  This paper addresses distributed average tracking for a group of physical
double-integrator agents under an undirected graph with reduced requirement on
velocity measurements. The idea is that multiple agents track the average of
multiple time-varying input signals, each of which is available to only one
agent, under local interaction with neighbors. We consider two cases. First, a
distributed discontinuous algorithm and filter are proposed, where each agent
needs the relative positions between itself and its neighbors and its
neighbors' filter outputs obtained through communication but the requirement
for either absolute or relative velocity measurements is removed. The agents'
positions and velocities must be initialized correctly, but the algorithm can
deal with a wide class of input signals with bounded acceleration deviations.
Second, a distributed discontinuous algorithm and filter are proposed to remove
the requirement for communication and accurate initialization. Here each agent
needs to measure the relative position between itself and its neighbors and its
own velocity but the requirement for relative velocity measurements between
itself and its neighbors is removed. The algorithm can deal with the case where
the input signals and their velocities and accelerations are all bounded.
Numerical simulations are also presented to illustrate the theoretical results.
