1. April 20111 Bug Algorithms Shmuel Wimer Bar Ilan Univ., School of Engineering

2. April 20112 Bug1 and Bug2 Algorithm Move towards the goal, unless an obstacle is encountered. Circumnavigate the obstacle until motion toward the goal is again allowable. Robot is assumed to be a point with perfect positioning. Robot has a contact sensor which detects the obstacle boundary if it touches it. The robot can measure the distance d(x,y) between any two points. The workspace is bounded.

3. April 20113 The Bug1 algorithm successfully finds the goal.

4. April 20114 Bug1 exhibits two behaviors: –motion to goal, and –boundary following. The robot moves along a line from q start to q goal until it hits an obstacle at a hit point - q 1, hit. It circumnavigate the obstacle until it returns the hit point. It then determines the nearest point to q goal and traverses along the boundary to that leave point - q 1, leave. From q 1, leave it heads straight to q goal again. The algorithm terminates when q goal is reached or the planner determines that q goal is not reachable.

5. April 20115 The Bug1 algorithm reports the goal is unreachable.

6. April 20116 The Bug2 algorithm successfully finds the goal.

7. April 20117 The Bug2 algorithm reports the goal is unreachable.

8. April 20118 Bug2 also exhibits two behaviors: –motion to goal, and –boundary following. The motion line is fixed, connecting q start to q goal. From a hit point q i, hit it circumnavigate an obstacle until it reaches a new point along the motion line, closer to q goal. If it returns to q i, hit the goal is not reachable. At first glance it seems that Bug1 is more effective than Bug2, yielding a shorter path. This is not always the case.

9. April 20119

10. 10 For Bug1, when the robot hits an obstacle it completely circumnavigate the boundary and then returns to the leave point, traversing it 1.5 times in the worst case. If there are n obstacles then: Let the motion line connecting q start to q goal intersects and obstacle n i times. Bug2 may perform a complete traversal of the boundary on half of those point. Therefore: L Bug2 can be arbitrarily longer than L Bug1.

11. April 201111 Tangent Bug The robot has an azimuth distance sensor with infinitesimal angular resolution. For every point of an obstacle, azimuth distance is defined: The range of the sensor is usually limited.

12. April 201112 ρ R is piecewise continuous. The tangent Bug planner assumes that the robot can detect discontinuities in ρ R. Intervals of continuity: [O 1,O 2 ], [O 3,O 4 ], [O 5,O 6 ] and [O 7,O 8 ]

13. April 201113 Like Bug1 and Bug2, Tangent Bug has motion-to-goal and boundary-following behaviors. Unlike Bug1 and Bug2, its motion-to-goal behavior may have both straight and boundary following phases. Similarly, in boundary-following behavior it may have a straight motion phase. The robot starts in a motion-to-goal by moving straight towards the goal until it senses an obstacle at distance of R units. By definition, the line connecting the robot to the goal must intersect an interval of continuity.

14. April 201114 The robot is sensing WO 1 and WO 2, but ignores WO 1. After touching WO 2 the first time, an interval [O 1,O 2 ] of continuity is defined. The robot then moves towards O i that maximally decreases a heuristic distance to goal, for example, d(x,O i )+d(O i,q goal ).

15. April 201115 Motion-to-goal is also following boundary