Grounded natural language understanding in Human-Robot Interaction (HRI) requires integrating linguistic, visual, and world knowledge to ensure effective task execution. We propose an approach that enhances Multi-Modal Large Language Models (MLLMs) with a novel explicit dialogue planning phase, allowing robotic agents to systematically refine their understanding of ambiguous commands through structured clarification steps. This reduces hallucinations and improves task feasibility.To evaluate this approach, we introduce a novel dataset of over 1,100 annotated dialogues in English and Italian, designed for fine-tuning and assessing Multi-Modal models in HRI scenarios. Experimental results show that dialogue planning improves response accuracy and quality, and contributes to cross-lingual generalisation, enabling models trained in one language to transfer effectively to another. To the best of our knowledge, this is the first application of structured, goal-driven, and explicit dialogue planning in Multi-Modal LLMs for grounded interaction.