L1-MPPI: L1 Adaptive Model Predictive Path Integral for Agile UAV Control

Lukáš Kotek; Ondřej Procházka; Vojtěch Vonásek; Martin Saska; Robert Pěnička

cs.ROSep 29, 2026

L1-MPPI: L1 Adaptive Model Predictive Path Integral for Agile UAV Control

Authors: Lukáš Kotek, Ondřej Procházka, Vojtěch Vonásek, Martin Saska, Robert Pěnička

Organizations: Multi-robot Systems Group, Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic

Abstract

This work proposes the L1 Adaptive Model Predictive Path Integral (L1-MPPI). It cascades L1 adaptive control with the Model Predictive Path Integral (MPPI) to improve tracking of high-speed UAV trajectories. Thanks to the L1augmentation, the tracking remains accurate even under model uncertainties and external disturbances, such as an additional payload or a mismatch in the modeled aerodynamic drag. In contrast to existing MPPI approaches for UAV control that do not explicitly model aerodynamic effects, varying payloads, and typically neglect the dynamics of low-level motor controllers, our L1-MPPI approach enhances the dynamic model used in the MPPI by incorporating the low-level flight controller and motor dynamics, as well as an iterative mixing scheme that reflects the approach of the low-level controller. The proposed method demonstrates improved tracking performance in both simulation and the real world, even when the UAV is subjected to an unknown payload. In flight with 35% mass increase, our approach lowers the RMSE by 58.61% with respect to plain MPPI. Compared to the same MPPI using an online mass estimator in place of the L1 augmentation, the RMSE is lower by 38.59%. During the real-world experiments the UAV reaches speeds up to 13.50 m/s and accelerations up to 2.5 g.

Figures & tables

Fig. 1: Real-world agile flight of the UAV controlled by the proposed $\mathcal{L}_{1}$ -MPPI at speeds up to $13.00\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$ and accelerations reaching $2.5\text{\,}\mathrm{g}$ . The UAV carries a payload of unknown weight, and the $\mathcal{L}_{1}$ augmentation compensates for the resulting model mismatch online. The composite image shows the flown trajectory, with a detail of the UAV with the attached payload.

Panel of Figure 2 — Fig. 2: The proposed $\mathcal{L}_{1}$ -MPPI control architecture. The state estimate $\mathbf{p},\mathbf{v},\mathbf{q},\bm{\omega},\bm{\Omega}$ is provided to both the MPPI and $\mathcal{L}_{1}$ adaptive controllers. The MPPI controller computes the nominal control input $F_{MPPI},\bm{\omega}_{MPPI}$ based on the reference trajectory $\mathcal{T}_{ref}$ , while the $\mathcal{L}_{1}$ controller generates the adaptive compensation command $F_{\mathcal{L}1},\bm{\omega}_{\mathcal{L}1}$ . The combined command $t_{c},\bm{\omega}_{c}$ is sent to the PID-based low-level flight controller, which computes individual rotor throttle commands $\bm{r}_{c}$ for the UAV. The entire control architecture operates at $100\text{\,}\mathrm{Hz}$ .

Fig. 3: Example of desaturation of two motors by our controller without changing the collective thrust. The image is adapted from [ 27 ] .

Panel of Figure 4 — Fig. 4: The architecture of the $\mathcal{L}_{1}$ adaptive controller is composed of three main blocks: the observer, adaptation law, and control law. Based on the observed state $\hat{\bm{z}}$ , uncertainties $\hat{\bm{\sigma}}=[\hat{\bm{\sigma}}_{m},\hat{\bm{\sigma}}_{um}]^{T}$ are estimated using an adaptation law. The control law then yields the $\mathcal{L}_{1}$ adaptive controller command $\bm{u}_{\mathcal{L}1}$ based on the estimated uncertainties.

Fig. 5: The mean motor throttle response to a step command, highlighting the delay

\Delta t

between the applied throttle command and the motor response controlled by the low-level controller.

Fig. 6: Reference and tracked trajectories under an additional payload using the proposed $\mathcal{L}_{1}$ -MPPI controller and plain MPPI.

Traj.	Controller	Figure 8		Hypotrochoid
Traj.	Controller	pos. RMSE [m]	Gain [%]	pos. RMSE [m]	Gain [%]
No change	MPPI (plain)	$0.673\pm 0.025$	–	$0.609\pm 0.021$	–
	Ours	$0.529\pm 0.026$	$21.35$	$0.437\pm 0.024$	$28.20$
	Ours (no delay)	$0.529\pm 0.023$	$21.36$	$0.439\pm 0.010$	$27.90$
	Ours ( $\mathcal{L}_{1}$ tr. only)	$\bm{0.509\pm 0.019}$	$\bm{24.35}$	$0.451\pm 0.011$	$25.85$
	Ours (no $\mathcal{L}_{1}$ )	$0.524\pm 0.015$	$22.16$	$0.439\pm 0.014$	$27.86$

TABLE I: Results of the tracking experiments.

Condition	Ours [m]	Ours ( $\mathcal{L}_{1}$ tr. only) [m]	Ours (no $\mathcal{L}_{1}$ ) [m]
No change	$0.703$	$0.707$	$\bm{0.654}$
Mass mismatch	$\bm{0.727}$	$0.981$	$1.266$
Real payload	$\bm{0.621}$	$0.699$	–

TABLE II: RMSE results of tracking figure 8 in the real world.

Fig. 7: Commands from the MPPI and

\mathcal{L}_{1}

adaptive controller during the real-world figure 8 tracking experiment. The force plots show the collective thrust of each controller over the entire trajectory and its beginning. The top-right plot illustrates the rotational dynamics compensation by the

\mathcal{L}_{1}

adaptive controller. Bottom-right plot compares the roll rate command of MPPI and

\mathcal{L}_{1}

adaptive controller.

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OA-MPPI: Occlusion-Aware Model Predictive Path Integral Control for UAV Flight

Vittorio Palladino, Teaya Yang, Ruiqi Zhang, Mark W. Mueller

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Model Predictive Path Integral Unmanned Aerial Vehicles Obstacle Avoidance Dynamic Environments Path

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Autonomous UAV flight through cluttered and partially unknown environments requires reasoning not only about observed obstacles but also about occluded regions that the sensor cannot observe. We present OA-MPPI, an obstacle- and occlusion-aware extension of Model Predictive Path Integral (MPPI) control for quadrotor flight that accounts for potential moving agents emerging from these regions into the vehicle's path. At every planning step, we extract a 3D occlusion boundary from the online occupancy map and use it to model the regions that hidden agents could reach over the prediction horizon. We penalize trajectories that enter these expanding regions within MPPI rollouts generated using nonlinear quadrotor dynamics and accounting for individual rotor thrust limits. We validate the proposed approach in simulation and hardware flight experiments, with the complete pipeline running onboard the vehicle in real time. Results show increased clearance from occlusion boundaries compared to baseline MPPI in both settings, as well as avoidance of an agent emerging from occlusion in simulation.

Abstract

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