Several stars do indeed seem to follow slightly wavy paths through space.
One problem is that the errors inherent in making the observations and measurements are about the same size as the planetary- induced wiggles astronomers are seeking, making it very difficult to be sure if a measured wobble is real. So far there have been no uncontested detections of planets from stellar wobbles. In 1963, Peter van de Kamp, then director of Swarthmore College's Sproul Observatory, announced that, based on an analysis of its motion, Barnard's Star had an unseen companion. Van de Kamp estimated that the companion was 50 percent heavier than Jupiter, much too small to be a star. Six years later, van de Kamp revised his analysis and declared that Barnard's Star actually had two planetary companions, one 0.7 times the mass of Jupiter, the other half Jupiter's mass.