In the field of autonomous vehicles (AVs), accurately discerning commander intent and executing linguistic commands within a visual context presents a significant challenge. This paper introduces a sophisticated encoder-decoder framework, developed to address visual grounding in AVs.Our Context-Aware Visual Grounding (CAVG) model is an advanced system that integrates five core encoders-Text, Image, Context, and Cross-Modal-with a Multimodal decoder. This integration enables the CAVG model to adeptly capture contextual semantics and to learn human emotional features, augmented by state-of-the-art Large Language Models (LLMs) including GPT-4. The architecture of CAVG is reinforced by the implementation of multi-head cross-modal attention mechanisms and a Region-Specific Dynamic (RSD) layer for attention modulation. This architectural design enables the model to efficiently process and interpret a range of cross-modal inputs, yielding a comprehensive understanding of the correlation between verbal commands and corresponding visual scenes. Empirical evaluations on the Talk2Car dataset, a real-world benchmark, demonstrate that CAVG establishes new standards in prediction accuracy and operational efficiency. Notably, the model exhibits exceptional performance even with limited training data, ranging from 50% to 75% of the full dataset. This feature highlights its effectiveness and potential for deployment in practical AV applications. Moreover, CAVG has shown remarkable robustness and adaptability in challenging scenarios, including long-text command interpretation, low-light conditions, ambiguous command contexts, inclement weather conditions, and densely populated urban environments. The code for the proposed model is available at our Github.