Unconstraining Multi-Robot Manipulation: Enabling Arbitrary Constraints in ECBS with Bounded Sub-Optimality

TL;DR

This work addresses the bottleneck in applying conflict-based search to multi-robot-arm motion planning by removing the strict trade-off between completeness and efficiency. It introduces Generalized ECBS, a framework that supports arbitrary, potentially incomplete constraints while preserving completeness and a bounded sub-optimality guarantee, via lazy CT expansion, multiple focal queues, and dynamic constraint-priority learning (Dynamic Thompson Sampling). The authors formalize M-RAMP, adapt CBS/ECBS to accommodate new constraint types (e.g., sphere and step-priority), and demonstrate substantial performance gains across 4, 6, and 8-robot scenarios with realistic manipulators. The approach achieves higher success rates and competitive runtimes compared to baselines like ECBS and classical motion planners, underscoring the practical impact of principled constraint design in high-DoF multi-robot manipulation. Overall, Gen-ECBS enables robust, scalable MAPF-based planning for complex M-RAMP problems, with broad implications for autonomous assembly and coordination in cluttered workspaces.

Abstract

Multi-Robot-Arm Motion Planning (M-RAMP) is a challenging problem featuring complex single-agent planning and multi-agent coordination. Recent advancements in extending the popular Conflict-Based Search (CBS) algorithm have made large strides in solving Multi-Agent Path Finding (MAPF) problems. However, fundamental challenges remain in applying CBS to M-RAMP. A core challenge is the existing reliance of the CBS framework on conservative "complete" constraints. These constraints ensure solution guarantees but often result in slow pruning of the search space -- causing repeated expensive single-agent planning calls. Therefore, even though it is possible to leverage domain knowledge and design incomplete M-RAMP-specific CBS constraints to more efficiently prune the search, using these constraints would render the algorithm itself incomplete. This forces practitioners to choose between efficiency and completeness. In light of these challenges, we propose a novel algorithm, Generalized ECBS, aimed at removing the burden of choice between completeness and efficiency in MAPF algorithms. Our approach enables the use of arbitrary constraints in conflict-based algorithms while preserving completeness and bounding sub-optimality. This enables practitioners to capitalize on the benefits of arbitrary constraints and opens a new space for constraint design in MAPF that has not been explored. We provide a theoretical analysis of our algorithms, propose new "incomplete" constraints, and demonstrate their effectiveness through experiments in M-RAMP.

Figures (4)

• Figure 1: A team of 4 manipulators collaborating in a bin picking task. Popular MAPF algorithms such as CBS can be applied to multi-arm manipulation but may be ineffective due to their conservative approach to conflict resolution. Our proposed algorithm allows for more efficient planning, by capitalizing on stronger "incomplete" constraints, without compromising theoretical guarantees.
• Figure 2: Given agent $\mathcal{R}_{i}$ in $q^{i}_{4}$ and $\mathcal{R}_{j}$ in $q^{j}_{4}$ conflicting at time $t=4$ and point $p$ (leftmost), we illustrate the constraint landscape when replanning for $\mathcal{R}_{j}$ (top row) and for $\mathcal{R}_{i}$ (bottom row) alongside examples of invalid configurations under the constraint (marked with dashed outlines). When applicable, we include agent configurations (e.g., $q^{i}_{4}$) or sequence of configurations (e.g., $\pi^i$) in the robot base link. From left to right: vertex constraints forbid an agent from taking on its conflicting configuration at $t$. Sphere constraints forbid collisions with a sphere centered at $p$ at time $t$. Avoidance constraints disallow collisions with the conflicting configuration of the other agent at $t$. Priority constraints force an agent to plan around the current path of the other. Rightmost: examples of incompleteness in the sphere and avoidance constraints. We illustrate valid conflict-free configurations between $\mathcal{R}_{i}$ and $\mathcal{R}_{j}$ where each invalidates its imposed constraints. This scenario shows that sphere and avoidance constraints are not mutually disjunctive, and therefore are not complete within CBS.
• Figure 3: Illustration of the CT and priority queues in Generalized ECBS. Each CT node shows its number of conflicts (left subscript), and sum of costs (left superscript). The active priority queue sampled by DTS has a bold perimeter. (a) After the root node $R$ has been expanded, its children are generated lazily (dashed). (b) Node $E$ is chosen from $\text{FOCAL}_\beta$ and evaluated. Upon DTS resampling, $FOCAL_\alpha$ is activated. (c) Node $C$ is chosen and evaluated. (d) Node $C$ was chosen (a second time) and lazily expanded. (e) Node $I$ is chosen and evaluated. (f) Node $I$ is expanded and marked as a goal. We note that the one-step-lazy evaluations may allow for significantly reduced work relative to naively evaluating all child nodes upon expansion -- an operation that does not scale with the number of constraints.
• Figure 4: Comparing planning algorithms in realistic M-RAMP problems. Left: Renders of the planning scenes. Two scenes, with 4 and 8 robots, exhibit dense obstacle clutter while the scene with 6 robots is more open. Right: success rate, planning time, and cost results across 50 tests ($\mu \pm \sigma$). Through a high success rate, we see that Generalized ECBS scales with the number of robots and handles clutter. Middle: a pairwise comparison between Generalized ECBS and the other methods. Looking at tests where both methods succeeded, we report the average ratio of Generalized ECBS's path cost and planning time to that of the other. The path cost is nearly identical among search-based planners. Since Generalized ECBS solves more problems than the others, the pairwise comparison focuses on simpler tests, where Generalized ECBS planning time may show a slight overhead.

Theorems & Definitions (10)

• Definition 1: Complete Constraints
• Definition 2: Vertex Constraint
• Definition 3: Avoidance Constraint
• Definition 4: Priority Constraint
• Definition 5: Sphere Constraints
• Definition 6: Step-Priority Constraints
• Lemma 1
• proof
• Lemma 2
• proof