24-354 General Robotics
Spring-02. Prof. Howie Choset

Problem #5 (15 points)

In class most of the mobile robot discussion was limited to robots that can only translate in the plane, i.e. were parameterized by configuration Q = (x, y).
Consider a non-circularly symmetric robot which can translate and rotate in the plane.

(a.) What is the dimension of the configuration space of this robot?

(b.) What does the L1 metric look like for the robot? (write it out algebraically) Note: In class, the L1 metric was defined as D(A, B) = |Ax - Bx| - |Ay - By|.

(c.) If we were to use the wavefront planner to generate a path in the configuration space for this robot, how could we adapt the L1 metric to favor translation over rotational motion?