The ability of robots to recognize human gestures facilitates a natural and accessible human-robot collaboration. However, most work in gesture recognition remains rooted in reference frame-dependent representations. This poses a challenge when reference frames vary due to different work cell layouts, imprecise frame calibrations, or other environmental changes. This paper investigated the use of invariant trajectory descriptors for robust hand palm motion gesture recognition under reference frame changes. First, a novel dataset of recorded Hand Palm Motion (HPM) gestures is introduced. The motion gestures in this dataset were specifically designed to be distinguishable without dependence on specific reference frames or directional cues. Afterwards, multiple invariant trajectory descriptor approaches were benchmarked to assess how their performances generalize to this novel HPM dataset. After this offline benchmarking, the best scoring approach is validated for online recognition by developing a real-time Proof of Concept (PoC). In this PoC, hand palm motion gestures were used to control the real-time movement of a manipulator arm. The PoC demonstrated a high recognition reliability in real-time operation, achieving an $F_1$-score of 92.3%. This work demonstrates the effectiveness of the invariant descriptor approach as a standalone solution. Moreover, we believe that the invariant descriptor approach can also be utilized within other state-of-the-art pattern recognition and learning systems to improve their robustness against reference frame variations.