Back-In Parking
 Swan "back-in parks" itself between two parallel-parked cars, the ways human drivers do.  The robot scans the front of two mock-up cars with its sonars, computes an intermediate position and direction at the entrance of the narrow parking space, moves itself to the position/direction with zero curvature in the end, drives along the center line defined by the two cars, and stops. Swan waits four seconds before leaving the parking space.   In the first video, Back-In Parking, the side gap between Swan and each neighbor is 50 mm. Click here to see the trajectory. In the second video, Back-In Parking: Tight, the side gap is only 10 mm! Click here to see the trajectory. This parking motion is reliable and repeatable.   The width of Swan robot is 270 mm, and the mock-up cars have the same dimensions as those of Swan.   The key to this back-in-parking algorithm is for a robot to place itself at an intermediate position and direction at zero curvature. This is a geometrical problem. Symmetric Geometry solves all car-like-robot problems, including this one, and precisely executes planned motions. Modern control theory and Euclidean Geometry are not effective for this purpose.   This performance surpasses any human driver's skills because humans are not equipped with Symmetric Geometry. The technology can be easily applied to every automobile to make driving safer and drivers happier. Rental car companies assert that parking lots are the most common places where car accidents occur, and this technology could solve that problem.     These parking functions possess a further advantage; the technology uses sonars, rather than images sensors, so it does not need light, which means a car can execute back-in parking or parallel parking in low light, such as at dusk, or without light, after dark.

 Videos 1 . Back-In Parking 2 . Back-In Parking: Tight