Dual Gradient Consensus for Adaptive Learning to Transient Out-of-Distribution Disturbances in Quadrotor Control

Mingtian Tan; Vasileios Tzoumas

cs.ROOct 25, 2026

Dual Gradient Consensus for Adaptive Learning to Transient Out-of-Distribution Disturbances in Quadrotor Control

Authors: Mingtian Tan, Vasileios Tzoumas

Abstract

Quadrotor trajectory tracking under unmodeled disturbances often relies on online residual adaptation, but short out-domain residuals can corrupt the learned disturbance model when constant-step updates treat every residual gradient uniformly. We propose Dual Gradient Consensus (DGC), an adaptive-learning method for mixed in-domain/out-domain disturbances that retains the random Fourier feature model, offline BPTT policy, and least-squares adaptation of a prior domain-adaptive residual policy (DAPL) while modifying the online update step size. DGC compares each residual gradient with long- and short-term gradient memories, classifies the current adaptation regime, and uses a confidence map to suppress unreliable updates while recovering adaptation after persistent domain shifts. We evaluate DGC in numerical quadrotor trajectory tracking under four residuals that mix an in-domain component with short out-domain events. Compared with $L_1$ -augmented MPC, RFF-based MPC, constant-step DAPL, and a frozen-parameter baseline, DGC achieves the lowest mean position RMSE in all four cases.

Figures & tables

Fig. 1: Overview of Dual Gradient Consensus for online adaptive learning under mixed in-domain/out-domain disturbances. Left: the residual pipeline forms a packed gradient $g_{t}$ from the RFF predictor, a low-pass residual, and the least-squares loss. Center: Long-Term Gradient (LTG) and Short-Term Gradient (STG) memories classify $g_{t}$ into four regimes; only $(0,1)$ hands LTG over to STG. Right: a confidence map sets the step length of the $(\hat{\bm{\alpha}},\hat{\sigma})$ update on mixed in-domain/out-domain residuals. Bottom: the applied learning step size remains high in-domain, drops on transients, and recovers after a completed domain shift.

$s^{\mathrm{L}}$	$s^{\mathrm{S}}$	Meaning	Action
$1$	$1$	In-domain	Keep LTG; $\varphi$ -step
$0$	$0$	Shift/noise	Keep LTG; no step
$1$	$0$	Transient	Keep LTG; $\varphi$ -step
$0$	$1$	New domain	LTG $\leftarrow$ STG; $\varphi$ -step

TABLE I: Two-bit classification of

g_{t}

in Definition 1 . (agreement is

\cos(\cdot,\cdot)>0

Symbol	Meaning	Value
$N_{\mathrm{L}}$	LTG length	$20$
$N_{\mathrm{S}}$	STG length and LPF ( 5 )	$5$
$\tau$	Center of $\varphi$	$0.5$
$k$	Slope of $\varphi$	$10$
$\varepsilon_{\min}$	Hold threshold on raw $\\|\hat{\bm{h}}-\bm{h}\\|$	$0.2$
$W$	Moving-average window of $\eta$	$10$

TABLE II: Hyper-parameters of Dual Gradient Consensus.

Fig. 2: Representative rollouts for the four cases in Section IV-C . Columns: (a) step domain shift with out-domain pulse (Case 1); (b) stationary domain with out-domain pulses (Case 2); (c) periodic domain shift with out-domain pulse (Case 3); (d) ramp domain shift with out-domain pulse (Case 4). Rows, top to bottom: applied disturbances (one coordinate,

\mathrm{m/s}^{2}

), residual prediction error (

\mathrm{m/s}^{2}

), position tracking error (

\mathrm{m}

), and Dual Gradient Consensus rates

\eta_{\bm{\alpha}}

and

\eta_{\sigma}

. Shaded bands mark impulse intervals. Controllers: MPC (L1-E), MPC (RFF), DAPL, DAPL (w/o

\sigma

\bm{\alpha}

update), and DGC (ours).

Case	1	2	3	4
MPC (L1-E)	$1.921$ $\pm 0.524$	$0.017$ $\pm 0.002$	$0.312$ $\pm 0.037$	$0.190$ $\pm 0.030$
MPC (RFF)	$5.660$ $\pm 1.508$	$0.022$ $\pm 0.002$	$0.207$ $\pm 0.036$	$0.565$ $\pm 0.496$
DAPL	$0.929$ $\pm 0.525$	$0.162$ $\pm 0.044$	$0.255$ $\pm 0.056$	$0.133$ $\pm 0.077$
DAPL (w/o $\sigma$ , $\bm{\alpha}$ update)	$1.812$ $\pm 0.001$	$0.052$ $\pm 0.002$	$0.191$ $\pm 0.001$	$0.531$ $\pm 0.001$
Ours	$\mathbf{0.478}$ $\pm 0.006$	$\mathbf{0.006}$ $\pm 0.001$	$\mathbf{0.145}$ $\pm 0.004$	$\mathbf{0.068}$ $\pm 0.010$

TABLE III: Position RMSE (m) for the four cases in Section IV-C , mean

\pm

standard deviation over ten rollouts. Best mean in each column in bold .

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Quadrotor control studies how to stabilize, guide, and adapt aerial robots under demanding flight conditions and physical constraints.

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Efficient Domain-Adaptive Policy Learning via Kernel Representation with Application to Quadrotor Control under Non-Stationary Disturbances

Hongyu Zhou, Mingtian Tan, Vasileios Tzoumas

University of Michigan, Ann Arbor

Quadrotor Control Adaptive Control

Open paper AskPDF arXiv

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.

Abstract

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