Physics-Informed and Data-Driven Composite Disturbance Separation and Predictive Control for Airborne Electro-Optical Gimbals with Multiple Constraints

Yaokun Lu; Yifan Li; Zhixuan Zhang; Enmei Wang; Hao Teng; Jianzhong Qiao

cs.ROOct 26, 2026

Physics-Informed and Data-Driven Composite Disturbance Separation and Predictive Control for Airborne Electro-Optical Gimbals with Multiple Constraints

Authors: Yaokun Lu, Yifan Li, Zhixuan Zhang, Enmei Wang, Hao Teng, Jianzhong Qiao

Organizations: School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191, China · Hangzhou Innovation Institute of Beihang University, Hangzhou, 311115, China · School of Instrumentation Science and Optoelectronic Engineering, Beihang University, Beijing, 100191, China

Abstract

This paper studies the constrained pointing control problem of airborne electro-optical gimbals subjected to composite periodic and aperiodic disturbances. Under carrier vibration, input delay, and actuator constraints, achieving line-of-sight stabilization and tracking is challenging. A disturbance-separated model predictive control (MPC) scheme is proposed to compensate these heterogeneous disturbances according to their physical characteristics. An adaptive periodic observer predicts multi-harmonic vibrations over the MPC horizon using linear-regression frequency estimation. A linear observer estimates the aperiodic disturbance, and a bounded long short-term memory (LSTM) network predicts its change over the input delay. Embedding periodic predictions into the MPC model while applying aperiodic compensation outside the optimizer limits amplification of aperiodic estimation errors and improves pointing accuracy under frequency changes and parameter mismatch. On the stated headroom envelope, input-set tightening provides feasible commands within the prescribed limits, and a regional practical tracking bound is established under explicit input-sequence and predicted-state margin conditions. A UAV-mounted two-axis gimbal platform is assembled for comparative indoor hovering experiments, complemented by simulations under frequency changes and parameter mismatch. In the reported trials, the proposed method achieves yaw and pitch relative-angle root-mean-square errors (RMSEs) of 0.770 degrees and 0.350 degrees, reducing tracking errors by 25.1% and 45.9% compared with linear active disturbance rejection control.

Figures & tables

Figure 1: Proposed MPC architecture with physics-informed and data-driven disturbance separation.

	Calibrated, steady				Calibrated, switch
Method	RMSE	Rel.	Sat.	Fail.	RMSE	Rel.	Sat.	Fail.
MPC	0.389	$+24.0$	0.1	0	0.382	$+27.9$	0.1	0
MPC-DO	0.320	0	0.1	0	0.303	0	0.1	0
MPC-APDO	0.295	$-3.4$	1.2	0	0.333	$+15.4$	0.9	0
MPC with fixed frequency	0.934	$+201$	90.4	17	0.916	$+219$	90.9	11
MPC with adaptive frequency	0.898	$+188$	88.7	7	0.874	$+197$	88.3	3

Table 1: Test results over 40 runs per entry (10 seeds

\times

4 base frequencies). RMSE in deg; Rel.: paired change relative to MPC-DO (%); Sat.: share of samples with

|u|\geq u_{\max}

(%); Fail.: count of high-error runs with RMSE

\geq 1

deg.

Figure 2: Distribution of the pointing RMSE over 40 test runs on the calibrated plant (boxes: quartiles; whiskers: minimum and maximum; dotted line: 1 deg high-error threshold).

Figure 3: Representative run on the calibrated plant,

f_{0}=1

Hz with the switch to

1.6f

t=20

s (dashed vertical line): (a) tracking error, with an inset showing 16–18 s; (b) integer speed-command level of MPC-DS with the input limit and the tightened limit

u_{\max}-m

Figure 4: Frequency estimates in the run of Fig. 3 : proposed linear-regression law ( 14 ) and the gradient law of [ 41 ] , both with the same prefilter input.

Figure 5: Ablation on the calibrated plant: paired RMSE change relative to MPC-DO, without mismatch and with

\pm 30\%

parameter mismatch (hatched).

Figure 6: Mean RMSE on the calibrated plant versus the bound of the uniform mismatch in

K

\tau_{m}

and

T_{d}

(40 runs per point, parameters not retuned).

Figure 7: Experimental platform and indoor flight. (a) Hardware close-up; dashed boxes identify the SIYI ZR10 electro-optical gimbal, Intel N100 onboard computer, and LiDAR. (b) Video frame of the multirotor hovering inside a netted indoor test area.

Figure 8: Two-axis angular tracking during indoor hovering. (a)–(d) Measured angular trajectories for PID, LADRC, MPC-DS w/o LR, and MPC-DS (Proposed) over 5–28 s; the dashed circle is the reference, and black segments with open circles mark four simultaneous reference/measurement pairs in the same reference cycle. The circle-center values give the joint two-axis RMSE, defined from simultaneous yaw and pitch errors. (e), (f) Signed yaw and pitch error densities over the same interval, with colors matching (a)–(d); white dots and dark segments denote medians and interquartile ranges, and the numbers give RMSEs in degrees. Each method contributes one 30 s trial; the densities describe time samples within that trial. PID is the plain-PID trial collected in a separate flight batch.

Feedback Control

Feedback control uses ongoing measurements to adjust actions, stabilize dynamical systems, track goals, and respond to disturbances and constraints.

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Quantile-Based Command-Reserve MPC for Current-Command Gimbal Pointing

Yaokun Lu, Yifan Li, Enmei Wang, Hao Teng+2

School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191, China · Hangzhou Innovation Institute of Beihang University, Hangzhou, 311115, China · School of Instrumentation Science and Optoelectronic Engineering, Beihang University, Beijing, 100191, China

Model Predictive Control Disturbance Rejection

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This paper studies the constrained line-of-sight pointing control problem of a two-axis current-command gimbal subjected to mismatched mechanical disturbances. Friction, torque ripple, current-response lag, model mismatch, and limited drive commands make accurate pointing more challenging yet interesting. A quantile disturbance predictor is proposed to compensate predictable acceleration residuals and describe their remaining uncertainty, with the aid of learning median and outer quantiles from state, command, and reference histories. A tube-inspired model predictive controller is proposed to reserve command headroom according to prediction uncertainty, with the aid of calibrated radii and stage-dependent input margins. The median improves the nominal prediction, while the radius adapts the command reserve without adding optimization variables. A finite-horizon tube inclusion result is established for a specified linear error model and fixed ancillary policy; its conditions are distinguished from the approximations used in hardware. Native command bounds and a final command limiter keep the sent commands within their prescribed range. On a two-axis embedded platform, four controller configurations are compared in seven repeated trials each. The proposed configuration achieves a two-dimensional pointing root-mean-square error of

3.94 \pm 0.10

mrad with no command-limit samples in the evaluation windows. Its performance supports the combined use of residual prediction and adaptive command margins in the tested operating condition. Solver times and logged loop overruns are reported separately for the nominal 100 Hz implementation.

Abstract

Feedback Control

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