Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane

This dissertation studies the dynamics and stability of legged locomotion in the horizontal plane. Motivated by experimental studies of insects, we develop a three-degree-of freedom rigid body model with the tripod support stance phases replaced with a single ‘effective’ massless compliant leg placed in contact with, and lifted from, the ground in a stereotypical manner requiring minimal sensory feedback. The model is free to rotate and translate on a frictionless plane, subject to intermittent constraints due to foot placement.; Initially, we study the behavior of the model as it is subjected to prescribed forces at the feet, characteristic of force profiles for a summed tripod of legs. We find that behavior is very sensitive to leg touchdown position and force orientation. It is found that while nonrotating forces always yield unstable gaits, allowing the forces to rotate with the body can produce stable, albeit unrealistic motions for large leg touchdown angles.; The passive models considered next incorporate mechanical feedback of force directions and magnitudes in an energetically conservative framework, through the representation of the virtual leg as a linear elastic spring. The resulting mechanical systems exhibit periodic gaits whose stability characteristics are due to intermittent foot contact, and are largely determined by geometrical criteria. One of the major findings is that these models belong to a class of mechanical models for which neural or other detailed feedback is not necessary for stability, The purely mechanical effect of angular momentum transfer from foot to foot can produce strong asymptotic stability of mass center heading and body angular velocity.; Subsequently, we include dissipation and energy inputs via active muscles in two forms: via prescribed torques at the ‘hip’ pivot, and via an active spring element of variable length. We again find stable gaits, but now with the additional effect of speed stabilization.; Finally, we discuss the relevance of our idealized models to experiments and simulations on insect running, showing that their gait and force characteristics match observations reasonably well. We perform parameter studies and suggest that our model is relevant to the understanding of locomotion dynamics across species.