Source-linked AI summary
OA-MPPI: Occlusion-Aware Model Predictive Path Integral Control for UAV Flight
Vittorio Palladino, Teaya Yang, Ruiqi Zhang, Mark W. Mueller
TL;DR
UAVs in cluttered, partially unknown environments must account for obstacles and agents emerging from occlusion. OA-MPPI adds occupancy-map occlusion boundaries and expanding hidden-agent keep-out regions to MPPI rollouts. It increased clearance in simulation and hardware scenarios, and avoided a simulated emerging agent that collided with baseline MPPI.
Problem
UAV flight in cluttered, unknown environments must handle obstacles and potential collisions with moving agents emerging from sensor-occluded regions.
Source: §I · p. 1Method
OA-MPPI extracts occlusion boundaries from the local occupancy map and penalizes MPPI rollouts that enter expanding keep-out regions for potential hidden agents.
Source: §I · p. 2, §VI · p. 8Results
OA-MPPI increased clearance from occlusion boundaries in three hardware scenarios and avoided a simulated emerging agent that collided with baseline MPPI.
Source: B. Simulation Tests · p. 6, C. Flight Experiments · p. 7Takeaways & Limitations
The complete perception and control pipeline ran onboard during hardware flights while the occlusion-aware trajectories maintained greater clearance from boundaries.
Source: C. Flight Experiments · p. 7, §VI · p. 8The hardware flight experiments did not include dynamic obstacles.
Source: §VI · p. 8
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
UAV control in cluttered, unknown environments must address vehicle dynamics and actuator limits, real-time obstacle avoidance, and agents emerging from unobserved regions. OA-MPPI adds occlusion-aware costs to MPPI rollouts, targeting a gap in aerial planning and improving safety near occlusion boundaries.
I. INTRODUCTION
- UAV control in cluttered, unknown environments must account for nonlinear dynamics and actuator limits, real-time obstacle avoidance, and collisions with agents emerging from unobserved regions.Source: §I · p. 1
- NMPC combines dynamics, actuator limits, and collision constraints, but its nonconvex optimization can be computationally demanding in real time; MPPI instead evaluates sampled rollouts without derivatives.Source: §I · p. 1
- MPPI’s rollout costs can directly evaluate complex, nonconvex collision costs, providing a basis for including risks from unobserved regions.Source: §I · p. 1
II. RELATED WORK
- Occlusion-aware planning has received comparatively less attention in aerial robotics than in ground-vehicle research, where approaches model phantom agents and bound their motion or risk.Source: §I · p. 1, Occlusion-aware planning · p. 2
I. INTRODUCTION
- OA-MPPI extracts 3D occlusion boundaries and expands potential collision regions over the prediction horizon, evaluating occlusion and observed-obstacle costs within MPPI rollouts.The reported results show safer trajectories near occlusion boundaries than a controller without the occlusion-aware cost.Source: §I · p. 2
II. RELATED WORK
- Aerial planners for partially mapped environments address navigation through unexplored space, while OA-MPPI additionally predicts hidden agents’ possible occupancy of currently known free space.Source: Planning in unknown environments · p. 2
III. PRELIMINARIES
MPPI samples candidate action sequences, evaluates their rollout costs, and uses cost-based weights to update the nominal sequence. It applies the first updated action and shifts the horizon for the next planning cycle.
A. Model Predictive Path Integral Control
- MPPI samples candidate action sequences and combines them into an improved sequence based on rollout costs.Source: A. Model Predictive Path Integral… · p. 2
- Each rollout perturbs the nominal action sequence with Gaussian noise, starts from the estimated state, and propagates through the quadrotor dynamics.The rollout cost includes stage costs across the horizon and a terminal cost.Source: A. Model Predictive Path Integral… · p. 2
- A softmax transform converts rollout costs into normalized importance weights, which update the nominal sequence using the sampled disturbances.Subtracting the minimum cost supports numerical stability; the temperature parameter controls the trade-off between averaging disturbances and selecting the best rollout.Source: A. Model Predictive Path Integral… · p. 2
- Only the first action of the updated sequence is applied; the remaining actions initialize the next planning cycle as the horizon shifts forward.Source: A. Model Predictive Path Integral… · pp. 2–3
IV. METHODOLOGY
The quadrotor state comprises position, attitude, velocity, and body rate, while MPPI commands collective thrust and desired body rate. Sampled inputs are projected onto feasible rotor-thrust limits before the state is propagated.
