Motion planning and control of mobile robot using Linear Matrix Inequalities (LMIs)

A new motion planning algorithm is proposed for point and disc robots. In this approach, the problem is first formulated as a Binary Integer Programming with variables taken from Delaunay Triangulation of the 2D or n-D Free Configuration Space, and then transformed into LMIs and solved to obtain an optimal channel made of connected triangles. The channel is then used to build safe and short paths within from Start to Goal. It is also possible to weight certain passageways of the space so that the robot can avoid costly routes, which is especially useful for traffic control applications. Finally, a tracking control strategy along trajectory based on preplanned path is applied for a synchronous drive robot. The algorithm is simple, complete, and does not suffer from local minima. It is also extendable to 3 and higher C-spaces.