TY - GEN

T1 - Spatial distribution statistics for two-agent optimal navigation with cone-shaped local observation

AU - De Mot, Jan

AU - Feron, Eric

N1 - Generated from Scopus record by KAUST IRTS on 2021-02-18

PY - 2005/9/1

Y1 - 2005/9/1

N2 - In this paper, we study spatially synchronous two-agent navigation on a structured partially unknown graph. The general edge cost statistics are given, and the agents gather and share exact information on the cost of local edges. The agents purpose is to traverse the graph as efficiently as possible. In previous work, we formulate the problem as a Dynamic Program, and exploit the structure of an equivalent Linear Program to compute the optimal value function. Here, we use the optimal policy to formulate a Markov chain with an infinite number of states whose properties we analyze. We present a method that computes the steady state probability distribution of the agent separation, exploiting the repetitive structure of the Markov chain as the agent separation goes to infinity. The results confirms and quantify the intuition that the less rewards, the more beneficial for the agents to spread out. ©2005 AACC.

AB - In this paper, we study spatially synchronous two-agent navigation on a structured partially unknown graph. The general edge cost statistics are given, and the agents gather and share exact information on the cost of local edges. The agents purpose is to traverse the graph as efficiently as possible. In previous work, we formulate the problem as a Dynamic Program, and exploit the structure of an equivalent Linear Program to compute the optimal value function. Here, we use the optimal policy to formulate a Markov chain with an infinite number of states whose properties we analyze. We present a method that computes the steady state probability distribution of the agent separation, exploiting the repetitive structure of the Markov chain as the agent separation goes to infinity. The results confirms and quantify the intuition that the less rewards, the more beneficial for the agents to spread out. ©2005 AACC.

UR - http://www.scopus.com/inward/record.url?scp=23944443826&partnerID=8YFLogxK

M3 - Conference contribution

SP - 1877

EP - 1882

BT - Proceedings of the American Control Conference

ER -