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OmniRisk: Omnidirectional Trajectory-Risk Learning for Agile Quadrotor Dynamic Avoidance

Yifan He, Yang Liu, Wenhao Zhao, Hai Lin, Deping Zhang, Mingze Ma, Xin Zhou, Fei Gao, Huan Yu, Zipeng Dai, Ziming Ding

arXiv:2609.18191v2cs.RO

TL;DR

Sparse range observations do not directly reveal obstacle motion, and online planners trade latency against reliability in dense, high-speed encounters. OmniRisk learns trajectory-level risk offline and scores candidate primitives in a single forward pass. The paper reports full-tensor success rates of at least 92.0% across geometries and a 4.0% average dynamic collision rate.

  • Problem

    Sparse range data does not directly reveal obstacle motion, while online planners either scale with obstacle count or lose avoidance success in dense, fast encounters.

    Source: §I · p. 1

  • Method

    OmniRisk combines range, dynamic masks, and surface velocities, then uses an asymmetric motion-aligned risk field to supervise single-pass scoring of candidate trajectories.

    Source: §I · p. 1, 5) Online Objective · p. 3, 1) Limitations of Proximity Metrics · p. 5

  • Results

    At least 92.0% success across geometries and 4.0% average dynamic collision rate are reported for the full input tensor.

    Source: B. Input Representation Ablation · p. 6

  • Takeaways & Limitations

    The framework’s onboard planning latency remains below the 50 ms control budget across obstacle counts.

    Source: §VII · p. 8

    Proximity-based risk formulations are causally symmetric, isotropic, and can produce gradients that vanish almost everywhere under rigid distance thresholds.

    Source: 1) Limitations of Proximity Metrics · p. 4

Abstract

from arXiv · show

Agile quadrotor avoidance of fast-moving obstacles requires anticipating collisions and selecting feasible maneuvers within short reaction windows. Reliable predictive avoidance remains challenging because sparse range observations do not directly reveal obstacle motion, while online trajectory optimizers either scale poorly with obstacle count or remain efficient at the expense of reliability in dense, high-speed encounters. We present OmniRisk, an omnidirectional planning framework that learns trajectory-level risk offline for efficient onboard evasion. A fixed-dimensional tensor combines LiDAR range panoramas, dynamic masks, and Cartesian surface velocities to represent geometry and motion jointly. We formulate an asymmetric risk field aligned with obstacle velocity that emphasizes approaching interactions and attenuates receding ones. Accumulating this risk along predicted relative trajectories provides dense supervision and discourages unnecessary hesitation after obstacles pass. A dual-branch circular convolutional network predicts terminal boundary states and dynamic risks for candidate primitives over an omnidirectional anchor lattice in a single forward pass, followed by selection and closed-form reconstruction of the selected candidate primitive. This formulation removes online risk accumulation along trajectories and makes risk-inference cost independent of obstacle count. OmniRisk enables efficient onboard avoidance, with real-world flights demonstrating consecutive evasive maneuvers at relative encounter speeds up to 15 m/s without fine-tuning. Code is available at https://github.com/VANdexj/OmniRisk.

I. INTRODUCTION

Agile quadrotor avoidance is constrained by short reaction windows, while existing planners trade latency against reliability in dense, fast encounters. OmniRisk shifts trajectory-risk evaluation offline and scores candidate maneuvers in one forward pass, combining metric geometry, dynamic motion, and static clearance.

I. INTRODUCTION

  • Full spatiotemporal planners scale latency with obstacle count, while lightweight local refinement loses avoidance success in dense, fast encounters.Planning latency consumes the narrow reaction margin available before impact.Source: §I · p. 1
  • OmniRisk shifts continuous trajectory-risk evaluation offline, then scores every candidate primitive in one inference whose cost is independent of dynamic obstacle count.The selected primitive is reconstructed in closed form rather than obtained by refining one locally chosen trajectory.Source: §I · p. 1
  • In real-world flight, the vehicle traverses static rock clutter via the static clearance cost and evades a crossing thrown ball at closest approach using the asymmetric dynamic risk field.The demonstration reaches the goal along a time-colored quintic trajectory without replanning stalls, using surface-velocity channels.Source: §I · pp. 1–2

A. Omnidirectional Perception and the Planning Interfaces

  • The unified planning tensor combines metric range, dynamic masks, and Cartesian surface velocities to represent obstacle geometry and motion under sparse LiDAR returns.Its fixed-dimensional representation is independent of dynamic obstacle count.Source: §I · p. 2, A. Omnidirectional Perception and the… · p. 2

I. INTRODUCTION

  • The obstacle-velocity-aligned asymmetric risk field penalizes closing threats while attenuating penalties on receding obstacles.This is one of the paper’s stated contributions alongside the unified input tensor and offline trajectory-risk learning.Source: §I · p. 2

B. Spatiotemporal Risk Fields and Trajectory Optimization

OmniRisk replaces obstacle-dependent online optimization with fixed-lattice feed-forward scoring, using offline trajectory-risk labels from an asymmetric, velocity-aligned field. Its planning frame and tracked-obstacle state define the local geometry and motion used by this formulation.

