Brachytherapy (BT) is an essential component in the treatment of cervical cancer as it allows for locally delivering a high dose to the tumour with minimal trauma to surrounding tissues and organs at risk (OARs). However, in advanced cervical cancer patients commercially available BT applicators are particularly ill-adapted and therefore result in suboptimal local control and frequent occurrence of substantial tissue morbidity. Additionally, cervical cancer BT is associated with large dosimetric uncertainty which has been shown to significantly impact the delivered dose and the occurrence of normal tissue complications. The clinical outcomes of treatment may be improved through combined efforts in sophisticated applicator design and robust treatment optimisation. Patient-tailored BT applicators have been introduced to improve dose conformity, but currently rely on manual indication of needle channels. Automated needle channel planning software exists, but does not account for OAR dose constraints or uncertainty in planning. Robust treatment optimisation potentially improves the dose conformity of plans in the presence of uncertainty, but relies on the questionable presumption that optimisation of dwell times can fully correct for suboptimal dwell positions. In this thesis, the freedom of source placement that 3D-printed applicators allow and the principle of robust treatment optimisation are leveraged to develop robust needle channel planning software for personalised applicators. This thesis was accordingly divided into three parts. In the first part, literature was reviewed to establish the dosimetric uncertainty budget and evaluate geometric uncertainty of OARs. Inter and intra-fraction uncertainty are likely the greatest contributors to the uncertainty budget, possibly increasing the delivered dose to OARs with up to 4.0±20% (k = 1). Using dose-response models it was established that this may realistically increase the occurrence of moderate to severe morbidity of the bladder or rectum by 1.5 and 3.7% respectively. The BT needle channel planning problem under uncertainty was accordingly defined as the problem of computing multiple feasible, non-intersecting curvature- constrained channels under probabilistic or bounded spatial uncertainty of OARs. In the second part, a tool termed motion-planning quality function deployment (MP-QFD) was developed to select a suitable motion planning class. Using the results from a pilot study among nine medical specialists, this tool substantiated the preferred choice for an incremental sampling-based motion planning algorithm. In the last part, robust variants of sampling-based planners were introduced that are capable of computing trajectories for non-holonomic agents in environments under uncertainty. In a two-dimensional simulated patient case, it was shown that these planners were able to generate near-optimal trajectories that (probabilistically) guaranteed not exceeding OAR dose constraints. Subsequent dose-based optimisation showed that (robust) trajectory planning could theoretically yield treatment plans with improved dose conformity over those generated for conventional applicators. Due to modelling assumptions, robust motion planning did not result in improved dose conformity over a nominal motion planning approach in a worst-case scenario. Future work should therefore focus on improving our understanding of OAR movement in and during BT treatment and validating this theoretical work in a patient case series.