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Extended Version: Multi-Robot Motion Planning with Cooperative Localization

Anne Theurkauf, Nisar Ahmed, Morteza Lahijanian

TL;DR

This work addresses uncertain multi-robot motion planning with cooperative localization (CL-MRMP), where inter-robot measurements create correlations that must be accounted for to guarantee safety. It formalizes the problem as a chance-constrained planning task and extends a belief-based, sampling-based planner by leveraging a centralized estimator to propagate the expected belief $\mathbf{b}(X_k)=\mathcal{N}(\hat{X}_k, \Gamma_k)$, preserving probabilistic completeness. The authors introduce Belief-RRT and Belief-EST adaptions, along with efficient, conservative methods to validate chance constraints through probability contours and per-type allocation ($p_{obs}$, $p_{rob}$, $p_{ eg CL}$). To improve performance, three biasing techniques—State Cloning, Distance Weighting, and Re-Branching—encourage cooperative sensing behaviors, with benchmarks showing context-dependent gains. Overall, the approach yields safe, coordinated plans under uncertainty and CL requirements, while acknowledging scalability limitations and pointing to decoupled planning as a path for future work.

Abstract

We consider the uncertain multi-robot motion planning (MRMP) problem with cooperative localization (CL-MRMP), under both motion and measurement noise, where each robot can act as a sensor for its nearby teammates. We formalize CL-MRMP as a chance-constrained motion planning problem, and propose a safety-guaranteed algorithm that explicitly accounts for robot-robot correlations. Our approach extends a sampling-based planner to solve CL-MRMP while preserving probabilistic completeness. To improve efficiency, we introduce novel biasing techniques. We evaluate our method across diverse benchmarks, demonstrating its effectiveness in generating motion plans, with significant performance gains from biasing strategies.

Extended Version: Multi-Robot Motion Planning with Cooperative Localization

TL;DR

This work addresses uncertain multi-robot motion planning with cooperative localization (CL-MRMP), where inter-robot measurements create correlations that must be accounted for to guarantee safety. It formalizes the problem as a chance-constrained planning task and extends a belief-based, sampling-based planner by leveraging a centralized estimator to propagate the expected belief , preserving probabilistic completeness. The authors introduce Belief-RRT and Belief-EST adaptions, along with efficient, conservative methods to validate chance constraints through probability contours and per-type allocation (, , ). To improve performance, three biasing techniques—State Cloning, Distance Weighting, and Re-Branching—encourage cooperative sensing behaviors, with benchmarks showing context-dependent gains. Overall, the approach yields safe, coordinated plans under uncertainty and CL requirements, while acknowledging scalability limitations and pointing to decoupled planning as a path for future work.

Abstract

We consider the uncertain multi-robot motion planning (MRMP) problem with cooperative localization (CL-MRMP), under both motion and measurement noise, where each robot can act as a sensor for its nearby teammates. We formalize CL-MRMP as a chance-constrained motion planning problem, and propose a safety-guaranteed algorithm that explicitly accounts for robot-robot correlations. Our approach extends a sampling-based planner to solve CL-MRMP while preserving probabilistic completeness. To improve efficiency, we introduce novel biasing techniques. We evaluate our method across diverse benchmarks, demonstrating its effectiveness in generating motion plans, with significant performance gains from biasing strategies.

Paper Structure

This paper contains 23 sections, 2 theorems, 17 equations, 14 figures, 6 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Robot Dynamics
  4. Robot Measurements
  5. Centralized Estimation and Cooperative Localization
  6. Motion Plan and Control
  7. Probabilistic Objectives
  8. CL-MRMP Problem
  9. Sampling-Based Planner Framework
  10. Belief-$\mathcal{A}$ for CL-MRMP
  11. Efficient Validation of Chance Constraints
  12. Probability allocation
  13. Robot-Obstacle Collision Checking
  14. Robot-Robot Collision Checking
  15. CL Condition
  16. ...and 8 more sections

Key Result

Theorem 1

The validity checking Alg. alg:RobotRobotCollision guarantees the satisfaction of the robot-robot collision constraint $P^{ij_k}_{coll} \leq p_{rob}$ if it returns True.

Figures (14)

  • Figure 1: CL-MRMP solution plan for 2 robots with motion and sensing uncertainties (initial states are near the bottom of the figure, and their goal regions are indicated by red and cyan circles). Cyan robot lacks onboard sensors, but the solution plan enables it to use the red robot as a sensor, reducing its uncertainty and allowing it to successfully navigate to its goal region. Afterward, the plan guides the red robot to its goal. (trajectory circles: 2$\sigma$ bounds).
  • Figure 2: Test Environments
  • Figure 3: Two Robot Environments
  • Figure 4: Benchmarking results for (a)-(b) collision rates of 2 robots in Random Env., and (c) success rates for 2-6 robots in Pincer Env.
  • Figure 5: Random Results
  • ...and 9 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof