Deep Learning with Transfer Learning Method for Error Compensation

of Cable-driven Robot

Aydar Akhmetzyanov

, Maksim Rassabin

, Alexander Maloletov

, Mikhail Fadeev

and Alexandr Klimchik

Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia

Keywords:

Cable-driven Robot, Kinematics Compensation, Deep Learning, Transfer Learning, Robotics.

Abstract:

This paper proposes the application of Deep Learning methods for kinematic error compensation. Particular

attention is paid to simulation-based error estimation and the use of the Transfer Learning method for error

compensation to reduce physical experiments with a real robot. The obtained results were applied and vali-

dated for 4-dof (degrees of freedom) cable-driven parallel robot. The problem of error compensation for the

cable-driven parallel robot is highly non-linear. Nevertheless, deep learning-based methods for a considerable

training dataset provides better accuracy than simple linear error compensators. To overcome this drawback,

we applied the transfer learning method and used the knowledge of robot kinematics simulated in Unity. Unity

cable-driven robot simulation was implemented, and the central hypothesis was veriﬁed ﬁrst in the simulated

environment. The proposed Transfer Learning method allowed to speed up the process of robotics system

integration and recalibration due to the signiﬁcant sample efﬁciency improvement.

1 INTRODUCTION

The cable-driven parallel robot is a wide class of

robots that ﬁnd their application in many areas, for

example, warehousing (Alias et al., 2018), (Rasheed

et al., 2020), 3D printing (Izard et al., 2017), surgery

(Wang et al., 2016), etc. Their advantages include

larger workspace (Morris and Shoham, 2009), rela-

tively small robot mass, ability to handle large pay-

load, ability to operate with high speed and accel-

eration. The main disadvantage of parallel cable-

controlled robots is associated with the complexity of

physical modeling and, as a result, with the complex-

ity of non-linear compensation of geometric and non-

geometric errors. In this paper, we address the prob-

lem of non-linear inverse kinematics error of cable-

driven robot.

In an industrial environment, additional on-line or

off-line error compensation methods are used to im-

prove robot positioning accuracy (Wu et al., 2015). In

the cable-driven parallel robot, the error compensa-

https://orcid.org/0000-0003-3698-2977

https://orcid.org/0000-0002-3468-9331

https://orcid.org/0000-0002-7312-2944

https://orcid.org/0000-0002-9503-1242

https://orcid.org/0000-0002-2244-1849

tion algorithm can be realized employing adjustment

cable lengths, which change the end-effector position.

In this case, the error compensation algorithm is rela-

tively simple, since it does not require controller mod-

iﬁcation while updating higher-level inputs only. To

achieve the desired positioning accuracy, it is often

required to give as input reference trajectory that dif-

fers from the target one (Klimchik et al., 2013). In

this case, the input trajectory is usually changed on

the value of correction, which is computed either it-

eratively using the kinematic model or based on the

Jacobian matrix (Klimchik et al., 2014).

In general, the error compensation algorithms can

be split into two big groups: based on some sophis-

ticated model (Klimchik et al., 2014) or model-free

compensation (Zhao et al., 2019). The ﬁrst group can

be easily adopted within the robot workspace but it is

not able to take into account any factor that is not de-

scribed by the model. The second group does not need

any preliminary knowledge on the robot, may take

into account all possible factor inﬂuences on the robot

positioning accuracy, but frequently requires either a

considerable amount of data for training (for machine

learning-based algorithms) or real-time estimation of

the end-effector position. Real-time estimation of the

end-effector position is usually not possible on the in-

dustrial ﬂoor; that is why this approach is commonly

Akhmetzyanov, A., Rassabin, M., Maloletov, A., Fadeev, M. and Klimchik, A.

Deep Learning with Transfer Learning Method for Error Compensation of Cable-driven Robot.

DOI: 10.5220/0009905605530559

In Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2020), pages 553-559

ISBN: 978-989-758-442-8

553

used for some validations in the lab only. Recent re-

search in kinematic error compensation shows the ef-

ﬁciency of Deep learning and Reinforcement learn-

ing methods (Pane et al., 2019). The most straight-

forward approach to compensate robot positioning er-

rors is based on the simple linear regression model

which provides acceptable results for the majority of

real cases.

