Ideally, people who navigate together in a complex indoor space share a mental model that facilitates explanation. This paper reports on a robot control system whose cognitive world model is based on spatial affordances that generalize over its perceptual data. Given a target, the control system formulates multiple plans, each with a model-relevant metric, and selects among them. As a result, it can provide readily understandable natural language about the robot’s intentions and confidence, and generate diverse, contrastive explanations that reference the acquired spatial model. Empirical results in large, complex environments demonstrate the robot’s ability to provide human-friendly explanations in natural language.