How Tuning, Reference Preview, Actuator Modeling, and Fallback Policies Change Quadrotor Controller Comparisons: A Reproducible Simulation Study

Xuan-Quy Dao; Le-Minh Nguyen; Ngoc-Bich Le

cs.ROOct 26, 2026

How Tuning, Reference Preview, Actuator Modeling, and Fallback Policies Change Quadrotor Controller Comparisons: A Reproducible Simulation Study

Authors: Xuan-Quy Dao, Le-Minh Nguyen, Ngoc-Bich Le

Organizations: Eastern International University Binh Duong, Vietnam · Industrial University of Ho Chi Minh City Ho Chi Minh City, Vietnam

Abstract

Quadrotor controller comparisons commonly report a single tracking error, although the resulting ranking also depends on tuning effort, reference information, actuator prediction, optimizer fallback, and command timing. We quantify these effects for cascade PID, hover LQR, boundary-layer sliding-mode control (BL-SMC), linear MPC with LQR fallback (LMPC-F), a preview-enabled LMPC-F, and a geometric $SO(3)$ controller on a common nonlinear plant with rotor gyroscopic coupling, motor lag, and saturation. A primary study (556 episodes at 50Hz) combines matched twelve-candidate tuning, 400 paired evaluation episodes, and a 48-cell MPC factorial; a confirmation study (1462 episodes) repeats the evaluation on 50 fresh realizations with tuning budgets of 12, 24, and 48 candidates. A matched twelve-candidate tuning protocol changed the mean-RMSE ordering obtained with the fixed baseline settings, moving BL-SMC from last to first; the new ordering recurred on the fresh realizations, and a 48-candidate budget left it unchanged. Reference preview substantially reduced MPC tracking error and, on the figure-eight task, removed fallback activity. On an abrupt step, the outcome depended on the interplay between fallback policy, predictor, and actuator authority. Command timing also changed the outcome: replaying measured command-call delays terminated three of four nominal MPC configurations on a desktop computer and all four on a Raspberry Pi5, whereas capping the solver at 100 iterations removed every deadline miss in the tested nominal timing profiles. Controller rankings therefore depend not only on tracking accuracy but also on the tuning protocol, reference information, fallback behavior, and implementation timing. We propose a reporting checklist covering tracking accuracy, tuning effort, completion and failure rates, fallback activity, applied-input variation, and command timing.

Figures & tables

Framework	Plant	Focus	Evaluation design
Martini et al. [ 20 ]	Nonlinear quadrotor, motor lag and saturation	Linear and nonlinear controllers	Seven architectures, six missions
Safe-Control-Gym [ 21 ]	Cart-pole, 1D/2D quadrotor	Constraints, disturbances, safe learning	Reduced-dimensional tasks
gym-pybullet-drones [ 22 ]	PyBullet multi-rotor	Learning-based, multi-agent control	Gym environments
Zhang et al. [ 23 ]	RotorPy quadrotor	Adaptive vs. non-adaptive control, stress, delays	Control-library comparison
This study	16-state plant with rotor lag, saturation, gyroscopic coupling	Tuning budget, preview, predictor, fallback, tilt constraints, timing	Paired randomized evaluation, factorial MPC contrasts, measured-delay replay

Table 1: Documented features of related quadrotor benchmark frameworks and of the present study.

Symbol	Value	Unit
$m$	0.468	kg
$l$	0.225	m
$g$	9.81	m/s 2
$I_{xx},I_{yy}$	$4.856\times 10^{-3}$	kg m 2
$I_{zz}$	$8.801\times 10^{-3}$	kg m 2
$k$	$2.98\times 10^{-6}$	N s 2

Table 2: Physical and numerical parameters. Physical coefficients follow [ 35 ] ; actuator lag and speed ceiling are assumed.

Panel of Figure 1 — Figure 1: Shared evaluation pipeline. All controllers use the same plant, allocator, motor model, and 50 Hz clock. † LMPC-F only. ‡ Active only in the timing replay of Section 4.6 .

Method	Settings	Dev.+val.	Selected ID	Val. score	Wall min
PID	12	24 + 3	11	0.187	1.2
LQR	12	24 + 3	8	0.225	1.1
SMC	12	24 + 3	10	0.119	1.2
MPC	12	24 + 3	3	0.354	2.2

Table 3: Matched tuning budget. Each method has 12 candidate settings (two development episodes each) and three validation finalists. IDs are zero-based. Wall time sums concurrent worker time.

