oxictl 0.1.1

Pure Rust Real-Time Control Systems Framework
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
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243

use crate::core::scalar::ControlScalar;
use crate::kinematics::forward::Transform3D;

/// SCARA robot configuration parameters.
///
/// SCARA (Selective Compliance Assembly Robot Arm):
///   - 2 revolute joints in horizontal plane (q1, q2)
///   - 1 prismatic joint for vertical motion (d3)
///   - 1 revolute joint for end-effector rotation (q4)
///
/// DH parameters (simplified):
///   Joint 1: a1, α=0, d=0, θ=q1
///   Joint 2: a2, α=π, d=0, θ=q2
///   Joint 3: a=0, α=0, d=d3, θ=0
///   Joint 4: a=0, α=0, d=d4, θ=q4
#[derive(Debug, Clone, Copy)]
pub struct ScaraConfig<S: ControlScalar> {
    /// Link 1 length (m).
    pub a1: S,
    /// Link 2 length (m).
    pub a2: S,
    /// Offset from joint 4 to end-effector (m).
    pub d4: S,
    /// Base height (m).
    pub d1: S,
    /// Joint limits: (min, max) for each joint.
    pub q_min: [S; 4],
    pub q_max: [S; 4],
}

impl<S: ControlScalar> ScaraConfig<S> {
    /// Typical desktop SCARA: 200mm + 200mm reach.
    pub fn desktop() -> Self {
        let two_pi = S::TWO * S::PI;
        Self {
            a1: S::from_f64(0.2),
            a2: S::from_f64(0.2),
            d4: S::from_f64(0.05),
            d1: S::from_f64(0.35),
            q_min: [-two_pi; 4],
            q_max: [two_pi; 4],
        }
    }
}

/// SCARA robot kinematics.
pub struct ScaraRobot<S: ControlScalar> {
    pub config: ScaraConfig<S>,
    /// Current joint values: [q1, q2, d3, q4].
    pub q: [S; 4],
}

impl<S: ControlScalar> ScaraRobot<S> {
    pub fn new(config: ScaraConfig<S>) -> Self {
        Self {
            config,
            q: [S::ZERO; 4],
        }
    }

    /// Set joint values (clamped to limits).
    pub fn set_joints(&mut self, q: [S; 4]) {
        for (i, &qi) in q.iter().enumerate() {
            self.q[i] = qi.clamp_val(self.config.q_min[i], self.config.q_max[i]);
        }
    }

    /// Forward kinematics: compute end-effector position and Z-rotation.
    ///
    /// Returns (x, y, z, psi) where:
    ///   x, y: horizontal position
    ///   z: vertical position (height = d1 - d3 + d4)
    ///   psi: end-effector rotation angle
    pub fn forward(&self) -> (S, S, S, S) {
        self.fk_impl(&self.q)
    }

    fn fk_impl(&self, q: &[S; 4]) -> (S, S, S, S) {
        let q1 = q[0];
        let q2 = q[1];
        let d3 = q[2];
        let q4 = q[3];

        let c1 = q1.cos();
        let s1 = q1.sin();
        let c12 = (q1 + q2).cos();
        let s12 = (q1 + q2).sin();

        let x = self.config.a1 * c1 + self.config.a2 * c12;
        let y = self.config.a1 * s1 + self.config.a2 * s12;
        let z = self.config.d1 - d3 + self.config.d4;
        let psi = q1 + q2 + q4;

        (x, y, z, psi)
    }

    /// Inverse kinematics: compute joint angles for desired (x, y, z, psi).
    ///
    /// SCARA IK has two solutions (elbow-up, elbow-down).
    /// Returns `[q1, q2, d3, q4]` for the elbow-down solution.
    /// Returns `None` if target is unreachable.
    pub fn inverse(&self, x: S, y: S, z: S, psi: S) -> Option<[S; 4]> {
        let r2 = x * x + y * y;
        let r = r2.sqrt();
        let a1 = self.config.a1;
        let a2 = self.config.a2;

        // Check reachability
        let r_max = a1 + a2;
        let r_min = (a1 - a2).abs();
        if r > r_max || r < r_min {
            return None;
        }

        // Solve for q2 using cosine rule: r² = a1² + a2² + 2*a1*a2*cos(q2)
        let cos_q2 = (r2 - a1 * a1 - a2 * a2) / (S::TWO * a1 * a2);
        let cos_q2_clamped = cos_q2.clamp_val(-S::ONE, S::ONE);
        let q2 = -cos_q2_clamped.acos(); // elbow-down: q2 negative

        // Solve for q1: atan2(y, x) - atan2(a2*sin(q2), a1 + a2*cos(q2))
        let sin_q2 = q2.sin();
        let k1 = a1 + a2 * cos_q2_clamped;
        let k2 = a2 * sin_q2;
        let q1 = y.atan2(x) - k2.atan2(k1);

