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Planning and Navigation

                             a) Classical Potential                                            271

                                                                    Goal





                            b) Rotation Potential
                                 with parameter β
                                                                    Goal






                           Figure 6.6
                           Comparison between a classical potential field and an extended potential field. Image courtesy of
                           Raja Chatila [84].



                           a gain factor which reduces the repulsive force when an obstacle is parallel to the robot’s
                           direction of travel, since such an object does not pose an immediate threat to the robot’s
                           trajectory. The result is enhanced wall following, which was problematic for earlier imple-
                           mentations of potential fields methods.
                             The task potential field considers the present robot velocity and from that it filters out
                           those obstacles that should not affect the near-term potential based on robot velocity. Again
                           a scaling is made, this time of all obstacle potentials when there are no obstacles in a sector
                                 Z
                                                             Z
                           named   in front of the robot. The sector   is defined as the space which the robot will
                           sweep during its next movement. The result can be smoother trajectories through space. An
                           example comparing a classical potential field and an extended potential field is depicted in
                           figure 6.6.
                             A great many variations and improvements of the potential field methods have been pro-
                           posed and implemented by mobile roboticists [67, 111]. In most cases, these variations aim
                           to improve the behavior of potential fields in local minima while also lowering the chances
                           of oscillations and instability when a robot must move through a narrow space such as a
                           doorway.
                             Potential fields are extremely easy to implement, much like the grassfire algorithm
                           described in section 6.2.1.2. Thus it has become a common tool in mobile robot applica-
                           tions in spite of its theoretical limitations.
                             This completes our brief summary of the path-planning techniques that are most popular
                           in mobile robotics. Of course, as the complexity of a robot increases (e.g., large degree of
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