Shakebot: A Low-cost, Open-source Robotic Shake Table for Earthquake Research and Education (2024)

I Introduction

For decades, researchers have used shake tables to simulate the effects of earthquakes on structures, systems, and materials, which provides a critical approach to earthquake research and education[jacobsen1929vibration, lu2008shake]. Simulated earthquake conditions can help civil engineers identify potential weaknesses in the design and suggest ways to improve the structure’s resilience[bogdanovic2019shake, rakicevic2021hybrid]. In a controlled laboratory setting, shake tables can also be used to study the behavior of fragile geological features, which aids seismologists in finding upper-bound constraints on ground motions[purvance2008freestanding]. By simulating earthquakes in the classroom, students can better understand the forces involved and the factors that influence the behavior of structures[elgamal2005line], inspiring the next generation of engineers and seismologists.

An important application of shake tables is to examine the dynamics of precariously balanced rocks (PBRs), which are free-standing rocks balanced on, but not attached to sub-horizontal pedestals[brune1996precariously, shi1996rocking, anooshehpoor2004methodology]. Because an earthquake ground motion of sufficient amplitude and duration may topple PBRs, the fragile configurations of PBRs provide upper-bound constraints on ground motions, refining probabilistic seismic hazard analysis[anderson2014precarious, rood2020earthquake]. The dynamics of the PBR overturning process are non-linear [yim_rocking_1980, purvance2008freestanding]. Purvance et al. [purvance2008freestanding] used a shake table to study the PBR overturning dynamics. However, difficulties can arise when using conventional shake tables to repeat overturning experiments. For example, when analyzing PBR fragility, shake experiments would involve accurate and repeated positioning of a large boulder on the shake table to record the overturning responses given ground motions. These boulders are often so heavy that the use of a crane or forklift is needed, and repositioning them precisely is difficult (e.g., [saifullah2022seismic]), complicating experiment repeatability.

In an effort to reduce variability, explore a broad parameter space of ground motions, and automate PBR overturning analyses, our previous study developed a virtual shake robot in simulation [chen2024virtual], which is a digital twin of the Shakebot. The virtual shake robot utilized core technologies in robotics, such as Robot Operating System (ROS), Gazebo simulation toolbox, and Bullet physics engine. Although the virtual shake robot allows us to conduct overturning experiments in simulation, the results need to be validated through physical experiments. To complete this validation, we designed and built a low-cost, small-scale shake table, called Shakebot (Fig.1).

The Shakebot provides a reverse method for simulation validation. Physics engines have been used for robotic development. However, when robotic systems are transitioned from simulations to the real world, simulation gaps may cause critical failures (e.g., in the arena of reinforcement learning[zhao2020sim, ding2020challenges]). When using a physics engine for scientific studies, we also need to address the simulation gap to calibrate and scale-up the simulation experiments. Using the Shakebot, we test the overturning dynamics of down-scaled, 3D-printed PBRs. We build the same PBR models in simulation and validate the overturning dynamics using our virtual shake robot. Following this approach, we are able to compare the overturning patterns obtained from the Shakebot and the virtual shake robot, further allowing us to quantify the uncertainty in simulation. The Shakebot serves as a validation tool for simulation studies, aiding in learning more about the real-time dynamics of the PBRs and potentially calibrating physics engine parameters to reduce the simulation gaps.

The paper is structured as follows. In Sec.II, we discuss commercial and academic shake tables available for civil engineering and seismology, and highlight a few of their capabilities and limitations. From Sec.III to Sec.VI, we describe the mechanical design, the perception system, the motion system, and the calibration system. In Sec.VII, we discuss the results of our experiments, followed by our conclusions and future directions in Sec.VIII.

II Related Work

Full- or large-scale shake tables and tabletop shake tables have different applications for research and education. Full-scale shake tables are designed to simulate earthquakes on full-scale buildings, bridges, and other large structures [gavridou2017shake]. Full-scale shake tables, which usually incorporate acceleration and displacement sensors for ground motion estimations, are expensive to build and maintain. The high cost limits their availability in research and education. Full-scale shake tables may also involve safety considerations in operation and damage prevention.

