In this paper, we consider the problem of deploying a robot from a
specification given as a temporal logic statement about some properties
satisfied by the regions of a large, partitioned environment. We assume that
the robot has noisy sensors and actuators and model its motion through the
regions of the environment as a Markov Decision Process (MDP). The robot
control problem becomes finding the control policy maximizing the probability
of satisfying the temporal logic task on the MDP.
In this paper we present a method for automatically planning robust optimal
paths for a group of robots that satisfy a common high level mission
specification. Each robot's motion in the environment is modeled as a weighted
transition system, and the mission is given as a Linear Temporal Logic (LTL)
formula over a set of propositions satisfied by the regions of the environment.
In addition, an optimizing proposition must repeatedly be satisfied.
We consider the problem of finding a control policy for a Markov Decision
Process (MDP) to maximize the probability of reaching some states while
avoiding some other states. This problem is motivated by applications in
robotics, where such problems naturally arise when probabilistic models of
robot motion are required to satisfy temporal logic task specifications. We
transform this problem into a Stochastic Shortest Path (SSP) problem and
develop a new approximate dynamic programming algorithm to solve it.
In this paper we present a method for automatically planning optimal paths
for a group of robots that satisfy a common high level mission specification.
Each robot's motion in the environment is modeled as a weighted transition
system. The mission is given as a Linear Temporal Logic formula. In addition,
an optimizing proposition must repeatedly be satisfied. The goal is to minimize
the maximum time between satisfying instances of the optimizing proposition.
Our method is guaranteed to compute an optimal set of robot paths.