Transformer based Collision Detection Approach by Torque Estimation using Joint Information

2.1 Problem formulation

The motion of a robot manipulator is elicited in response to the torque applied to each joint. When control input torque and externally applied torque are exerted on the manipulator, the dynamics of the robot are expressed by as

Where q, $$ \dot{\mathit{q}}$$, and $$ \ddot{\mathit{q}}\in {\mathbb{R}}^{n\times 1}$$ denote the joint angle vector, angular velocity vector, and angular acceleration vector, respectively. $$ \mathbf{M}\left(\mathit{q}\right)\in {\mathbb{R}}^{n\times n}$$ is the inertia matrix, $$ \mathbf{C}\left(\mathit{q},\dot{\mathit{q}}\right)\in {\mathbb{R}}^{n\times 1}$$ represents the centrifugal and Coriolis forces, $$ \mathbf{g}\left(\mathit{q}\right)\in {\mathbb{R}}^{n\times 1}$$ denotes the gravity force, τ_u and τ_ext $$ \in {\mathbb{R}}^{n\times 1}$$ denotes the control input torque and external torque, respectively. The τ_ext encompasses disturbances such as friction within its scope, but in this paper, it is delimited to torque resulting from external impacts. Computed torque control (CTC) is a method for controlling robots by applying torque to each joint, considering dynamics, to enable the robot to achieve motion as desired. CTC estimates the dynamics of the robot system using dynamical models, thereby inversely calculating the angles and angular velocities of each joint to control or generate the desired force using Jacobian Transpose. In the situation of controlling the robot using CTC, if disturbances forces apply to the robot, its motion deviates from the intended motion represented by the control torque. In this paper, we present a collision detection approach using a Transformer network utilizing input torque and joint information in the absence of external forces. Subsequently, we identify disparities arising from the influence of external forces to ascertain collisions.

[Fig. 1] illustrates the structure of the proposed torque estimator network and collision discriminator network operating within the framework of a general robot control system. The controller receives joint angle information from the robot systems and computes torque input values for various robot control objectives, such as the desired position of the end-effector $$ {\mathit{x}}_{\mathrm{d}}\in {\mathbb{R}}^{3\times 1}$$, desired joint angle q_d, angular velocity $$ {\dot{\mathit{q}}}_{\mathrm{d}}$$, and desired force $$ {\mathit{f}}_{\mathrm{d}}\in {\mathbb{R}}^{3\times 1}$$, to be transmitted to the robot.

[Fig. 1]

Overview of collision detection approach

The torque estimator shown in [Fig. 1] estimates the control input torque for the next step using received joint information from the robot. In this paper, to estimate the control input torque using only the joint information of the manipulator, we use a Transformer architecture based on the RNN to construct the network. The collision discriminator discerns disturbances of the robot by contrasting the control input torque values imposed by the controller onto the robot with the torque values estimated by the torque estimator. While the collision discriminator proposed in this paper solely conducts basic collision detection, for future research on external force estimation through external torque estimation, the collision discriminator is also constructed with a network architecture using a Transformer.

Ultimately, the proposed method consists of a torque estimation network and a collision discriminator network utilizing Transformer architecture. The torque estimator estimates the joint-based input torque $$ \widehat{\mathit{\tau }}(\mathit{q},\dot{\mathit{q}},\ddot{\mathit{q}})$$ in scenarios without the influence of external forces (τ_ext= 0). The collision discriminator detects situations where disturbances unexpectedly occur (τ_ext ≠ 0) by comparing the estimated input torque with the actual control input torque.

2.2 System overview

[Fig. 2] illustrates the system overview of a data processing pipeline for detecting collisions using a robot joint information dataset. At each control step, joint angle data are collected and used to estimate torque for the torque estimator network. The torque estimator estimates the torque between (t - α) and t intervals by utilizing data from the (t - 2α) to (t - α) interval. This estimated torque is then compared with the actual torque calculated from robot controller. The collision detection model performs inference at time step t, using a data window from (t - α) to t. The parameter α serves as a constant determining the amount of data utilized for collision detection.