A. Quadrotor Dynamics
- The state is x = [p, q, v, ω], and the controller commands collective thrust c and desired body rate ωd.The state variables are position, attitude, velocity, and body rate.Source: A. Quadrotor Dynamics · p. 3
- Each sampled input is projected by saturating desired rates, recovering and clipping individual rotor thrusts, then mapping back to feasible thrust and torque.Every sampled input passes through this feasibility projection before propagation.Source: A. Quadrotor Dynamics · p. 3
- The projected inputs propagate the state using a semi-implicit Euler discretization of Newton’s and Euler’s laws, with attitude integrated over each time step.The discretization also clips speed to vmax.Source: A. Quadrotor Dynamics · p. 3
B. Safety handling
Because MPPI averaging does not guarantee collision-free trajectories or zero terminal velocity, the controller validates plans and uses a deterministic braking tail. It falls back to hovering at the last verified-safe state when safety checks fail.
B. Safety handling
- Averaging individually collision-free rollouts can produce an unsafe nominal trajectory, so each cycle checks the averaged trajectory and every rollout over the full horizon.The nominal sequence is forward-simulated and checked against the map; individual rollouts are marked infeasible if any predicted state collides.Source: B. Safety handling · p. 3
- If the averaged plan fails validation or all rollouts are infeasible, the controller hovers at the last predicted state previously verified safe.Tracking resumes only when a freshly computed plan passes both checks.Source: B. Safety handling · p. 3
- A deterministic braking tail replaces sampled control at the end of each rollout to promote zero terminal velocity and level attitude.Its sufficient tail length bounds the time to cancel velocity and level attitude, but perturbations, disturbances, and model mismatch mean it does not guarantee every rollout ends at rest.Source: B. Safety handling · p. 4
C. Perception of Obstacles and Occlusion
The method builds an online occupancy map, extracts 3D occlusion boundaries from silhouette edges, and uses those boundaries to represent where hidden agents could emerge. Map-based extraction supports multiple sensing modalities and accumulated observations.
C. Perception of Obstacles and Occlusion
- The online occupancy grid labels cells occupied, known-free, or unknown, while its sliding local extent bounds memory and query time.The map is updated from LiDAR measurements, with traversed ray cells marked free and the terminating cell updated in log-odds.Source: C. Perception of Obstacles and Occlusion · p. 4
- Figure 3 shows the nearest occlusion voxel and the keep-out radius expanding over the horizon around the closest boundary point.The top view colors radius from t = 0 s to t = 3 s; the 3D view marks occlusion lines of sight and expanding keep-out spheres.Source: Figure 3 · p. 4
- At each planning cycle, the occlusion boundary B samples silhouette edges between known-free and unknown space shadowed by occupied regions; these mark locations from which hidden agents could emerge.Adjacent angular bins with sufficiently different ranges identify edges; sampled radial gate segments extend outward from the nearer bin, with edge points placed at the bin boundary to remove half-bin bias.Source: C. Perception of Obstacles and Occlusion · pp. 4–5
- Map-based boundary extraction is sensor-agnostic when a sensor supplies point clouds that can be integrated into the map.The approach applies to spinning and nonrepetitive LiDARs and depth cameras; accumulated map observations can preserve shadows from structures no longer in the instantaneous field of view.Source: C. Perception of Obstacles and Occlusion · p. 5
D. Definition of the Cost
The cost combines goal-seeking terms with hard rejection of rollouts that collide with mapped obstacles or enter a time-growing occlusion keep-out radius. It also regularizes control effort and input changes.
D. Definition of the Cost
- Equations (12) and (13) reject rollouts intersecting mapped obstacles or entering the time-growing keep-out radius around an occlusion boundary.The radius bounds exposure to a hidden agent that could have moved into the vehicle’s path since the boundary was last observed.Source: D. Definition of the Cost · p. 5
- Equations (9)–(11) favor reaching the goal at the horizon and increasingly discourage residual velocity as the vehicle nears the goal.The terminal goal term is weighted more heavily than the term for approaching the goal along the way.Source: D. Definition of the Cost · p. 5
- Figure 4 contrasts baseline MPPI, which collides with the emerging agent, with OA-MPPI, which avoids the collision.The simulated agent speed is 0.4 m/s.Source: Figure 4 · p. 6
A. Experimental Setup
The setup uses the same MPPI parameters in simulation and hardware, with parallel rollout evaluation and onboard processing. Sensor, map, and rollout settings define the test configuration.
