147 lines
4.0 KiB
Python
Executable File
147 lines
4.0 KiB
Python
Executable File
import numpy as np
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np.seterr(divide="ignore", invalid="ignore")
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from scipy.integrate import odeint
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from scipy.interpolate import interp1d
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import cvxpy as opt
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from .utils import *
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from .mpc_config import Params
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P = Params()
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def get_linear_model_matrices(x_bar, u_bar):
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"""
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Computes the LTI approximated state space model x' = Ax + Bu + C
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"""
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x = x_bar[0]
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y = x_bar[1]
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v = x_bar[2]
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theta = x_bar[3]
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a = u_bar[0]
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delta = u_bar[1]
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ct = np.cos(theta)
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st = np.sin(theta)
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cd = np.cos(delta)
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td = np.tan(delta)
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A = np.zeros((P.N, P.N))
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A[0, 2] = ct
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A[0, 3] = -v * st
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A[1, 2] = st
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A[1, 3] = v * ct
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A[3, 2] = v * td / P.L
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A_lin = np.eye(P.N) + P.DT * A
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B = np.zeros((P.N, P.M))
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B[2, 0] = 1
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B[3, 1] = v / (P.L * cd**2)
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B_lin = P.DT * B
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f_xu = np.array([v * ct, v * st, a, v * td / P.L]).reshape(P.N, 1)
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C_lin = (
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P.DT
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* (
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f_xu - np.dot(A, x_bar.reshape(P.N, 1)) - np.dot(B, u_bar.reshape(P.M, 1))
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).flatten()
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)
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# return np.round(A_lin,6), np.round(B_lin,6), np.round(C_lin,6)
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return A_lin, B_lin, C_lin
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class MPC:
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def __init__(self, state_cost, final_state_cost, input_cost, input_rate_cost):
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""" """
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nx = P.N # number of state vars
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nu = P.M # umber of input/control vars
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if len(state_cost) != nx:
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raise ValueError(f"State Error cost matrix shuld be of size {nx}")
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if len(final_state_cost) != nx:
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raise ValueError(f"End State Error cost matrix shuld be of size {nx}")
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if len(input_cost) != nu:
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raise ValueError(f"Control Effort cost matrix shuld be of size {nu}")
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if len(input_rate_cost) != nu:
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raise ValueError(
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f"Control Effort Difference cost matrix shuld be of size {nu}"
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)
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self.dt = P.DT
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self.control_horizon = P.T / P.DT
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self.Q = np.diag(state_cost)
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self.Qf = np.diag(final_state_cost)
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self.R = np.diag(input_cost)
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self.P = np.diag(input_rate_cost)
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self.u_bounds = np.array([P.MAX_ACC, P.MAX_STEER])
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self.du_bounds = np.array([P.MAX_D_ACC, P.MAX_D_STEER])
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def optimize_linearized_model(
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self,
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A,
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B,
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C,
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initial_state,
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target,
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verbose=False,
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):
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"""
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Optimisation problem defined for the linearised model,
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:param A:
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:param B:
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:param C:
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:param initial_state:
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:param target:
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:param verbose:
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:return:
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"""
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assert len(initial_state) == self.state_len
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# Create variables
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x = opt.Variable((self.state_len, control_horizon + 1), name="states")
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u = opt.Variable((self.action_len, control_horizon), name="actions")
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cost = 0
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constr = []
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for k in range(self.control_horizon):
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cost += opt.quad_form(target[:, k] - x[:, k + 1], self.Q)
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cost += opt.quad_form(u[:, k], self.R)
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# Actuation rate of change
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if k < (self.control_horizon - 1):
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cost += opt.quad_form(u[:, k + 1] - u[:, k], self.P)
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# Kinematics Constrains
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constr += [x[:, k + 1] == A @ x[:, k] + B @ u[:, k] + C]
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# Actuation rate of change limit
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if k < (self.control_horizon - 1):
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constr += [
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opt.abs(u[0, k + 1] - u[0, k]) / self.dt <= self.du_bounds[0]
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]
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constr += [
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opt.abs(u[1, k + 1] - u[1, k]) / self.dt <= self.du_bounds[1]
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]
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# Final Point tracking
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cost += opt.quad_form(x[:, -1] - target[:, -1], self.Qf)
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# initial state
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constr += [x[:, 0] == initial_state]
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# actuation magnitude
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constr += [opt.abs(u[:, 0]) <= self.u_bounds[0]]
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constr += [opt.abs(u[:, 1]) <= self.u_bounds[1]]
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prob = opt.Problem(opt.Minimize(cost), constr)
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solution = prob.solve(solver=opt.OSQP, warm_start=True, verbose=False)
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return u[:, 0].value
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