Lecture 7
16-311 Introduction to Robotics
Prof. Howie Choset

---

---

• Controls
• Lab 4: Low Level Mobile Base Control
  • Explanation of Lab4
• Motion Planning
  
  • Motion planning is concerned with how a robot traces a trajectory (velocities/accelerations); Path planning is only concerned with the generation of a path to follow.
  • Applications for path planning include:
    • Navigation
    • Mapping
    • Coverage
    
    
  • An obstacle is convex if all points on a line connecting any two points in the object belong to the object.
  • A path planner is complete if it returns a path in a finite time or returns that no path exists in a finite time.
  • The BUG 2 Algorithm
    • Head toward the goal in a straight line.
    • If you hit an obstacle, circumvent it until you reach the line connecting the start and goal, called the mline.
    • If the leave point is closer to the hit point continue toward the goal in a straight line
      • Else, continue around the obstacle
    • If you return to the same hit point without defining a leave point, then you have gone completely around the obstacle and the goal is not reachable (return failure.)
      

      BUG2 with LEFT direction		BUG2 with RIGHT direction

  • Motion Planning: Potential Functions
    • Charge-analogy
      
    • Distance Function (L1 and L2)
      
      
      
      D(x) = min d_i(x)
    • Attractive/Repulsive Potential Functions
      • Attractive: Distance to goal
      • Repulsive: Distance to obstacles
    
    
  • Continue with Potential functions
  • Attractive/Repulsive Potential Functions
    • Attractive: Distance to goal
      
      
    • Repulsive: Distance to obstacles
      
      
  • Local Minimum Problem
    
• Configuration Space (Planar)
  WORKSPACE
  CONFIG SPACE
  
• Distance metrics:
  • The most common and familiar is the L2 distance metric. This is the typical square-root of the sum of the squares approach. The contours of constant depth are made up of circles.
  • Another metric often used in robotics is the L1 or Manhattan distance metric. This distance is the absolute value sum of the orthogonal distances and can be thought of as the distance that a taxi cab might have to travel between two locations along city streets. Constant distance contours for L1 distance are diamonds as shown (Notice that obstacles "bend" the contours):
    
  • Wavefront (Distance Transformation)