Himanshu Gupta

Date: 1/11/2024

LSN Lecture

MAPF + Hybrid A*

Layout

• What is the formal definition of MAPF?
   
• What are some state-of-the-art solvers for MAPF?
  • Learn about one of them
     
• Hybrid A*
   
• Demo!

MAPF

MAPF

• It is defined by
  • a graph \(G(V,E)\)
  • Set of k agents \(A_1, A_2 ... A_k\)
  • \(s_i \in V\) - starting state for agent i
  • \(g_i \in V\) - goal position for agent i
  • At every time step, the agent can either move or wait (both have same cost)
     
• Goal : Find a sequence of actions to move all agents from their \(s_i\) to \(g_i\) while avoiding collisions and minimizing the total execution time.
  • Collision - two agents occupying the same region in the environment  at  the  same  time

How to solve MAPF problems?

• Early Days (Before 2012)
  • Coupled Approaches: Finds optimal solution but don't scale well.
    • Integer Linear Programming (ILP)
      • an optimization problem with constraints. Only worked well for problems with relatively small numbers of agents and grid sizes.
    • A* and its Variants
  • Decoupled Approaches: Doesn't find the optimal solution but scales well.
    • Sequential Approaches
      • assign every agent a priority value
      • Find path for every agent while considering the path used by the previous agents. 

How to solve MAPF problems?

• 2012  :
  • How can we merge benefits of both the coupled and the decoupled approaches?
  • Welcome CBS!
  • CBS - Conflict Based Search
    • ​Came out in 2012, but was accepted in 2015
      • because of error in optimality guarantee proofs
         
• After 2012 :
  • ICBS - Iterative CBS
  • ECBS - Enhanced CBS
  • The list goes on.....

CBS

• Conflict-Based Search (CBS) algorithm
  • a two-level algorithm for solving MAPF problems optimally.

CBS

CBS

• High-level decision maker 
  • Only finds and adds constraints
     
• Low-level decision maker
  • Finds a solution/path for an agent.
  • Can be any algorithm of the user's choice.
     
• Easily extends to robotics problems we care about!!
  • And yet wasn't done till 2022

K-CBS - Kidodynamic CBS

• Low level planner - RRT

CL-MAPF - Car Like MAPF 

• Low level planner - Hybrid A*

Hybrid A*

• A*, but for continuous state space!
  • Just do discretization smartly.
  • Search in continuous space, but discretize states and put them in bins.
     
• Due to the discretization of the state space, it loses optimality guarantees that \(A^*\) has.
   
• So for a Dubin's car, it will find a drivable path but not the best path (reasonably good though)!

Demo

Steps for MAPF demo

• Install Julia
   
• Clone this repository
  
  https://github.com/himanshugupta1009/MultiAgentPathFinding.jl
   
• Follow the instructions in the README

Steps for Hybrid A* demo

• Install Julia
   
• Open Julia REPL
  • Add the Hybrid A* package using these commands
    
    using Pkg
    Pkg.add("HybridAStar")
     
• Follow the example files available here
  
  https://github.com/CU-ADCL/HybridAStar.jl/tree/master

How can we do this?