Deep learning is also related to representation or

feature learning term, the process of ﬁnding an ap-

propriate representation of data. In our case, the

neural network can learn inverse kinematics without

predeﬁned knowledge of the robot structure. This

method ﬁrst proved its efﬁciency on image classiﬁca-

tion tasks (Krizhevsky et al., 2017) and later was ex-

panded to other functions including robot kinematics

(Duka, 2014). The primary drawback of deep learn-

ing compensation methods is the requirement of the

extensive training dataset, resulting in increased cal-

ibration time. In this paper, we address the Transfer

Learning paradigm to reduce the demand for the train-

ing set with real robots for neural network training.

Transfer learning is the improvement of learning

in a new task through the transfer of knowledge from

a related task that has already been learned (Torrey

et al., 2009). Transfer learning also can be character-

ized as a process of knowledge transfer from one task

to another, which is visualized in Fig 1.

Figure 1: Traditional ML and transfer learning scheme.

Transfer learning is a broad research ﬁeld. Its

application includes the Natural Language Process-

ing ﬁeld with word2vec (Mikolov et al., 2013), Re-

inforcement learning with Curriculum (Narvekar and

Stone, 2018), etc. The beneﬁt of transfer learning

is visualized in Fig. 2 (Torrey et al., 2009). It al-

lows us to improve initial accuracy, improve the slope

of the training curve, or increase the asymptote. In

our robotics case, transfer learning can be potentially

used to compensate different payload applied to our

robot or to speed up the process of regular robot re-

calibration.

Employing testing the initial idea of applying a

Figure 2: Learning performance.

transfer learning approach for cable-driven robot cal-

ibration, we modeled the robot in Unity with an inte-

grated Nvidia PhysX simulation engine. The original-

ity of this work corresponds to the reduction of train-

ing set size required for the neural network through

Transfer Learning application and validation of the

proposed approach on 4-dof cable-driven robot.

2 SYSTEM OVERVIEW

2.1 Cable-driven Robot Description

The approach developed in this paper is tested on a

prototype of the cable-driven parallel robot presented

in Fig.3. The cable robot consists of a frame, sev-

eral winches with cables, and a mobile platform (Fig

4). Winch mechanisms are located at the bottom of

the frame. The cables are thrown through the guide

rollers in the upper part of the frame. Mountings of

guide rollers can rotate around a vertical axis, pro-

viding an orientation of the cables in the direction of

the mobile platform. The free ends of the cables are

attached to a mobile platform on which various equip-

ment can be placed.

Figure 3: Photo of cable-driven parallel robot prototype

used for validation.

The 4-cable robot is an underactuated system. In

this system, it is possible to control the position of the

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

554

Figure 4: The design scheme of the cable robot: 1 - mobile

platform, 2 - guide roller, 3 - spool, 4 - movable guide roller.

mobile platform, but it is impossible to control its ori-

entation. In addition, cables sagging affects the end-

effector positioning accuracy of the mobile platform.

Formally, 4 actuators should provide control of

4 degrees of freedom, for example, they should al-

low to control the position of the mobile platform and

the angle of rotation around a certain axis. However,

the cables are non-restraining geometric connections,

which are closed only due to external forces acting on

the mobile platform. In other words, cables can only

work in tension. Therefore, using 4 cables, control

of 4 generalized coordinates is possible only in such

conﬁgurations of the cable system in which one of the

cables is an antagonist for the other three cables and

at the same time its tension is ensured by the external

forces of the system. In the conﬁguration of the cable

robot under consideration, the mobile platform is sus-

pended from 4 cables. Therefore, none of the cables

can be as an antagonist to the rest. And this means

that to control 4 generalized coordinates, at least one

of the cables must work in compression, which is im-

possible.

The robot control system solves the inverse kine-

matics problem by determining the cable lengths ac-

cording to the given position of the mobile platform,

taking into account the peculiarities of the winding

mechanism and the guide rollers construction (Malo-

letov et al., 2019). However, this system does not take

into account sagging cables and other possible factors

affecting the positioning accuracy of the mobile plat-

form.

The control system provides the ability to enter a

compensating factor to improve the accuracy of robot

control (Fadeev and Maloletov, 2019). But the prob-

lem is the complexity of a fairly accurate estimate of

the value of the compensating factor. Direct measure-

ment of the positioning error of the mobile platform

during the operation of the robot is not always pos-

sible. A more accurate dynamic model of the robot,

taking into account many parameters, requires large

computational costs during the operation of the robot

and the time required for calibration to determine the

values of these parameters. Accordingly, a high-speed

neural network is a good solution, provided that due

the Transfer Learning the time spent on retraining the

network on a particular robot will be comparable to

the time spent on calibrating the dynamic model.