B. Spatiotemporal Risk Fields and Trajectory Optimization

  • The proposed risk field is aligned with obstacle velocity and asymmetric in time, with discretized path integrals converted into continuous training labels for a feed-forward network.The formulation contrasts with symmetric pointwise potentials and fragile online optimization.Source: B. Spatiotemporal Risk Fields and… · p. 2

C. Learning-Based Low-Latency Avoidance

  • Learning-based alternatives often lack explicit surface-velocity channels or metric safety margins, while OmniRisk scores minimum-jerk primitives with kinodynamically bounded terminal states.The framework evaluates candidate primitives over a fixed omnidirectional anchor lattice in one forward pass.Source: C. Learning-Based Low-Latency Avoidance · p. 2, 1) Reformulation · p. 2

1) Reformulation:

  • A single forward pass scores every candidate primitive on a fixed omnidirectional lattice, shifting spatiotemporal risk integration into offline training and making evaluation independent of obstacle count.The resulting latency follows a fixed-size forward pass rather than the number of dynamic obstacles.Source: 1) Reformulation · p. 2, Figure 2 · p. 3

2) Notation:

  • The local planning frame is gravity-aligned and vehicle-anchored, and each dynamic track carries a centroid, metric velocity, extent, and persistent identity.These definitions situate the platform state and confirmed obstacle tracks used by the planner.Source: 2) Notation · pp. 2–3

3) Planning Input Tensor:

The planner uses a fixed-dimensional spherical-grid tensor to combine range, dynamic-track membership, and surface motion. Its action set contains fixed omnidirectional anchors, each supporting a candidate primitive whose terminal state adapts to observed static geometry.

3) Planning Input Tensor:

  • The planning input combines a metric nearest-surface range panorama, a dynamic-return mask, and Cartesian surface-velocity channels that are zero outside dynamic pixels.The representation is fixed-dimensional and decouples its complexity from point-cloud density and dynamic obstacle count.Source: 3) Planning Input Tensor · p. 3

4) Action Space:

  • The action lattice has 36 fixed unit-direction anchors across 12 azimuth bins and three elevation bands, with full 360° azimuthal coverage.The anchors and their count do not vary at runtime.Source: 4) Action Space · p. 3
  • Each anchored candidate is a minimum-jerk quintic primitive whose terminal boundary state adapts to observed static geometry within that anchor’s angular cell.Primitives that exceed velocity or acceleration limits are marked infeasible and excluded during selection.Source: 4) Action Space · p. 3

5) Online Objective:

OmniRisk moves continuous trajectory-risk evaluation into offline training, then scores candidate primitives onboard with a learned surrogate. Its online objective combines goal progress, control smoothness, and learned risk, using a range panorama built from spherical LiDAR projections.

5) Online Objective:

  • The learned risk surrogate estimates accumulated spatiotemporal risk directly from the planning tensor, bypassing iterative online optimization.Goal displacement and integrated squared jerk provide closed-form progress and smoothness costs.Source: 5) Online Objective · p. 3

1) Offline Stage:

  • Inverse-CPA sampling concentrates simulated training encounters in near-collision regimes before supervised regression trains a network to predict continuous trajectory risk.The offline pipeline accumulates risk along candidate primitives in privileged simulation.Source: 1) Offline Stage · p. 3

2) Online Stage:

  • At 20 Hz, static and dynamic heads score candidate primitives in parallel; an SO(3) controller tracks the selected primitive at 50 Hz.Asynchronous decoupling lets the controller continue tracking the previously committed trajectory if planning is delayed.Source: 2) Online Stage · pp. 3–4

1) Range Panorama Construction:

  • LiDAR points are projected into an H×W spherical grid whose cells store the minimum measured range along each bearing.The continuous spherical-to-pixel operator maps points to panorama cells.Source: 1) Range Panorama Construction · p. 4

2) Temporal Depth Completion:

The perception front end densifies sparse depth panoramas and synchronizes tracked dynamic obstacles to planning time. It then rasterizes confirmed tracks into the dynamic mask and velocity channels.

