In this paper; the problem of motion planning in environments with both known static obstacles and unpredictable dynamic constraints is considered. A methodology is introduced in which the motion plan for the static environment is modified on-line to accommodate the unpredictable constraints in such a way that the completeness properties of the original motion plan are preserved. At the heart of the approach is the idea that Navigation functions are indeed Lyapunov functions; and that the traditional method of forcing the robot to track the negative gradient of field is not the only input which stabilizes the system. This extra freedom in selecting the input is used to accommodate the dynamic constraints. A computational method for selecting the appropriate inputs is given. The method is used to solve two sample problems. The constraints in these cases are used to model collisions with other robots and, in the second example, a team of robots traveling in formation. Finally, some preliminary work on extending the approach to nonholonomic systems is presented
