A Neural Network Approach towards Real-Time Knot Point Density Estimates for the Nonlinear Quadrotor

Autonomous systems that navigate their environment need methods to quickly assess the feasibility and safety of desired trajectories. Traditional solutions that rely on numerical integration can be computationally heavy, while fast data-driven surrogates lack the formal guarantees that numerical approaches provide. This work demonstrates a framework that uses (1) a neural network with a spectral backbone to learn trajectories and quantile bands with built-in constraints (initial conditions and stability); (2) a modified conformal quantile regression to provide calibrated, joint trajectory-level coverage; and (3) interval arithmetic to extend noise-free coverage guarantees to control points. After refactoring the network for inference, the trajectory inference time for a quadrotor under a closed-loop linear quadratic regulator is 3.45ms on a Raspberry Pi Zero 2 W. The total pipeline time, including trajectory inference time, is 9.81ms, or approximately 100~Hz, consistent with typical control rates.

We present an algorithm for efficient domain-adaptive policy learning via kernel representations. Learning domain-adaptive policies is challenging since it requires an environment representation that is both sufficiently expressive to model complex sim-to-real gaps during offline training, and computationally efficient enough to support rapid online adaptation during deployment. For instance, a quadrotor may encounter time-varying, non-stationary disturbances, such as sudden gusts of wind, payload shifts, or transitions between distinct flight regimes with and without ground effects. To address these challenges, we model unknown disturbances using a differentiable kernel approximation based on random Fourier features. During the offline training phase, we randomly sample kernel coefficients and bandwidth parameters to generate a rich diversity of disturbance profiles. We then optimize the control policy via differentiable simulation with analytical gradients, a process that takes only 50 seconds of training time on an RTX 4090 GPU. During hardware deployment, the policy adapts to non-stationary environments in real time by updating both the kernel coefficients and bandwidth through online least-squares estimation. We evaluate our method on quadrotor trajectory tracking tasks across high-fidelity numerical simulations and hardware experiments using Crazyflie, subjected to various disturbances, including complex aerodynamic effects, wind, ground effects, and payload fluctuations.

Quadrotors flying in tight formations are severely affected by turbulent aerodynamic interactions, such as downwash, that can cause catastrophic collisions if left unmodeled. To compensate for these effects, we propose a physics-informed residual dynamics learning framework that captures complex aerodynamic interactions while ensuring the joint multi-quadrotor system remains differentially flat. We leverage this preserved flatness to design a computationally efficient feedback linearization controller that is easily tunable with linear control techniques and cancels aerodynamic disturbances via feedforward compensation. Hardware experiments demonstrate our framework reduces average tracking errors by 31% compared to nominal baselines. Crucially, our lightweight approach matches the tracking performance of state-of-the-art nonlinear model predictive control (NMPC) while requiring an order of magnitude less computation. We are the first to show that stable, tight formation flight can be achieved with under 30 seconds of training data and a 5ms loop rate, unlocking high-fidelity aerodynamic compensation for compute-constrained flight stacks.