Motion planning for rigid body robots
Tan, Liek Foo
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Given a non-holonomic disc model, D, its motion constraints in terms of maximum curvature (K (max)), a set W of rectilinear polygonal obstacles which assemble an office-like environment, and two configurations of S and G in free(W), this thesis investigates the planning of a smooth free path which satisfies the following condition: D is allowed backing up motions at the end portions of the path, but the middle is to be of class C(2) in its entirety. Although the motion planning problem of D amidst polygonal obstacles has been extensively studied, the paths considered are mostly class C(2) and piecewise C(2) only, and are subject only to the K(max) constraint. Typically, such paths consist of straight line segments and circular ars which have curvature discontinuity at the junction points. In order for D to follow such paths physically, D has to stop abruptly at each junction point to change curvature. The C(2) path investigated in this thesis allows non-stopping motion of D. It is also subject to a further K(mas) constraint to avoid turns that exceed the rate of change of curvature constraint. A class of smooth curves called cubic spirals are adopted for planning C(2) paths. Properties of the cubic spiral are examined in detail. A framework of layered motion planning approach is proposed to divide and conquer the motion planning problem. A novel sensor-oriented method is presented. It plans a spine net which facilitates D carry out deviation correction using sonar sensors while following a motion path.
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