Keywords

1 Introduction

The design for free-form timber structures fabricated/constructed by robotic automation is a complex and multi-disciplinary system. To clarify the research questions, different factors related to the research field need comprehensive considerations.

Robotic fabrication: Since the 1990s, industrial robots dominated robotics research, and the technical necessities determined areas of investigation for robotics [1]. Efficiency is highly valued to achieve production sustainability and economic growth in the manufacturing industry. Under the notion of “Industry 4.0” calling for a highly automated, autonomous, flexible system, robotic automation as a new technique has been gradually applied to construction in academics and industries.

Free-form timber structure: The current standard form of architecture could not meet the variety of demands of human Aesthetic needs. Non-standard and free-form architecture becomes more and more acceptable. Based on the attention paid to sustainable environmental design, timber is a perfect building material to meet the measurements for environmental construction efficiency. Freeform structures using timber as the main materials are driven by digital technologies in design methods and product fabrication for irregular geometries [2].

One question for robotic timber fabrication for free-form structure is how to consider the technical aspect and material properties throughout the whole design process. The conventional way of taking a robotic arm as a fabrication method is shown in Fig. 1a–c. The research aims to extract the appropriate features of geometry for the LSTM method and to develop a method to transform the predicted geometry data into robotic information for fabrication.

Fig. 1.
figure 1

Fabrication consideration in a different stage of the design process

Full size image

2 Related Work

Digital fabrication technologies have enabled timber structures becoto become irregular and complex. Compared with Computational Numerical Control (CNC) technique, the mobility, and not high requirements for the working condition of robotic fabrication system are more flexible [3]. And this advantage conforms to the development trend–that is to take the design information as the input to produce construction automatedly [4]. Now, the robotic timber fabrication technique has not only been researched in laboratories but also applied in some large-scale construction applications [3, 5,6,7]. According to different forms of the components designed by different based-factors, different robotic fabrication types are needed such as cutting, milling, sewing, driand lling on different timer products from natural wood to engineering timber products [8]. More and more cases of using robotic fabrication automation have been demonstrated [9,10,11,12]. In summary, robotic fabrication can be applied throughout the whole design process in different phases from preparation to customised fabrication.

The rationality of free-form morphology means the design can be fabricated and constructed which is a complex work for architects and engineers [13]. Machine learning (ML) is derived from statistics, and the quality of an ML system is determined by the low error rate of prediction or classification [14]. ML can generate data which can be applied in generative design work using technique like deep neural networks (DNNs) [15]. One of the DNN model that has demonstrated the ability to be applied in geometry generation is the generative adversarial network (GAN) [16]. The model built through GAN can learn from the existing 2D images and transfer the empirical data into the generative design in 2D form [17]. 2D application of GAN is only limited to the 2D plan or façade generations. In ML area, many attempts have been made to generate 3D objects.

Other machine learning networks has potential to deal with 3D geometry. The data type of the current LSTM applications is in time-sequence, and the results prove the effectiveness and accuracy in predicting time sequential data like wind or air quality [18, 19]. As for the image or 2D data type which is not in sequence technically, one step to transform image into sequence data is needed additionally [20]. As for 3D geometric data, LSTM or other machine learning methods have not been widely used, especially in architectural design field.

In this paper, LSTM method is applied to predict the free-form surface morphology to improve the rationality of free-form structure considering material properties of timber and robotic fabrication. The first step is to transform the geometric data into sequential data types, and the simulation environment for the robotic is set up. The experiment of applying LSTM model to predict the morphology of free-form curves would be taken in to testify the feasibility of the transformed data to be applied in LSTM. After the prediction experiment, the methods of testifying for the singularities and the limitation of the robotic fabrication would be operated. The results of the experiments and the method would be discussed in the discussion and conclusion part.

3 Methodology

3.1 Workflow

To improve the rationality of the free-form morphology design, the impact of characteristics (6 Degree-of-freedom) and constraints (the type of fabrication, the dimensions of working space) of robotics as a technique on architectural geometry design are considered. To generate the initial geometry of free-form timber morphology, this research would discuss using LSTM machine learning to fulfil the constraints of timber material and robotic fabrication in conceptual design.

Based on the morphological design requirements of free-form timber structures, the pathway of machine learning for predicting the curve is developed as follows, shown in Fig. 2:

Fig. 2.
figure 2

Workflow of the LSTM prediction and robotic testing

Full size image
  1. 1.

    Choose the appropriate input and output.

  2. 2.

    Transform the input and output into a training set (in numbers or figures).

  3. 3.

    Select the training method.

  4. 4.

    Test the training accuracy.

3.2 Data Transformation

To complete the prediction learning task, the appropriate free-form model mattes in the learning task. This research takes the Center Pompidou-Metz Model as a case to extract the data for LSTM (Fig. 3).

Fig. 3.
figure 3

3D model of the case

Full size image

As LSTM works well for the sequential data, the geometric data of the model would be transformed. The main difficulty is the geometric design is stored in a three-dimension form (like 3 dm, obj) while machine learning deals with numbers. If the model is presented in the figures from perspective views, there would be a loss of geometric information. The idea of data transformation is to find the proper way to store geometric information that fits the LSTM method and could be exported to the robot arm to generate fabrication commands (Fig. 4).