Tabletop shake tables, on the other hand, are typically used to test smaller models and structure components. Because of their low cost, these tables are also useful in educational settings to teach students about the behavior of structures under earthquake conditions. TABLE I compares existing tabletop shake tables and the Shakebot. Existing tabletop shake tables are comparatively expensive [web:qanser_st2, baran2011construction, web:testbox_shaketable] or only allow a fixed ground motion pattern [web:kelvin_es]. None of the existing tabletop shake tables have open-sourced their hardware. Another limitation of existing shake tables is that they solely employ accelerometers to measure ground motions.

III System Description

In this section, we discuss the mechanical design, motor selection strategy, and safety mechanism. The system is designed to satisfy the ground motion requirements—maximum dynamic acceleration of 11.8 $m/s^{2}$ (1.2 $\mathbf{g}$), maximum velocity of 0.5 $m/s$, and maximum displacement of 0.45 $m$, with maximum specimen (e.g., PBR) payload mass of 2 $kg$.

III-C Safety Mechanism

The design incorporates two levels of safety features. The first level consists of a pair of limit emergency switches situated at either end of the carriage’s range of motion, as shown in Fig. 2. These switches link to the emergency stop function on the stepper motor driver. Once either of these switches is triggered, the stepper motor is disabled. The second level of protection is supplied by an emergency push button in the control box, which disconnects the power supply from the stepper motor driver. The emergency push button can be manually activated by the Shakebot’s operator. Fig. 2 shows a top-down view of the Shakebot.

IV Perception System

The perception system estimates the status of the bed using a camera and an accelerometer. Four fiducial markers are affixed to the corners of the bed (Fig.1(b) and Fig.2). A top-down view camera (FLIR Chameleon^®3 Color Camera CM3-U3-13Y3C-CS 1/2") captures the position and orientation of the bed using the ROS package apriltag_ros [malyuta2017mt, Wang2016]. Additionally, an accelerometer (Wit Motion HWT905-TTL) attached underneath the bed measures acceleration (ground motion acceleration). We directly obtain ground motion displacement and acceleration from the fiducial marker detection and accelerometer, respectively. We additionally estimate the ground motion velocities by fusing the information from the fiducial marker detection and accelerometer.

IV-C Velocity Estimation

We estimate ground motion velocity by fusing the derived velocities from the fiducial marker detection and accelerometer data. Fig.3 illustrates the velocity fusion process. During a shake experiment, the timestamped ground motion displacements and accelerations are recorded. After the shake experiment, we implement numerical derivation to obtain velocity $v_{d}(t)$ from the ground motion displacements d(t).From the ground motion accelerations $a(t)$, we conduct numerical integration to obtain velocity $v_{a}(t)$.

From the recordings of fiducial markers and acceleremeter, we obtain two sets of derived velocities: $\mathbf{v_{d}}=\{v_{d}(t_{1}),...,v_{d}(t_{M})\}$ and $\mathbf{v_{a}}=\{v_{a}(t_{1}),...,v_{a}(t_{N})\}$. We phrase the ground motion velocity estimation as a regression problem with an objective function that minimizes the square of errors between estimated and derived velocities,

$$\arg\min_{\theta}||\hat{v}(t;\theta)-\mathbf{v_{s}}(t)||$$

(3)

where $\hat{v}(t;\theta)$ is a parametric ground motion velocity function, and $\mathbf{v_{s}}=\mathbf{v_{d}}\cup\mathbf{v_{a}}$ is a set of velocities derived from measurements. In this ground motion velocity estimation setting, $\{v_{d}(t)\}$ and $\{v_{a}(t)\}$ need not be synchronized, simplifying the electronic hardware configuration of our Shakebot. The fiducial marker detection and accelerometer have different frame rates. The parametric regression function $\hat{v}(t;\theta)$ has many options. We use a 6^rd order polynomial function for demonstration in Sec.VII.

V Motion System

The Shakebot has a hierarchical motion system and a user interface (UI) to facilitate shake experiments. The hierarchical motion system provides two options to emulate ground motions: single-pulse cosine displacement motion and realistic ground motion from seismogram acceleration recordings. The UI assists users in repeating the shake experiment where single-pulse cosine displacement motions are deployed with different ground motion parameters.

VI System Calibration

The Shakebot needs to be calibrated before conducting the shake experiments. We first calibrate the camera intrinsics and fiducial marker detection, and this calibrated perception system is used to facilitate velocity controller calibration.

