Optimal and Conforming Motion of a Point in a Constrained Plane

This paper deals with automatic generation of the motion of a point under both geometric and kinematic constraints. Optimal point paths are generated which are not only free of collisions with polygonal obstacles representing geometric constraints but also conform to kinematic constraints such as limits on velocity and acceleration. A specified minimum clearance from the boundaries of the obstacles is also satisfied. The new computational tools employed are an efficient representation of the free space, and a new motion generation algorithm with a computational time complexity of only O(n³ log n), where n is the total number of obstacle vertices. The algorithm finds the shortest or fastest curved path that also conforms with preset constraints on the motion of the point.