Track	Method	Complete	Fail	Failure CI (%)	Mean RMSE [95% CI] (m)	Mean $V$ (s -1 )
fixed	PID	50/50	0/50	[0.0, 7.1]	0.372 [0.359, 0.387]	0.140
fixed	LQR	50/50	0/50	[0.0, 7.1]	0.300 [0.285, 0.315]	1.710
fixed	SMC	50/50	0/50	[0.0, 7.1]	1.105 [0.795, 1.453]	0.474
fixed	MPC	50/50	0/50	[0.0, 7.1]	0.396 [0.380, 0.413]	400.873
tuned	PID	50/50	0/50	[0.0, 7.1]	0.226 [0.218, 0.235]	0.335
tuned	LQR	50/50	0/50	[0.0, 7.1]	0.238 [0.226, 0.250]	1.588

Table 4: Evaluation of complete controller implementations over 20 s (50 paired realizations per method and track). RMSE and

V

use complete episodes. Failure intervals are exact (Clopper–Pearson) 95%; RMSE intervals are episode-bootstrap 95%. Zero observed failures does not imply zero risk.

Method	$\Delta$ RMSE (m)	95% CI	$\Delta V$ (s -1 )	95% CI
PID	$-0.146$	[ $-0.152$ , $-0.141$ ]	0.195	[0.170, 0.224]
LQR	$-0.062$	[ $-0.066$ , $-0.059$ ]	$-0.122$	[ $-0.149$ , $-0.099$ ]
SMC	$-0.990$	[ $-1.331$ , $-0.688$ ]	0.738	[0.634, 0.856]
MPC	$-0.019$	[ $-0.026$ , $-0.011$ ]	$-37.468$	[ $-99.309$ , 30.538]

Table 5: Tuned minus fixed paired differences (50 both-complete pairs per method; bootstrap 95% CIs, unadjusted).

Figure 2: Left: tuned-minus-fixed RMSE differences for each realization (dots), with paired mean and bootstrap 95% interval (black); the symmetric-log axis preserves the SMC tail. Right: failure counts out of 50 for every method and track, with exact 95% binomial intervals.

Method	Fixed: RMSE [CI] (m), Fail	Budget 12 (m)	Budget 24 (m)	Budget 48 (m)	$V_{12}$ (s -1 )	FB 12 (%)
PID	0.385 [0.363, 0.408], 0	0.231 [0.219, 0.242]	0.231 [0.219, 0.242]	0.223 [0.212, 0.234]	0.332	–
LQR	0.295 [0.283, 0.307], 0	0.235 [0.225, 0.246]	0.235 [0.225, 0.246]	0.235 [0.225, 0.246]	1.530	–
BL-SMC	1.096 [0.791, 1.437], 2	0.128 [0.113, 0.146]	0.128 [0.113, 0.146]	0.128 [0.113, 0.146]	1.175	–
LMPC-F	0.385 [0.371, 0.399], 0	0.370 [0.356, 0.383]	0.352 [0.339, 0.364]	0.351 [0.340, 0.363]	193.6	5.7
LMPC-F+P	0.301 [0.289, 0.313], 0	0.268 [0.257, 0.280]	0.249 [0.238, 0.259]	0.249 [0.238, 0.259]	1.299	0.0
Geometric	0.544 [0.499, 0.593], 0	0.341 [0.314, 0.369]	0.345 [0.317, 0.376]	0.345 [0.317, 0.376]	0.171	–

Table 6: Confirmation study on 50 fresh realizations (Section 4.4 ). Mean RMSE over complete episodes with bootstrap 95% CI; “Fail” counts terminations out of 50. Budget columns use the setting selected from the first 12, 24, or 48 candidates; identical selections give identical values.

V

and fallback percentage refer to the 12-candidate selection.

Figure 3: Confirmation study on 50 fresh realizations: mean RMSE with bootstrap 95% intervals (left) and mean applied-input variation (right) for fixed settings and for the settings selected with budgets of 12, 24, and 48 candidates. Both axes are logarithmic.

Case	Preview	Predictor	Fallback	Outcome	Post RMSE (m)	FB (%)	Pred. error (m)
RA	no	motor	projected	F 3.44	2.837 ∗	11.6	0.00005
RA	no	motor	raw	F 4.32	2.521 ∗	29.6	0.00062
RA	no	rigid	projected	F 3.46	2.830 ∗	7.5	0.00007
RA	no	rigid	raw	F 4.62	2.277 ∗	30.7	0.00205
RA	yes	motor	projected	complete	0.512	1.4	0.00001
RA	yes	motor	raw	F 4.36	2.387 ∗	34.4	0.00059

Table 7: Abrupt-step factorial (Matrix A, fixed weights, hard-initial tilt). “F

t

” denotes termination at

t

s; starred RMSE values are partial post-step diagnostics excluded from ranking. FB: percentage of fallback calls. Pred. error: mean one-step position-prediction error evaluated along each configuration’s own trajectory. Because trajectories and operating states differ across configurations, these values are descriptive and should not be interpreted as a matched-state comparison of predictor accuracy.

