  An intermediate step to modelling behaviour of active matter is understanding
interactions of active objects (AOs) with inanimate matter, which often lead to
a range of rich behaviour. We present a range of simulations of the interaction
of a self-energised AO with three-dimensional granular matter and develop a
first-principles theoretical model to describe the observed phenomena. The AO
oscillates horizontally, which causes it to either rise against gravity or
sink, depending on the oscillation amplitude and frequency. We identify two
competing mechanisms that drive the vertical motion. When the AO moves below a
critical speed, $v_c$, it generates a jammed stagnant zone ahead of it, which
effects an upward force and leads to the rise. Above $v_c$ and certain kinetic
energy, the medium around the AO fluidises and the AO sinks into the layer
supporting it. The duration of the rising and sinking phases depend
non-trivially on the AO's amplitude and frequency leading to an intricate
nonlinear dynamics. We derive the equation of motion for the time-dependent
depth from first-principles and show that its solutions agree well with a wide
range of computer simulations, which we perform within the range of parameters
allowed by the finiteness of the simulated system.