Fig. 4.
figure 4

Data transformation

Full size image

For the data transformation in this condition, assuming the number of curves to be analysed in N, every curve has been divided into \((M-1)\) parts evenly. There are eight parameters to describe this curve, the position of the division-point \(\mathrm{ P}(\mathrm{x},\mathrm{y},\mathrm{z}) \), curvature \(\mathrm{ K }\), the position of the point on the curve \({t}_{1}\), the tangent of the points \(T\left( {a,b,c} \right)\)\(.\) Every curve can be described by a matrix, which is \({Q}_{m\times 8}\).

The detailed of matrix \(Q\) is shown as:

$$ Q_{M \times 8} = \left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {\begin{array}{*{20}c} {x_1 } & {y_1 } & {z_1 } \\ {x_2 } & {y_2 } & {z_2 } \\ \ldots & \ldots & \ldots \\ \end{array} } \\ {\begin{array}{*{20}c} {x_M } & {y_M } & {z_M } \\ \end{array} } \\ \end{array} } & {\begin{array}{*{20}c} {t_1 } \\ {t_2 } \\ \ldots \\ {t_M } \\ \end{array} } & {\begin{array}{*{20}c} {K_1 } \\ {K_2 } \\ \ldots \\ {K_M } \\ \end{array} } & {\begin{array}{*{20}c} {\begin{array}{*{20}c} {a_1 } & {b_1 } & {c_1 } \\ {a_2 } & {b_2 } & {c_2 } \\ \ldots & \ldots & \ldots \\ \end{array} } \\ {\begin{array}{*{20}c} {a_M } & {b_M } & {c_M } \\ \end{array} } \\ \end{array} } \\ \end{array} } \right] $$
(1)

According to the features of the discrete numbers extracted from the curves of the timber columns and beams, the LSTM training model is selected to predict the six variables of every curve for the best result. The workflow is shown in Fig. 5. After the LSTM learning network, the predicted parameters can interpolate the predicted curve which can be compared with the test one.

Fig. 5.
figure 5

LSTM learning process

Full size image

3.3 Robotic Setup

To operate the technical analysis of robotic in both Cartesian space and joint space which is unique for robotic system, DH method is applied to build the model of robotic arm. The x–y-z coordinate of the components can connect the geometry model of the component with robotic arm.

In robot motion control, there is a corresponding matrix map** between the joint velocity and the corresponding end-effector velocity and angular velocity as in the correspondence of the previous section, and this map** reflecting the interrelationship between joint velocity and end velocity is known in robotics as the "Jacobi matrix ". It is expressed as follows,

$$ V_e = J\left[ q \right] \cdot \dot{q} $$
(2)

Whether \(\left|J[q]\right|\ne 0\) is the way to testify the singularities.

4 Experiment

4.1 Training

Four timber beams from the geometric model are selected, and 16 curves are extracted to get the division points. In the prediction for 21 divided-points, the geometric information of 15 curves are selected and one curve is set as the test data and the training process is shown in Fig. 6. Figures 7 and 8 present the prediction error compared with the test data. To further test the prediction accuracy, the predicted tangent vector and the corresponding curvatures of the divided points are applied to fit the curve. The angles between the predicted tangent vector and the original one are shown in Fig. 9a.

Fig. 6.
figure 6

Training results with 21 points

Full size image
Fig. 7.
figure 7

Test results with 21 points

Full size image
Fig. 8.
figure 8

Histogram of the MSE of the prediction

Full size image
Fig. 9.
figure 9

Comparison of the generated curve and the tested curve

Full size image

4.2 Robotic Simulation

Based on the robotic working space cell, the limitation including the obstacles and the range or the movement can be visualised as shown in Fig. 10.

Fig. 10.
figure 10

Robotic working limits

Full size image

The determination of whether the toolpath of the fabrication of the free-form components satisfies the constraints of the robotic arm is shown in Fig. 11.

Fig. 11.
figure 11

Workflow of the robotic testification

Full size image

5 Discussion and Conclusion

The results of the prediction experiment shows that the transformed 3D geometric data in sequential form fits for the LSTM to operate the prediction learning task. The converged training results illustrates the feasibility of LSTM in predicting the morphology of free-form. By comparing the test and predict datasets, the predicted vectors match the test data sets while the predicted curvature is more oscillatory and deviates to some extent from the test ones. By transforming the predicted curve into 3D model, the predicted geometry can be compared with the test model directly in 3D environment. Figure 9 shows the deviation between the predicted vectors and original vectors where color blue stands for the predicted curve. Based on the predicted curve model, the curve is extended into timber beam which would be fabricated by robotic arm. The robotic work cell case presents the workflow of transforming the predicted timber component information into the fabrication data which can be turned into robotic commands.

In conclusion, this research first proposes one method to extract the geometric features to describe the free-form curve which could be transformed into the sequential data for LSTM prediction learning. The experiments demonstrate the workflow of taking LSTM to predict the curve with the curvatures that meet the restrictions of timber properties and the results proves the effectiveness of LSTM taking \(\{x, y, z, t, K, a,b,c\}\) as sequential features. When applying the robotic arm to fabricate the structure component which is transformed from the predicted free-form curve, DH method is applied to build the model of robotic arm in Matlab which a process to connect the geometric information in Rhino to the robotic simulation and analysis in Matlab. The working space limit can be computed by Monte Carlo method and the singularities of the robotic arm are derived based on the Jacob matrix to testify the tool path of the predicted free-form structure components.