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

Highlights: What are the main findings? A Hamiltonian neural differential model (HDM) is proposed, which formulates quadrotor dynamics on the SE(3) manifold with learnable inertia parameters and a neural network-approximated control input matrix. The model is reformulated into a control-affine form, enabling controller synthesis withcontrol Lyapunov functions (CLFs) for stability and exponential control barrier functions(ECBFs) for rigorous safety guarantees. What are the implications of the main findings? The HDM provides a physically interpretable and plausible dynamics representation by incorporating physical priors (e.g., SE(3) constraints, energy conservation), overcoming the limitations of handcrafted and black-box models. The integrated safety-critical control framework ensures stable and safe trajectory tracking in obstacle-dense environments, advancing the reliability of autonomous quadrotor operations. 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 (Formula presented.) 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 (Formula presented.) 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.