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. One goal in developing legged robot systems is to provide a high degree of agility. Intuitively, being agile means that future states (i.e., position and velocity variables de ning snapshots of the dynamic robot as it moves) are not deterministically pre-ordained and can instead be controlled to a high degree. For example, a robot that repeats a constant, low-level gait sequence arguably lacks agility, no matter how robust it is to terrain variability. In this work, we introduce two related concepts of agility: many-to-one and one-to-many control authority. By many-to-one, we mean that a system should be capable of arriving at the same nal state (e.g., landing at the far side of a ditch-like obstacle) from a large set of initial conditions; similarly, the system should be capable of recovering from many di erent perturbations to return back to one particular, nominal gait. As a complementary notion, one-to-many agility implies that a robot starting at one particular initial condition (e.g., sit
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