Holonomic planar motion from non-holonomic driving mechanisms: the front-point method

There are many methods that address navigation and path planning for mobile robots with non-holonomic motion constraints using clever techniques and exploiting application-specific data, but it is always better not to have any such constraints at all. In this document we re-examine the capabilities of some popular driving mechanisms from a different perspective and describe a method to obtain holonomic motion using those mechanisms. The main idea is to not concentrate on the center of the driving mechanism (which is the usual choice) as the reference point for our calculations, but to select another point whose motion in the x-y plane is not constrained in any direction, and which is also a logical and useful substitute for the center. In addition to the derivation of the forward and inverse kinematics equations for the new reference point, we also explain how to further simplify the design of a controller which uses the described method to compute motion commands for the robot. In order to illustrate the ideas, we present graphs that were plotted using the actual parameter values for a synchronous-drive research robot.