Generalized Landing for Small and Micro UAS

This paper develops an approach to landing small uncrewed multirotors on inclined surfaces via backwards reachable sets. It is assumed that upon contact the vehicle's ``foot'' does not slip and is modeled as a pin joint. The backward computation has three stages: (1) beginning with the vehicle stationary with all feet on the landing surface, conservation of energy is used to compute the set of feasible vehicle states immediately post contact that result in safe landing; (2) conservation of momentum is then used to determine the pre-contact set of vehicle states that lead to the safe post-contact states; (3) finally kinematics is used to determine the trigger states: the set of that result in safe pre-contact states assuming a particular landing maneuver. This set of safe states and trigger maneuver is then tested in a higher order simulation and compared with a landing policy computed using reinforcement learning. The comparison shows that the low order approach successfully computes a landing policy for arbitrarily inclined landing surfaces and that higher order dynamics (such as impact dynamics and leg flexibility) are critical at the boundaries of the safe landing set but do not adversely affect landings triggered from near the centroid of the safe landing set.