  Decentralized control of robots has attracted huge research interests.
However, some of the research used unrealistic assumptions without collision
avoidance. This report focuses on the collision-free control for multiple
robots in both complete coverage and search tasks in 2D and 3D areas which are
arbitrary unknown. All algorithms are decentralized as robots have limited
abilities and they are mathematically proved.
  The report starts with the grid selection in the two tasks. Grid patterns
simplify the representation of the area and robots only need to move straightly
between neighbor vertices. For the 100% complete 2D coverage, the equilateral
triangular grid is proposed. For the complete coverage ignoring the boundary
effect, the grid with the fewest vertices is calculated in every situation for
both 2D and 3D areas.
  The second part is for the complete coverage in 2D and 3D areas. A
decentralized collision-free algorithm with the above selected grid is
presented driving robots to sections which are furthest from the reference
point. The area can be static or expanding, and the algorithm is simulated in
MATLAB.
  Thirdly, three grid-based decentralized random algorithms with collision
avoidance are provided to search targets in 2D or 3D areas. The number of
targets can be known or unknown. In the first algorithm, robots choose vacant
neighbors randomly with priorities on unvisited ones while the second one adds
the repulsive force to disperse robots if they are close. In the third
algorithm, if surrounded by visited vertices, the robot will use the
breadth-first search algorithm to go to one of the nearest unvisited vertices
via the grid. The second search algorithm is verified on Pioneer 3-DX robots.
The general way to generate the formula to estimate the search time is
demonstrated. Algorithms are compared with five other algorithms in MATLAB to
show their effectiveness.
