DQ-MPCC: Dual-Quaternion MPCC for Quadrotor Racing

Bryan S. Guevara; Luis F. Recalde; Guanrui Li; Tiago Nascimento

cs.ROSep 29, 2026

DQ-MPCC: Dual-Quaternion MPCC for Quadrotor Racing

Authors: Bryan S. Guevara, Luis F. Recalde, Guanrui Li, Tiago Nascimento

Organizations: Laboratory of Systems and Robotics Engineering (LASER), Center of Informatics (CI), Federal University of Para´ıba (UFPB), Jo˜ao Pessoa, PB 58051-900, Brazil · Department of Robotics Engineering, Worcester Polytechnic Institute (WPI), Worcester, MA 01609, USA

Abstract

Quadrotor racing demands aggressive attitude and progress control while passing through every gate, and conventional quadrotor MPCC formulations state the prediction model in inertial coordinates and the attitude error in the body frame. We present a Dual-Quaternion Model Predictive Contouring Control (DQ-MPCC) for quadrotor racing in which the pose is a unit dual quaternion and the contouring errors are projected onto the tangent space of the dual quaternion manifold, expressed in the desired body frame: the same rigid-body dynamics as the conventional model, in unified pose-twist coordinates in the body frame. We compare DQ-MPCC against a baseline MPCC through Monte Carlo software-in-the-loop simulations and real-world racing on an eight-gate circuit of 11x4.5x3.65 m. With the same gains in simulation and hardware, DQ-MPCC keeps every crossing of its completed flights within the prescribed geometric margin, whereas the baseline exceeds it, its median worst-gate offset growing by 71.5% sim-to-real against a 10.1% decrease for DQ-MPCC. Among the configurations that keep every simulated gate crossing within the geometric margin, DQ-MPCC also reduces the minimum lap time by 6.7%, and by 10.5% in the real-world flights, while running onboard at 100 Hz.

Figures & tables

Fig. 1 : Real-world experiment of the proposed DQ-MPCC through the $8$ -gate circuit (top). The bottom plots show the gate crossings of all racing laps, with red markers for the DQ-MPCC and blue markers for the MPCC baseline.

Feature	[ 7 ]	[ 10 ]	[ 9 ]	[ 11 ]	[ 18 ]	Ours
Control type	PF	PF	PF	PF	TK	PF
Dynamics model	Bicycle	Point mass	Full 6-DoF	Full 6-DoF	Full 6-DoF	Full 6-DoF
Pose error space	$\mathbb{R}^{2}$	$\mathbb{R}^{3}$	$\mathbb{R}^{3}\!\times\!\mathfrak{so}(3)$	$\mathbb{R}^{3}\!\times\!\mathfrak{so}(3)$	$\mathfrak{se}(3)$	$\mathfrak{se}(3)$
Rotation repr.	—	—	Quat	Quat	DQ	DQ
Unified coords., body frame	—	—	✗	✗	✓	✓
Lag and cont. in $\mathfrak{se}(3)$	✗	✗	✗	✗	—	✓

TABLE I : MPCC vs DQ control formulations. Quat: unit quaternion; DQ: unit dual quaternion; PF: path following; TK: tracking. † Non-uniform grid (Section IV-B ).

\mathfrak{se}(3)

is the formulation of ( 21 ), deployed with

\bm{J}_{l}^{-1}{\approx}\bm{I}

Platform		Solver / OCP
$m$	$1.08$ kg	solver	acados SQP-RTI
$\tau_{rc}$	$30$ ms	integrator	ERK4
$f$	$[0,49.05]$ N	horizon $N$	$31$
$\|\Delta f\|$	$\leq 500$ N/s	$T_{p}$	$1.48$ s
$\|\omega_{\mathrm{cmd},i}\|$	$\leq 20$ rad/s	loop rate	$100$ Hz
$\|a_{s}\|$	$\leq 5g$	regularization	PROJECT $+$ LM ( $10^{-2}$ )

TABLE II : System and OCP Parameters.

Metric	MPCC	DQ-MPCC	exact $\bm{J}_{l}^{-1}$ †
$T_{\min}$ [s]	$3.457\,{\pm}\,0.010$	$\mathbf{3.226\,{\pm}\,0.007}$	$3.141\,{\pm}\,0.012$
$T_{\rm avg}$ [s]	$3.478\,{\pm}\,0.006$	$\mathbf{3.252\,{\pm}\,0.004}$	$3.164\,{\pm}\,0.011$
$\delta_{\max}$ [cm]	$\mathbf{{17.88}\,{\pm}\,0.62}$	${24.53}\,{\pm}\,0.73$	$24.55\,{\pm}\,0.80$
$\delta_{\rm avg}$ [cm]	$\mathbf{12.01\,{\pm}\,0.20}$	$15.85\,{\pm}\,0.20$	$15.44\,{\pm}\,0.44$
$e_{c}$ RMSE [cm]	$\mathbf{5.23\,{\pm}\,0.14}$	$12.70\,{\pm}\,0.11$	$12.04\,{\pm}\,0.22$
$e_{\ell}$ RMSE [cm]	$\mathbf{1.44\,{\pm}\,0.02}$	$1.60\,{\pm}\,0.04$	$1.57\,{\pm}\,0.04$

