Supplementary material from "A bio-inspired configuration and algorithm for vibration source localization and its biological implications"

Vibration source localization is an interdisciplinary topic with applications in both engineering and biology. To inspire technologies for use in engineering and understand how spiders may localize a vibration source, we develop a bio-inspired vibration source localization configuration and algorithm. The algorithm first calculates leg inputs using a backward filter forward smoother algorithm with leg responses; it then estimates the source angle, source distance, substrate wave speed and decay rate through optimization, utilizing the time and amplitude relationships between the calculated leg inputs. The algorithm effectiveness is validated through simulations. Results show that the algorithm gives accurate estimation of the source angle and wave speed with varying source distance, source angle, wave speed and decay rate, with errors typically within 3 deg (absolute) and 6% (relative), respectively. The algorithm cannot estimate the source distance. To locate the position, two spider-like agents would be used collaboratively. The algorithm works well even for leg responses with low signal-to-noise ratio. Results also show that the four-leg combination which includes front and back two legs is the minimum leg requirement. Increasing the leg–substrate contact damping can improve the algorithm accuracy. These results also give us new insights into how spiders may localize a vibration source.