We discovered a specific rule for generating typical quadrupedal gaits (the order of the movement of four legs) through a simulated quadrupedal locomotion, in which unprogrammed gaits (diagonal/lateral sequence walks, left/right-lead canters, and left/right-lead transverse gallops) spontaneously emerged because of leg loading feedbacks to the CPGs hard-wired to produce a default trot. Additionally, all gaits transitioned according to speed, as seen in animals. We have therefore hypothesized that various gaits derive from a trot because of posture control through leg loading feedback. The body tilt on the two support legs of each diagonal pair during trotting was classified into three types (level, tilted up, or tilted down) according to speed. The load difference between the two legs led to the phase difference between their CPGs via the loading feedbacks, resulting in nine gaits (32: three tilts to the power of two diagonal pairs) including the aforementioned.
This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.
We aim to design a neuromorphic controller for the locomotion of a quadruped robot with muscle-driven leg mechanisms. To this end, we use a simulated cat model; each leg of the model is equipped with three joints driven by six muscle models incorporating two-joint muscles. For each leg, we use a two-level central pattern generator consisting of a rhythm generation part to produce basic rhythms and a pattern formation part to synergistically activate a different set of muscles in each of the four sequential phases (swing, touchdown, stance, and liftoff). Conventionally, it was difficult for a quadruped model with such realistic neural systems and muscle-driven leg mechanisms to walk even on flat terrain, but because of our improved neural and mechanical components, our quadruped model succeeds in reproducing motoneuron activations and leg trajectories similar to those in cats and achieves stable three-dimensional locomotion at a variety of speeds. Moreover, the quadruped is capable of walking upslope and over irregular terrains and adapting to perturbations, even without adjusting the parameters.
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