A self-organizing model of walking patterns of insects

Abstract

Insects generate walking patterns which depend upon external conditions. For example, when an insect is exposed to an additional load parallel to the direction in which it is walking, the walking pattern changes according to the magnitude of the load. Furthermore, even after some of its legs have been amputated, an insect will produce walking patterns with its remaining legs. These adaptations in insect walking could not previously be explained by a mathematical model, since the mathematical models were based upon the hypothesis that the relationship between walking velocity and walking patterns is fixed under all conditions. We have produced a mathematical model which describes self-organizing insect walking patterns in real-time by using feedback information regarding muscle load (Kimura et al. 1993). As part of this model, we introduced a new rule to coordinate leg movement, in which the information is circulated to optimize the efficiency of the energy transduction of each effector organ. We describe this mechanism as ‘the least dissatisfaction for the greatest number of elements’. In this paper, we introduce the following aspects of this model, which reflect adaptability to changing circumstances: (1) after one leg is exposed to a transient perturbation, the walking pattern recovers swiftly; (2) when the external load parallel to the walking direction is continuously increased or decreased, the pattern transition point is shifted according to the magnitude of the load increment or decrement. This model generates a walking pattern which optimizes energy consumption at a given walking velocity even under these conditions; and (3) when some of the legs are amputated, the model generates walking patterns which are consistent with experimental results. We also discuss the ability of a hierarchical self-organizing model to describe a swift and flexible information processing system.