Motion planning using navigation measure

Navigation measure is introduced as a new tool to solve the motion planning problem in the presence of static obstacles. Existence of the navigation measure guarantees collision free convergence to the final destination set. Navigation measure can be viewed as a dual to the navigation function, a popular tool used in the motion planning literature today. While navigation function has its minimum at the final destination set and peaks at the obstacle sets, the navigation measure on the other hand takes maximum value at the destination set and is zero on the obstacle set. A linear programming formalism is proposed for the construction of navigation measure. Set oriented numerical methods are used to obtain finite dimensional approximation of the navigation measure.