Optimizer

Objective

Generate an optimized velocity profile that minimizes energy,

while keeping velocity and time within given constraints

User input data

, distance, dist_step, time , min_velocity, max_stop_velocity

Pre-determined data

map_data : //describe data type

stop_profile :

• generated from map_data

elev_profile :

• generated from map_data

max_velocity

Code Breakdown

load_course_map()

• Parameters: The name of the course we’re trying to load in (course_name)

• Returns: The map of elevations on said course (elev_profile).

• The map of elevations has dimensions num_points x 2, with column 1 (Index 0) representing the y-coordinates and column 2 (Index 1) representing the x-coordinates.

generate_initial_profile()

• Parameters: The maximum allowable time to cover a distance in seconds (time), the distance to be covered in meters (distance), the list of pitches map of elevations that the car must travel (e_profile), the minimum allowable velocity (min_velocity), and the list of indices where the car must stop (stop_profile)

• Returns: initial_profile : A map of the same dimensions as the map of elevations with each element representing the average velocity required for the car to move at each point on the map of elevations (initial_profile).

• Ex. initial_profile[2] = 10 means that according to the initial profile, the car should be moving 10 m/s at point 3 (Index 2) on the map of elevations.

• This function basically generates the naive/initial solution that will be improved upon through the optimization function later in the program.

• Only three possible velocity values are stored in initial_profile.

  • Cruise avg_velocity when we can

  • When we can't, we just go max_v or min_velocity

MAIN (functions below are inside main):

objective()

• Parameters: The velocity profile (v_profile)

• Returns: The amount of energy used by the car as a result of driving at the stated velocities in v_profile throughout each point on the map of elevations (energy / 100000). The energy usage is calculated by a function located in car_model.py

• This objective function will be minimized by the optimization function later in the program because we’d want to minimize how much energy the car uses.

time_constraint()

• Parameters: The velocity profile (v_profile)

• Returns: Time spent driving as a result of moving at the stated velocities in v_profile throughout each point on the map of elevations subtracted from the maximum allowable time by the competition. (time-sum(time_used))

• Basically returns how much more time we used than is allowed.

• Time used by the v-profile shouldn’t be greater than the maximum time allowed by the competition.

• Used as a constraint for the optimization function later in the program.

speed_constraint()

• Parameters: The velocity profile (v_profile)

• Returns: The negative sum of how much the car’s velocity in v_profile is greater than the maximum velocity at each point in the map of elevations (error)

• If the velocity in v_profile isn’t greater than the maximum velocity at a certain point, the error variable will not be incremented.

• The maximum velocity is calculated by calling the max_velocity function from car_model.py

Solution

• Calculated using scipy.optimize’s minimize function with the objective function as the function that will be minimized, v0 as the initial profile (naive solution), the bounds being the minimum and maximum velocity, Sequential Least SQuares Programming (SLSQP) optimizer as the method of minimizing the objective function, and the constraints being the speed_constraint and time_constraint function.