Variable Time-Step MPC for Agile Multi-Rotor UAV Interception of Dynamic Targets

TL;DR

The paper tackles dynamic target interception and persistent monitoring with agile multi-rotor UAVs by introducing a Variable Time-step MPC (VT-MPC) that jointly optimizes time-step lengths $t_k$ with control inputs over a horizon $N_h$. By modeling target reward dynamics with a Butterworth-based sensor function and leveraging the differential-flatness of quadrotor dynamics through a simplified point-mass with jerk input, the method achieves long horizons without increasing the number of prediction steps. The authors formulate a comprehensive OCP that maximizes collected rewards while respecting velocity, acceleration, jerk, and heading constraints, along with a travel-budget terminal constraint, and provide an online re-planning framework for receding-horizon operation with onboard estimation and warm-start. Validation spans offline 2D/3D KOP benchmarks and real-world field deployments, demonstrating higher-quality solutions, dynamic feasibility, and effective moving-target interception under dynamic reward scenarios. The approach promises improved planning performance for persistent monitoring and agile interception, with open-source code to enable replication and extension.

Abstract

Agile trajectory planning can improve the efficiency of multi-rotor Uncrewed Aerial Vehicles (UAVs) in scenarios with combined task-oriented and kinematic trajectory planning, such as monitoring spatio-temporal phenomena or intercepting dynamic targets. Agile planning using existing non-linear model predictive control methods is limited by the number of planning steps as it becomes increasingly computationally demanding. That reduces the prediction horizon length, leading to a decrease in solution quality. Besides, the fixed time-step length limits the utilization of the available UAV dynamics in the target neighborhood. In this paper, we propose to address these limitations by introducing variable time steps and coupling them with the prediction horizon length. A simplified point-mass motion primitive is used to leverage the differential flatness of quadrotor dynamics and the generation of feasible trajectories in the flat output space. Based on the presented evaluation results and experimentally validated deployment, the proposed method increases the solution quality by enabling planning for long flight segments but allowing tightly sampled maneuvering.

Figures (12)

• Figure 1: A solution to a 3D variant of the Tsiligirides 2 benchmark instance of the KOP determined by the proposed variable time-step method with the travel budget of 40s with the visualization of the vehicle velocity for each prediction step.
• Figure 2: Analysis of the velocity profile from the trajectory depicted in \ref{['fig:cover-page']} with respect to (w.r.t.) the kinematic constraints imposed by meyer2023top (blue cuboids) and constraints imposed by the proposed method (green sphere). About 84.4% of the velocity profile (green trajectory) lies outside the cuboidal constraints but within the proposed spherical constraints.
• Figure 3: Example of the variable time-step lengths distribution for a data collecting trajectory of the Tsiligirides 2 instance extended to 3D. The optimal solution utilizes shorter time-steps in areas of reward collection and frequent input changes due to maneuvering.
• Figure 4: An example single-dimensional jerk-input trajectory where time-step sampling of the VT-MPC is shown as the top x-axis and of the MPC as the bottom x-axis. With the MPC times-step of $0.2s$, the formulation requires 20.0 prediction steps to reach full fidelity on the prediction horizon $4s$. The VT-MPC set at $t\textsubscript{min}=0.2s$, $t\textsubscript{max}=0.6s$ and $t\textsubscript{sum}=4s$ utilizes only 10.0 prediction steps. The first optimization time-step is always constrained at $t\textsubscript{min}$.
• Figure 5: Snapshots of the UAV performing the monitoring mission in a field test. The UAV is encircled in each image.