Robot Formations Motion Dynamics Based on Scalar Fields

Non-holonomic systems may appear in several forms, including combinations between holonomic and nonholonomic constraints for vehicle formations. Examples of the latter are non-holonomic formation constraints with holonomic vehicles or holonomic formation constraints with non-holonomic vehicles. In this paper the problem of non-holonomic systems with holonomic or non-holonomic constraints is addressed by reformulating the problem using scalar fields. This has the advantage of leading to a definition of force which allows to formulate the motion of a team of nonholonomic vehicles in matrix form, both for holonomic and non-holonomic constraints. Furthermore, the constraints can be systematically included in this formulation.