Layered Dynamic Obstacle Representation

• Layered representation of dynamic obstacles is a structured framework that divides static and dynamic elements to support precise, risk-aware planning.
• It employs specialized data layers such as OctoMap for static mapping and LiDAR clustering for dynamic detection to optimize collision avoidance.
• Reactive control systems integrate chance-constrained MPC and dynamic costmaps to adapt trajectories in real time based on predicted obstacle behavior.

A layered representation of dynamic obstacles is a structured framework for environment modeling that explicitly separates static and dynamic components in spatiotemporal mapping and planning systems. Originating in the context of mobile robotics and UAV navigation, this approach enables robust, risk-aware trajectory generation and obstacle avoidance by partitioning the perceived environment into dedicated layers, each with specialized data structures, semantic roles, and dynamic behaviors. Two recent methodologies exemplify this paradigm: (i) the OctoMap/static-vs-dynamic object model with chance-constraint MPC for UAVs (Xu et al., 2021) and (ii) the layered costmap with a movable-obstacles layer for ground robots in ROS2 Nav2 (Stan et al., 17 Oct 2025).

1. Motivation and Fundamentals

Layered representations address key limitations in traditional mapping techniques, where static and dynamic objects are merged in a monolithic occupancy grid, resulting in loss of temporal specificity, confusion in collision checking, and poor reactive performance. By organizing environmental data along semantic or operational lines, layered schemes enable:

• Efficient collision and traversability queries against persistent (static) infrastructure
• Independent modeling, tracking, and prediction of moving or transient objects
• Selective risk assignment and adaptive behavior based on obstacle mobility or interaction feedback

A conceptual summary is:

Layer Type	Function	Example Data Structure
Static	Persistent obstacles	OctoMap, occupancy grid
Dynamic (movable)	Time-varying objects	Gaussians+ellipsoids, costmap clusters
Short-lived (scan)	Immediate returns	ObstacleLayer (ROS2)

This modularization enables application-specific logic in each layer, such as minimum-snap QPs in the static map, and stochastic prediction or adaptive cost escalation in the dynamic/movable layer.

2. Static Environment Modeling

In UAV trajectory planning (Xu et al., 2021), the static layer is implemented using an OctoMap occupancy grid $M$ (per Hornung et al. 2013), which serves one role: binary collision checking for candidate trajectories. No ESDF or occupancy-probability formulas are introduced.

For ground robots in partially mapped spaces (Stan et al., 17 Oct 2025), the static layer consists of a 2D occupancy grid generated offline via SLAM. Each cell is marked as either free or maximally occupied, representing immovable infrastructure (walls, pillars).

Both frameworks use the static layer to define the non-negotiable operational space: these obstacle maps are immutable except by remapping.

3. Dynamic and Movable Obstacle Representation

Dynamic and movable obstacles are managed via structurally and semantically distinct layers:

• In real-time UAV planning (Xu et al., 2021), each moving obstacle $i$ at step $k$ is characterized by a Gaussian pose distribution

$$p_o^k \sim \mathcal{N}(\overline{p}_o^k, \Sigma_o^k)$$

and modeled as a minimum bounding ellipsoid (axes $a,b,c$) enclosing the obstacle's axis-aligned bounding box. Motion is predicted by a constant-velocity model:

$$p_o^{k+1} = p_o^k + v_o^k \Delta t \ \Sigma_o^{k+1} = \Sigma_o^k + \Sigma_{o,v}^k (\Delta t)^2$$

where velocity and its uncertainty derive from computer vision detection/tracking. These parameters are propagated and injected into the MPC's chance constraints.

• For ground robots (Stan et al., 17 Oct 2025), a Movable Obstacles Layer identifies all LiDAR returns that are absent from the static occupancy grid. Isolated clusters of these new points, detected via 4-connected component labeling, are interpreted as "tentatively movable" objects and assigned a traversal cost that is systematically lower than that for fixed structure. The clustering ensures consistent object identification across scans, and cost inflation is applied based on spatial proximity.

