Building autonomous mobile agents has been a major research effort for a while
with cooperative mobile robotics receiving a lot of attention in recent times. Motion
planning is a critical problem in deploying autonomous agents. In this research we
have developed two novel global motion planning schemes for a group of mobile agents
which eliminate some of the disadvantages of the current methods available. The first
is the homotopy method in which the planning is done in polynomial space. In this
method the position in local frame of each mobile agent is mapped to a complex
number and a time varying polynomial contains information regarding the current
positions of all mobile agents, the degree of the polynomial being the number of
mobile agents and the roots of the polynomial representing the position in local
frame of the mobile agents at a given time. This polynomial is constructed by finding
a path parameterized in time from the initial to the goal polynomial (represent the
initial and goal positions in local frame of the mobile agents) so that the discriminant
variety or the set of polynomials with multiple roots is avoided in polynomial space.
This is equivalent to saying that there is no collision between any two agents in going
from initial position to goal position. The second is the homogeneous deformation
method. It is based on continuum theory for motion of deformable bodies. In this
method a swarm of vehicles is considered at rest in an initial configuration with no
restrictions on the initial shape or the locations of the vehicles within that shape. A
motion plan is developed to move this swarm of vehicles from the initial configuration to a new configuration such that there are no collisions between any vehicles at
any time instant. It is achieved via a linear map between the initial and desired
final configuration such that the map is invertible at all times. Both the methods
proposed are computationally attractive. Also they facilitate motion coordination
between groups of mobile agents with limited or no sensing and communication
