Ballistically-Launched Multirotor Vehicles

• Ballistically-launched multirotor vehicles are deployable aerial robots designed for rapid transition from impulsive, ballistic launch to fully controlled multirotor flight.
• They employ folding architectures, passive aerodynamic stabilization, and rapid release mechanisms, achieving deployment within 137 ms and attitude settling in about 2.1 s.
• Integrated autonomous control pipelines using IMUs, vision sensors, and barometers ensure precise GPS-independent stabilization for emergency-response and exploratory applications.

Ballistically-launched multirotor vehicles are deployable aerial robots engineered for rapid transition from a ballistic trajectory to fully controlled multirotor flight. These systems integrate high-acceleration launch mechanisms, folding airframe architectures, passive aerodynamic stabilization, and automated midair transition, enabling reliable deployment from stationary or moving platforms and operation in constrained, unstructured, or GPS-denied environments (Pastor et al., 2019, Bouman et al., 2019).

1. Ballistic Launch Mechanisms and Trajectory Dynamics

Ballistic deployment is achieved via impulsive propulsion—typically pneumatic or CO₂-based—within a launch tube or barrel, imparting velocities between 12–15 m/s and peak accelerations of 21–50 g to a compacted, folded multirotor. Launch tubes range from 3 in (83 mm) to 6 in (152 mm) diameter; acceleration is transmitted via a foam-sealed, rigid carrier or direct interaction with the pressurized gas (Pastor et al., 2019, Bouman et al., 2019).

The launch phase is governed by gravity–drag dynamics:

• The forces along the trajectory are gravity ($-mg$) and a quadratic aerodynamic drag ($F_d = \frac{1}{2}\rho C_D A v^2$).
• The equations of motion in Earth-fixed coordinates:

$$m \frac{d^2x}{dt^2} = -F_d \frac{v_x}{v},\quad m \frac{d^2z}{dt^2} = - mg - F_d \frac{v_z}{v}$$

with $v = \sqrt{v_x^2 + v_z^2}$, $C_D$ (drag coefficient, canonical value ≈1.0 for folded vehicle), and $A$ (body frontal area, e.g. 0.018 m²). Analytical solutions do not exist for these dynamics under drag; numerical integration is standard for mission profile prediction (Pastor et al., 2019, Bouman et al., 2019).

2. Folding Architectures and Deployment Mechanisms

To satisfy volumetric constraints of launch tubes and withstand high G-forces, arm and fin assemblies employ spring-loaded hinges with passive, mechanical retention and rapid midair deployment. Arm hinges are preloaded (e.g., 1.04 N·m torque closed) and retained by monofilament loops or carrier assemblies. Release mechanisms include nichrome burn-wires—activated by an electrical pulse to sever the monofilament—or physical triggers upon exit from the carrier (Pastor et al., 2019, Bouman et al., 2019).

Typical deployment timing is as follows:

• Barrel exit to deployment initiation: 20–55 ms.
• Full arm and fin deployment: within 70–137 ms.
• Latching or mechanical end-stop engagement: immediate upon deployment completion.

All structural components (arms, risers, hinges) utilize impact-resistant, fiber-reinforced polymers or carbon fiber. Propeller booms are designed to fold back ≈90° beyond horizontal, permitting propeller stowage entirely within the body cylinder (Pastor et al., 2019).

3. Aerodynamic Stability and Passive Transition

Maintaining trajectory and attitude stability during the ballistic and post-deployment phases is ensured by tailored mass and aerodynamic center (AC) placement, plus strategic deployment of ring-fins and folding aerodynamic surfaces. Design criteria require the AC to be downstream of the center of mass (COM) by a margin (e.g., 5 cm or 0.14 m) for weathercock stability. Restoring moments in roll and yaw are quantified as

$$M_\phi \approx K_\phi \phi,\qquad M_\psi \approx K_\psi \psi$$

where $K_\phi = \frac{1}{2}\rho V^2 C_{L\alpha} S_f e$ and $e = x_{AC} - x_{COM}$ (Bouman et al., 2019). The ring-fin and/or deployable fins supply significant normal force and damping, yielding pitch oscillation periods on the order of 0.6 s.