4. Layer Integration in Planning and Control

Each framework fuses its layers differently:

• UAVs (Xu et al., 2021): The static layer generates an initial, collision-free trajectory using an iterative box-corridor minimum-snap quadratic program.
  • The dynamic layer constrains the system in real time during execution, using a chance-constrained MPC—the optimization minimizes both tracking error and control input over a horizon $k=1\ldots N$.
  • The crucial analytic chance constraint is:

  $$a^{kT}(\overline{y}^k) - 1 \ge \mathrm{erf}^{-1}(1-2\delta) \sqrt{2a^{kT}(\Sigma_{r,t}^k + \Sigma_{o,t}^k)a^k}$$

  which encapsulates collision risk (with selectable probability) as a linear inequality applied at each trajectory timestep. When obstacles are encountered, a "temporal goal" replaces the reference trajectory locally, shifting the system away from the obstacle and smoothly back onto the original plan.

• ROS2 Nav2 (Stan et al., 17 Oct 2025): All three costmap layers—Static, Obstacle, and Movable—are queried in a fixed sequence on each update. The Movable Obstacles Layer writes cells either as low-cost "light" obstacles or, upon interaction cues from the progress checker, escalates to "heavy" or "lethal" statuses. Integration with Nav2 is achieved by standard plugin interfaces, with parameters set for clustering resolution, inflation radii, and escalation thresholds.

5. Cost and Risk Assignment Mechanisms

Explicit cost assignment and escalation formulas underpin safe, efficient operation:

• Movable obstacles (Stan et al., 17 Oct 2025) employ:

$$C_\mathrm{master}(x) = \min(C_\mathrm{max},\; C_0(k) \exp\left(-\frac{d(x,k)}{\sigma}\right))$$

where $$C_0(k) \in \{ C_\mathrm{light}, C_\mathrm{heavy}, C_\mathrm{lethal}\}$$, $d(x,k)$ is the closest distance from cell $x$ to the cluster $k$, and $\sigma$ is the decay length. The initial value is light (50), rising to heavy (100) or lethal (254) upon robotic interaction failures.

• In the stochastic chance-constraint MPC (Xu et al., 2021), the effective "cost" of planned risk is the quantified collision probability, set by $\delta$. The risk margin is incorporated via an analytic form involving the difference of means and aggregate covariance.

6. Reactive Feedback and Adaptation

Feedback mechanisms dynamically adjust the representation and cost/risk assignments:

• "Slow-Pose Progress Checker" (Stan et al., 17 Oct 2025): During navigation, if the robot's actual velocity $v_\mathrm{act}$ lags behind the commanded value $v_\mathrm{cmd}$ by more than a ratio $\rho$ over a freeze period, the nearest obstacle is escalated in its assigned cost—first to heavy, then to lethal if stalling persists. This logic is implemented as a ROS2 plugin, operating at ≈10 Hz.
• Temporal goal tracking (Xu et al., 2021): The reference for the MPC planner switches from the original plan to a locally generated avoidance target when an encounter is predicted. This process is formalized via Algorithms 2 and 3 of the paper, favoring targets beyond both proximity and velocity-angle thresholds.

These mechanisms ensure that dynamic obstacles and ambiguous objects (e.g., potentially movable debris) are reclassified and handled with increased caution upon direct robot interaction or near-miss predictions.

7. Implementation and Performance Considerations

Both approaches are designed for real-time deployment with computational efficiency:

• The UAV framework (Xu et al., 2021) employs Quadprog++ for corridor QPs and ACADO for MPC, operating entirely on CPU and using analytic forms for all collision and chance constraints.
• The layered costmap in ROS2 (Stan et al., 17 Oct 2025) is implemented as a plugin stack with configuration via costmap_params.yaml. Key parameters include light/heavy/lethal costs, wall distance thresholds, inflation radii, decay lengths, and progress checking time constants.

Reported performance for the ROS2 method shows 100% success in light-object scenarios and 80–95% in heavy/immovable tests, with drastically fewer deadlocks and traversal times comparable to static-only baselines.

A notable limitation is that both methods require the static map to be a faithful and relatively current depiction of truly immovable structure; significant deviations (e.g., unseen destroyed walls) may lead to conservative or failed planning unless mechanisms for map updating are explicitly layered.

Collectively, layered representations of dynamic obstacles provide a reproducible and computationally tractable solution to planning, risk management, and adaptation in robotic navigation within complex, partially known, and evolving environments (Xu et al., 2021, Stan et al., 17 Oct 2025).