A Simple Extension of Inverted Pendulum Template to Explain Features of Slow Walking

Locomotion involves complex interactions between an organism and its environment. Despite these complex interactions, many characteristics of the motion of an animal's center of mass (COM) can be modeled using simple mechanical models such as inverted pendulum (IP) and spring-loaded inverted pendulum (SLIP) which employ a single effective leg to model an animal's COM. However, because these models are simple, they also have many limitations. We show that one limitation of IP and SLIP and many other simple mechanical models of locomotion is that they cannot model many observed features of locomotion at slow speeds. This limitation is due to the fact that the gravitational force is too strong, and, if unopposed, compels the animal to complete its stance in a relatively short time. We propose a new model, AS-IP (Angular Spring modulated Inverted Pendulum), in which the body is attached to the leg using springs which resist the leg's movement away from the vertical plane, and thus provides a means to model forces that effectively counter gravity. We show that AS-IP provides a mechanism by which an animal can tune its stance duration, and provide evidence that AS-IP is an excellent model for the motion of a fly's COM. More generally, we conclude that combining AS-IP with SLIP will greatly expand our ability to model legged locomotion over a range of speeds.