2) Temporal Depth Completion:

  • A sliding buffer of motion-compensated LiDAR sweeps fills unobserved panorama rays using edge-preserving nearest-neighbor propagation capped at r_max.The resulting panorama is described as dense and metrically consistent, capturing thin obstacles and free-space boundaries with negligible computational overhead.Source: 2) Temporal Depth Completion · p. 4

B. Dynamic Masking and Velocity Rasterization

  • M-detector segments moving returns, and Hungarian association links clusters across frames to maintain six-dimensional position-and-velocity track states.A track is confirmed after consistent associations over τ_track, with extrapolation bounded within τ_pred.Source: B. Dynamic Masking and Velocity… · p. 4
  • A closed-form ballistic model propagates measured states to planning time, after which synchronized tracks populate the dynamic mask and velocity channels.The propagation accounts for vertical gravitational acceleration during measurement latency.Source: B. Dynamic Masking and Velocity… · p. 4

C. Domain Invariance and Sim-to-Real Transfer

The sim-to-real interface preserves consistent geometry and motion channels, while mask corruption discourages reliance on occupancy alone. The static clearance cost biases selected trajectories toward wider corridors, and the dynamic risk field addresses limitations of proximity-based penalties.

1) Channel Alignment:

  • Matching spherical discretization, circular azimuth boundaries, and accumulation windows across simulation and reality keeps channel geometry consistent for zero-shot deployment.Depth completion is restricted to range so it does not dilate the binary dynamic mask or Cartesian surface-velocity channels.Source: 1) Channel Alignment · p. 4

2) Mask-Channel Corruption:

  • Independent false-positive and false-negative mask perturbations assign spurious regions zero velocity, guiding the network to evaluate risk through surface kinematics rather than binary occupancy alone.Source: 2) Mask-Channel Corruption · p. 4

A. Static Clearance Cost

  • The exponential static-clearance penalty retains repulsive gradients within nominally safe margins, biasing trajectory selection toward wider corridors.It is evaluated against an analytical ESDF at uniform collocation points along each candidate primitive.Source: A. Static Clearance Cost · p. 4

1) Limitations of Proximity Metrics:

  • Proximity-based dynamic penalties treat receding and closing obstacles alike, remain isotropic, and can yield step-like labels with gradients that vanish almost everywhere.These limitations motivate a velocity-aligned, causally asymmetric risk field with dense, continuous supervision; Fig. 3 depicts pointwise risk and candidate primitives colored by dynamic risk.Source: 1) Limitations of Proximity Metrics · pp. 4–5, Figure 3 · p. 5

2) Anisotropic Relative Metric:

The dynamic risk metric represents candidate-obstacle interactions in relative coordinates and elongates clearance along obstacle travel. A causal gate amplifies approaching risk and attenuates receding risk.

2) Anisotropic Relative Metric:

  • A constant-velocity forecast expresses candidate-obstacle separation and relative velocity in relative coordinates, with the spatial metric aligned to obstacle travel.The anisotropic Gaussian elongates along-track clearance while retaining lateral bounds, and its longitudinal scale expands with obstacle speed.Source: 2) Anisotropic Relative Metric · p. 5

3) Softplus Causal Gate:

  • The softplus causal gate amplifies approaching risk and lets receding risk decay toward zero, so crossing obstacles are penalized mainly before closest approach.Deceleration or re-approach departs from the constant-velocity forecast and is reflected after tracked velocity updates.Source: 3) Softplus Causal Gate · p. 5

4) Directed Path Integral:

OmniRisk aggregates relative-motion risk along candidate primitives for training, then predicts candidate geometry and dynamic risk with a dual-branch network. Separating geometry generation from dynamic scoring keeps obstacle motion from changing candidate geometry.

4) Directed Path Integral:

  • The dynamic risk of each candidate primitive aggregates pointwise risk, and uniform sampling makes this a scaled Riemann sum of time-integrated risk that mainly penalizes collision-course primitives.The scale K/T is absorbed into w_scale.Source: 4) Directed Path Integral · p. 5

1) Network Architecture:

  • A dual-branch circular convolutional network predicts terminal boundary states and dynamic risks in one forward pass.The static head estimates candidate geometry and static costs; the dynamic head predicts risk for that geometry.Source: 1) Network Architecture · p. 5

2) Head Isolation:

  • The dynamic head evaluates candidate geometry generated exclusively by the static head.Dynamic inputs cannot alter candidate geometry; isolating the heads suppresses trajectory chattering and promotes spatial consistency across replanning cycles.Source: 2) Head Isolation · p. 5

3) Training Objective:

Training separates terminal-state and static-cost objectives from dynamic-risk prediction, while online selection scores a fixed set of candidates and reconstructs the chosen primitive in closed form. The paper then evaluates the framework in simulation and real-world environments.