In the experiments, we used a mobile platform,

in which all 4 cables are attached to a single point

and the position of the mobile platform is determined

by the coordinates of this point. To obtain the real

position of the mobile platform, the VantageE laser

tracker is used, which measures the absolute reﬂector

position with the accuracy of 20 µm + 5 µm/m. To

measure the coordinates of the mobile platform, the

reﬂector was mounted on the platform above the ca-

bles’ attachment point.

Test positions of a mobile platform were measured

for 1183 points located in nodes of a regular grid of

13x13x7 points. Sizes of the investigated working

space: ξ ∈ [-3500 mm, 3500 mm], η ∈ [-1500 mm,

1500 mm], ζ ∈ [0 mm, 1200 mm]. Experimental stud-

ies were carried out for 3 different payloads: for the

masses equal to 5, 17 and 33 kg. The difference be-

tween the target and obtained positions of the mobile

platform corresponds to the error that should be com-

pensated in the control loop.

2.2 Unity Robot Simulation

To collect data for transfer learning we created the

unity simulation of the cable-driven parallel robot that

integrated the physical engine. The robot structure

screenshot is available in Fig. 5. The robot consists of

4 elastic prismatic joints, the end-effector, and cable

end object which connects prismatic joints to the end-

effector. We can control joint lengths and thus move

the end-effector inside the robot workspace. The end

effector mass inﬂuences the tension of robot springs

and changes the kinematics of the robot.

To collect the dataset for the transfer learning ex-

periment we deﬁned a set of the target position and

estimated their end-effector positions in the simulated

environments (Fig. 6). The randomly generated joint

length allowed to collect the dataset for different situ-

ations. We performed the data collection for 2 differ-

ent masses which allowed to estimate the advantage

Deep Learning with Transfer Learning Method for Error Compensation of Cable-driven Robot

555

Figure 5: Cable-driven parallel robot structure in the Unity

environment.

from neural network weight transfer for the training

of the new error compensator.

Figure 6: Unity model parallel simulation.

The resulting dataset consists of the tar-

get and the measured positions in the unity

frame for 2 different masses and available un-

der simulated kinematicsMass1.csv and simu-

lated kinematicsMass2.csv ﬁles in the dataset folder

(Akhmetzyanov, 2019). To further apply this dataset

to the real robot, the coordinate frame should be

converted to the robot coordinate system.

3 IMPLEMENTATION AND

RESULTS

To check the transfer learning viability for robot cal-

ibration tasks, we implemented the following exper-

iments. In the ﬁrst one, we modeled a robot with

Unity and implemented simple inverse kinematics.

Using this simulator, we collected the inverse kine-

matics reference error dataset. In the second one, we

trained the error compensator on it. In the third one,

we modiﬁed robot parameters to simulate the uncali-

brated robot behavior with additional weight applied

to the end-effector and used transfer learning to speed

up the process of compensatory training. In the fourth

experiment, we tried to verify the viability of transfer

learning to train compensators on the data from real

robots. Finally, we applied different weighed pay-

loads on the robot and recalibrated the compensator

in a new usage scenario. The results, the dataset, the

source code, and the unity project are available in the

GitHub repository (Akhmetzyanov, 2019).

3.1 Unity Model Compensation

We developed a neural network model that is capable

to ﬁt kinematics and outperform linear model that has

been taken as a baseline. We implemented our model

with Keras framework with a TensorFlow backend.

We provide XYZ coordinates as the input to the net-

work (3 ﬂoat inputs). Output in our case is a correc-

tion signal for XYZ coordinates (3 ﬂoat outputs). The

best results were obtained with the neural network

model with one hidden layer containing 7 neurons,

the hyperbolic tangent activation function, and input

normalization. We provided the target position as in-

put and kinematic error as a prediction target. Thus,

our neural network must accept the coordinates of the

position of the mobile platform and provide the pre-

dicted value of the positioning error, which we can

use as a compensating factor in the control system of

the cable robot.

We tested sigmoid, linear, tanh, and ReLU acti-

vation functions with different neural network archi-

tectures. The Hyperbolic tangent activation function

gave the best results, because of its range symmetry

around zero which is true for linear activation as well.

We provide the visualization of kinematics error

data (Fig. 7) as a difference between reference (trian-

gular dots) and measured (round dots) positions. The

codirected shift in positions exists and can be com-

pensated. Errors are not linear relative to the position

in the workspace and thus the non-linear model is re-

quired to compensate errors. MAE for the weight #1

dataset is 25.09 mm, for the weight #2 is 33.93 mm.

