Solving a generalized constrained optimization problem with both logic ANDand OR relationships by a mathematical transformation and its application to robot motion planning

The logic relationship among the equality and inequality constraints in a s tandard constrained optimization problem (SCOP) is the logical AND. Various efficient, convergent and robust algorithms have been developed for such a SCOP. The logic relationship among the equality and inequality constraints in a standard constrained optimization problem (SCOP) is the logical AND. Various efficient, convergent and robust algorithms have been developed for such a SCOP, Motivated by a practical application, a more general constrai ned optimization problem (GCOP) with not only logic AND but also OR relatio nships is proposed in this paper. In order to solve such a generalized prob lem, a mathematical transformation which can transfer a set of inequalities with logic OR into one inequality is developed. This transformation provid es a necessary and sufficient condition which enables us to use the algorit hms developed for SCOP's to solve the generalized optimization problems. Th e research is motivated by the requirements of developing an efficient, rob ust, and reliable navigation algorithm for a mobile robot such as an Autono mous Underwater Vehicle (AUV), The original contributions of the paper incl ude threefold: First, from the viewpoint of optimization theory, this paper , to our best knowledge, Is the first one to propose such a GCOP, Second, a method is developed to solve such a GCOP, Third, from the viewpoint of rob ot path planning, this paper presents a new way of using classical optimiza tion approach to solve robot path planning. It is our belief that some othe r engineering problems may also be cast as such a generalized form of optim ization problem and benefit from the solution given in this paper. Results are presented for path planning in three dimensions, showing its effectiven ess, efficiency and the approach Is being implemented for European Communit y MAST project CT97-0083.