Measuring the stability of highly-dynamic bipedal locomotion is a challenging but essential task for more capable human-like walking. By discretizing the walking dynamics, we treat the system as a Markov chain, which lends itself to an easy quantification of failure rates by the expected number of steps before falling. This meaningful and intuitive metric is then used for optimizing and benchmarking given controllers. While this method is applicable to any controller scheme, we illustrate the results with two case demonstrations. One scheme is the now-familiar hybrid zero dynamics approach and the other is a method using piece-wise reference trajectories with a sliding mode control. We optimize low-level controllers, to minimize failure rates for any one gait, and we adopt a hierarchical control structure to switch among low-level gaits, providing even more dramatic improvements on the system performance.
Legged systems should exploit non-steady gaits both for improved recovery from unexpected perturbations and also to enlarge the set of reachable states toward negotiating a range of known upcoming terrain obstacles. We present a 4-link planar, bounding, quadruped model with compliance in its legs and spine and describe design of an intuitive and effective low-level gait controller. We extend our previous work on meshing hybrid dynamic systems and demonstrate that our control strategy results in stable gaits with meshable, low-dimension step- to-step variability. This meshability is a first step toward enabling switching control, to increase stability after perturbations compared with any single gait control, and we describe how this framework can also be used to find the set of n-step reachable states. Finally, we propose new guidelines for quantifying "agility" for legged robots, providing a preliminary framework for quantifying and improving performance of legged systems.