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 L1 -MPPI at speeds up to 13.00ms−1 and accelerations reaching 2.5g . The UAV carries a payload of unknown weight, and the L1 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.
Fig. 2: The proposed L1 -MPPI control architecture. The state estimate p,v,q,ω,Ω is provided to both the MPPI and L1 adaptive controllers. The MPPI controller computes the nominal control input FMPPI,ωMPPI based on the reference trajectory Tref , while the L1 controller generates the adaptive compensation command FL1,ωL1 . The combined command tc,ωc is sent to the PID-based low-level flight controller, which computes individual rotor throttle commands rc for the UAV. The entire control architecture operates at 100Hz .
Fig. 3: Example of desaturation of two motors by our controller without changing the collective thrust. The image is adapted from [ 27 ] .
Fig. 4: The architecture of the L1 adaptive controller is composed of three main blocks: the observer, adaptation law, and control law. Based on the observed state z^ , uncertainties σ^=[σ^m,σ^um]T are estimated using an adaptation law. The control law then yields the L1 adaptive controller command uL1 based on the estimated uncertainties.
Fig. 5: The mean motor throttle response to a step command, highlighting the delay Δt 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 L1 -MPPI controller and plain MPPI.
Traj.
Controller
Figure 8
Hypotrochoid
pos. RMSE [m]
Gain [%]
pos. RMSE [m]
Gain [%]
No change
MPPI (plain)
0.673±0.025
–
0.609±0.021
–
Ours
0.529±0.026
21.35
0.437±0.024
28.20
Ours (no delay)
0.529±0.023
21.36
0.439±0.010
27.90
Ours ( L1 tr. only)
0.509±0.019
24.35
0.451±0.011
25.85
Ours (no L1 )
0.524±0.015
22.16
0.439±0.014
27.86
TABLE I: Results of the tracking experiments.
Condition
Ours [m]
Ours ( L1 tr. only) [m]
Ours (no L1 ) [m]
No change
0.703
0.707
0.654
Mass mismatch
0.727
0.981
1.266
Real payload
0.621
0.699
–
TABLE II: RMSE results of tracking figure 8 in the real world.
Fig. 7: Commands from the MPPI and L1 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 L1 adaptive controller. Bottom-right plot compares the roll rate command of MPPI and L1 adaptive controller.
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.
Vittorio Palladino, Teaya Yang, Ruiqi Zhang +1
High Performance Robotics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720, United States
Flapping-wing micro aerial vehicles offer quieter and safer operation than rotary-wing drones, yet achieving precise autonomous control of bird-scale ornithopters remains challenging: lift, airspeed, and turning authority are tightly coupled and governed by only a few control inputs. Conventional cascaded controllers treat altitude, speed, and heading independently, producing persistent tracking errors during complex maneuvers, while time-parameterized trajectory tracking requires predefined speed profiles that existing methods cannot robustly produce for these coupled dynamics. We address both limitations simultaneously with a Model Predictive Contouring Control (MPCC) approach that tracks arc-length-parameterized trajectories while optimizing progress online, eliminating the need for predefined timing. However, MPCC requires a dynamical model that captures the coupled aerodynamics without exceeding the computational budget of real-time nonlinear optimization. Here, we propose a compact, continuously differentiable model that captures the dominant couplings of bird-scale ornithopters, enabling real-time predictive control. We validated the method with the XFly ornithopter flying along circular and three-dimensional racing trajectories and achieved a mean deviation from the reference trajectory between 6.5 and 9 cm at speeds up to 3 m/s, which represents an almost 10-fold improvement over prior ornithopter control methods.
Charbel Toumieh, Jack Zeng, Niel Mistry +1
Laboratory of Intelligent Systems, Ecole Polytechnique Federale de Lausanne (EPFL), CH1015 Lausanne, Switzerland
Classical proportional--integral--derivative (PID) control remains widely used in industrial control systems, while model predictive control (MPC) is actively studied to achieve higher performance for systems with nonlinear dynamics. Model predictive path integral (MPPI) control is a sampling-based MPC method that optimizes control inputs without gradient calculations and can handle non-differentiable models and objective functions. However, conventional MPPI directly samples control-input sequences, which can produce large temporal input increments and causes the optimization dimension to grow with the prediction horizon. This study proposes MPPI--PID control, which uses MPPI to optimize PID gains online instead of directly optimizing the control-input sequences. By replacing high-dimensional input-sequence optimization with low-dimensional gain-space optimization while retaining the PID structure, the proposed formulation improves sampling efficiency and promotes smoother control inputs. Theoretical analyses are provided for a unified path-integral update, the relation between optimization dimension and effective sample size, and the temporal correlation of input perturbations induced by the PID structure. The method is evaluated on a learning-based path following of a mini forklift using a residual-learning dynamics model that combines a physical model and a neural network identified from real-machine driving data. Numerical results show that MPPI--PID improves tracking performance over fixed-gain PID, yields smaller input increments than conventional MPPI, and maintains favorable performance under reduced sampling budgets.
Teruki Kato, Koshi Oishi, Seigo Ito
Toyota Central R&D Labs., Inc., Nagakute 480-1192, Japan