A two-degrees-of-freedom impulsive mechanical system known as compass-gait biped is one of the simplest models of a walking machine. Nevertheless, its dynamics is reach enough to possess various truly nonlinear phenomena observed in
physically built biped mechanisms. For instance, for shallow down-hill slopes it possesses stable and unstable limit cycles with symmetric gait patterns without any actuation. For larger slopes passive symmetric gaits are not any longer available but are replaced
with non-symmetric ones consisting of several steps in one period. The regions of attraction for stable gaits can be estimated via numerical simulations. They are quite narrow but the dynamics can tolerate a certain class of perturbations so that such a gait
is possible to reproduce in a hardware experiment. Surprisingly enough it is still not understood how much a single control input can improve versatility of an achievable passive walking gait or induce a better one.
In this talk we discuss some questions natural both for passive and actuated (with under-actuation degree one) compass-gait walkers but for which it is difficult to find comprehensive answers in the literature:
How many passive cycles might exist for the walker on a particular slope? How to find all the passive gaits? How to build a Lyapunov function to validate orbital asymptotic stability (or instability) of a passive gait? How to estimate the region of attraction
for a passive gait? How to use the active torque from a single motor to induce gaits with better characteristics than the ones for passive ones? How to stabilize such gaits, to estimate or to enlarge their regions of attraction, to reduce the sensitivity with
respect to small variations in the parameters such as the walking slope? Comprehensive constructive answers to these questions are expected to lead to new systematic approaches for mechanical-model-based analysis of existing high degrees of freedom biped walkers
and to improving and redesigning their feedback control systems.