A General Theory of Motion Planning Complexity: Characterizing Which Gadgets Make Games Hard

12/10/2018
by   Erik D. Demaine, et al.
0

We build a general theory for characterizing the computational complexity of motion planning of robot(s) through a graph of "gadgets", where each gadget has its own state defining a set of allowed traversals which in turn modify the gadget's state. We study two families of such gadgets, one which naturally leads to motion planning problems with polynomially bounded solutions, and another which leads to polynomially unbounded (potentially exponential) solutions. We also study a range of competitive game-theoretic scenarios, from one player controlling one robot to teams of players each controlling their own robot and racing to achieve their team's goal. Under small restrictions on these gadgets, we fully characterize the complexity of bounded 1-player motion planning (NL vs. NP-complete), unbounded 1-player motion planning (NL vs. PSPACE-complete), and bounded 2-player motion planning (P vs. PSPACE-complete), and we partially characterize the complexity of unbounded 2-player motion planning (P vs. EXPTIME-complete), bounded 2-team motion planning (P vs. NEXPTIME-complete), and unbounded 2-team motion planning (P vs. undecidable). These results can be seen as an alternative to Constraint Logic (which has already proved useful as a basis for hardness reductions), providing a wide variety of agent-based gadgets, any one of which suffices to prove a problem hard.

READ FULL TEXT

page 2

page 11

page 16

research
06/09/2018

Computational Complexity of Motion Planning of a Robot through Simple Gadgets

We initiate a general theory for analyzing the complexity of motion plan...
research
05/07/2020

Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets

We analyze the computational complexity of motion planning through local...
research
06/01/2023

Complexity of Motion Planning of Arbitrarily Many Robots: Gadgets, Petri Nets, and Counter Machines

We extend the motion-planning-through-gadgets framework to several new s...
research
07/14/2022

PSPACE-Completeness of Reversible Deterministic Systems

We prove PSPACE-completeness of several reversible, fully deterministic ...
research
03/06/2019

The Parameterized Complexity of Motion Planning for Snake-Like Robots

We study the parameterized complexity of a variant of the classic video ...
research
03/07/2020

Complexity of Planning

This is a chapter in the Encyclopedia of Robotics. It is devoted to the ...
research
03/25/2021

Shadoks Approach to Low-Makespan Coordinated Motion Planning

This paper describes the heuristics used by the Shadoks team for the CG:...

Please sign up or login with your details

Forgot password? Click here to reset