Modular Deep Recurrent Neural Network: Application to Quadrotors

Nima Mohajerin; Steven L. Waslander

cs.LGSep 3, 2026

Modular Deep Recurrent Neural Network: Application to Quadrotors

Authors: Nima Mohajerin, Steven L. Waslander

Organizations: Dept. of Mechanical and Mechatronics Engineering University of Waterloo, Waterloo, ON,Canada

Abstract

A modular deep Recurrent Neural Network (RNN) is introduced to facilitate the process of deploying various architectures of RNNs, and to automatically compute derivatives for gradient-based learning methods. The modularity leads to a set of new architectures, one of which includes feedforward inter-layer connections. By adding feedforward inter-layer connections in a multi-layer RNN, it is observed that the capability of the RNN to learn and model high-order dynamics and nonlinearities is significantly improved. The problem of vanishing/exploding gradient in space for a multilayer RNN is also alleviated using feedforward connections. These results are demonstrated using a quadrotor case study, for which a model of the altitude dynamics is learned with our particular network structure, while existing methods are unable to generalize as quickly or at all.

Figures & tables

Panel of Figure 1 — Fig. 1: A 3 layer MODERNN, with output $\mathbf{y}(k)$ equal to $\mathbf{y}_{3}(k)$ .

Panel of Figure 2 — Fig. 2: A 3 layer MODERNN,with output $\mathbf{y}(k)$ equal to $\Big[\mathbf{y}_{1}^{T}(k)\hskip 5.0pt\mathbf{y}_{3}^{T}(k)$ ] .

Fig. 4: Comparison between Hessian condition numbers.

Recurrent Neural Networks

Recurrent neural networks process sequences by updating a persistent hidden state, enabling temporal modeling, memory, and streaming computation.

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First-order reinforcement learning with differentiable simulation is promising for quadrotor control, but practical progress remains fragmented across task-specific settings. To support more systematic development and evaluation, we present a unified differentiable framework for multi-task quadrotor control. The framework is wrapped, extensible, and equipped with deployment-oriented dynamics, providing a common interface across four representative tasks: hovering, tracking, landing, and racing. We also present the suite of first-order learning algorithms, where we identify two practical bottlenecks of standard first-order training: limited state coverage caused by horizon initialization and gradient bias caused by partially non-differentiable rewards. To address these issues, we propose Amended Backpropagation Through Time (ABPT), which combines differentiable rollout optimization, a value-based auxiliary objective, and visited-state initialization to improve training robustness. Experimental results show that ABPT yields the clearest gains in tasks with partially non-differentiable rewards, while remaining competitive in fully differentiable settings. We further provide proof-of-concept real-world deployments showing initial transferability of policies learned in the proposed framework beyond simulation.

Abstract

Recurrent Neural Networks

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