lqr 0.1.0

A generic LQR feedback controller
Documentation 
1
2
3
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
53
54
55
56
57
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

use lqr::{compute_target, find_closest_indices};
use nalgebra as na;
use std::error::Error;

#[test]
fn compute_target_1() {
    let trajectory = na::Matrix5x2::new(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.1);
    let expected = na::Matrix5x1::new(0.5, 0.0, 0.0, 0.5, 0.05);
    let target = compute_target(&trajectory, (0, 0.5f64), (1, 0.5f64));
    assert_eq!(expected, target);
}

#[test]
fn compute_target_2() {
    let trajectory = na::Matrix5x2::new(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.1);
    let expected = na::Matrix5x1::new(0.25, 0.0, 0.0, 0.25, 0.025);
    let target = compute_target(&trajectory, (0, 0.25), (1, 0.75));
    assert_eq!(target, expected);
}

#[test]
fn compute_target_3() {
    let trajectory = na::Matrix5x2::new(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.1);
    let expected = na::Matrix5x1::new(0.75, 0.0, 0.0, 0.75, 0.07500000000000001);
    let target = compute_target(&trajectory, (0, 0.75), (1, 0.25));
    assert_eq!(target, expected);
}

#[test]
fn compute_target_4() {
    let trajectory = na::Matrix5x2::new(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.1);
    let expected = na::Matrix5x1::new(0.0, 0.0, 0.0, 0.0, 0.0);
    let target = compute_target(&trajectory, (0, 0.0), (1, f64::MAX));
    assert_eq!(target, expected);
}

#[test]
fn index_search() {
    let current_state = na::Matrix5x1::new(0.5, 0.0, 0.0, 0.0, 0.0);
    let trajectory = na::Matrix5x2::new(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);

    match find_closest_indices(&current_state, &trajectory) {
        Ok((lower, upper)) => {
            assert_eq!(lower.0, 0);
            assert_eq!(lower.1, 0.5f64);
            assert_eq!(upper.0, 0);
            assert_eq!(upper.1, 0.5f64);
        }
        Err(_) => {
            assert!(false, "failed to find closest index")
        }
    }
}

#[test]
fn index_search_before_path() {
    let current_state = na::Matrix5x1::new(-1.0, 0.0, 0.0, 0.0, 0.0);
    let trajectory = na::Matrix5x2::new(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);

    match find_closest_indices(&current_state, &trajectory) {
        Ok((lower, upper)) => {
            assert_eq!(lower.0, 0);
            assert_eq!(lower.1, 1.0);
            assert_eq!(upper.0, 0);
            assert_eq!(upper.1, 1.0);
        }
        Err(_) => {
            assert!(false, "failed to find closest index")
        }
    }
}

#[test]
fn index_search_after_path() {
    let current_state = na::Matrix5x1::new(2.0, 0.0, 0.0, 0.0, 0.0);
    let trajectory = na::Matrix5x2::new(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);

    match find_closest_indices(&current_state, &trajectory) {
        Ok((lower, upper)) => {
            assert_eq!(lower.0, 1);
            assert_eq!(lower.1, 1.0);
            assert_eq!(upper.0, 1);
            assert_eq!(upper.1, 1.0);
        }
        Err(_) => {
            assert!(false, "failed to find closest index")
        }
    }
}

#[test]
fn lqr_optimization() -> Result<(), Box<dyn Error>> {
    // Define state
    let _x: f64 = 2.0;
    let _y: f64 = 2.0;
    let theta: f64 = 0.34;
    let v: f64 = 3.0;

    // Define controls
    let delta: f64 = 0.0;
    let _acc: f64 = 0.0;

    // wheelbase
    let l = 2.0;

    // compute matrices for the LQR controller
    let a = na::Matrix4::<f64>::new(
        0.0,
        0.0,
        -v * theta.sin(),
        theta.cos(),
        0.0,
        0.0,
        v * theta.cos(),
        theta.sin(),
        0.0,
        0.0,
        0.0,
        delta.tan() / l,
        0.0,
        0.0,
        0.0,
        0.0,
    );
    let b = na::Matrix4x2::<f64>::new(
        0.0,
        0.0,
        0.0,
        0.0,
        v / (l * delta.cos().powf(2.0)),
        0.0,
        0.0,
        1.0,
    );
    let q = na::Matrix4::identity();
    let r = na::Matrix2::identity();

    let mut controller = lqr::LQRController::new()?;
    controller.compute_gain(&a, &b, &q, &r, 1e-12)?;

    // hand calculated results
    let real_gain = na::Matrix2x4::<f64>::new(0.0, 0.0, 15.0, 0.0, 0.0, 0.0, 0.0, 2.0);

    let mut gain_result = controller.k.unwrap().clone();

    // 0 out the gain
    gain_result.apply(|v| {
        if v.abs() < 1e-6 {
            *v = 0.0f64;
        }
    });

    assert_eq!(real_gain, gain_result);

    Ok(())
}