I want my coffee hot! Learning to find people under spatio-temporal constraints

In this paper we present a probabilistic model for spatio-temporal patterns of human activities that enable robots to blend themselves into the workflows and daily routines of people. The model, called spatial affordance map, is a non-homogeneous spatial Poisson process that relates space, time and occurrence probability of activity events. We describe how learning and inference is made and present a novel planning algorithm that produces paths which maximize the probability to encounter a person. We show that the problem is a special class of the orienteering problem that can be solved as a finite horizon Markov decision process. We develop a simulator of populated office environments to validate the model and the planning algorithm. The simulated agents follow activity patterns learned by administering a questionnaire to 27 colleagues over two weeks. The experiments shows that the model is statistically valid with respect to both the Anderson-Darling test and the expected waiting time estimation. They further show that the proposed algorithm is able to find optimal paths.