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Five types of basic maneuver patterns, where the arrow shows the orientation of the robot. The robot changes motion directions from forward to backward or vice versa at each sharp intersection.

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Conference Paper
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Navigation of a car-like robot in environments with unknowns requires effective on-line planning of nonholonomic trajectories. We propose a set of basic maneuver patterns based on Bezier curves that allow either forward or backward motion as building blocks to create nonholonomic trajectories quickly, given a sequence of knot positions/points (e.g....

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Context 1
... , P n , and P n+1 indicate a turn formed by two line segments. The figure also shows four types of transition curves, which are Bezier curves with P n as the common control point. We now describe how to use these four types of Bezier curves to construct maneuver patterns. For an arbitrary angle  formed by P n-1 , P n , and P n+1 , as shown in Fig. 4, if  is sufficiently large, the straightforward turning curve v 1 v 2 can be followed by a car-like robot to make the turn while satisfying inequality (4) under its velocity at P n-1 . Thus, the curve v 1 v 2 is a maneuver pattern, called maneuver 1. Now if there is an obstacle to block the maneuver along v 1 v 2 , a different ...
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... the curve v 1 v 2 is a maneuver pattern, called maneuver 1. Now if there is an obstacle to block the maneuver along v 1 v 2 , a different maneuver policy involving additional straight-line movements, called maneuver 2, can be used to achieve the same turn, as shown in Figure 4. Note that v 7 v 8 is executed by the robot by moving backward. ...
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... pair of patterns maneuver 1 and maneuver 2 provide two alternatives for a car to achieve the same turn while satisfying the nonholonomic constraint, i.e., inequality (4). If  is too small so that the maneuver 1 and maneuver 2 patterns cannot be applied to the robot without violating the nonholonomic constraint, the patterns maneuver 3 and maneuver 4 (see Figure 4) can be used to make the turn by reversing the robot. The smaller  is, the larger the angle  is, and therefore, it is more likely that (4) will be satisfied. ...
Context 4
... 5, also shown in Figure 4, is another alternative pattern to execute a sharp turn by reversing the robot. Although reversing the robot may not meet the requirement of certain turn by itself, it can be a necessary intermediate movement that leads to a correct turn eventually. ...

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