Exact Thrust-Reversal Limits of Bidirectional Propellers under Bounded Motor Inputs

Bidirectional thrust grants quadrotors a second equilibrium condition and increased control authority, expanding the envelope of possible aggressive maneuvers and enabling inverted flight, perching, and sensing. Prior geometric control approaches extend differential flatness through Hopf fibration-based attitude representations to support bidirectional thrust, but struggle with actuator saturation and motor reversal delay during inversions, requiring heuristic thrust posture scheduling and waypoint tuning. We propose a learning-based framework that modulates a constant reference trajectory to perform compact, position-constrained quadrotor inversions while remaining compatible with traditional trajectory generation and tracking across flight regimes. Separate policies are trained via reinforcement learning for nominal-to-inverted and inverted-to-nominal transitions. In JAX-based simulation, the proposed method achieves the lowest position deviation and settling time across all evaluated baselines, reducing position root mean square error (RMSE) by 32% and settling time by 57% relative to the strongest optimization-based baseline. Hardware experiments demonstrate successful inversion across multiple yaw configurations with position RMSE below 0.35m, and compatibility with downstream trajectory generation and control through circular flight in both regimes. Additionally, we provide an open-source implementation of the proposed framework.

Traversing crests, ledges, and ditches at high speed often launches vehicles into the air, and a mishandled landing presents a substantial crash hazard. We show that the airborne phase is barely controllable: on a 1383 kg platform the wheel angular-momentum budget caps the recoverable pitch-rate change at roughly $9$-$13^\circ$/s in the tighter nose-up direction under drive at typical takeoff wheel speeds, and at about twice that in the reverse-inclusive braking direction; driving the wheels to their drivetrain hard limit raises the measured nose-up ceiling to only $16$-$18^\circ$/s. Takeoff pitch-rate disturbances beyond this directional budget are physically unrecoverable in flight, so the decisive leverage lies before takeoff. DART (Dual-Axis Airborne Reachability-Gated Torque-Reaction) back-propagates the landing constraint into a closed-form certified feasible-takeoff set, which supplies a conservative go/no-go condition and a pre-takeoff speed-shaping law. In flight, DART regulates pitch and roll via steer-resolved wheel-reaction torque, governed by a per-flight roll latch derived from the yaw-coupling analysis. In deterministic full-scale simulation in BeamNG.tech, a calibrated pre-takeoff speed regulator reduces touchdown speed by 36% and raises on-target landings from 0/30 to 30/30. Under the same steep-lip approach the airborne law completes 29/30 safe landings under crash-avoidance bounds versus 0/30 for reaction-wheel-style PD (RW-PD) and time-optimal bang-bang (TOBB). On banked run-ups DART holds the median pitch error at or below $2^\circ$ at every cross-slope, with the largest baseline separation at $γ=12^\circ$. Across disturbance regimes, the latch preserves pitch-only allocation on low-disturbance entries and enables dual-axis control when roll becomes binding. All results are from simulation; hardware validation remains open.

Aerodynamic promptness quantifies how rotor-speed variations generate multirotor wrench variations, but its Euclidean formulation assigns the same local cost to a given rotor acceleration at every operating speed. This work develops a capacity-aware extension for redundant multirotors with arbitrary numbers of heterogeneous rotors and wrench components. Under bounded motor torque and aerodynamic drag, each generally asymmetric instantaneous rotor-acceleration interval contains a largest zero-centered subset whose radius defines the symmetric acceleration capacity (SAC). The SAC induces a Riemannian metric on the positive-capacity rotor-speed region. Propagating its co-metric through the nonlinear rotor-speed-to-wrench differential yields a state-attached task-rate capability matrix and ellipsoid. The corresponding inverse quadratic form equals the minimum normalized rotor-acceleration effort required to realize a prescribed wrench rate, while the ellipsoid volume defines the drag-aware aerodynamic manipulability (DAAM) index. Fiberwise DAAM maximization provides a task-coordinate-invariant criterion for selecting task-equivalent actuator states; its maximizing set exists on compact regular domains and can be nonconvex and set valued. Low-dimensional two- and three-rotor studies make the resulting fiberwise geometry and parameter dependence directly visible. A complementary two-rotor use case shows how DAAM can inform a continuous allocation section subject to directional motor-torque feasibility. For two heterogeneous propulsion systems, the resulting sections reduce saturation-induced force-tracking degradation relative to the pseudoinverse in the faster command bands