Newer
Older
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
np.seterr(divide="ignore", invalid="ignore")
import cvxpy as opt
class MPC:
def __init__(self, model, T, DT, state_cost, final_state_cost, input_cost, input_rate_cost):
"""
Args:
vehicle ():
T ():
DT ():
state_cost ():
final_state_cost ():
input_cost ():
input_rate_cost ():
"""
self.nx = 3 # number of state vars
self.nu = 2 # number of input/control vars
if len(state_cost) != self.nx:
raise ValueError(f"State Error cost matrix shuld be of size {self.nx}")
if len(final_state_cost) != self.nx:
raise ValueError(f"End State Error cost matrix shuld be of size {self.nx}")
if len(input_cost) != self.nu:
raise ValueError(f"Control Effort cost matrix shuld be of size {self.nu}")
if len(input_rate_cost) != self.nu:
raise ValueError(
f"Control Effort Difference cost matrix shuld be of size {self.nu}"
)
self.robot_model = model
self.dt = DT
# how far we can look into the future divided by our dt
# is the number of control intervals
self.control_horizon = int(T / DT)
# Weight for the error in state
self.Q = np.diag(state_cost)
# Weight for the error in final state
self.Qf = np.diag(final_state_cost)
# weight for error in control
self.R = np.diag(input_cost)
self.P = np.diag(input_rate_cost)
# Instantiate the optimizer
self.optimizer = Optimizer(self.nx, self.nu, self.control_horizon, self.Q, self.Qf, self.R, self.P)
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
def get_linear_model_matrices_roomba(self,x_bar,u_bar):
"""
Computes the approximated LTI state space model x' = Ax + Bu + C
Args:
x_bar (array-like): State vector [x, y, theta]
u_bar (array-like): Input vector [v, omega]
Returns:
A_lin, B_lin, C_lin: Linearized state-space matrices
"""
x = x_bar[0]
y = x_bar[1]
theta = x_bar[2]
v = u_bar[0]
omega = u_bar[1]
ct = np.cos(theta)
st = np.sin(theta)
# Initialize matrix A with zeros and fill in appropriate elements
A = np.zeros((self.nx, self.nx))
A[0, 2] = -v * st
A[1, 2] = v * ct
# Discrete-time state matrix A_lin
A_lin = np.eye(self.nx) + self.dt * A
# Initialize matrix B with zeros and fill in appropriate elements
B = np.zeros((self.nx, self.nu))
B[0, 0] = ct
B[1, 0] = st
B[2, 1] = 1
# Discrete-time input matrix B_lin
B_lin = self.dt * B
# Compute the non-linear state update equation f(x, u)
f_xu = np.array([v * ct, v * st, omega]).reshape(self.nx, 1)
# Compute the constant vector C_lin
C_lin = (self.dt * (f_xu - np.dot(A, x_bar.reshape(self.nx, 1)) - np.dot(B, u_bar.reshape(self.nu, 1))).flatten())
return A_lin, B_lin, C_lin
def get_linear_model_matrices(self, x_bar, u_bar):
"""
Computes the approximated LTI state space model x' = Ax + Bu + C
Args:
x_bar (array-like):
u_bar (array-like):
Returns:
"""
x = x_bar[0]
y = x_bar[1]
v = x_bar[2]
theta = x_bar[3]
a = u_bar[0]
delta = u_bar[1]
ct = np.cos(theta)
st = np.sin(theta)
cd = np.cos(delta)
td = np.tan(delta)
A = np.zeros((self.nx, self.nx))
A[0, 2] = ct
A[0, 3] = -v * st
A[1, 2] = st
A[1, 3] = v * ct
A[3, 2] = v * td / self.robot_model.wheelbase
A_lin = np.eye(self.nx) + self.dt * A
B = np.zeros((self.nx, self.nu))
B[2, 0] = 1
B[3, 1] = v / (self.robot_model.wheelbase * cd**2)
B_lin = self.dt * B
f_xu = np.array([v * ct, v * st, a, v * td / self.robot_model.wheelbase]).reshape(
self.nx, 1
)
C_lin = (
self.dt
* (
f_xu
- np.dot(A, x_bar.reshape(self.nx, 1))
- np.dot(B, u_bar.reshape(self.nu, 1))
).flatten()
)
return A_lin, B_lin, C_lin
def step(self, initial_state, target, prev_cmd):
A, B, C = self.get_linear_model_matrices_roomba(initial_state, prev_cmd) # Use Roomba model
# Use the Optimizer class to solve the optimization problem
x_opt, u_opt = self.optimizer.solve(initial_state, target, prev_cmd, A, B, C, self.robot_model, self.dt)
if __name__ == "__main__":
# Example usage:
dt = 0.1
Q = [20, 20, 20] # state error cost
Qf = [30, 30, 30] # state final error cost
R = [10, 10] # input cost
P = [10, 10] # input rate of change cost
mpc = MPC(roomba, 5, dt, Q, Qf, R, P)
x_bar = np.array([0.0, 0.0, 0.0])
u_bar = np.array([1.0, 0.1])
A_lin, B_lin, C_lin = mpc.get_linear_model_matrices_roomba(x_bar, u_bar)
print(A_lin)
print(B_lin)
print(C_lin)