  Contact-based decision and planning methods are becoming increasingly
important to endow higher levels of autonomy for legged robots. Formal
synthesis methods derived from symbolic systems have great potential for
reasoning about high-level locomotion decisions and achieving complex
maneuvering behaviors with correctness guarantees. This study takes a first
step toward formally devising an architecture composed of task planning and
control of whole-body dynamic locomotion behaviors in constrained and
dynamically changing environments. At the high level, we formulate a two-player
temporal logic game between the multi-limb locomotion planner and its dynamic
environment to synthesize a winning strategy that delivers symbolic locomotion
actions. These locomotion actions satisfy the desired high-level task
specifications expressed in a fragment of temporal logic. Those actions are
sent to a robust finite transition system that synthesizes a locomotion
controller that fulfills state reachability constraints. This controller is
further executed via a low-level motion planner that generates feasible
locomotion trajectories. We construct a set of dynamic locomotion models for
legged robots to serve as a template library for handling diverse environmental
events. We devise a replanning strategy that takes into consideration sudden
environmental changes or large state disturbances to increase the robustness of
the resulting locomotion behaviors. We formally prove the correctness of the
layered locomotion framework guaranteeing a robust implementation by the motion
planning layer. Simulations of reactive locomotion behaviors in diverse
environments indicate that our framework has the potential to serve as a
theoretical foundation for intelligent locomotion behaviors.
