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

Yaokun Lu; Yifan Li; Enmei Wang; Hao Teng; Pengwei Hu; Jianzhong Qiao

cs.ROOct 26, 2026

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

Authors: Yaokun Lu, Yifan Li, Enmei Wang, Hao Teng, Pengwei Hu, 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 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.

Figures & tables

Figure 1: Conceptual architecture for current-command gimbal pointing. The predictor provides a median and outer quantiles. The adaptive command reserve sets the input margin $m_{j|k}$ . Analytical tube propagation is distinguished from the hardware command-margin implementation in Section 3.3 . The disturbance sources shown are physical sources affecting the plant; separate identification of each source is not claimed.

Figure 2: Embedded two-axis current-command gimbal platform. A Radxa X4 controller exchanges commands and measurements over CAN. The inset shows the integrated elevation drive.

Method	Azimuth RMSE (mrad)	Elevation RMSE (mrad)	2D RMSE (mrad)	Command-limit samples
MPC	$4.60\pm 0.17$	$5.88\pm 1.18$	$7.49\pm 1.03$	$3.9\pm 2.7$
MPC-P	$2.92\pm 0.16$	$3.54\pm 0.39$	$4.59\pm 0.35$	$1.3\pm 1.3$
Fixed Tube-MPC	$4.55\pm 0.06$	$4.06\pm 0.63$	$6.11\pm 0.43$	$0.0\pm 0.0$
Proposed	$2.86\pm 0.06$	$2.70\pm 0.20$	$3.94\pm 0.10$	$0.0\pm 0.0$

Table 1: Hardware comparison: mean

\pm

sample standard deviation over seven trials per configuration; statistics use

t\geq 5

s in each

18

s run.

Figure 3: Representative hardware trial. (a,b) Processed acceleration-residual labels, logged median predictions, and calibrated symmetric prediction bands for azimuth and elevation. The nominal scalar target is

90\%

; the reported coverage is empirical. The right panels show residual prediction error normalized by the radius. (c) Angle tracking and pointing-error distributions.

Figure 4: Representative four-configuration hardware comparison under the outer command limits. (a) Two-dimensional pointing error. (b) Azimuth command; markers denote samples at the command boundary. (c) Pointing-error distributions. This comparison includes conditional component comparisons, but does not isolate adaptive versus fixed radii at a shared median correction.

Quantity	Value
Maximum MPC solve time	$2.789$ ms
Maximum active-loop duration	$44.012$ ms
Overruns, entire runs	$100/12\,588$ ( $0.794\%$ )
Overruns, $t\geq 5$ s	$70/9\,094$ ( $0.770\%$ )

Table 2: Logged timing for Proposed across seven trials. An overrun means the measured active-loop work exceeds

10

ms.

Model Predictive Control

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Feedback Control Disturbance Rejection Model Predictive Control

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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.

Abstract

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