  Robots are required to not only learn spatial concepts autonomously but also
utilize such knowledge for various tasks in a domestic environment. Spatial
concept represents a multimodal place category acquired from the robot's
spatial experience including vision, speech-language, and self-position. The
aim of this study is to enable a mobile robot to perform navigational tasks
with human speech instructions, such as `Go to the kitchen', via probabilistic
inference on a Bayesian generative model using spatial concepts. Specifically,
path planning was formalized as the maximization of probabilistic distribution
on the path-trajectory under speech instruction, based on a
control-as-inference framework. Furthermore, we described the relationship
between probabilistic inference based on the Bayesian generative model and
control problem including reinforcement learning. We demonstrated path planning
based on human instruction using acquired spatial concepts to verify the
usefulness of the proposed approach in the simulator and in real environments.
Experimentally, places instructed by the user's speech commands showed high
probability values, and the trajectory toward the target place was correctly
estimated. Our approach, based on probabilistic inference concerning
decision-making, can lead to further improvement in robot autonomy.