        // Prismatic joint: d3 = d1 + d4 - z
        let d3 = self.config.d1 + self.config.d4 - z;

        // End-effector rotation
        let q4 = psi - q1 - q2;

        // Check joint limits
        let q = [q1, q2, d3, q4];
        for (i, &qi) in q.iter().enumerate() {
            if qi < self.config.q_min[i] || qi > self.config.q_max[i] {
                return None;
            }
        }

        Some(q)
    }

    /// Compute the Jacobian (4×4: dx, dy, dz, dpsi vs dq1, dq2, dd3, dq4).
    pub fn jacobian(&self) -> [[S; 4]; 4] {
        let q1 = self.q[0];
        let q2 = self.q[1];
        let s1 = q1.sin();
        let c1 = q1.cos();
        let s12 = (q1 + q2).sin();
        let c12 = (q1 + q2).cos();
        let a1 = self.config.a1;
        let a2 = self.config.a2;

        [
            // dx/dq1, dx/dq2, dx/dd3, dx/dq4
            [-a1 * s1 - a2 * s12, -a2 * s12, S::ZERO, S::ZERO],
            // dy/dq1, dy/dq2, dy/dd3, dy/dq4
            [a1 * c1 + a2 * c12, a2 * c12, S::ZERO, S::ZERO],
            // dz/dq1, dz/dq2, dz/dd3, dz/dq4
            [S::ZERO, S::ZERO, -S::ONE, S::ZERO],
            // dpsi/dq1, dpsi/dq2, dpsi/dd3, dpsi/dq4
            [S::ONE, S::ONE, S::ZERO, S::ONE],
        ]
    }

    /// FK using Transform3D composition (for visualization or chaining).
    pub fn forward_transforms(&self) -> [Transform3D<S>; 4] {
        let q = &self.q;
        let t1 = Transform3D::rot_z(q[0]).compose(&Transform3D::translate(
            self.config.a1,
            S::ZERO,
            S::ZERO,
        ));
        let t2 = t1
            .compose(&Transform3D::rot_z(q[1]))
            .compose(&Transform3D::translate(self.config.a2, S::ZERO, S::ZERO));
        let t3 = t2.compose(&Transform3D::translate(S::ZERO, S::ZERO, -(q[2])));
        let t4 = t3.compose(&Transform3D::rot_z(q[3]));
        [t1, t2, t3, t4]
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    fn build_scara() -> ScaraRobot<f64> {
        ScaraRobot::new(ScaraConfig {
            a1: 0.3,
            a2: 0.2,
            d4: 0.05,
            d1: 0.4,
            q_min: [-core::f64::consts::PI * 2.0; 4],
            q_max: [core::f64::consts::PI * 2.0; 4],
        })
    }

    #[test]
    fn fk_at_zero_config() {
        let mut robot = build_scara();
        robot.set_joints([0.0, 0.0, 0.0, 0.0]);
        let (x, y, z, _psi) = robot.forward();
        // At q=[0,0,0,0]: arm along x, x = a1+a2 = 0.5
        assert!((x - 0.5).abs() < 1e-10, "x={}", x);
        assert!(y.abs() < 1e-10, "y={}", y);
        // z = d1 - 0 + d4 = 0.4 + 0.05 = 0.45
        assert!((z - 0.45).abs() < 1e-10, "z={}", z);
    }

    #[test]
    fn ik_fk_roundtrip() {
        let mut robot = build_scara();
        let q_orig = [0.3_f64, -0.5, 0.05, 0.2];
        robot.set_joints(q_orig);
        let (x, y, z, psi) = robot.forward();
        let q_sol = robot.inverse(x, y, z, psi).expect("IK should succeed");
        // Re-run FK with solved joints
        robot.set_joints(q_sol);
        let (x2, y2, z2, psi2) = robot.forward();
        assert!((x2 - x).abs() < 1e-6, "x error: {} vs {}", x2, x);
        assert!((y2 - y).abs() < 1e-6, "y error: {} vs {}", y2, y);
        assert!((z2 - z).abs() < 1e-6, "z error: {} vs {}", z2, z);
        assert!((psi2 - psi).abs() < 1e-6, "psi error: {} vs {}", psi2, psi);
    }

    #[test]
    fn unreachable_target_returns_none() {
        let robot = build_scara();
        // Target beyond arm reach (a1+a2=0.5)
        let result = robot.inverse(0.6, 0.0, 0.45, 0.0);
        assert!(result.is_none());
    }

    #[test]
    fn jacobian_shape() {
        let mut robot = build_scara();
        robot.set_joints([0.3, 0.5, 0.0, 0.0]);
        let j = robot.jacobian();
        // z row should be [0, 0, -1, 0]
        assert!((j[2][2] - (-1.0)).abs() < 1e-10);
        assert!(j[2][0].abs() < 1e-10);
    }
}