  This work tries to contribute to the design of legged robots with
capabilities boosted through thruster-assisted locomotion. Our long-term goal
is the development of robots capable of negotiating unstructured environments,
including land and air, by leveraging legs and thrusters collaboratively. These
robots could be used in a broad number of applications including search and
rescue operations, space exploration, automated package handling in residential
spaces and digital agriculture, to name a few. In all of these examples, the
unique capability of thruster-assisted mobility greatly broadens the locomotion
designs possibilities for these systems. In an effort to demonstrate thrusters
effectiveness in the robustification and efficiency of bipedal locomotion
gaits, this work explores their effects on the gait limit cycles and proposes
new design paradigms based on shaping these center manifolds with strong
foliations. Unilateral contact force feasibility conditions are resolved in an
optimal control scheme.
