This paper deals with automatic generation of the motion of a point un
der both geometric and kinematic constraints. Optimal point paths are
generated which are not only free of collisions with polygonal obstacl
es representing geometric constraints but also conform to kinematic co
nstraints such as limits on velocity and acceleration. A specified min
imum 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 comput
ational time complexity of only O(n3 log n), where n is the total numb
er of obstacle vertices. The algorithm finds the shortest or fastest c
urved path that also conforms with preset constraints on the motion of
the point.