VII Experiments and Discussion

We conducted experiments to demonstrate an application of the Shakebot in PBR fragility studies and to test its performance in validating simulation. These experiments focused on a PBR at the Double Rock site in coastal Central California [rood2020earthquake]. The PBR, as shown in Fig.5, was mapped by an unpiloted aerial vehicle and constructed using structure from motion and Poisson reconstruction algorithms [chen2024virtual].

The first experiment demonstrates the Shakebot application in studying the fragility anisotropy of PBRs. We down-scaled the Double Rock PBR from 151.0 cm to 12.0 cm in height and 3D-printed it with PLA material. The resulting PBR, denoted as 3D-printed PBR(a), had a total mass of 105g. Because of the asymmetric geometry of 3D-printed PBR(a), the overturning responses were expected to vary with different ground motion directions. To investigate this fragility anisotropy idea, we placed the 3D-printed PBR(a) with two initial orientations (yaw angles of 0° and 270°, as shown in Fig.5) on the bed. Using the UI, we obtained the response diagrams from a set of ground motions, as shown in Fig.6. The response diagrams indicated that 3D-printed PBR(a) oriented at a yaw angle of 0° was more fragile than at yaw angle of 270°. This result is consistent with previous studies showing that PBRs with smaller minimal contact angles along the motion direction are more fragile [purvance2008freestanding, haddad2012estimating]. Addtionally, the resulting boundary curves closely resembled the simulation results of the Double Rock PBR with original shape [chen2024virtual].

In the second experiment, we used the Shakebot to evaluate the overturning simulation. The Double Rock PBR was down-scaled to 12.8 cm in height and 3D-printed with the PETG material. The resulting PBR, denoted as 3D-printed PBR(b), had a total mass of 404 g. We imported the 3D model of the down-scaled PBR to Gazebo and conducted overturning experiments using the virtual shake robot [chen2024virtual]. To examine the simulation results, we used the Shakebot to overturn 3D-printed PBR(b). In both simulation and real-world experiments, the PBR had a yaw angle of 0°. As shown in Fig.7, the overturning boundary curves from the real-world and simulation experiments are similar. Future work should explore the causes of their difference. For example, we observed that Gazebo reduced the precision of configuration parameters when passing those parameters to the Bullet physics engine. The data from real-world experiments will aid in calibrating and improving the simulation experiments.

Fig.8 shows the estimation results of acceleration, displacement, and velocity from the input PGA of 0.98 $m/s^{2}$ and PGV/PGA of 0.1 $s$. According to the PGA and PGV/PGA, the desired PGV and peak ground displacement are 0.1 $m/s$ and 0.01 $m$, respectively. The acceleration estimation and displacement estimation can be improved with better measurement equipment such as a better-quality accelerator and motion capture system. Our velocity estimation method used the 6^rd order polynomial function to fuse data from afford sensors, resulting in a PGV estimate of 0.12 $m/s$. The resulting velocity estimation is better than individual velocities derived from the accelerometer and fiducial marker detection. Future work should quantify uncertainties in displacement, velocity, and acceleration estimates. Investigations on other regression models (e.g., Gaussian process regression) and real-time state estimation may also improve the ground motion estimation.

Because validating ground motion estimation requires future investment in expensive measurement equipment, we assumed that the actual ground motions were the same as the desired ground motions during the overturning experiment. This assumption is reasonable given our hierarchical control system and calibration processes. However, future work should verify this assumption. We also anticipate that the PBR response status registration can be automated by an object detection system and PBR placement can be implemented by a robotic arm. By automating the overturning experiments, we can save on human labor and ensure accurate PBR placement for reliable results.

VIII Conclusion

We introduced a low-cost, open-source shake table named Shakebot for earthquake research and education. Leveraging concepts and tools from robotics, we simplified and advanced the hardware and software compared to the existing shake tables. We presented the technical details of the perception and motion systems, which are important for the open-source community to upgrade or customize the Shakebot. Experiments showed the applications of the Shakebot for PBR studies. Our work demonstrates an interdisciplinary method of using robotics for natural sciences, providing a step towards robotics-enabled automated geoscience [chen2022automated]. The Shakebot provides an affordable platform for education, outreach, and other ground motion experiments.

ACKNOWLEDGEMENTS

This research was supported by the Pacific Gas and Electric Company and Southern California Earthquake Center (Contribution No. 21137). SCEC is funded by NSF Cooperative Agreement EAR-1600087 and USGS Cooperative Agreement G17AC00047. Thank you to Chris Madugo for his support and advice in the research.

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