COVER:COverage-VErified Roadmaps for Fixed-time Motion Planning in Continuous Semi-Static Environments

TL;DR

COVER addresses fixed-time motion planning in semi-static environments by constructing coverage-verified roadmaps that partition the obstacle configuration space and verify feasibility per partition. It introduces per-edge swept-volume envelopes and decomposition trees to produce binary signatures that encode edge validity, enabling exact problem-space coverage estimation and fixed-time query guarantees. The approach supports heterogeneous obstacle sizes and continuous placements, and is coupled with a coverage estimator to quantify the guaranteed solvable fraction of obstacle configurations. Empirical validation on a 7-DOF Panda demonstrates superior problem-space coverage and faster, reliable query resolution compared with a discretized baseline, illustrating practical impact for industrial robotics in semi-static settings.

Abstract

Having the ability to answer motion-planning queries within a fixed time budget is critical for the widespread deployment of robotic systems. Semi-static environments, where most obstacles remain static but a limited set can vary across queries, exhibit structured variability that can be systematically exploited to provide stronger guarantees than in general motion-planning problems. However, prior approaches in this setting either lack formal guarantees or rely on restrictive discretizations of obstacle configurations, limiting their applicability in realistic domains. This paper introduces COVER, a novel framework that incrementally constructs a coverage-verified roadmap in semi-static environments. By partitioning the obstacle configuration space and solving for feasible paths within each partition, COVER systematically verifies feasibility of the roadmap in each partition and guarantees fixed-time motion planning queries within the verified regions. We validate COVER with a 7-DOF simulated Panda robot performing table and shelf tasks, demonstrating that COVER achieves broader coverage with higher query success rates than prior works.

Figures (5)

• Figure 1: (a) Semi-static motion-planning problem: the robot must grasp a white cylinder while two obstacles may lie anywhere in the dark-blue region. (b)–(d)) Three sampled instances. cover guarantees that for all covered placements, a valid motion plan can be retrieved.
• Figure 2: (a): Simple example with a roadmap containing two edges. Dashed lines indicate the approximate end-effector trajectory of the robot along each edge. (b): Envelopes generated for the two edges. (c) Envelopes of the edges used for partitioning the obstacle configuration space of $o_i$ into disjoint regions. These partitions are organized in a binary space partitioning tree, with each leaf corresponding to an equivalent binary signature.
• Figure 3: Demonstration of cover with two movable obstacles $o_1$ and $o_2$. (a) The roadmap $\mathcal{G}\xspace$ is initialized with start and goal configurations. $\mathcal{M}_1$ and $\mathcal{M}_2$ are partitioned into subregions (\ref{['alg:decompose']}), resulting in distinct subdivisions due to different obstacle sizes. (b) A path (green edge) is added under the assumption of no movable obstacles, after which the decomposition trees of $\mathcal{M}_1$ and $\mathcal{M}_2$ are refined with the new edges. (c) A composite motion planning problem is formed by $o_1$ assuming configurations that invalidate the new edge and $o_2$ assuming configurations that block goal configuration $g_2$. A feasible path is then added to $\mathcal{G}\xspace$. The process repeats until $\mathcal{M}_\text{uncov}$ is exhausted or a set number of consecutive failures occurs.
• Figure 4: Semi-static environments with 2 movable obstacles, used for evaluating the object-pick tasks. (a)Table-Pick with target object and movable obstacles on a table surface. (b)Shelf-High with target and obstacles on the upper rack. (c)Shelf-Low with target and obstacles on the lower rack.
• Figure 5: Problem-space coverage across environments. (a) Median coverage of app and cover over five trials for each obstacle-size pair. Bars show median values, with green bars denoting the maximum feasible coverage after filtering problems with all starts or all goals invalid. (b) Coverage relative to the initial disjoint paths used to warm-start both methods. Dots indicate individual trial results for cover and Squares correspond to trial results of app.