In this paper we consider whether an animal or an agent (a 'shadower')
can actively camouflage its movements whilst tracking another animal
or agent (a 'shadowee'). It is shown that, under certain conditions, t
he shadower can conceal its motion if it moves along a trajectory such
that it emulates the optic flow produced by a stationary object, as v
iewed by the moving shadowee. Algorithms for determining trajectories
which enable the shadower to camouflage its motion whilst tracking a s
hadowee, or whilst moving toward a stationary or moving target, are de
veloped and tested. The proposed strategies work regardless of whether
the shadower is viewed against a homogeneous or a structured backgrou
nd. It is of interest to investigate the relevance of active motion ca
mouflage in contexts such as 'shadowing' behaviour in hoverflies, capt
ure of prey by predators and military manoeuvres.