Aspect Sentiment Triplet Extraction (ASTE) is a challenging task in natural language processing (NLP) that aims to extract triplets from comments. Each triplet comprises an aspect term, an opinion term, and the sentiment polarity of the aspect term. The neural network model developed for this task can enable robots to effectively identify and extract the most meaningful and relevant information from comment sentences, ultimately leading to better products and services for consumers. Most existing end-to-end models focus solely on learning the interactions between the three elements in a triplet and contextual words, ignoring the rich affective knowledge information contained in each word and paying insufficient attention to the relationships between multiple triplets in the same sentence. To address this gap, this study proposes a novel end-to-end model called the Dual Graph Convolutional Networks Integrating Affective Knowledge and Position Information (DGCNAP). This model jointly considers both the contextual features and the affective knowledge information by introducing the affective knowledge from SenticNet into the dependency graph construction of two parallel channels. In addition, a novel multi-target position-aware function is added to the graph convolutional network (GCN) to reduce the impact of noise information and capture the relationships between potential triplets in the same sentence by assigning greater positional weights to words that are in proximity to aspect or opinion terms. The experiment results on the ASTE-Data-V2 datasets demonstrate that our model outperforms other state-of-the-art models significantly, where the F1 scores on 14res, 14lap, 15res, and 16res are 70.72, 57.57, 61.19, and 69.58.