Techniques for determining a distance between a point and a spiral line segment

1 . An autonomous vehicle comprising:

one or more sensors;

one or more processors; and

one or more computer-readable media storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising:

receiving a reference line segment associated with a road segment located within an environment, the reference line segment defined by a segment of a spiral;

determining a first line that is perpendicular to the reference line segment at a starting point of the reference line segment;

determining a second line that is perpendicular to the reference line segment at an ending point of the reference line segment;

determining a set of regions associated with the reference line segment based at least in part on the first line and the second line;

receiving sensor data from the one or more sensors;

determining, based at least in part on the sensor data, a location of an object within the environment;

determining that the location of the object corresponds to a region from the regions;

determining, based at least in part on the location of the object corresponding to the region, a minimum distance between the location of the object and the reference line segment; and

causing the autonomous vehicle to perform an action based at least in part on the minimum distance.

2 . The autonomous vehicle as recited in claim 1 , wherein determining the minimum distance between the location of the object and the reference line segment comprises at least:

determining that the region is associated with the starting point of the reference line segment; and

determining the minimum distance as a distance between the location of the object and the starting point of the reference line segment.

3 . The autonomous vehicle as recited in claim 1 , wherein determining the minimum distance between the location of the object and the reference line segment comprises at least:

determining, based at least in part on the region, a first distance between the location of the object and the starting point of the reference line segment;

determining, based at least in part on the region, a second distance between the location of the object and the ending point of the reference line segment; and

determining the minimum distance as a shortest distance between the first distance and the second distance.

4 . The autonomous vehicle as recited in claim 1 , wherein determining the minimum distance between the location of the object and the reference line segment comprises at least determining, using an optimization function, the minimum distance between the location of the object and the reference line segment.

5 . The autonomous vehicle as recited in claim 1 , the operations further comprise:

determining at least a third line corresponding to a Voronoi edge associated with the reference line segment,

and wherein determining the minimum distance between the location of the object and the reference line segment comprises at least:

determining that the location of the object corresponds to a sub-region of the region, the sub-region being associated with a portion of the region that is located proximate the third line;

determining a rule that is associated with the sub-region; and

determining the minimum distance based at least in part the location of the object and the rule.

6 . A method comprising:

receiving a reference line segment associated with a road segment;

determining a first line normal to the reference line segment at a first point along the reference line segment;

determining a second line that is normal to the reference line segment at a second point along the reference line segment;

determining, based at least in part on the first line and the second line, a set of regions associated with the reference line segment;

determining that a location corresponds to a region from the set of regions;

determining, based at least in part on the region, a minimum distance between the location and the reference line segment;

determining, based at least in part on the minimum distance, at least an action for a vehicle; and

causing the vehicle to perform an action based at least in part on the minimum distance.

7 . The method as recited in claim 6 , wherein determining the minimum distance between the location and the reference line segment comprises at least:

determining that the region is associated with an endpoint of the reference line segment; and

determining the minimum distance as a distance between the location and the endpoint of the reference line segment.

8 . The method as recited in claim 6 , wherein determining the minimum distance between the location and the reference line segment comprises at least:

determining, based at least in part on the region, a first distance between the location and a first endpoint of the reference line segment;

determining, based at least in part on the region, a second distance between the location and a second endpoint of the reference line segment; and

determining the minimum distance as a shortest distance between the first distance and the second distance.

9 . The method as recited in claim 6 , wherein determining the minimum distance between the location and the reference line segment comprises at least determining, using an optimization function, the minimum distance between the location and the reference line segment.

10 . The method as recited in claim 6 , wherein determining the minimum distance between the location and the reference line segment comprises at least:

determining that the location corresponds to a sub-region of the region; and

determining, based at least in part on the sub-region, the minimum distance between the location and the reference line segment.

11 . The method as recited in claim 10 , wherein determining the minimum distance between the location and the reference line segment comprises at least:

determining a rule associated with the sub-region, the rule indicating at least one of:

the minimum distance is associated with a first endpoint of the reference line segment;

the minimum distance is associated with a second endpoint segment;

the minimum distance is associated with at least one of the first endpoint or the second endpoint, or

the minimum distance is determined using an optimization function; and determining the minimum distance using at least the rule.

12 . The method as recited in claim 10 , further comprising:

determining that the first line is normal to a first endpoint of the reference line segment;

determining that the second line is normal to a second endpoint of the reference line segment; and

determining a third line that connects to at least the first point on the first line and the second point on the second line,

wherein determining that the location corresponds to the sub-region of the region comprises determining a position of the location relative to the third line.

13 . The method as recited in claim 10 , further comprising:

determining an evolute associated with the reference line segment,

wherein determining that the location corresponds to the sub-region of the region comprises determining a position of the location relative to the evolute.

14 . The method as recited in claim 6 , wherein determining the regions associated with the road segment comprises at least:

determining that the first line is normal to a first endpoint of the reference line segment;

determining that the second line is normal to a second ending point of the reference line segment;

determining a first region that is associated with a first portion of the first line and a first portion of the second line;

determining a second region that is associated with the first portion of the first line and a second portion of the second line;

determining a third region that is associated with a second portion of the first line and the first portion of the second line; and

determining a fourth region that is associated with the second portion of the first line and the second portion of the second line.

15 . The method as recited in claim 6 , wherein determining the action for the vehicle to perform comprises at least:

determining, based at least in part on the minimum distance, a cost associated with a trajectory of the vehicle; and

determining the action based at least in part on the cost.

16 . One or more non-transitory computer-readable media storing instructions that, when executed by one or more processors, cause the one or more processors to perform operations comprising:

receiving a reference line segment associated with a road segment of an environment;

determining a first line normal to the reference line segment at a first point along the reference line segment;

determining a second line normal to the reference line segment at a second point along the reference line segment;

determining a set of regions associated with the reference line based at least in part on the first line and the second line ;

determining that a location within the environment is associated with a region from the set of regions;

determining, based at least in part on the region, a minimum distance between the location and the reference line segment; and

causing a vehicle to perform an action based at least in part on the minimum distance.

17 . The one or more non-transitory computer-readable media as recited in claim 16 , wherein determining the minimum distance between the location and the reference line segment comprises at least:

determining that the region is associated with a first endpoint of the reference line segment; and

determining the minimum distance as a distance between the location and the first endpoint of the reference line segment.

18 . The one or more non-transitory computer-readable media as recited in claim 16 , wherein determining the minimum distance between the location and the reference line segment comprises at least:

determining, based at least in part on the region, a first distance between the location and a first endpoint of the reference line segment;

determining, based at least in part on the region, a second distance between the location and a second endpoint of the reference line segment; and

determining the minimum distance as a shortest distance between the first distance and the second distance.

19 . The one or more non-transitory computer-readable media as recited in claim 16 , wherein determining the minimum distance between the location and the reference line segment comprises at least determining, using an optimization function, the minimum distance between the location and the reference line segment.

20 . The one or more non-transitory computer-readable media as recited in claim 16 , wherein determining the minimum distance between the location and the reference line segment comprises at least:

determining that the location corresponds to a sub-region of the region; and

determining, based at least in part on the sub-region of the region, the minimum distance between the location and the reference line segment.