Couple of things - may be better to have controls in their own group (desktop, mobile) and if on mobile - System create object > up, down, etc. etc.
Why only a space bar on mobile to jump? Better to separate the arrows - left/right on left side of screen - up/down on right side, since the spacebar sprite only jumps on mobile.
This way you can easily manage the events/actions - touch right - move right. touch up - jump. Easy peasy.
Also, mobile controls are very small, and collision polygon should be a bit larger than the actual arrow. Difficult to get him moving on mobile. I kept missing the buttons.