A Mathematical Model That Learns an Adaptively Generated Novel Pattern in Quadruped Locomotion

Quadrupeds show several locomotion patterns when adapting to environmental conditions. An immediate transition among walk, trot, and gallop implies the existence of a memory for locomotion patterns. In this article, we postulate that motion pattern learning necessitates the repetitive presentation of the same environmental conditions and aim at constructing a mathematical model for new pattern learning. The model construction considers a decerebrate cat experiment in which only the left forelimb is driven at higher speed by a belt on a treadmill. A central pattern generator (CPG) model that qualitatively describes this decerebrate cat's behavior has already been proposed. In developing this model, we introduce a memory mechanism to store the locomotion pattern, where the memory is represented as the minimal point of the potential function. The recollection process is described as a gradient system of this potential function, while in the memorization process a new pattern learning is regarded as a new minimal point generation by the bifurcation from an already existing minimal point. Finally, we discuss the generalization of this model to motion adaptation and learning.