  We study a generic model for the polarisation and motility of self-propelled
soft objects, biological cells or biomimetic systems, interacting with a
viscous substrate. The active forces generated by the cell on the substrate are
modelled by means of oscillating force multipoles at the cell-substrate
interface. Symmetry breaking and cell polarisation for a range of cell sizes
naturally `emerge' from long range mechanical interactions between oscillating
units, mediated both by the intracellular medium and the substrate. However,
the harnessing of cell polarisation for motility requires substrate-mediated
interactions. Motility can be optimised by adapting the oscillation frequency
to the relaxation time of the system or when the substrate and cell viscosities
match. Cellular noise can destroy mechanical coordination between
force-generating elements within the cell, resulting in sudden changes of
polarisation. The persistence of the cell's motion is found to depend on the
cell size and the substrate viscosity. Within such a model, chemotactic
guidance of cell motion is obtained by directionally modulating the persistence
of motion, rather than by modulating the instantaneous cell velocity, in a way
that resembles the run and tumble chemotaxis of bacteria.
