Quadrotors are increasingly deployed in applications such as agriculture, infrastructure inspection, and maintenance. In each of these applications, the robot must navigate complex scene geometry while remaining strictly collision-free. Unlike in ground domains, even minor collisions for aerial vehicles can result in the loss of the robot. This safety requirement induces a pair of technical challenges. First, the environment must be represented with sufficient fidelity to encode complex structure, even when no ground-truth obstacle data is available. Second, a motion planner must leverage this representation to determine a collision-free path to the goal. This paper proposes a system that addresses these complementary challenges. The proposed method, AirSplan, adopts a normalized variant of 3D Gaussian Splatting that encodes high-fidelity scene geometry. It then applies a novel reachability-based motion planner that leverages the differential flatness of quadrotors to compute continuous-time collision constraints that tightly overapproximate the robot's occupancy. Experiments demonstrate that AirSplan successfully finds a path in 81.2% of challenging test cases, a significant improvement over the nearest baseline method's 51.2%.
Figures & tables
Fig. 1: AirSplan generates safe quadrotor trajectories in cluttered environments. The robot occupancy is tightly overapproximated using a reachable set (shown in pink) based on differential flatness. The scene is modeled as a Normalized 3D Gaussian Splat. A sampling-based planner jointly reasons over both representations to compute safe paths between waypoints (yellow) to the goal (red).
Fig. 2: AirSplan plans safe quadrotor trajectories through cluttered environments represented as normalized Gaussian Splats. It combines three key components. First, differential flatness is used to construct a tight sphere-based overapproximation of the robot volume along a trajectory. Second, the collision probability between each sphere and the normalized 3D Gaussian Splat is efficiently computed using a Bounding Volume Hierarchy (visualized with gray wireframe boxes). Third, a GPU-parallel sampling-based optimizer evaluates many candidate trajectories to efficiently find safe paths through dense environments.
Fig. 3: Examples of images used to reconstruct the tree environments used in planning experiments. Trees were procedurally generated using L-Systems. 3DGS models were reconstructed from these simulated observations.
Symbol
Description
Value
nσ
Gaussian culling level
10
nB
BVH buffer size
16,384
β
Risk threshold
0.01
T
Planning horizon
1s
nS
Number of trajectory samples
96
nI
Max optimizer iterations
20
TABLE I: Key planning, reachability, and collision-checking parameters used in the motion planning experiments
Fig. 4: The precision and recall of various collision-checking methods between spheres and radiance fields are evaluated with multiple risk parameters; outlined entries indicate the values used by each method during planning. The proposed collision check yields results that are equivalent to or better than the baselines, with significantly lower computational complexity.
Method
Mean Time
Std. Dev.
Splanning
122.1 ms
89.1 ms
Ours
42.2 ms
4.9 ms
TABLE II: Mean and standard deviation of time required to evaluate the collision constraint.
Method
% Success
% Stuck
% Collide
SPL
Splat-Nav
51.2%
48.8%
0 %
0.47
CATNIPS
28.8%
70.4%
0.8%
0.26
Ours
81.2%
18.8%
0%
0.66
TABLE III: Each planner ran 500 trials total, then collision-checked against the scene. SPL is success weighted by path length [ 36 ] .
Flat
PZ
Samp.
Success
Stuck
Collision
FRS
Reach.
Opt.
%
%
%
✗
✗
✗
16.2%
83.8%
0%
✗
✓
✓
49.8%
50.2%
0%
✓
✓
✗
25.2%
74.8%
0%
✓
✓
✓
81.2%
18.8%
0%
TABLE IV: Ablation study over key system components. Each row replaces proposed components with existing baselines.
Machines in Motion Lab, Tandon School of Engineering, New York University · Department of Smart Systems Technologies, University of Klagenfurt, Austria. · Artificial and Natural Intelligence Toulouse Institute (ANITI)