation between encoder values and cable length. Approaches to calibrate CDPRs are presented in [7
] and even automated in [8
]. Both methods need measurement input at different poses in the workspace. In [7
], this input comes from a laser tracker, in [8
] from the internal position and cable force sensors. This requires to move the robot for calibration, which is not always possible depending on the application. A mathematical approach to model cable creep can be found in [9
]. However, due to the non-linearity and variety of influencing factors, accurate models for cable creep are challenging.
There are two possibilities to address the elongation error due to cable elasticity. The first one is to model cable elongation effects mathematically. In [2
], a simple elongation model is developed, implemented, and tested on the IPAnema 3 cable robot which results in an accuracy increase of the average error of almost 40%. The method calculates a cable force distribution at the actual pose. The external forces applied on the platform (the external wrench) are considered to be constant. Any additional external force leads to errors. The cable force distribution algorithm could be changed to consider a changing wrench, but this would require knowledge of the external forces such as the weight of a handled object. In [1
], elasticity, including cable sagging, is considered in the inverse kinematic model. Furthermore, visual servoing is used for pose estimation. This leads to the second possibility: the compensation of cable elasticity and creep effects with feedback from additional external sensors. This feedback can come from cameras like in [1
] which requires the platform to be always visible for the camera. In [11
], angular sensors at the proximal anchor points of a CDPR are proposed and a simulation evaluating the accuracy improvement is presented. An experimental evaluation is not included. In [12
], a similar approach with cable orientation sensors for a CDPR with two and three cables is presented. With regard to accuracy improvement, it is stated that especially for large-scale CDPRs, the cable orientation must be very accurate. Extending the principle for cable robots with more than three cables is part of future research.
Two different approaches to get feedback about the real cable length can be found in [3
]. They present a method to directly measure the cable length with different measurement principles. In [3
], the idea is to use a hall sensor and small strips of magnetic tape attached to the cable in a known distance or, also in [3
], to use colored marks which can be detected by an IR optical sensor. In [14
], the method with colored marks has been further elaborated. However, to get the initial cable length (calibration of the home pose), this method requires moving the robot. In this paper’s example, the required movement of the cable in average accounts for 0.622 m. The resolution depends on the length of the cable, the number of the color sensors used, and the distance of the color sensors and marks. In the given examples, the best resolution for a cable of 60 m is 0.1 m, with 84 marks on the cable and 15 color sensors.
The use of friction pulleys for direct cable length measurement is another suggestion which can be found in [15
] (p. 362). However, aside from the idea itself, to the best of the authors’ knowledge, no further investigation of this idea can be found in the literature.
This paper presents a new device to measure the cable length directly, based on a laser distance sensor. More precisely, the cable length of the standard pulley kinematic, assuming cables as straight lines and thus the geometrical length is determined. The measured feedback cable length is a first step towards the correction of cable length inaccuracies due to cable elasticity or creep. Thus, the accuracy of CDPRs can be improved.
The paper is structured as follows: In Section 2
, the concept, kinematic, an analysis of the measurement error due to cable sagging, and the mechanical design of the direct cable length measurement sensor are explained. In Section 3
, the direct cable length measurement sensors are experimentally evaluated and the results are discussed. Finally, the paper closes with a conclusion and outlook.
3. Experimental Accuracy Evaluation
The DCLM-Sensor accuracy is evaluated on the cable robot demonstrator IPAnema 3 at Fraunhofer IPA. The IPAnema 3 is a redundantly constrained cable robot with eight cables. The geometrical parameters are given in Table 3
. A picture of the experimental setup is shown in Figure 6
In the experiments, DCLM-Sensors are attached to each cable. As ground truth measurement of the cable length, a Leica laser tracker AT960 (https://www.hexagonmi.com/de-de/products/laser-tracker-systems/leica-absolute-tracker-at960
, accessed on 4 February 2021) with a T-Mac attached to the platform is employed. With the T-Mac, it is possible to measure all six degrees of freedom with an accuracy given in Table 4
. The DCLM-Sensor cable length measurement accuracy is evaluated with a grid of 25 static poses in an x-y-plane with z = 0 m. For the 25 evaluated poses and the specified laser tracker accuracy, the worst-case error for the measurement of the ground truth cable length amounts to ±0.337 mm. Worst-case means that the position measurement of the T-Mac has a maximum measurement error in addition to a maximum rotational accuracy error.