[Fig. 2]

Timeline of the data pipeline for the collision discriminator

The torque estimator network utilizes this window to estimate the torque values based on the joint angle, angular velocity, and angular acceleration. These estimated torque values are then subtracted from the actual torque values to determine discrepancies indicative of abnormal behavior, such as collisions. The collision discriminator module takes the discrepancy between the estimated and actual torques and determines whether a collision has occurred. The collision events are encoded as a binary collision indicator, with a positive indication signaling a collision at the respective time frame. The collision indicator is represented as a binary sequence for each control step, where 0 denotes collision-free instances and 1 indicates collision events. This system design enables real-time monitoring of robotic operations to identify collision events, enhancing the safety and reliability of automated processes.

2.3 Network architecture

In our proposed architecture, we use the Synchronous Time-step Encoding (STE) for positional encoding, tailored for handling time-series data involving joint angle, angular velocities, and angular accelerations as shown in [Fig. 3]. This technique addresses the challenge of preserving temporal coherence when these sequences are concatenated, ensuring accurate temporal interpretation of each data point. STE continuously discriminates neighboring time-steps by applying temporal identifiers from a single sinusoid, thereby maintaining the temporal relationship and sequence of movements, even when multiple features are combined into a single vector. This aspect is crucial for tasks like collision detection that demand an intricate understanding of sequential dynamics. To ensure temporal consistency, STE applies identical positional encoding at regular intervals within the concatenated sequences. This modification of the traditional sinusoidal embedding formula allows the model to understand that data points from q,$$ \dot{\mathit{q}}$$, and $$ \ddot{\mathit{q}}$$ at the same positions pertain to synchronous time steps. Such an embedding strategy enhances the model’s capability to interpret and predict complex time-series patterns by leveraging the temporal coherence of sequential data, thereby improving its performance in tasks requiring precise analysis of dynamic movements.

[Fig. 3]

Diagram of Synchronous Time-step Encoding with Transformer, tailored for time-series data of joint positions, angular velocities, and angular accelerations, ensuring temporal coherence

3.1 Computed torque controller

Since the proposed method outlined in Chapter 2 focuses on controllers managing the robot’s torque, the controller designed for the data collection process, utilizing Jacobian transpose control, is structured as

Where $$ \mathit{J}\in {\mathbb{R}}^{6\times n}$$ represents the basic Jacobian matrix for an n-DOF manipulator, τ_g denotes gravity compensation torque vector. $$ {\mathit{K}}_{\mathrm{p}}\in {\mathbb{R}}^{3\times 3}$$ and $$ {\mathit{K}}_{\mathrm{p}}\in {\mathbb{R}}^{3\times 3}$$ respectively denote the virtual spring gain matrix and damping matrix of the end-effector position in Cartesian space. x_d, $$ {\mathit{x}}_{\mathrm{c}}\in {\mathbb{R}}^{3\times 1}$$, and $$ \mathit{\delta }\mathit{\Phi }\in {\mathbb{R}}^{3\times 1}$$ represent the desired position, current position, and orientation error of end-effector, respectively. The joint friction compensation torque vector τ_fric serves to compensate for joint gear friction by adding a constant torque of predetermined slope k and magnitude $$ {\mathit{K}}_{\mathrm{c}}\in {\mathbb{R}}^{n\times n}$$ for each joint rotation direction. Since the proposed collision detection method is independent of the controller’s structure, intentional complexity is introduced by designing the controller to deliberately incorporate trigonometric functions and derivatives such as the hyperbolic tangent function and Jacobian.

3.2 Data collection

Simulation was divided into two scenarios involving free motion and collision situations, with details and the operational range for both scenarios depicted in [Fig. 5]. For free motion, we selected a workspace within the robot’s operational range where the robot commonly operates. Desired points were randomly designated within this workspace, and the robot was programmed to repetitively move to these points. In collision scenarios, the robot moved within specific areas, but rectangular obstacles were randomly placed to induce collisions. These obstacles were essential in creating collision events, offering crucial opportunities for the model to detect and learn from the variations in torque patterns resulting from unforeseen physical contacts. Time-series data for each joint, including joint positions and computed torques, were recorded at a frequency of 500 Hz. For collisions, occurrences were logged in a binary format, frame by frame at the same frequency. Angular velocities were derived by differentiating joint positions, and angular accelerations were obtained by further differentiation. All collected data were min-max normalized before being inputted into the model. The dataset for these experiments consisted of a total length of 11,585,405 data points per each joint. The size of recent data α as presented in [Fig. 2] was set to 1,000. [Fig. 6] shows the distribution of collision occurrences per link during the data collection process. For the following reasons, biased distributions appeared: Links 1 and 2, which rotate only and are closer to the base, experienced minimal collisions, while Link 5, characterized by its longer length, exhibited relatively higher collision rates. Links 6 and 7 exhibited relatively fewer occurrences of collisions due to their smaller size and volume compared to links 3, 4, and 5. [Table 1] lists the accuracy of collision detection based on the collision link. It confirms that biased collision data does not affect the collision detection algorithm.