Yaw inertia increases substantially (up to ×5) after arm deployment, dissipating angular momentum and promoting rapid attitude settlement. No spin stabilization is employed; empirical tests confirm self-righting in crosswinds up to 17 m/s (full scale) and pitch/yaw stabilization margins consistent with theoretical modeling (Pastor et al., 2019, Bouman et al., 2019).

4. Control Architectures and Autonomous Transition

After deployment, multirotor operation transitions from passive stabilization to full autonomous control using onboard IMUs, barometers, rangefinders, and vision sensors. The control pipeline in the SQUID prototype consists of sequential engagement:

• IMU-only attitude hold and high-thrust spin-up immediately after ballistic deceleration (settling pitch/roll within 1–2 s).
• Barometric altitude control once launch-induced pressure transients decay (~3 s).
• Vision-Inertial Odometry (VIO) initialization (e.g., ROVIO EKF) as lateral/vertical velocities subside.
• Fusion of VIO into the PX4 EKF for GPS-independent 6-DoF control.

Dynamics are controlled by cascaded position–attitude loops:

$$J \dot{\omega} = \tau - \omega \times (J \omega),\qquad \tau = -K_p(\theta - \theta_{ref}) - K_d\omega$$

Position control uses proportional-derivative terms on altitude and planar coordinates, with thrust commanded to counter both gravity and aerodynamic loads. Full position-manifold stabilization is achieved within 15 s after launch, with post-settle RMS roll/pitch error of 1.6° and positional accuracy of 0.18 m (Bouman et al., 2019).

5. Propulsion, Thrust Budget, and Energy Management

Flight modules are configured to maximize thrust-to-weight for assured midair recovery from the ballistic launch phase. For example, a 0.53 kg vehicle (including 0.2 kg payload) with four T-Motors Air40 and 5-in DAL 5050 propellers delivers ≈6.4 kgf total thrust (≈12:1 ratio), with hover achieved at ~28% throttle (Pastor et al., 2019). Larger prototypes (SQUID) employ a 3.3 kg mass, six-rotor configuration, and 6000 mAh LiPo battery.

Key equations governing required thrust:

• Hover: $F_d = \frac{1}{2}\rho C_D A v^2$0.
• Translational: $F_d = \frac{1}{2}\rho C_D A v^2$1.

Power metrics include launch energies ≈1 kJ, motor spin-up and stabilization ≈0.2 Wh, and cruise hover at ≈200 W (Bouman et al., 2019).

6. Experimental Validation and Performance Metrics

Both static and moving-platform launches have demonstrated reliable, repeatable deployment and controlled flight transition. Key validation metrics from field trials include:

Metric	Value
Launch–to–motor–spin delay	0.15 s
Complete arm/fin deployment	≤137 ms
Attitude settling time (mean $F_d = \frac{1}{2}\rho C_D A v^2$2)	2.1 s
Passive deployment reliability	100% across 20+ tests
Active stabilization success	95% (1 incident: tether break)
RMS roll/pitch error (post-settle)	1.6°
RMS horizontal position error	0.18 m

Consecutive launches at up to 50 mph (22 m/s vehicle speed) validated deployment and transition reliability. Time-resolved IMU and flight logs corroborate aerodynamic model predictions for aggressive ballistic deceleration, aerodynamic self-alignment, and attitude settlement before pilot or autonomy intervention (Pastor et al., 2019, Bouman et al., 2019).

7. Applications, Scalability, and Integration

Ballistically-launched multirotor systems have demonstrated utility in emergency-response scenarios—enabling deterministic, rapid deployment even from unsteady, moving, or cluttered platforms (e.g., vehicles, ship decks, or mobile landing assets). In planetary exploration contexts, they extend the operational range and data collection footprint of surface landers or rovers, protecting valuable primary assets by spatially isolating the multirotor in a robust ballistic arc (Pastor et al., 2019, Bouman et al., 2019).

Scaling laws (Froude, Reynolds, nondimensional mass) indicate that aerodynamic stability and deployment timescales scale predictably with vehicle size and launch energy, supporting adaptation to larger or smaller platforms.

• "Design of a Ballistically-Launched Foldable Multirotor" (Pastor et al., 2019)
• "Design and Autonomous Stabilization of a Ballistically Launched Multirotor" (Bouman et al., 2019)