Figure 4: Abrupt step with scheduled preview in the reduced-authority (RA) case. The dashed trace (motor predictor, projected fallback) is the only RA configuration that completes. All variants share the allocator and plant; crosses mark terminations. The input-increment ratio is normalized by the componentwise QP limits

d_{u}

; bottom rows mark fallback calls. Projection restricts the requests but not the nonlinear state evolution.

Preview	Tilt policy	Outcome	Post RMSE	Max slack (rad)
no	hard-initial	F 4.62	2.277 ∗	0.00000
no	hard-future	F 4.62	2.277 ∗	0.00000
no	soft-future	F 4.62	2.278 ∗	0.00341
yes	hard-initial	F 3.36	2.787 ∗	0.00000
yes	hard-future	F 3.36	2.787 ∗	0.00000
yes	soft-future	F 6.44	2.679 ∗	0.12700

Table 8: RA abrupt step, rigid predictor, raw fallback (Matrix B). Hard-future omits only the

j=0

tilt bound; soft-future allows penalized slack. Starred values are partial.

Case	Prev.	Pred.	P99 (ms)	Miss (%)	Window (s)	Replay	Late/used	P99 (ms)	Miss (%)	Window (s)	Replay	Late/used
			Desktop					Raspberry Pi 5
nominal	no	rigid	101.8	8.9	20.00	F 3.56	13/178	121.1	9.6	20.00	F 3.58	14/179
nominal	yes	rigid	100.1	6.9	20.00	F 2.88	8/144	39.3	2.1	20.00	F 2.88	9/144
nominal	no	motor	32.2	1.5	20.00	complete	15/1000	37.4	1.6	20.00	F 3.74–3.80	16–17/187–190
nominal	yes	motor	95.1	5.9	20.00	F 3.10	26/155	147.5	11.1	20.00	F 3.60–3.80	35–41/180–190
RA	yes	rigid	43.8	7.1	3.36	no F in window	12/168	53.6	7.1	3.36	F 3.28	12/164

Table 9: Dedicated timing profiles (first call included, no warm-up) and exogenous command-arrival replay on a Windows desktop (Intel Core i5-8400) and a Raspberry Pi 5 (one pinned core, median of three repeats; ranges are shown when repeats differ). Call time includes reference and diagnostic computations and excludes setup, allocation, integration, and logging. “Window” is the profile duration available for replay; a window shorter than 20 s cannot establish completion. Late/used: deadline misses among the replayed calls.

Cap	Prev.	Pred.	P99 (ms)	Max (ms)	Miss (%)	Cap hits	Fallback (%)	No-delay RMSE (m)	Replay (3 runs)	Replay RMSE (m)
4000	no	rigid	121.1	140.6	9.6	14	3.5	0.650	F 3.58 (3/3)	–
4000	yes	rigid	39.3	123.9	2.1	6	3.0	0.568	F 2.88 (3/3)	–
4000	no	motor	37.4	191.6	1.6	4	2.0	0.568	F 3.74–3.80 (3/3)	–
4000	yes	motor	147.5	221.8	11.1	9	11.5	0.606	F 3.60–3.80 (3/3)	–
400	no	rigid	13.3	14.0	0.0	11	2.0	0.551	complete (3/3)	0.555–0.556
400	yes	rigid	13.6	14.3	0.0	34	4.0	0.537	complete (3/3)	0.542–0.550

Table 10: Deadline-aware OSQP iteration caps on the Raspberry Pi 5 (nominal step, raw fallback, three repeats each; median values, maximum over repeats for “Max”). Cap hits are calls out of 1000 that used the full iteration allowance; some of them still reached solved or solved inaccurate at the final convergence check and were accepted, so the fallback share can be smaller than the cap-hit share. RMSE is the post-step position RMSE.

Figure 5: Empirical CDF of command-call times on the Windows desktop for the nominal step (1000 sequential calls per predictor/preview variant, raw fallback). The dashed line marks the 20 ms deadline. Calls are correlated; observed maxima are not worst-case execution-time bounds.

Report	Evidence in this study
Tuning budget, search space, and selection data for every method	Ordering change, reproduced on fresh draws (Tables 4 , 6 )
Reference information (preview, feedforward) per method	Preview: 0.169 $\to$ 0.003 m; no fallback with preview (figure-eight)
Completion and failure counts with exact intervals before accuracy	0/50 primary vs. 2/50 fresh (fixed BL-SMC)
Solver acceptance rule and fallback frequency	9.6% fallback calls; 92.4% of $V$
Applied (not requested) input variation, including its distribution	LMPC-F: median 1.7, mean 194 s -1
Fallback policy and its interaction with authority	Raw 4/8 vs. projected 1/8 (step)

Table 11: Reporting checklist for quadrotor controller comparisons derived from this study.

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