3) Training Objective:

  • Terminal boundary states minimize smoothness, static clearance, anchor alignment, and acceleration effort without dynamic risk; static cost regression instead uses goal progress in place of anchor alignment.The static-cost regressor uses a smooth-L1 loss.Source: 3) Training Objective · p. 5
  • Equal-weighted losses are optimized jointly, with dynamic risk compressed logarithmically to prevent near-miss extremes from dominating gradients.Each minibatch recomputes static and dynamic targets from privileged ESDF geometry and ground-truth tracks, blocking gradients through both targets.Source: 3) Training Objective · p. 5

D. Online Selection

  • Runtime selection evaluates all 36 candidate primitives in one forward pass, with selection cost O(1) in dynamic obstacle count.The continuity and switching-hysteresis term suppresses trajectory chattering; the selected primitive’s polynomial coefficients are reconstructed in closed form and mapped to attitude-thrust setpoints.Source: D. Online Selection · p. 6

VI. EXPERIMENTAL VALIDATION

  • The framework is systematically evaluated across simulated and real-world environments.The quadrotor platform uses a Livox Mid-360 LiDAR, NVIDIA Jetson Orin NX, and NxtPX4v2 flight controller.Source: §VI · p. 6, Figure 4 · p. 6

A. Protocol and Baselines

The evaluation uses paired simulation trials with shared inputs for FAPP and SIMP, testing input representations, dynamic-risk mechanisms, and planning scalability. Results show that motion cues and directional risk improve avoidance, while the planner’s latency remains within the control budget in most tested conditions.

A. Protocol and Baselines

  • Trials use 50 paired evaluation seeds per condition and define a deadline miss as planning latency above 50 ms in the 20 Hz replanning loop.Sensing, detection, and track confirmation are shared by the methods and excluded from measured latency.Source: A. Protocol and Baselines · p. 6

B. Input Representation Ablation

  • At least 92.0% success across geometries and 4.0% average DCR with the full tensor, versus 22.0% crossing and 26.0% rear-pursuit success for Depth-Only.The full tensor includes Cartesian surface velocities, making lateral relative motion observable where range alone and a dynamic mask lack metric kinematic cues.Source: B. Input Representation Ablation · p. 6, Table I · p. 6

C. Dynamic Risk Field Ablation

  • 96.2% directional accuracy and 4.0% DCR with the full risk formulation; removing directional projection yields 51.8% A–R accuracy and 34.0% DCR.Removing future prediction lowers future-collision AUC to 0.735; the full field combines along-track elongation with monotonic risk decay for receding obstacles.Source: C. Dynamic Risk Field Ablation · p. 6, Table II · p. 7

D. Computational Scalability

  • 42.2–45.8 ms P95 latency and 3.0% deadline misses at six obstacles; OmniRisk remains below SIMP’s >1400 ms and 96.3% misses, though FAPP is faster at about 17 ms with no misses.Network inference stays nearly constant at 20.0–20.5 ms P95; residual latency variation comes from rasterization.Source: D. Computational Scalability · p. 7

E. Multi-Threat Closed-Loop Safety

In the most adversarial simulated condition, OmniRisk outperforms FAPP on clearance and success rate. Frozen weights also transfer to real-world flights against unseen projectiles at encounter speeds up to 15 m/s, while the conclusion reports P95 planning latency below the 50 ms budget across obstacle counts.

E. Multi-Threat Closed-Loop Safety

F. Real-World Flight Performance

  • Frozen weights achieved zero-shot real-world evasion against unseen projectiles at relative encounter speeds up to 15 m/s; the weakly reflective foam basketball had the lowest success rates, 86.0% indoors and 82.0% outdoors.In the three-obstacle trial, minimum clearance was 0.24 m.Source: F. Real-World Flight Performance · pp. 7–8, Table VI · p. 8

VII. CONCLUSION

  • The conclusion reports P95 planning latency below the 50 ms control budget across obstacle counts and identifies decentralized multiagent cooperative avoidance as a future direction.The framework uses onboard sensing and computation and evaluates all candidates in a single forward pass.Source: §VII · p. 8
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