A. Experimental Setup
- The simulation uses a ray-casting sensor model and ROG-Map; hardware processing runs onboard a Jetson Orin Nano with 8 GB of RAM.Both settings use the same MPPI parameters.Source: A. Experimental Setup · p. 6
- The ROG-Map grid covers 20 × 20 × 6 m at 0.1 m resolution, with a 4 m query range and a 3 m gate length.The gate length was chosen to exceed the distance a briskly walking person could cross within one replanning cycle.Source: A. Experimental Setup · p. 6
- Figure 5 depicts flight over an occluding box and a side view in the xz-plane at 2.1 s, where OA-MPPI takes a higher path than baseline MPPI.The caption reports that the higher path increases clearance from the occlusion boundary.Source: Figure 5 · p. 6
- MPPI evaluates 500 rollouts over a 30-step horizon with Δt = 0.1 s.The simulation and hardware tests use the same MPPI parameters, and rollouts are evaluated in parallel with OpenMP.Source: A. Experimental Setup · p. 6
- The MID-360 has a native vertical field of view from −7° to 52°, is mounted with a 20° forward tilt, and provides point clouds at approximately 10 Hz.Its range-jump threshold τ suppresses small range variations, including sensor noise, when identifying silhouette edges.Source: A. Experimental Setup · p. 6
B. Simulation Tests
In simulation, OA-MPPI steers around expanding keep-out regions near occlusion boundaries. The tests include an emerging-agent crossing and a case where an agent could emerge vertically.
B. Simulation Tests
- When an agent emerges from occlusion and crosses the vehicle’s path, baseline MPPI collides with it, while OA-MPPI avoids it by steering around the expanding keep-out region.The scenario is evaluated in simulation to avoid the risk of a physical collision.Source: B. Simulation Tests · p. 6
- For a predominantly horizontal occlusion boundary where a hidden agent could emerge vertically, OA-MPPI takes a higher path over the obstacle than baseline MPPI, increasing clearance.The keep-out region expands at 0.4 m/s in both simulation tests.Source: B. Simulation Tests · pp. 6–7
C. Flight Experiments
Across three hardware flight scenarios, OA-MPPI stays farther from occlusion boundaries than baseline MPPI, with longer routes and slower goal-reaching. The onboard planner runs with a modest update-rate reduction.
C. Flight Experiments
- The three scenarios use a single wall, a central pillar, and a two-wall corridor, with the same start and goal positions for baseline MPPI and OA-MPPI.The keep-out expansion speed is 0.4 m/s for the single-wall and two-wall scenarios and 0.3 m/s for the pillar.Source: C. Flight Experiments · p. 7
- The planner averages 8.47 Hz with the occlusion cost enabled, about 12% slower than the occlusion-agnostic planner.The reported overhead comes from the boundary extractor and kd-tree queries against the nearest boundary voxel at each rollout timestep; onboard replanning remains fast enough in the tested scenarios.Source: C. Flight Experiments · p. 7
- In all three flight scenarios, OA-MPPI arcs farther from occlusion boundaries but reaches the goal more slowly along a longer path; Table II compares time, distance, and mean velocity.The passage attributes the detour to staying clear of the expanding keep-out region, not failure to converge.Source: Table II · p. 7, C. Flight Experiments · p. 7
VI. CONCLUSION AND FUTURE WORK
OA-MPPI extends MPPI to reason about regions occluded by obstacles, penalizing trajectories that enter expanding keep-out regions. Simulation and hardware results show increased clearance, while the authors identify limits in motion modeling, hardware testing, and constrained environments.
VI. CONCLUSION AND FUTURE WORK
- OA-MPPI extracts occlusion boundaries from the local occupancy map and penalizes trajectories entering an expanding keep-out region within nonlinear quadrotor MPPI rollouts.The expansion uses an assumed hidden-agent speed bound without assuming a specific trajectory.Source: §VI · pp. 7–8
- Simulation showed increased clearance and avoidance of an emerging agent that collided with baseline MPPI; increased clearance was also observed in three onboard hardware flight scenarios.The full perception and control pipeline ran onboard the vehicle.Source: §VI · p. 8
- The method uses a fixed hidden-agent speed bound, hardware tests omit dynamic obstacles, and expanding keep-out regions may restrict paths in narrow or heavily occluded environments.The authors suggest adapting the bound or using agent-specific reachable sets, testing dynamic obstacles in flight, and using active perception to reduce uncertainty.Source: §VI · p. 8