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204    S. Pr¨uter et al.
                           hardware is capable of running this task in real-time and that the algorithm
                           adapts to environmental changes such as moving obstacles. Section 6 con-
                           cludes this chapter with a brief discussion including on outline of possible
                           future research.


                           2 The Slip Problem

                           As is well known, robots are moving by spinning their wheels. The resulting
                           direction of the robot depends on the wheels’ speeds relative to each other.
                           Usually, PID controllers regulate the motors by comparing the target speed
                           with the tick-count delivered by the attached wheel encoders. However, the
                           PID controllers are not always able to archive this goal when controlling omni-
                           directional drives, because some wheels occasionally slip. As a consequence,
                           the robot deviates from its expected path. This section uses self-organizing
                           Kohonen feature maps [3, 6] to precisely control the wheels.

                           2.1 Slip and Friction

                           Slip occurs when accelerating or decelerating a wheel in case the friction
                           between wheel and ground is too low. In case of slipping wheels the driven
                           distance does not match the distance that corresponds to the measured wheel
                           ticks. In other words, the robot has moved a distance shorter (acceleration)
                           or longer (deceleration) than it “thought”. Fig. 4 illustrates the effect when
                           wheel 3 is slipping.
                              Friction is another problem that leads to similar effects. It results from
                           mechanical problems between moving and non-moving parts and also between
                           the robot parts and the floor. In most cases, but not always, servo loops
                           can compensate for those effects. Similarly to the slip problem, friction leads
                           to imprecise positions. In addition, high robot speeds, non-constant friction
                           values, and real-world noise make this problem even worse.


                                         slip at wheel 3               no slip
                                       2                          2       2        2
                                    1  A                      1 A     1 B      1 C
                                       3                          3       3        3
                                              2
                                            B
                                          1
                                             3        2
                                                  1
                                                   C
                                                     3
                             Fig. 4. A slipping wheel, e.g., wheel 3, may lead to a deviating moving path
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