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

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.

From neuron to behavior: dynamic equation-based prediction of biological processes in motor control

This article presents the use of continuous dynamic models in the form of differential equations to describe and predict temporal changes in biological processes and discusses several of its important advantages over discontinuous bistable ones, exemplified on the stick insect walking system. In this system, coordinated locomotion is produced by concerted joint dynamics and interactions on different dynamical scales, which is therefore difficult to understand. Modeling using differential equations possesses, in general, the potential for the inclusion of biological detail, the suitability for simulation, and most importantly, parameter manipulation to make predictions about the system behavior. We will show in this review article how, in case of the stick insect walking system, continuous dynamical system models can help to understand coordinated locomotion.

Deriving neural network controllers from neuro-biological data: implementation of a single-leg stick insect controller

This article presents modular recurrent neural network controllers for single legs of a biomimetic six-legged robot equipped with standard DC motors. Following arguments of Ekeberg et al. (Arthropod Struct Dev 33:287-300, 2004), completely decentralized and sensori-driven neuro-controllers were derived from neuro-biological data of stick-insects. Parameters of the controllers were either hand-tuned or optimized by an evolutionary algorithm. Employing identical controller structures, qualitatively similar behaviors were achieved for robot and for stick insect simulations. For a wide range of perturbing conditions, as for instance changing ground height or up- and downhill walking, swing as well as stance control were shown to be robust. Behavioral adaptations, like varying locomotion speeds, could be achieved by changes in neural parameters as well as by a mechanical coupling to the environment. To a large extent the simulated walking behavior matched biological data. For example, this was the case for body support force profiles and swing trajectories under varying ground heights. The results suggest that the single-leg controllers are suitable as modules for hexapod controllers, and they might therefore bridge morphological- and behavioral-based approaches to stick insect locomotion control.