Virtual Confinement Zone (VCZ) for Symbolic Control

This repository implements the Virtual Confinement Zone (VCZ) framework, as described in the research paper: "Scalable and Approximation-free Symbolic Control for Unknown Euler-Lagrange Systems".

The project builds upon the foundational SCOTS Toolbox (Symbolic Control of Transition Systems) to provide robust control strategies for Euler-Lagrange systems with unknown dynamics.

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Overview

Traditional symbolic control requires precise models or conservative approximations. The VCZ approach enables:

• Scalable Synthesis: Efficiently handles complex systems by confining them within parameterized zones.
• Model-Free Guarantee: Provides safety and reachability even when system dynamics are unknown.
• Integrated Workflow: Combines C++ for high-performance controller synthesis with MATLAB for simulation and visualization.

Getting Started

Prerequisites

• A C++11 compliant compiler (Clang recommended).
• MATLAB (for post-processing and simulation).
• CUDD Library (Colorado University Decision Diagram).

Installation

1. Clone the Repository:

   git clone https://github.com/FocasLab/Virtual-Confinement-Zone.git
   cd Virtual-Confinement-Zone

2. Install CUDD: Follow the instructions in INSTALL_CUDD.md to build the library locally.

Docker-based Execution

For a quick setup without manual C++ dependency management:

1. Build/Run: Refer to DOCKER_INSTRUCTIONS.md for commands to build the image and run containers with volume mounting.
2. Inside Container: Use the same synthesis steps as described in the Manipulator workflows.
3. Visualization: All outputs are synced to your local machine for use in MATLAB.

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Repository Structure

• ./examples/: Contains benchmark implementations:
  • one_arm: Single-arm manipulator using SCOTS + MATLAB.
  • two_arm: Two-arm manipulator (2R) using SCOTS + MATLAB.
  • MultiAgent: Multi-agent system implemented entirely in MATLAB.
• ./doc/: Doxygen-generated C++ documentation.
• ./mfiles/: Core MATLAB functions for symbolic control and VCZ visualization.
• ./src/: Underlying SCOTS header-only library.

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Example Workflows

1. One-Arm & Two-Arm Manipulators

These examples use the SCOTS toolbox for controller synthesis.

1. Build: Navigate to examples/one_arm (or two_arm) and run make.
2. Synthesize: Execute ./one_arm_scots (or ./two_arm_scots) to generate controller.scs.
3. Export: Open MATLAB, cd to the example folder, and run to_csv.m to convert the controller to csv format.
4. Simulate: Run the main manipulator script (e.g., One_arm_manipulator.m) to simulate and visualize the results.

2. Multi-Agent Systems

This example is handled directly within MATLAB.

1. Synthesize: Run VCZ.m to compute the VCZ center trajectory and save poses.csv.
2. Control: Run VCZ_control2.m to track the simulated trajectory.

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Citation

If you use this work in your research, please cite:

@misc{das2025scalableapproximationfreesymboliccontrol,
      title={Scalable and Approximation-free Symbolic Control for Unknown Euler-Lagrange Systems},
      author={Ratnangshu Das and Shubham Sawarkar and Pushpak Jagtap},
      year={2025},
      eprint={2509.19859},
      archivePrefix={arXiv},
      primaryClass={eess.SY},
      url={https://arxiv.org/abs/2509.19859},
}

@inproceedings{rungger2016scots,
      author={Rungger, Matthias and Zamani, Majid},
      title={SCOTS: A Tool for the Synthesis of Symbolic Controllers},
      booktitle={Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control (HSCC)},
      year={2016},
      doi={10.1145/2883817.2883834}
}

Acknowledgments

We acknowledge Matthias Rungger for the original SCOTS toolbox. This branch extends the toolbox to support VCZ-based control for Euler-Lagrange systems.