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# Park Atomic Motions

A Park Atomic Motion moves a vehicle from a start frame q0 = (p0, θ0) = ((x0, y0), θ0) to a destination frame q1 = (p1, θ1) = ((x1, y1), θ1) with p0p1, forward or backward, and stops the vehicle at q1. The curvature must be continuous and must be 0 at the start and destination. We denote this Park Problem < q0, q1>. In real life, we have to solve Park Problems in this general problem setting. All of the sample park motions shown in [5.3] to [5.6] belong to this general problem format. We call this general Park-Problem definition [A]:

Park-Problem Definition [A]: < q0, q1 >

On the other hand, there exists another useful Park-Problem definition. Let us define Q0 = ((0, 0), 0) an identity frame. We deal with a Park Problem, in which the vehicle moves the vehicle from Q0 to q1Park medleys [5.1] and [5.2] deal with Park motions in this format. We call this Park-Problem definition [B]:

Park-Problem Definition [B]: < Q0, q1 >

We can easily prove that Problem definitions [A] and [B] are equivalent. MotionLab has worked on Park problems in [B] format. The Park-Atomic-Motion algorithm adopts a more sophisticated one than the ones for the other four Atomic-Motion types; the algorithm computes the solution in real time. This algorithm, in a way, minimizes the cost of the entire curve (on Path Complexity or Driving Skills page).

A Park Atomic Motion is an algorithm for an exact motion, not an exponentially converging one.

### [5.1] Park-Forward Medley by Science Robot

This medley presents eleven distinct
Park-Forward Atomic Motions.

Each of these motions corresponds to each of the eleven
Park-Backward Motions in [5.2].

### [5.2] Park-Backward Medley by Science Robot

This medley presents eleven distinct
Park-Backward Atomic Motions.

Each of these motions corresponds to
each of the eleven
Park-Forward motions in [5.1]

### [5.3] Parallel-Parking Motion by the Swan Robot

This super-tight Parallel-Parking motion
is an application of backward/forward
Park Atomic Motions for Swan.

The robot’s sonars sense the positions of the two “parking vehicles” and the “curb”
to plan the entire motion.

This motion is reproducible.

### [5.4] Back-In Parking Motion by the Swan Robot

This motion is another application of
Park Atomic Motions.
The Swan robot creates a super-tight
Back-In Parking.
The robot’s sonars sense the positions of
the two “parking vehicles” and the “curb”
to plan the entire motion.

When the Swan parks, there are only
1-cm gaps on both sides of the body.

This motion is reproducible.

### [5.5] Sea Urchin by Science Robot

This Sea Urchin motion creates 16
forward/backward park-motion pairs.
Each pair of park motions radially rotates by 360/16 = 22.5º around the origin (0, 0).

A user inputs an integer n between 1 and 32. In this particular motion, n = 16.

### [5.6] Random Park by Science Robot

This motion executes a series of
forward/backward park-motion pairs. In each park motion, two random numbers determine the destination position and direction.
All destination positions are on a given circle.

The sophisticated Park algorithm
efficiently finds
each solution in real time.