## T2b-dtspn - Data collection path planning with curvature-constrained trajectory - Dubins TSPN

The main task is to implement two approaches solving the curvature-constrained Traveling Salesman Problem with neighborhoods.

 Deadline November 29, 2020, 23:59 PST Points 5 Label in BRUTE t2b-dtspn Files to submit archive with DTSPNSolver.py Resources T2b resources

### Decoupled Approach

In the plan_tour_decoupled function implement the decoupled solution for the Dubins TSP with Neighborhoods (DTSPN) with disk-shaped regions.

The decoupled approach comprises the following basic steps

1. Estimate sequence of visits by Euclidean TSP connecting centers of the regions.
2. For each region, sample boundary points and heading angles.
3. Find the shortest feasible tour comprising Dubins maneuvers connecting the regions, where the sequence of visits is estimated from the ETSP.

The plan_tour_decoupled function has the following prescription:

def plan_tour_decoupled(goals, sensing_radius, turning_radius):
"""
Compute a DTSPN tour using the decoupled approach.

Parameters
----------
goals: list (float, float)
list of the TSP goal coordinates (x, y)
neighborhood of TSP goals
turning radius for the Dubins vehicle model

Returns
-------
list (float,float,float), path_length (float)
tour as a list of robot configurations (x, y, phi) densely sampled
"""

### Noon-Bean Transform Approach

In the plan_tour_noon_bean function implement the Noon-Bean trasnform solution for the Dubins TSP with Neighborhoods (DTSPN) with disk-shaped regions.

The Noon-Bean approach comprises the following basic steps

1. For each region, sample boundary points and heading angles.
2. Construct a distance matrix using the Noon-Bean transform (from lectures) where the individual regions correspond to the NoonBean's Generalized TSP sets.
3. Find the shortest feasible tour created from Dubins maneuvers by solving the Asymmetric TSP problem characterized by the distance matrix.

The plan_tour_noon_bean function has the following prescription

def plan_tour_noon_bean(goals, sensing_radius, turning_radius):
"""
Compute a DTSPN tour using the NoonBean approach.

Parameters
----------
goals: list (float, float)
list of the TSP goal coordinates (x, y)
neighborhood of TSP goals
turning radius for the Dubins vehicle model

Returns
-------
list (float,float,float), path_length (float)
tour as a list of robot configurations (x, y, phi) densely sampled
"""

The LKH solver seems to be very sensitive to the choice of bigM constant for Noon-Bean transformation. It influences the computational time significantly. The lower the bigM constant is, the faster it computes; but if it is too small, it can violate the original assumption to visit each set only once. The reference sets bigM to be the length of the longest Dubins path and use it also for representing infinity. The distance matrix is normalized before solving by LKH, and thus it cannot contains infinity values. (Alternatively, you can use a slightly smaller number of samples.)

### Appendix

#### Installation of the Prepared Dependencies

pip3 install dubins # or our favorite way to install the package
./install.sh