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DR-TVFC of Multi-Agent Systems under Disturbances

Distributed Robust Time-Varying Formation Control for Multi-Agent Systems under Disturbances

Authors: Guang-Ze Yang¹ and Zi-Jiang Yang²

DR-TVFC Framework

Abstract​

This work considers the problem of time-varying formation tracking control of second-order multi-agent systems under disturbances. The DR-TVFC (Distributed Robust Time-Varying Formation Control) approach is proposed, including distributed finite-time estimators of the leader's states and sliding mode time-varying formation controllers.

Key Contributions:

  1. Distributed Finite-Time Estimation: Each agent can quickly estimate the leader's states through the communication network using distributed finite-time estimators based on sliding mode estimation.

  2. Sliding Mode Formation Controller: Utilizing the estimates of the leader's states, a sliding mode time-varying formation controller is designed using the prescribed time modification function.

  3. Enhanced Robustness: Unlike traditional distributed control laws relying on the exchange of agents' states, the proposed control design achieves great robustness and stability of the overall system by exchanging the estimates of the leader's states.

  4. Theoretical Guarantees: According to Lyapunov stability analysis, we prove that the proposed approach enables the sliding variables to achieve fast finite-time convergence.

Publication Status

This work has been accepted by the 2024 63rd Annual Conference of SICE.

Research Framework​

Research Conclusion

The framework demonstrates the integration of distributed estimation and robust control techniques for achieving time-varying formation control in multi-agent systems.

Source Code and Implementation​

GitHub Repository

Source Code: https://github.com/youkoutaku/DR-TVFC

The complete implementation includes MATLAB simulation code, documentation, and visualization tools.

Program Structure​

Core Configuration​

  • config.m: System parameters and control parameters configuration

Signal Generation​

  • Leader_state.m: Generate reference signal (trajectory) and plot figures
  • Formation_shape.m: Generate time-varying formation shape and plot figures

Main Implementation​

  • main.m: Main simulation file containing:
    • Distributed finite-time estimator implementation
    • Prescribed time modification functions
    • Sliding mode formation controller
    • Complete system simulation

Visualization Programs (Plot/ directory)​

Main Figures​

  1. fig_motion.m: 3D plotting of agents' movement trajectories
  2. fig_error_e.m: Estimation errors of the distributed estimator
  3. fig_states.m: State evolution of all agents
  4. fig_error_pro.m: Formation controller tracking errors
  5. fig_input.m: Control input signals
  6. Animation.m: Real-time animation of agents' movement (run after fig_states.m)

Additional Analysis Figures​

  1. fig_states_e.m: Estimator state evolution
  2. fig_vinput.m: Virtual input signals of the estimator
  3. fig_em.m: Modified formation tracking errors
  4. fig_xi.m: Prescribed time modification function visualization
  5. fig_sliding.m: Sliding variable evolution

Running the Simulation​

To execute the complete simulation and analysis:

build.m

This script will run the entire simulation pipeline and generate all visualization results.

Key Technical Features​

1. Distributed Finite-Time Estimation​

  • Sliding Mode Based: Robust estimation against disturbances
  • Finite-Time Convergence: Fast convergence to true leader states
  • Network Communication: Efficient information exchange protocol

2. Prescribed Time Modification​

  • Time-Varying Formation: Dynamic formation shape changes
  • Prescribed Convergence: Guaranteed convergence within specified time
  • Disturbance Rejection: Robust performance under external disturbances

3. Sliding Mode Control​

  • Robust Control: Inherent robustness to uncertainties and disturbances
  • Finite-Time Convergence: Fast system response
  • Chattering Reduction: Advanced techniques to minimize control chattering

Development History and Updates​

Recent Updates​

2024-08-01

  • Enhanced Animation.m program for improved presentation capabilities

2024-06-25

  • Globalized agent states to utilize matrix computation instead of iterative loops
  • Improved computational efficiency

Major Milestones​

2024-01-21

  • Implemented time-varying formation shape using SMFC algorithm

2023-11-26

  • Introduced distributed state estimation for consensus tracking control
  • Enhanced leader state estimation capabilities

2023-09-08

  • Integrated prescribed time modification function to formation tracking errors in SMFC

2023-07-30

  • Developed sliding mode formation controller (SMFC) for centralized leader-follower architecture

Ongoing Research​

2023-03-11

  • Collision avoidance for multi-agent systems (ongoing development)

2023-11-06

  • Neural network integration for disturbance handling (experimental phase)

Applications and Impact​

Robotics Applications​

  • Autonomous Vehicle Formation: Coordinated movement of autonomous vehicles
  • Drone Swarms: Formation flying and collaborative missions
  • Mobile Robot Teams: Warehouse automation and logistics

Industrial Applications​

  • Manufacturing Systems: Coordinated robotic assembly lines
  • Process Control: Multi-unit chemical process coordination
  • Smart Grid: Distributed energy system coordination

Research Significance​

  • Theoretical Advancement: Novel approach to distributed robust control
  • Practical Implementation: MATLAB-based tools for research and education
  • Community Contribution: Open-source implementation for reproducible research

Future Directions​

  1. Enhanced Collision Avoidance: Integration of sophisticated obstacle avoidance algorithms
  2. Machine Learning Integration: Neural network-based disturbance estimation and compensation
  3. Experimental Validation: Hardware implementation and real-world testing
  4. Scalability Studies: Performance analysis with larger agent populations

Author Information​

¹ Guang-Ze Yang
Department of Mechanical Systems Engineering, Ibaraki University, Hitachi, Japan
Tel: +81-294-38-5205
Email: 24nm499s@vc.ibaraki.ac.jp

² Zi-Jiang Yang
Department of Mechanical Systems Engineering, Ibaraki University, Hitachi, Japan
Tel: +81-294-38-5205
Email: shikoh.yoh.zijiang@vc.ibaraki.ac.jp

Research Impact

This research contributes to the advancement of distributed control theory and provides practical tools for multi-agent system formation control applications. The open-source implementation facilitates further research and development in the field.