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
// Copyright (c) 2025 Junior Sundar
//
// SPDX-License-Identifier: BSD-3-Clause
use rand::Rng;
use std::f64::consts::PI;
use crate::base::{
error::{StateSamplingError, StateSpaceError},
space::StateSpace,
state::SO3State,
};
/// A state space representing 3D rotations (the Special Orthogonal group SO(3)).
///
/// States are represented by unit quaternions.
#[derive(Clone)]
pub struct SO3StateSpace {
/// The bounds of the space, as a `(center_rotation, max_angle)` tuple.
pub bounds: (SO3State, f64),
longest_valid_segment_fraction: f64,
}
impl SO3StateSpace {
/// Creates a new `SO3StateSpace`.
///
/// # Arguments
///
/// * `bounds_option` - An optional tuple `(center_rotation, max_angle)` where `max_angle` is
/// the maximum allowed angular distance from the center in radians.
/// - If `None`, the space is considered "unbounded": the center is the identity rotation and
/// the `max_angle` is set to `PI`, covering all possible rotations.
/// - If `Some`, the provided bounds are validated.
///
/// # Errors
///
/// * `StateSpaceError::InvalidAngularDistance` if the provided `max_angle` is negative.
///
/// # Examples
///
/// ```
/// use oxmpl::base::space::SO3StateSpace;
/// use oxmpl::base::state::SO3State;
/// use std::f64::consts::PI;
///
/// // Create an unbounded space (covers all rotations)
/// let unbounded_space = SO3StateSpace::new(None).unwrap();
/// assert_eq!(unbounded_space.bounds.0, SO3State::identity());
/// assert_eq!(unbounded_space.bounds.1, PI);
///
/// // Create a space bounded to a 30-degree cone around the identity rotation
/// let center = SO3State::identity();
/// let max_angle = 30.0f64.to_radians();
/// let bounded_space = SO3StateSpace::new(Some((center, max_angle))).unwrap();
/// ```
pub fn new(bounds_option: Option<(SO3State, f64)>) -> Result<Self, StateSpaceError> {
let bounds = match bounds_option {
Some((center_rotation, max_angle)) => {
if max_angle < 0.0 {
return Err(StateSpaceError::InvalidAngularDistance { lower: max_angle });
}
let clamped_max_angle = max_angle.min(PI);
(center_rotation, clamped_max_angle)
}
None => {
let center = SO3State::identity();
let max_angle = PI;
(center, max_angle)
}
};
Ok(Self {
bounds,
longest_valid_segment_fraction: 0.05,
})
}
/// Returns the maximum possible distance in this space, which is always 0.5*PI.
pub fn get_maximum_extent(&self) -> f64 {
0.5 * PI
}
/// Sets the fraction used to determine motion checking resolution.
pub fn set_longest_valid_segment_fraction(&mut self, fraction: f64) {
if fraction > 0.0 && fraction <= 1.0 {
self.longest_valid_segment_fraction = fraction;
} else if fraction <= 0.0 {
self.longest_valid_segment_fraction = 0.;
} else {
self.longest_valid_segment_fraction = 1.;
}
}
}
impl StateSpace for SO3StateSpace {
type StateType = SO3State;
/// Computes the shortest angle between two rotations using the quaternion dot product.
fn distance(&self, state1: &Self::StateType, state2: &Self::StateType) -> f64 {
let abs_dot =
(state1.x * state2.x + state1.y * state2.y + state1.z * state2.z + state1.w * state2.w)
.abs();
let clamped_dot = abs_dot.min(1.0);
2.0 * clamped_dot.acos()
}
/// Performs Spherical Linear Interpolation (SLERP) between two states.
///
/// The resulting state's components are calculated as:
/// `out_state.values[i] = from.values[i] + t * (to.values[i] - from.values[i])`
fn interpolate(
&self,
from: &Self::StateType,
to: &Self::StateType,
t: f64,
out_state: &mut Self::StateType,
) {
let mut dot = from.x * to.x + from.y * to.y + from.z * to.z + from.w * to.w;
let sign = if dot < 0.0 { -1.0 } else { 1.0 };
dot *= sign;
const DOT_THRESHOLD: f64 = 0.9995;
if dot > DOT_THRESHOLD {
// LERP
out_state.x = from.x + t * (to.x * sign - from.x);
out_state.y = from.y + t * (to.y * sign - from.y);
out_state.z = from.z + t * (to.z * sign - from.z);
out_state.w = from.w + t * (to.w * sign - from.w);
let norm = (out_state.x.powi(2)
+ out_state.y.powi(2)
+ out_state.z.powi(2)
+ out_state.w.powi(2))
.sqrt();
out_state.x /= norm;
out_state.y /= norm;
out_state.z /= norm;
out_state.w /= norm;
} else {
// SLERP
let theta = dot.acos();
let sin_theta = theta.sin();
let s0 = ((1.0 - t) * theta).sin() / sin_theta;
let s1 = (t * theta).sin() / sin_theta * sign;
out_state.x = from.x * s0 + to.x * s1;
out_state.y = from.y * s0 + to.y * s1;
out_state.z = from.z * s0 + to.z * s1;
out_state.w = from.w * s0 + to.w * s1;
}
}
/// Projects a state onto the boundary of the valid "cone of freedom" if it is out of bounds.
fn enforce_bounds(&self, state: &mut Self::StateType) {
match state.normalise() {
Ok(norm) => *state = norm,
Err(_) => *state = SO3State::identity(),
};
if self.satisfies_bounds(state) {
return;
};
let (center_rotation, max_angle) = &self.bounds;
let actual_distance = self.distance(center_rotation, state);
if actual_distance < 1e-9 {
return;
}
let t = *max_angle / actual_distance;
let original_state = state.clone();
self.interpolate(center_rotation, &original_state, t, state);
}
/// Checks if a state is within the defined "cone of freedom" bounds.
fn satisfies_bounds(&self, state: &Self::StateType) -> bool {
let (center_rotation, max_angle) = &self.bounds;
let deviation = self.distance(center_rotation, state);
deviation <= *max_angle
}
/// Generates a uniformly random rotation within the defined bounds.
///
/// # Arguments
///
/// * `rng` - A mutable reference to a random number generator.
///
/// # Errors
///
/// This function will not return an error, as the constructor ensures the bounds are always
/// valid. The `Result` is returned to satisfy the `StateSpace` trait.
fn sample_uniform(&self, rng: &mut impl Rng) -> Result<SO3State, StateSamplingError> {
let (center_rotation, max_angle) = &self.bounds;
if *max_angle < 1e-9 {
return Ok(center_rotation.clone());
}
// The rejection sampling
loop {
let x: f64 = rng.random_range(-1.0..1.0);
let y: f64 = rng.random_range(-1.0..1.0);
let z: f64 = rng.random_range(-1.0..1.0);
let w: f64 = rng.random_range(-1.0..1.0);
let norm_sq = x * x + y * y + z * z + w * w;
if norm_sq > 1e-9 && norm_sq < 1.0 {
let norm = norm_sq.sqrt();
let random_quat = SO3State {
x: x / norm,
y: y / norm,
z: z / norm,
w: w / norm,
};
let distance = self.distance(center_rotation, &random_quat);
if distance <= *max_angle {
return Ok(random_quat);
}
}
}
}
fn get_longest_valid_segment_length(&self) -> f64 {
self.get_maximum_extent() * self.longest_valid_segment_fraction
}
}