[Fig. 5]

Snapshots of the data collection process in the simulation environment: (a) Free random motion scenario, (b) Collision scenario caused by a random box

[Fig. 6]

Distribution of collisions about each link

[Table 1]

Accuracy of collision detection by link

3.3 Performance of torque estimator network

[Fig. 7] depicts the actual input torque and the torque estimated by the network for each joint in free motion scenarios. [Fig. 8] illustrates the joint information, specifically for the 5th link, during collision situations. Due to the collision, there are changes in the trends of the desired torque and angular velocity. The discrepancy between the torque estimated by the network and the trend seems to serve as the basis for collision detection judgments.

[Fig. 7]

Graphs of estimated and control torque for each joint in free motion

[Fig. 8]

Graphs of joint angle, angular velocity, both torque, and collision detection during collision scenarios

To evaluate the performance of network architectures for the collision detection problem, we first examined the performance of the torque estimator network. KL divergence is used to measure how closely the probability distribution of the predictions made by our model matches the actual distribution observed in the training data. After training for 100 epochs, the estimated torque values on the validation set were compared to the target torque values using KL-divergence loss as

Where N represents the batch size. i denotes the class index.

[Table 2] lists the results using RNN architecture, while [Table 3] lists the outcomes with the Transformer architecture. Despite having a generally higher number of network parameters, the Transformer architecture offers shorter inference times than RNNs.

[Table 2]

Performance of RNN-based torque estimator

[Table 3]

Performance of Transformer-based torque estimator

This efficiency stems primarily from parallel processing capabilities, which are made possible by its self-attention mechanism that allows for the simultaneous processing of all input data elements. In contrast, RNNs process data sequentially, necessitating the completion of one element’s before proceeding to the next. In the context of online collision detection, where rapid detection and response to collisions are crucial, the shorted inference time of the Transformer represents the advantage. This analysis underscores the Transformer’s efficacy in tasks requiring quick and efficient processing, marking it as a superior choice for real-time collision detection applications.

3.4 Performance of collision discriminator network

For the collision discriminator network, which predicts a binary tensor indicating the presence of a collision on a frame-by-frame basis, we conducted the following experiments to compare the performance across different architectures. Collisions are generated randomly in the workspace and the collision information is recorded for each joint. To determine whether the Transformer architecture is advantageous for the problem of collision detection, comparisons were made among a Multi-layer Perceptron (MLP), an RNN network, and a Transformer network. All three networks were trained for 100 epochs with a batch size of 16. The MLP consisted of three fully connected layers, the RNN had a hidden size of 100, and the Transformer used a hidden size of 100, with 8 heads and 6 encoder layers. Considering the potential imbalance in the class distribution between collision and no-collision instances, the F1 score is selected for its ability to balance both precision and recall of the model, offering a more nuanced evaluation of its performance in effectively handling both positive and negative classes. The proportion of collision in the total data is 21%. As listed in [Table 4], the Transformer demonstrates higher accuracy compared to other architectures and, when compared with the similarly performing RNNs, it exhibits faster inference time.

[Table 4]

Performance of collision discriminator according to network architectures

3.5 Ablation studies

To enhance the learning performance of the Transformer network, STE and decoder are naturally utilized; however, an ablation study was conducted to assess their respective impacts. Simulations were carried out to examine the effects of applying STE and attaching a decoder to the Transformer-based torque estimator network. This study aimed to explore two main aspects. The first aspect was the application of STE to enhance the network’s capability in handling time-series data with inherent temporal relationships. The second aspect involved attaching a decoder to the network with the hypothesis that it would improve the network’s ability to reconstruct and predict torque values more accurately. The findings from these experiments are systematically presented in [Table 5]. The results demonstrate that both the application of STE and the attachment of a decoder to the Transformer-based torque estimator network contributed to its improved performance.

[Table 5]

Ablation study on torque estimator