Body torsional flexibility effects on stability during trotting and pacing based on a simple analytical model

Quadruped animals use not only their legs but also their trunks during walking and running. Although many previous studies have investigated the flexion, extension, and lateral bending of the trunk, few studies have investigated the body torsion, and its dynamic effects on locomotion thus remain unclear. In this study, we investigated the effects of body torsion on gait stability during trotting and pacing. Specifically, we constructed a simple model consisting of two rigid bodies connected via a torsional joint that has a torsional spring and four leg springs. We then derived periodic solutions for trotting and pacing and evaluated the stabilities of these motion types using a Poincaré map. We found that the moments of inertia of the bodies and the spring constant ratio of the torsional spring and the leg springs determine the stability of these periodic solutions. We then determined the stability conditions for these parameters and elucidated the relevant mechanisms. In addition, we clarified the importance of the body torsion to the gait stability by comparison with a rigid model. Finally, we analyzed the biological relevance of our findings and provided a design principle for development of quadruped robots.