FU-MPC: Frontier- and Uncertainty-Aware Model Predictive Control for Efficient and Accurate UAV Exploration with Motorized LiDAR

Technical Summary: FU-MPC for Efficient and Accurate UAV Exploration with Motorized LiDAR

Problem Statement
Efficient autonomous exploration in unknown environments requires a system that simultaneously expands spatial coverage and maintains reliable localization. For conventional UAVs equipped with rigidly mounted LiDARs, the observable region is tightly coupled with the vehicle's pose and motion. Consequently, expanding vertical or lateral coverage often necessitates additional translational or rotational maneuvers. In geometrically challenging or confined environments, these maneuvers can be inefficient and may introduce LiDAR matching degeneracy, leading to SLAM errors and potential mission failure. While motorized rotating LiDARs offer an additional sensing degree of freedom by actively adjusting the viewing direction without altering UAV motion, existing exploration systems rarely exploit this scanning freedom as an explicit decision variable. Current approaches typically treat LiDAR scanning as a preset peripheral process, failing to link scan motion directly to the dual objectives of revealing frontier-rich unknown space and maintaining strong geometric constraints for localization.

Methodology
The authors propose FU-MPC (Frontier- and Uncertainty-Aware Model Predictive Control), a hierarchical framework designed for a UAV platform equipped with an independently actuated motorized LiDAR. The system operates through two primary layers:

1. Hardware and System Architecture:
   The platform features a front-mounted LiDAR with an independently actuated motor, tightly time-synchronized with IMU and encoder data via an STM32 microcontroller. This design decouples scanning motion from UAV flight dynamics, allowing LiDAR rotation speed to serve as a real-time, commandable control input.

2. Global Exploration Planning:
   The global planner organizes raw frontier observations into representative viewpoints. It employs a dynamic clustering strategy to merge frontier clusters that share overlapping visible regions, reducing target redundancy. A topology-aware global cost function sequences these viewpoints, explicitly accounting for path reachability, vertical motion burden, and heading consistency. This generates an efficient, executable global tour that avoids aggressive reorientations common in Euclidean-distance-based planners.

3. Local Scan Control (FU-MPC):
   Built upon the global flight trajectory, FU-MPC acts as a local receding-horizon controller that optimizes the LiDAR's angular velocity online. The controller formulates a joint optimization problem balancing two objectives:

   • Frontier-Aware Exploration Utility: A lightweight surrogate evaluates the potential gain of revealing new frontiers based on the predicted future scanning volume and environmental complexity.
   • Direction-Dependent Localization Uncertainty: A Fisher-information-based metric estimates the quality of geometric constraints for pose estimation based on the distribution of visible surface normals. The cost is defined as the trace of the inverse Fisher information matrix (A-optimality criterion).

   To ensure real-time execution on onboard hardware, the system utilizes lightweight piecewise-linear surrogates to approximate the predictive utility field and pre-computes uncertainty costs in lookup tables, avoiding expensive online matrix operations. The controller minimizes a cost function that balances exploration gain, localization quality, and control smoothness within a strict 0.1-second cycle.

Key Contributions

1. Hardware Integration: Development of a UAV platform with an independently actuated motorized LiDAR, elevating scan speed to a dedicated real-time control input rather than a fixed peripheral process.
2. Hierarchical Planning Framework: A global planner that sequences frontiers into representative viewpoints using a topology-aware cost, addressing the inefficiencies of fixed-FoV planning in cluttered 3D environments.
3. FU-MPC Controller: A novel local scan controller that jointly optimizes frontier discovery and localization accuracy. It explicitly couples controllable scan motion with exploration progress and estimation quality using predictive scanning and Fisher-information-based uncertainty metrics.
4. Real-Time Implementation: The use of lightweight surrogates and asynchronous table updates enables closed-loop scan optimization at high rates on embedded edge computing units.

Experimental Results
The system was validated through simulations in three large-scale scenes (a sinkhole, a spatial maze, and a lava tube) and real-world flight experiments.

• Efficiency: Compared to state-of-the-art baselines (EPIC, FUEL, ERRT), FU-MPC demonstrated significantly faster coverage accumulation. In the Spatial Maze, it reduced exploration time by 36.8% and trajectory length by 48.7% compared to EPIC. In the Lava Tube, it achieved a 61.6% reduction in time, primarily by avoiding the frequent heading changes required by fixed-LiDAR systems to adjust viewing angles.
• Accuracy: FU-MPC maintained robust localization performance. In the Sinkhole scenario, where EPIC suffered severe trajectory drift (RMSE ~59m), FU-MPC completed the task with bounded error (RMSE ~1.03m). Ablation studies confirmed that the adaptive rotation strategy outperformed fixed-speed baselines in both accuracy and efficiency, overcoming the traditional trade-off between fast sweeping and stable feature tracking.
• Real-World Performance: Field tests in outdoor environments (parking-lot tunnels and building-like structures) demonstrated the system's ability to scan interior regions from outside and adapt rotation speeds at sharp corners to improve localization without compromising safety.
• Computational Efficiency: On an x86 Intel-N305 edge unit, the Local Scan Control module consumed an average of only 1.88% CPU, confirming the viability of the lightweight surrogate approach for onboard execution.

Significance
The paper claims that FU-MPC addresses a critical gap in autonomous exploration by treating the scanning mechanism itself as an active decision variable. By explicitly regulating scan motion according to exploration demand and localization conditions, the system achieves a more efficient balance between rapid coverage expansion and robust state estimation. The work demonstrates that motorized LiDARs, when coupled with uncertainty-aware predictive control, can significantly enhance the performance of UAVs in complex, geometrically challenging environments where traditional fixed-sensor approaches struggle with efficiency and localization stability.