Training history is available in Figure 8. After com-

pensation mean error reduced to 0.8 mm.

3.2 Unity Model Transfer Learning

Low error for compensator training is possible due to

unlimited data availability from the simulation. It al-

lows us to estimate optimal model architecture. For

further experiments, we will use only a limited sub-

set of available simulation data. To verify our trans-

fer learning hypothesis, we are comparing sample re-

quirements for model training from scratch and with

inherited neural network weights from the previous

payload type. Besides, we will compare both models

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556

Figure 7: Kinematic errors on simulated data.

Figure 8: Training history on simulated data.

with a linear compensator as a baseline.

Figure 9: Train and test errors on Unity data.

The results of the experiments are presented in

Fig. 9. Here we present the error distance (training

and test set dist) for different training set sizes. The

Hypothesis was conﬁrmed and it seems that weight

transfer is more efﬁcient in terms of sample efﬁciency.

We see that 22 samples are enough to outperform

the linear model. But with transfer learning, 22 are

enough to adapt the previous model to the new task

with 2.5 times accuracy increase. The same accuracy

can be achieved with 100 samples for training from

scratch. We also increasing the number of training

epochs while increasing the number of training sam-

ples to improve training performance.

In our ﬁgures, we use epochs and loss dimensions.

In artiﬁcial neural network terms, an epoch stands for

one cycle of gradient descent and backpropagation

through the full training dataset. For the loss term,

we use mean absolute error or L1 Loss which value

is measured in millimeters, thus, naturally describes

the accuracy of our model. Our loss is the arithmetic

mean of absolute differences between our target ref-

erence and predicted values.

3.3 Real Robot Compensation

We collected 2000 samples from real robots for 17

and 33 kg masses. Visualizations of errors for 17 kg

payload available in Fig. 10. In the real robot dataset,

the linear shift of error also explicit. For 5 kg payload,

we have a 1.117m mean Z position and 1.085 m for

33 kg, which means that the bigger mass pulls the end

effector down. Our total error for 5kg: 0.198 m and

error for 33kg: 0.186 m. The training process is avail-

able in Fig. 11. Test error is 8.1 mm after training.

Figure 10: Kinematic error data based on real measure-

ments.

3.4 Real Robot to Real Robot with

Different Mass Compensation

In the production environment, we need to recalibrate

our robot or adapt our controller for the new pay-

load. This is the common application scenario of our

method. From our experiment, in the case of differ-

ent mass adaptation for real robots, transfer learning

strongly reasonable. The results are available in Fig.

Deep Learning with Transfer Learning Method for Error Compensation of Cable-driven Robot

557

Figure 11: Training history with real data.

12. This experiment proved that it is efﬁcient to apply

transfer learning when we need to speed up the pro-

cess of robot calibration or adaptation to a new end-

effector payload.

In Fig. 12 we see that for 20 samples we achieve

the same performance for linear and neural network

based compensator. For the same training set size

we achieved 30% in accuracy using proposed trans-

fer learning method. To achieve the same accuracy

we need 120 samples to train the neural network from

scratch which shows sample efﬁciency increase by the

order of magnitude.

Figure 12: Training and test errors.

3.5 Unity Simulation to Real Robot

Transfer Learning

Our experiments showed that in some cases, it is pos-

sible to improve the training process even when the

environment dynamics is different. In our case, we

used weights from simulated environments to train

the real robot error compensator. As a result, some

constraints emerge. For example, the frames should

be co-directed, and scales should be the same. Nor-

malization with zero mean and one standard deviation

help to achieve this task. Fig. 13 and Fig. 14 shows

these results.

Figure 13: Training and test errors for 5 kg.

Figure 14: Training and test errors for 33 kg.

4 CONCLUSIONS

Since modern manipulators is a complex non-linear

kinematic system, a system on neural networks can

be used to compensate for the errors of the displace-

ment of the end effector. However, for this type of

calibration, a large dataset is usually required, which

is an undoubted problem when calibrating with vari-

able parameters, such as mass, at the end of the end

effector. However, as discussed above, the use of sim-

ulation and a part of real data, in conjunction with the

use of the transfer learning technique, allows increas-

ing the accuracy of the manipulator operation with-

out increasing data collection. It is worth noting that

this work examined the application of the method us-

ing only one type of a manipulator - a cable-driven

robot, however, this area in the ﬁeld of robotics has

prospects and requires further study.

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

558

ACKNOWLEDGEMENTS

Work was supported by the RFBR (Russian Founda-

tion for Basic Research)(Grant No. 19-08-01234).

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