Mechanical models for insect locomotion: active muscles and energy losses.

We extend the analysis of simple, energy-conserving models for the dynamics of insect locomotion in the horizontal plane developed in Schmitt and Holmes (2000a,b, 2001), where gaits characteristic of steady cockroach running and turning were evoked. In this paper, we include dissipation and energy inputs via active "muscles" in three forms: via prescribed torques at the "hip" pivot, via an active spring element of variable length, and via a pair of Hill-type muscle models representing an extensor/flexor system. Due to mechanical feedback of passive elastic forces, the stable gaits of the conservative models are preserved, and now energy input and absorption balances to additionally stabilize a preferred speed, with only modest neural sensing and feedback being required. However, these bipedal models still cannot simultaneously match observed moment-yaw magnitudes and fore-aft dynamics.