The evaluated poses in relation to the cable robot are visualized with blue dots in Figure 7
. The eight proximal anchor points
of the IPAnema 3 are marked with orange dots. The poses are evaluated in the order following the red arrow. The coordinates and the associated ID are given in Table 5
. Compared to the size of the cable robot, the evaluated area is quite small, but due to the heavy end-effector the workspace of this cable robot setup is limited.
The measurement procedure at each pose is as follows:
The CDPR-platform moves to the measurement pose. After a waiting time of five seconds to let eventual vibrations subside, the pose measurements of the laser tracker and the cable length measurements of the DCLM-Sensors are logged and averaged over one second. After the measurement, the CDPR-platform moves to the next measurement pose and the measurement procedure starts again.
3.1. Accuracy Results of the DCLM-Sensor
The result of the accuracy evaluation is shown in Figure 8
. The grey dots (Error
) display the error between the cable lengths commanded by the CDPR-controller and the ground truth cable lengths measured with the laser tracker for each pose and all eight cables. The cable lengths of the CDPR-controller are calculated through the inverse kinematic (IK) [16
] and set with the motor encoders. The error of the cable lengths commanded by the CDPR-controller is between −5.19 mm and +6.02 mm. The mean value of the cable length error accounts to −0.292 mm and the standard deviation to 2.117 mm.
The red dots (Error ) show the error between the cable lengths measured with the DCLM-Sensors and the ground truth cable lengths measured with the laser tracker for each pose and all eight cables. The error of the DCLM-Sensors is in the range from −2.32 mm to +1.86 mm, with a mean of −0.145 mm and a standard deviation of 0.883 mm.
3.2. Discussion of the Experimental Evaluation
The experimental evaluation shows that the measurement principle works as intended. All measured cable lengths of the DCLM-Sensors are >4 m. This means that according to the technical data of the SICK laser sensor (Table 4
), the absolute measurement accuracy is equal to ±3 mm. Thus, the error of the cable length measurement is even less than specified in the data sheet of the SICK laser sensor.
Comparing the accuracy of the IK and the DCLM-Sensors, the standard deviation of the DCLM-Sensor measurement error is 58% lower. The maximum measurement error is reduced about 69%, the minimum about 55%. The mean error is close to zero for both cable length errors. Even taking the worst-case scenario of the ground truth cable length into account, there is a significant improvement in the determination of the cable length.
This means, using the cable length measurements of the DCLM-Sensors as feedback for the CDPR-controller, the cable lengths could be adjusted more accurately to the cable lengths calculated with the inverse kinematic. Increasing the cable length precision is assumed to also increase the pose accuracy of CDPRs.
The accuracy deviations of the DCLM-Sensor are assumed to be dependent on:
The measurement accuracy of the laser sensor;
Misalignment of cable and laser due to cable sagging.
The second point especially influences the measurement accuracy of the DCLM-Sensor at the wrench-feasible workspace borders, where the cable can be long and the cable force low. Thus, the cable sags and the laser is not aligned parallel to the cable (see Section 2.2
). In the worst-case scenario, the laser does not hit the reflector anymore. During the trials to evaluate the DCLM-Sensor accuracy with a larger grid than presented in this paper, it has been found that the sensor loses the reflector if the cable force is lower than 200 N, with a cable length above 10.7 m, and an angle between the cable and the horizontal plane below 8.8°. The point where the laser sensor loses its reflector is dependent on the cable force, the cable length, and the angle of the cable which influences the impact of the gravity on the cable.
To further improve the accuracy of the DCLM-Sensor, one could use a more accurate laser sensor and address the misalignment of the laser sensor. The alignment inaccuracy could be reduced through a counterweight which reduces the force of the DCLM-Sensor on the cable that increases the misalignment due to sagging.