A Hamiltonian Neural Differential Dynamics Model and Control Framework for Autonomous Obstacle Avoidance in a Quadrotor Subject to Model Uncertainty

Establishing precise and reliable quadrotor dynamics model is crucial for safe and stable tracking control in obstacle environments. However, obtaining such models is challenging, as it requires precise inertia identification and accounting for complex aerodynamic effects, which handcrafted models struggle to do. To address this, this paper proposes a safety-critical control framework built on a Hamiltonian neural differential model (HDM). The HDM formulates the quadrotor dynamics under a Hamiltonian structure over the SE(3) manifold, with explicitly optimizable inertia parameters and a neural network-approximated control input matrix. This yields a neural ordinary differential equation (ODE) that is solved numerically for state prediction, while all parameters are trained jointly from data via gradient descent. Unlike black-box models, the HDM incorporates physical priors—such as SE(3) constraints and energy conservation—ensuring a physically plausible and interpretable dynamics representation. Furthermore, the HDM is reformulated into a control-affine form, enabling controller synthesis via control Lyapunov functions (CLFs) for stability and exponential control barrier functions (ECBFs) for rigorous safety guarantees. Simulations validate the framework’s effectiveness in achieving safe and stable tracking control.