P_MDP_TG

Planner for Markov Decision Processes with Temporal Goals

@ARTICLE{8272366,
  author={M. {Guo} and M. M. {Zavlanos}},
  journal={IEEE Transactions on Automatic Control}, 
  title={Probabilistic Motion Planning Under Temporal Tasks and Soft Constraints}, 
  year={2018},
  volume={63},
  number={12},
  pages={4051-4066},
  doi={10.1109/TAC.2018.2799561}}

Description

This package contains the implementation for policy synthesis algorithms given a probabilistically-labeled Markov Decision Process (MDP) (as the robot motion model) and a Linear Temporal Logic (LTL) formula (as the robot task). It outputs a stationary and finite-memory policy consists of plan prefix and plan suffix, such that the controlled robot behavior fulfills the task with a given lower-bounded risk and minimizes the expected total cost.

Features

• Allows probabilistic labels on MDP states.
• Tunable trade-off between risk and expected total cost in the plan prefix.
• Linear programs for solving constrained stochastic shortest path (SSP).
• Optimization over both plan prefix and suffix.
• Relaxed policy generation for cases where no accepting end components (AECs) exist.
• Interface between LTL formula, Buchi Automaton, Deterministic Robin Automaton and NetworkX graph objects.
• Computing maximal accepting end components (MAEC) of MDPs.
• [New] Clean storage of product automaton via pickle, for translating later to PRISM language, see the interface.

from MDP_TG.mdp import Motion_MDP
from MDP_TG.dra import Dra, Product_Dra
from MDP_TG.lp import syn_full_plan

# construct your motion MDP
motion_mdp = Motion_MDP(node_dict, edge_dict, U, initial_node, initial_label)

# specify your LTL task
surv_task = "& G F a & G F b G F c"

# construct DRA 
dra = Dra(surv_task)

# construct product DRA and accepting pairs
prod_dra = Product_Dra(motion_mdp, dra)
prod_dra.compute_S_f()

# policy synthesis 
allowed_risk = 0.1
best_all_plan = syn_full_plan(prod_dra, allowed_risk)

• [New] Virtual experimental platform based on V_REP.

Dependence

• Install python packages like Networkx, ply
• Compile ltl2ba executable for your OS.
• Compile ltl2dstar executable for your OS.
• Gurobi solver for linear programs. Free for academic use.