Efficient Multi-Robot Motion Planning for Manifold-Constrained Manipulators by Randomized Scheduling and Informed Path Generation

TL;DR

The paper addresses multi-robot motion planning for high-DOF manipulators constrained to manifolds in narrow, shared workspaces by introducing Scheduling to Avoid Collisions (StAC). StAC combines a high-level coordination-space scheduler that imposes randomized pauses and priorities with a low-level manifold-constrained planner, and it uses an Experience-driven feedback loop via a Collision History and Collision Recorder to guide future sampling. The approach is shown to be probabilistically complete and achieves substantial reductions in low-level path queries (10–100×) and faster solve times on challenging doorway-like tasks compared with state-of-the-art baselines. This work advances scalable, complete MRMP in tight environments with manifold constraints, with implications for complex assembly, surgery, and other high-DOF robotic applications.

Abstract

Multi-robot motion planning for high degree-of-freedom manipulators in shared, constrained, and narrow spaces is a complex problem and essential for many scenarios such as construction, surgery, and more. Traditional coupled and decoupled methods either scale poorly or lack completeness, and hybrid methods that compose paths from individual robots together require the enumeration of many paths before they can find valid composite solutions. This paper introduces Scheduling to Avoid Collisions (StAC), a hybrid approach that more effectively composes paths from individual robots by scheduling (adding random stops and coordination motion along each path) and generates paths that are more likely to be feasible by using bidirectional feedback between the scheduler and motion planner for informed sampling. StAC uses 10 to 100 times fewer paths from the low-level planner than state-of-the-art baselines on challenging problems in manipulator cases.

Figures (8)

• Figure 1: We extend the classic planar doorway problem to high-DoF manipulators. The end effectors of the two arms are constrained to a manifold on the same plane. In this problem, robots must swap end-effector positions by navigating a narrow passage that only allows one robot at a time, requiring one arm to detour and wait to avoid collisions. As shown in \ref{['sce:doorway']}, StAC solves the problem in an average of 5 seconds, while the state-of-the-art hybrid method fails within 60 seconds.
• Figure 2: An illustration of Schedule(P). Robots $a$ and $b$ are in the environment with their start $a_s, b_s$ and goal $a_g, b_g$. Schedule(P) uses a set of individual robot paths to generate a candidate solution. The candidate solution is represented by a sequence of robot configurations. It is always in the same sequence as the path but with repetition of configurations as stops. To transition from composite state $i$ to $i+1$, each robot will either move or stop. If all robots stop, then state $i+1$ is trivial and should be removed.
• Figure 3: The Collision Recorder tracks the number of collisions occurring on each edge during coordination space planning for a given set of paths, $P$. Each path in $P$ initializes its Collision Record with a count of its edges, which is the path length minus one. The record for iteration $i$ is randomly initialized for illustration purposes. During each iteration, collision checking is performed on the candidate solution, and the counter for any edge involved in a collision is incremented by one. If a robot stops, the collision is not counted. For example, a collision between $a_{g}$ and $b_{1,2}$ in the grey region only increments the counter for $b_{1,2}$ from 25 to 26, since robot $a$ is stopped.
• Figure 4: Low-level planners will plan a new path using the previous path in the Collision History. The number near each edge is a normalized Collision Record of the edge. The yellow region is the collision region determined by the random walk algorithm with $c_1$ and $c_2$ as its end vertices. $c_d$ is the detour configuration. The new path is shown in the solid line.
• Figure 5: CDF (Cumulative Distribution Function) of solve time for the manipulator doorway setup with two 7-DOF Franka Panda arms (shown in \ref{['fig:arm_doorway']}. Note that CBSMP cannot solve this problem even once, as indicated by the horizontal line at 0.

Theorems & Definitions (8)

• Lemma 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof
• Theorem 4
• proof