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Distributed Autonomous Systems Project (2023-24)

Course Project: Distributed Classification and Multi-Robot Control

This project, developed as part of the Distributed Autonomous Systems course, focuses on two main tasks: distributed classification via logistic regression and multi-robot control using aggregative optimization. The project demonstrates advanced skills in distributed optimization, machine learning, and robotics, with implementations in Python and ROS 2.

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Task 1: Distributed Classification via Logistic Regression

Objective: Design and implement a distributed optimization algorithm to solve a nonlinear classification problem using logistic regression.

1. Distributed Optimization:

   • Implemented the Gradient Tracking algorithm to solve a consensus optimization problem of the form:
     [ \min_z \sum_{i=1}^N \ell_i(z), \quad z \in \mathbb{R}^d ]
     where (\ell_i) is a quadratic function.
   • Tested the algorithm on various graph topologies (e.g., cycle, path, star) with weights determined by the Metropolis-Hastings method.
   • Visualized the convergence of the cost function and gradient norms across iterations.

2. Centralized Classification:

   • Generated a dataset of (M) points in (\mathbb{R}^d) with binary labels.
   • Implemented a centralized gradient method to minimize the logistic regression cost function:
     [ \min_{w,b} \sum_{m=1}^M \log\left(1 + \exp(-p^m(w^\top \phi(D^m) + b))\right) ]
     where (\phi) is a nonlinear mapping (e.g., quadratic for elliptical separation).
   • Evaluated the algorithm on different dataset patterns and visualized convergence.

3. Distributed Classification:

   • Split the dataset into (N) subsets and extended the Gradient Tracking algorithm for distributed classification.
   • Tested the algorithm on various dataset sizes and patterns, demonstrating convergence to a stationary point.
   • Computed the percentage of misclassified points to evaluate solution quality.

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Task 2: Aggregative Optimization for Multi-Robot Systems

Objective: Develop a distributed control algorithm for a team of robots to maintain formation while moving toward private targets.

1. Problem Setup:

   • Formalized the problem as an aggregative optimization problem:
     [ \min_z \sum_{i=1}^N \ell_i(z_i, \sigma(z)), \quad \sigma(z) = \frac{1}{N} \sum_{i=1}^N \phi_i(z_i) ]
     where (\ell_i) is a cost function balancing formation tightness and target proximity.
   • Implemented the Aggregative Tracking algorithm in Python, enabling robots to:
     • Maintain a tight formation.
     • Move toward private targets.
   • Conducted simulations with varying cost function parameters, target locations, and moving targets.

2. ROS 2 Implementation:

   • Created a ROS 2 package in Python to implement the Aggregative Tracking algorithm.
   • Simulated robot behavior using RViz, demonstrating real-time distributed control.

3. Corridor Navigation:

   • Designed a new cost function to enable the robot team to navigate through a corridor without colliding with walls.
   • Tested the implementation in ROS 2, showcasing the team's ability to reach targets while maintaining formation and avoiding obstacles.

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Key Skills Demonstrated

• Distributed Optimization: Gradient Tracking, consensus optimization, and aggregative optimization.
• Machine Learning: Logistic regression, nonlinear classification, and dataset generation.
• Robotics: Multi-robot control, formation maintenance, and ROS 2 implementation.
• Programming: Python, MATLAB, ROS 2, and simulation tools (RViz).
• Data Visualization: Convergence plots, cost function evolution, and animated robot behavior.

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Impact and Results

• Successfully implemented distributed algorithms for classification and multi-robot control, demonstrating scalability and robustness.
• Achieved high classification accuracy and effective robot coordination in simulated environments.
• Provided insights into the trade-offs between formation tightness and target proximity in multi-robot systems.