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Multi-Robot Trajectory Planning via Constrained Bayesian Optimization and Local Cost Map Learning with STL-Based Conflict Resolution

Sourav Raxit, Abdullah Al Redwan Newaz, Jose Fuentes, Paulo Padrao, Ana Cavalcanti, Leonardo Bobadilla

TL;DR

This work proposes a two-stage framework integrating sampling-based online learning with formal STL reasoning, ensuring specification satisfaction while maintaining scalability and probabilistic completeness in multi-robot motion planning under Signal Temporal Logic specifications.

Abstract

We address multi-robot motion planning under Signal Temporal Logic (STL) specifications with kinodynamic constraints. Exact approaches face scalability bottlenecks and limited adaptability, while conventional sampling-based methods require excessive samples to construct optimal trajectories. We propose a two-stage framework integrating sampling-based online learning with formal STL reasoning. At the single-robot level, our constrained Bayesian Optimization-based Tree search (cBOT) planner uses a Gaussian process as a surrogate model to learn local cost maps and feasibility constraints, generating shorter collision-free trajectories with fewer samples. At the multi-robot level, our STL-enhanced Kinodynamic Conflict-Based Search (STL-KCBS) algorithm incorporates STL monitoring into conflict detection and resolution, ensuring specification satisfaction while maintaining scalability and probabilistic completeness. Benchmarking demonstrates improved trajectory efficiency and safety over existing methods. Real-world experiments with autonomous surface vehicles validate robustness and practical applicability in uncertain environments. The STLcBOT Planner will be released as an open-source package, and videos of real-world and simulated experiments are available at https://stlbot.github.io/.

Multi-Robot Trajectory Planning via Constrained Bayesian Optimization and Local Cost Map Learning with STL-Based Conflict Resolution

TL;DR

This work proposes a two-stage framework integrating sampling-based online learning with formal STL reasoning, ensuring specification satisfaction while maintaining scalability and probabilistic completeness in multi-robot motion planning under Signal Temporal Logic specifications.

Abstract

We address multi-robot motion planning under Signal Temporal Logic (STL) specifications with kinodynamic constraints. Exact approaches face scalability bottlenecks and limited adaptability, while conventional sampling-based methods require excessive samples to construct optimal trajectories. We propose a two-stage framework integrating sampling-based online learning with formal STL reasoning. At the single-robot level, our constrained Bayesian Optimization-based Tree search (cBOT) planner uses a Gaussian process as a surrogate model to learn local cost maps and feasibility constraints, generating shorter collision-free trajectories with fewer samples. At the multi-robot level, our STL-enhanced Kinodynamic Conflict-Based Search (STL-KCBS) algorithm incorporates STL monitoring into conflict detection and resolution, ensuring specification satisfaction while maintaining scalability and probabilistic completeness. Benchmarking demonstrates improved trajectory efficiency and safety over existing methods. Real-world experiments with autonomous surface vehicles validate robustness and practical applicability in uncertain environments. The STLcBOT Planner will be released as an open-source package, and videos of real-world and simulated experiments are available at https://stlbot.github.io/.
Paper Structure (10 sections, 19 equations, 5 figures, 1 table, 2 algorithms)

This paper contains 10 sections, 19 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Decoupled Robot Planning
  4. Signal Temporal Logic enhanced KCBS
  5. Experiments and Results
  6. STL Specification and Hierarchical Decomposition
  7. Indoor Experiments and Qualitative analysis
  8. Outdoor Experiments in a Lake environment
  9. Benchmark Results
  10. Conclusion

Figures (5)

  • Figure 1: STLcBOT planner applied to three UGVs navigating a cluttered indoor environment. Subfigures \ref{['subfig:gv_e_1']} and \ref{['subfig:gv_e_2']} demonstrate kinodynamically-constrained trajectories that enable accurate trajectory following and collision avoidance.
  • Figure 2: Comparison of RRT and cBOT planners for twelve robots under STL constraints in forest and cross-hall environments. Figures \ref{['subfig:sub1']} and \ref{['subfig:sub3']} show RRT-generated trajectories, while Figures \ref{['subfig:sub2']} and \ref{['subfig:sub4']} display cBOT-generated paths. cBOT produces notably shorter and smoother trajectories compared to the longer, less structured paths from RRT-based planning.
  • Figure 3: Field validation of STLcBOT using two ASVs in a lake environment with complex navigation scenarios. Figs.\ref{['subfig:asv_1']}--\ref{['subfig:asv_3']} show planned trajectories, while Figs.\ref{['subfig:asv_4']}--\ref{['subfig:asv_6']} display ASVs executing missions in the operational area.
  • Figure 4: STLcBOT planner applied to three ASVs navigating in a lake environment with challenging spatial configurations. Subfigures (\ref{['subfig:asv_3_1']}) and (\ref{['subfig:asv_3_2']}) show trajectory execution where ASVs reach their respective goals while avoiding fountain obstacles.
  • Figure 5: Benchmark comparison of multi-robot motion planning algorithms across four representative environments (Env. 1: empty, Env. 2: cross-hall, Env. 3: forest, Env. 4: bugtrap). The columns report success rates, runtimes, and path lengths as the number of robots increases. The proposed STLcBOT, together with other cBOT-based methods (KcBOT, PPcBOT) kottinger2022conflictma2019searching, consistently achieves near-perfect success and efficient paths with tractable runtimes. RRT-based methods (PPRRT, STLRRT, KRRT) lavalle2001randomizedkottinger2022conflictma2019searchingmaler2004monitoring degrade under clutter and density, while convex optimization–based approaches (PBS+STGCS, SP+STGCS, RP+STGCS) tang2025space and temporal sampling extension (SP+STRRT*) tang2025space generate competitive paths when successful but fail to scale, particularly in Env. 3.

Theorems & Definitions (4)

  • Definition 1: Signal Temporal Logic (STL) Semantics
  • Definition 2: MA-STL Formula
  • Definition 3: Kinodynamic Constraints
  • Definition 4: MA-STL Satisfaction with Robustness