Communication-aware Hierarchical Map Compression of Time-Varying Environments for Mobile Robots

TL;DR

The paper tackles compressing time-varying probabilistic occupancy grids for mobile robots under bandwidth limits. It introduces a map-innovation based reparameterization and enforces a hierarchical, multi-resolution quadtree encoder to balance distortion and transmission size, solving an ILP-like problem at each time step. The approach yields an online algorithm that can operate without prior knowledge of map dynamics and demonstrates effective compression and tracking in both static and dynamic environments. This framework enables scalable inter-agent map sharing and on-board memory efficiency in resource-constrained robotic networks.

Abstract

In this paper, we develop a systematic framework for the time-sequential compression of dynamic probabilistic occupancy grids. Our approach leverages ideas from signal compression theory to formulate an optimization problem that searches for a multi-resolution hierarchical encoder that balances the quality of the compressed map (distortion) with its description size, the latter of which relates to the bandwidth required to reliably transmit the map to other agents or to store map estimates in on-board memory. The resulting optimization problem allows for multi-resolution map compressions to be obtained that satisfy available communication or memory resources, and does not require knowledge of the occupancy map dynamics. We develop an algorithm to solve our problem, and demonstrate the utility of the proposed framework in simulation on both static (i.e., non-time varying) and dynamic (time-varying) occupancy maps.

Figures (9)

• Figure 1: (Bottom left) Finest-resolution $4\times 4$ grid with cells $\{x_1,\ldots,x_{16}\}$. (Bottom right) compressed grid aggregating cells $\{x_1,x_2,x_5,x_6\}$ to node $t_1$, cells $\{x_9,x_{10},x_{13},x_{14}\}$ to $t_2$, and so on. (Top) The quadtree tree $\mathcal{T}$ shown in black that corresponds to the compressed grid at right. The quadtree $\mathcal{T}_\mathcal{X}$ is the tree containing all the finest resolution cells $x_1,\ldots,x_{16}$ as leaf nodes, with the (sub)tree $\mathcal{T}_{\mathcal{X}(t_1)}$ shown by tree contained entirely within the dashed circle. $\mathcal{T}$ has seven leaf nodes (i.e., $\mathcal{N}_{\text{leaf}}(\mathcal{T}) = \{t_1,t_2,t_3,x_3,x_4,x_7,x_8\}$) with corresponding regions $S_1^{\mathcal{T}}=\{x_1,x_2,x_5,x_6\},~S_2^{\mathcal{T}}=\{x_9,x_{10},x_{13},x_{14}\}$, and so forth.
• Figure 2: Illustration of integer program constraints. (top) For the tree shown, the interior nodes (i.e., those nodes with children) are $\{t_1,t_2,t_3,t_4,t_5\}$. To represent an allowable pruning of the tree (bottom left), it must be the case that for any of the nodes $t_1,~t_2,~t_3$ or $t_4$ to be expanded, their parent $t_5$ must be expanded as well. (bottom right) An invalid pruning of the tree obtained by not enforcing the parental expansion constraint, with $t_3$ expanded without the expansion of $t_5$. By taking $[\mathbf z]_i$ to be the state (expanded or not) of node $t_i$, we see that for valid pruning we have $[\mathbf z]_i - [\mathbf z]_5 \leq 0$ for each $i = 1,\ldots,4$. Collecting these inequalities leads to \ref{['eq:encCons2']}.
• Figure 3: (a) The 128$\times$128 probabilistic environment. (b) Full-resolution 128$\times$128 probabilistic environment together with amoeba path for time-varying map compression. Grey scale intensity corresponds to probability that a cell is occupied.
• Figure 4: Distortion and number of leaf nodes (as percentage of finest-resolution map) vs. time-step. (a) Distortion vs. time-step. (b) Number of leaf nodes of the tree encoder solution vs. time-step with the constraint $b_k$ shown.
• Figure 5: Estimated map sequence $\hat{X}_k$.

Theorems & Definitions (2)

• Proposition 1
• proof