Simple analytical model reveals the functional role of embodied sensorimotor interaction in hexapod gaits

Abstract

Insects have various gaits with specific characteristics and can change their gaits smoothly in accordance with their speed. These gaits emerge from the embodied sensorimotor interactions that occur between the insect’s neural control and body dynamic systems through sensory feedback. Sensory feedback plays a critical role in coordinated movements such as locomotion, particularly in stick insects. While many previously developed insect models can generate different insect gaits, the functional role of embodied sensorimotor interactions in the interlimb coordination of insects remains unclear because of their complexity. In this study, we propose a simple physical model that is amenable to mathematical analysis to explain the functional role of these interactions clearly. We focus on a foot contact sensory feedback called phase resetting, which regulates leg retraction timing based on touchdown information. First, we used a hexapod robot to determine whether the distributed decoupled oscillators used for legs with the sensory feedback generate insect-like gaits through embodied sensorimotor interactions. The robot generated two different gaits and one had similar characteristics to insect gaits. Next, we proposed the simple model as a minimal model that allowed us to analyze and explain the gait mechanism through the embodied sensorimotor interactions. The simple model consists of a rigid body with massless springs acting as legs, where the legs are controlled using oscillator phases with phase resetting, and the governed equations are reduced such that they can be explained using only the oscillator phases with some approximations. This simplicity leads to analytical solutions for the hexapod gaits via perturbation analysis, despite the complexity of the embodied sensorimotor interactions. This is the first study to provide an analytical model for insect gaits under these interaction conditions. Our results clarified how this specific foot contact sensory feedback contributes to generation of insect-like ipsilateral interlimb coordination during hexapod locomotion.

Evolved embodied phase coordination enables robust quadruped robot locomotion

“…Because of the minimal de nition, TEGOTAE can also be combined with several di erent control systems making it an interesting candidate for control system research within the ER community. Most of the work dealing with TEGOTAE has focused on analyzing locomotion to show the advantages of the TEGOTAE sensory feedback mechanism [3], in this paper we extend that research to encompass ER and argue that TEGOTAE sensor feedback is versatile, can readily be combined with a complex CPG control system without the use of inverse kinematics, is robust in light of controller evolution and can work for complex quadruped robots.…”

“…From the graph we can see that the di erence in simulation is quite considerable, however, in the real world the two control systems perform equally well. 3 Videos of real-world evaluations: https://folk.uio.no/jorgehn/tegotae/video/ To test if the di erences in previous results, Figure 5a…”

“…Because TEGOTAE only a ects a small portion of the overall control structure it can easily be combined with di erent control approaches, widening its appeal for ER research. However, most of the work dealing with TEGOTAE so far has focused on analyzing locomotion to show the advantages of the TEGOTAE sensory feedback mechanism [3], using hand-tuned parameters and inverse kinematics or single jointed legs with low complexity controllers.…”

Dynamical determinants of different spine movements and gait speeds in rotary and transverse gallops

“…Because of the complex nature of the governing dynamics, there are limitations to the understanding of the mechanisms underlying different flight phases in the galloping gait types that can be gained from observations of animals alone. To overcome the limitations of the observational approach in animal locomotion, modeling approaches have attracted recent research attention ( Bertram and Gutmann, 2009 ; Alexander, 1988 ; Marques et al, 2014 ; Markowitz and Herr, 2016 ; Swanstrom et al, 2005 ; Aoi et al, 2017 ; Usherwood and Davies, 2017 ; Ambe et al, 2018 ; Fujiki et al, 2018 ; Aoi et al, 2019 ; Toeda et al, 2019 ). Because the essential contribution of the legs can be represented by springs, the spring-loaded inverted pendulum (SLIP) model was developed to investigate animal locomotion mechanism from a dynamic viewpoint, particularly for human running and walking ( Blickhan, 1989 ; McMahon and Cheng, 1990 ; Seyfarth et al, 2002 ; Geyer et al, 2005, 2006 ; Srinivasan and Holmes, 2008 ; Lipfert et al, 2012 ; Seethapathi and Srinivasan, 2019 ).…”

Honeybees Prefer to Steer on a Smooth Wall With Tetrapod Gaits

“… Couzin-Fuchs et al (2015) examined the role of proprioceptive feedback in cockroach locomotion and established pymetrozine as a useful tool for further studies of insect locomotion. Ambe et al (2018) proposed an analytical model to reveal the functional role of embodied sensorimotor interaction in hexapod gaits. In addition, Weihmann et al (2017) investigated high-speed locomotion and gait changes of the cockroach ( Nauphoeta cinerea ), on two substrates of different slipperiness.…”