A galloping quadruped model using left-right asymmetry in touchdown angles.

Among quadrupedal gaits, the galloping gait has specific characteristics in terms of locomotor behavior. In particular, it shows a left-right asymmetry in gait parameters such as touchdown angle and the relative phase of limb movements. In addition, asymmetric gait parameters show a characteristic dependence on locomotion speed. There are two types of galloping gaits in quadruped animals: the transverse gallop, often observed in horses; and the rotary gallop, often observed in dogs and cheetahs. These two gaits have different footfall sequences. Although these specific characteristics in quadrupedal galloping gaits have been observed and described in detail, the underlying mechanisms remain unclear. In this paper, we use a simple physical model with a rigid body and four massless springs and incorporate the left-right asymmetry of touchdown angles. Our simulation results show that our model produces stable galloping gaits for certain combinations of model parameters and explains these specific characteristics observed in the quadrupedal galloping gait. The results are then evaluated in comparison with the measured data of quadruped animals and the gait mechanisms are clarified from the viewpoint of dynamics, such as the roles of the left-right touchdown angle difference in the generation of galloping gaits and energy transfer during one gait cycle to produce two different galloping gaits

Adaptive Control Strategies for Interlimb Coordination in Legged Robots: A Review

Walking animals produce adaptive interlimb coordination during locomotion in accordance with their situation. Interlimb coordination is generated through the dynamic interactions of the neural system, the musculoskeletal system, and the environment, although the underlying mechanisms remain unclear. Recently, investigations of the adaptation mechanisms of living beings have attracted attention, and bio-inspired control systems based on neurophysiological findings regarding sensorimotor interactions are being developed for legged robots. In this review, we introduce adaptive interlimb coordination for legged robots induced by various factors (locomotion speed, environmental situation, body properties, and task). In addition, we show characteristic properties of adaptive interlimb coordination, such as gait hysteresis and different time-scale adaptations. We also discuss the underlying mechanisms and control strategies to achieve adaptive interlimb coordination and the design principle for the control system of legged robots

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

<div><p>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.</p></div

Evolution of the oscillator phases as a result of sensory feedback at each event.

<p>The sensory feedback provided at each event changes the relative phases.</p

Touchdown and liftoff events for the direct wave gait.

<p>Black and grey legs represent the stance and swing legs, respectively. Events T<i>i</i> and T(<i>i</i> + 3) (<i>i</i> = 1, 2, 3) have axial symmetry.</p

Simple physical model with rigid body and six massless spring legs.

<p>The body is represented by a flat plate here to show the geometric relationships between the model and the variables more clearly.</p

Maximum absolute eigenvalues of the direct and retrograde wave gaits of the simple model (Analysis) and the robot simulation (Simulation) for duty factor <i>β</i>.

<p><b>A</b>: <i>s</i>*/<i>a</i>* = 0, <b>B</b>: 0.15, and <b>C</b>: 0.3.</p

Physical parameters of the robot.

<p>Physical parameters of the robot.</p