$ $Acoustic-to-articulatory inversion (AAI) involves mapping from the acoustic space to the articulatory space. Signal-processing features like the MFCCs, have been widely used for the AAI task. For subjects with dysarthric speech, AAI is challenging because of an imprecise and indistinct pronunciation. In this work, we perform AAI for dysarthric speech using representations from pre-trained self-supervised learning (SSL) models. We demonstrate the impact of different pre-trained features on this challenging AAI task, at low-resource conditions. In addition, we also condition x-vectors to the extracted SSL features to train a BLSTM network. In the seen case, we experiment with three AAI training schemes (subject-specific, pooled, and fine-tuned). The results, consistent across training schemes, reveal that DeCoAR, in the fine-tuned scheme, achieves a relative improvement of the Pearson Correlation Coefficient (CC) by ${\sim}$1.81\% and ${\sim}$4.56\% for healthy controls and patients, respectively, over MFCCs. In the unseen case, we observe similar average trends for different SSL features. Overall, SSL networks like wav2vec, APC, and DeCoAR, which are trained with feature reconstruction or future timestep prediction tasks, perform well in predicting dysarthric articulatory trajectories.