Learning Parameter-Efficient Markovian Quadrotor Dynamics Models

Abstract

Operation of quadrotors through high-speed, high-acceleration maneuvers remains a challenging problem due to the complex aerodynamics in this regime. While standard physical models suffice for control in near-hover conditions, the primary challenge in executing aggressive trajectories is obtaining a model for the quadrotor dynamics that adequately models the aerodynamic effects present, including lift, drag, propeller interactions, and propeller downwash. Previous approaches have incorporated neural networks to learn the residual dynamics as a function of a sliding window of the most recent quadrotor states, eschewing the Markovian property traditionally associated with a state, or equivalently, expanding the size of the implicit Markovian state by a multiplicative factor equal to the length of the sliding window.

In this work, we propose a two-stage approach to fitting the residual dynamics unaccounted for by a simple physical model while retaining a concise Markovian state. (1) We fit an 18-parameter symmetric quadratic function to model aerodynamic forces on the quadrotor (2) The remaining dynamics are accounted for by additional parameters representing the evolution of a d-dimensional latent state in concert with the physical state, where d is a hyperparameter. We train models with these components to fit trajectory data from Bauersfeld et al. [1] using PyTorch, an automatic differentiation software. Under this model, we retain a Markovian state smaller than that of sliding window approaches by a factor of 16 while achieving strong fitting results. We run ablation tests to demonstrate that the addition of the state augmentation results in a more robust and accurate dynamics model, able to compensate for the removal of explicit modeling of blade flapping, and to an extent even the aerodynamic force fitting.

[1] Leonard Bauersfeld, Elia Kaufmann, Philipp Foehn, Sihao Sun, and Davide Scaramuzza. Neurobem: Hybrid aerodynamic quadrotor model. 07 2021. doi: 10.15607/RSS.2021.XVII.042.