TABLE III : SiL racing metrics,

n{=}100

Monte Carlo seeds; median

\,\pm\,

std over completed runs; bold = better of the two deployed controllers; † = same-gains ablation with the exact coordinate ( 21 ) (Section VI ); solve times: overhead vs. DQ-MPCC measured side by side

Fig. 4 : Racing laps for MPCC vs DQ-MPCC over the contour tube and gate rings, $XY$ (top) and $XZ$ (bottom): (a) software-in-the-loop, $92$ and $90$ completed runs of the $n{=}100$ campaigns; (b) Real-world experiments, six flights per controller.

	attempts	compl. ( $3$ laps)	failed	margin comp.
MPCC	$11$	$6$	$5$	$2/6$
DQ-MPCC	$7$	$6$	$\mathbf{1}$	$\mathbf{6/6}$

TABLE IV : Real-world trial accounting (racing attempts in flight).

Metric	MPCC	DQ-MPCC	$\Delta$
$T_{\min}$ [s]	$3.872\,{\pm}\,0.032$	$\mathbf{3.464\,{\pm}\,0.010}$	$\mathbf{-10.5\%}$
$T_{\rm avg}$ [s]	$3.906\,{\pm}\,0.030$	$\mathbf{3.493\,{\pm}\,0.009}$	$\mathbf{-10.6\%}$
$\delta_{\max}$ [cm]	$30.7\,{\pm}\,1.8$	$\mathbf{22.1\,{\pm}\,1.0}$	$\mathbf{-28.1\%}$
$\delta_{\rm avg}$ [cm]	$\mathbf{13.0\,{\pm}\,0.8}$	$14.7\,{\pm}\,0.4$	$+13.1\%$
$e_{c}$ RMSE [cm]	$\mathbf{11.5\,{\pm}\,0.9}$	$14.0\,{\pm}\,0.4$	$+21.3\%$
$e_{\ell}$ RMSE [cm]	$\mathbf{4.59\,{\pm}\,0.01}$	$4.82\,{\pm}\,0.01$	$+5.1\%$

TABLE V : RW racing metrics, median

\,\pm\,

std over the six completed flights per controller.

\Delta

vs MPCC; bold = better.

Ctrl.	$\Delta T_{\min}$	$\Delta\delta_{\max}$	$\Delta e_{c}$	$\Delta\|\bm{a}\|_{p99}$	$\Delta\omega_{\rm rms}$	$\Delta L_{p}$
MPCC	$+12.0\%$	$+71.5\%$	$+121\%$	$+17.5\%$	$+26.2\%$	$-5.2\%$
DQ-MPCC	$\mathbf{+7.4\%}$	$\mathbf{-10.1\%}$	$\mathbf{+9.7\%}$	$\mathbf{-4.1\%}$	$\mathbf{+13.9\%}$	$\mathbf{-4.8\%}$

TABLE VI : Sim-to-real gap (no retuning): per-controller RW-vs-SiL change. bold : smaller absolute RW-vs-SiL change. Relative changes use unrounded medians.

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Many aerial tasks involving quadrotors demand both instant reactivity and long-horizon planning for obstacle avoidance, energy efficiency, or trajectory tracking. High-fidelity models enable accurate control but are too slow for long horizons. Low-fidelity planners scale but cannot directly control the system, necessitating cascaded architectures. Prevailing hierarchical approaches plan with a simplified model and use a high-fidelity controller for tracking, yet this decomposition is inherently suboptimal. The controller is limited by the coarse plan, and conventional MPC alternatives shorten the horizon to stay real-time feasible. We present UNIQUE, an MPC architecture that replaces this hierarchical stacking with temporal cascading. The planning problem is formulated as the second-tail horizon of a single multi-phase MPC, rather than being solved separately. We align costs across horizons, derive feasibility constraints for the point-mass planning model, and introduce transition constraints that convert high-fidelity states into meaningful low-fidelity states. Parallel point-mass and mixed-integer solvers address nonconvexities while incorporating progressive 3D obstacle smoothing over the planning horizon. In simulations and real flights, under equal computational budgets, UNIQUE improves closed-loop tracking by up to 75% compared with standard MPC and hierarchical baselines. Ablations and Pareto analyses confirm performance gains across variations in horizon, constraint approximations, and smoothing schedules.

Abstract

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