Dom, cars don't fly! -- Or do they? In-Air Vehicle Maneuver for High-Speed Off-Road Navigation

1. Problem Statement

High-speed off-road navigation on uneven terrain often results in vehicles becoming airborne. While traditional off-road autonomy systems assume vehicles remain in contact with the ground (limiting speed to avoid rollovers or getting stuck), aggressive navigation requires leveraging terrain features to "fly" over obstacles to save time.

The core challenge addressed is controlling a ground vehicle's attitude (roll, pitch, yaw) while airborne using only existing ground vehicle controls (throttle and steering).

• The Constraint: Once airborne, the vehicle is under-actuated. Gravity dictates translational motion, and standard controls (throttle/steering) are designed for ground traction, not aerial dynamics.
• The Risk: Improper landing poses (e.g., nose-diving, tail-down, or rolling sideways) can cause catastrophic failure, mission termination, or vehicle damage.
• The Gap: Existing planners either avoid airborne states or pre-plan trajectories assuming simple gravity-based flight, lacking strategies for active in-air control to ensure a safe landing configuration.

2. Methodology

The authors propose a novel framework consisting of a hybrid dynamics model and a specialized motion planner.

A. Physics Principles of In-Air Control

The paper establishes that ground vehicle controls can influence aerial attitude through two physical mechanisms:

1. Inertial Effect: Accelerating or decelerating the wheels (changing RPM) generates reaction torques on the chassis due to the conservation of angular momentum.
2. Gyroscopic Effect: Steering the front wheel while it is spinning creates a precession torque that rotates the chassis.

• Note: Yaw control is largely unactuated by these controls and relies on initial conditions and environmental noise (e.g., air resistance).

B. PHLI: Physics and Learning based model for In-air vehicle maneuver

To accurately predict the vehicle's state during flight, the authors developed PHLI, a hybrid forward kinodynamic model:

• Hybrid Approach: Pure physics models are difficult to parameterize due to variable center of gravity, suspension movement, and tire expansion at high speeds. Pure data-driven models lack generalization.
• Structure:
  • $g_\phi$ (Data-Driven): A Multi-Layer Perceptron (MLP) that takes the current state and action as input and predicts the angular accelerations ($\ddot{roll}, \ddot{pitch}, \ddot{yaw}$). It is trained on IMU data to minimize the error between predicted and ground-truth accelerations.
  • $h_\xi$ (Physics-Based): A deterministic integrator that uses the predicted accelerations to update the state variables (angles, angular velocities, RPM, steering angle) over a time step $dt$.
• State Space ($S$): Includes roll, pitch, yaw, their angular velocities, wheel RPM, and steering angle.
• Action Space ($A$): Rate of change in wheel RPM ($\dot{rpm}$) and steering angle ($\dot{\psi}$).

C. Dom Planner: Fixed-Horizon Sampling-Based Planner

Named after Dominic Toretto (a pop-culture reference to flying cars), the Dom Planner is designed for the unique constraints of the "landing window."

• Fixed-Horizon: Unlike standard receding-horizon planners (like MPC), this planner plans over a fixed time window $T$ defined by the time remaining until landing. The goal is to reach a specific state exactly at time $T$.
• Sampling Strategy: The planner samples $N$ action sequences (combinations of $\dot{rpm}$ and $\dot{\psi}$) over the horizon.
• Cost Function: A weighted sum of state errors. Crucially, the weights $w_i(t)$ are time-dependent:
  • Early in flight: Prioritize aligning angles (roll/pitch) to the target.
  • Late in flight: Prioritize minimizing angular velocities and RPM to ensure a soft, flat landing.
• Feasibility Check: The planner verifies if the sampled trajectory can reach the goal within the remaining time, allowing for alternate goals if the primary one is unreachable to mitigate impact.

3. Key Contributions

1. Hybrid Dynamics Model (PHLI): A novel model combining physics principles (inertial/gyroscopic effects) with data-driven learning to predict in-air vehicle dynamics using only throttle and steering inputs.
2. Dom Planner: A fixed-horizon, sampling-based motion planner specifically designed to converge to a safe landing configuration within a strict, short time window.
3. Experimental Validation: Comprehensive testing on a 1/5th-scale vehicle using a 2-axis gimbal (to simulate weightlessness) and real-world outdoor ramp jumps, demonstrating the feasibility of "flying" ground vehicles.

4. Experimental Results

The system was tested on a Losi DBXL E2 vehicle (top speed 80+ km/h) against a baseline PID controller.

• Indoor Experiments (Gimbal Platform):

  • Trajectory Tracking: Dom Planner tracked continuous roll/pitch trajectories with significantly lower error (0.23 rad vs. 0.69 rad for PID) and 100% success rate (5/5) compared to PID (2/5).
  • Rapid State Change: Dom Planner reached random goal states faster (12.4s vs. 23.7s) and with higher precision.
  • Timed Goal Reaching: Successfully reached specific states at exact time points, a capability PID failed to achieve reliably.
  • State Stability: Under external disturbances, Dom Planner recovered 3x faster (0.74s vs. 1.20s) with lower latency.

• Outdoor Experiments:

  • The vehicle was launched off a 45° ramp at ~14 m/s.
  • Dom Planner successfully controlled the vehicle mid-air to land flat (zero roll/pitch) with wheel RPM set to 1000 to cushion the impact.
  • The system generalized well to real-world disturbances (air resistance, uneven weight distribution) without retraining.

5. Significance

This work fundamentally shifts the paradigm of off-road autonomy:

• Safety at Speed: It enables robots to navigate at physically feasible maximum speeds by actively managing the risks of airborne phases rather than avoiding them.
• Control Innovation: It proves that standard ground vehicle actuators (throttle/steering) are sufficient for complex 3D aerial maneuvers if the dynamics are correctly modeled and planned for.
• Mission Efficiency: By allowing vehicles to "fly" over obstacles rather than slowing down or detouring, mission completion times can be significantly reduced in time-sensitive scenarios.

In conclusion, the paper demonstrates that "cars do fly" in a controlled, autonomous manner, bridging the gap between ground robotics and aerial maneuvering through advanced kinodynamic modeling and planning.