中央研究院 資訊科學研究所

Curvature constraint is an essential constraint for smooth turning because of the physical limitation of vehicles on lateral acceleration during turning. In this research, we present three practical curvature-constrained smooth turning scenarios for autonomous vehicle maneuvering scenarios: ordinary turn, lane change on straight road, and lane change in roundabout. For each scenario, instead of using concatenated path segments of lower-order curves, like cubic Bezier curves, we use the equivalent 7th-degree Bezier curves of simplified η3 -splines to design smooth uni-directional turning paths. The scenarios serve well to illustrate that various curvature-constrained turning paths of 7th-degree Bezier form can be generated successfully through flexible selections of suitable parameter values by the user or an iterative-search-and-verify process to explore the feasible parameter set in a more intuitive and computationally simpler manner. Mathematical inductions and examples are given in each scenario, and the plots of the relationship between maximum curvature and the assigned parameter show how our methods work.

Definitions of the projective group and the projective space upon which it acts are given, and it is shown that these definitions are equivalent to the standard ones. The definitions presented here are fundamental in the sense that they do not depend on less primitive notions such as field and linear space.

Definitions of the projective group and the projective space upon which it acts are given, and it is shown that these definitions are equivalent to the standard ones. This is done by construction of affine subspaces and the field of throws in the sense of von Staudt.