TEST_F(QuaternionTest, quaternion_multiplied_with_its_inverse_should_be_identity)
{
const auto quat = create_random_quaternion();
const auto inverse = quaternion_inverse(quat);
const auto res = quat * inverse;
EXPECT_NEAR(1, res.w(), PRECISION);
EXPECT_NEAR(0, res.x(), PRECISION);
EXPECT_NEAR(0, res.y(), PRECISION);
EXPECT_NEAR(0, res.z(), PRECISION);
}
TEST_F(QuaternionTest, inverse_of_a_quaternion_is_the_conjugate_divded_by_the_norm_squared)
{
const auto quat = create_random_quaternion();
const auto res = quaternion_inverse(quat);
const auto normsquared = quaternion_norm(quat) * quaternion_norm(quat);
const auto inverse = quaternion_conjugate(quat) / normsquared;
EXPECT_FLOAT_EQ(inverse.w(), res.w());
EXPECT_FLOAT_EQ(inverse.x(), res.x());
EXPECT_FLOAT_EQ(inverse.y(), res.y());
EXPECT_FLOAT_EQ(inverse.z(), res.z());
}
/** [quaternion inverse example] */
static char * test_quaternion_inverse()
{
quaternion qA;
quaternion qInverse;
quaternion qIdentity;
quaternion_set_from_axis_anglef3(&qA, 1.0f, 1.0f, 1.0f, HYP_TAU / 4.0f);
quaternion_set(&qInverse, &qA);
quaternion_inverse(&qInverse);
quaternion_multiply(&qA, &qInverse);
quaternion_normalize(&qA);
quaternion_identity(&qIdentity);
test_assert(quaternion_equals(&qA, &qIdentity));
return 0;
}
/*
* Rotate vector v by unit quaternion q:
*
* v' = q q_v q^-1, where q_v = [0, v]
*/
void
quaternion_rotation(struct point_XYZ *ret, const Quaternion *quat, const struct point_XYZ *v)
{
Quaternion q_v, q_i, q_r1, q_r2;
q_v.w = 0.0;
q_v.x = v->x;
q_v.y = v->y;
q_v.z = v->z;
quaternion_inverse(&q_i, quat);
quaternion_multiply(&q_r1, &q_v, &q_i);
quaternion_multiply(&q_r2, quat, &q_r1);
ret->x = q_r2.x;
ret->y = q_r2.y;
ret->z = q_r2.z;
/* printf("Quaternion rotation: ret = {%f, %f, %f}, quat = {%f, %f, %f, %f}, v = {%f, %f, %f}\n", ret->x, ret->y, ret->z, quat->w, quat->x, quat->y, quat->z, v->x, v->y, v->z); */
}
void Estimator::run_estimator(const vector_t& accel, const vector_t& gyro, const uint64_t& imu_time)
{
_current_state.now_us = imu_time;
if (last_time == 0 || _current_state.now_us <= last_time)
{
last_time = _current_state.now_us;
return;
}
float dt = (_current_state.now_us - last_time) * 1e-6f;
last_time = _current_state.now_us;
// Crank up the gains for the first few seconds for quick convergence
if (imu_time < (uint64_t)params->get_param_int(Params::PARAM_INIT_TIME)*1000)
{
kp = params->get_param_float(Params::PARAM_FILTER_KP)*10.0f;
ki = params->get_param_float(Params::PARAM_FILTER_KI)*10.0f;
}
else
{
kp = params->get_param_float(Params::PARAM_FILTER_KP);
ki = params->get_param_float(Params::PARAM_FILTER_KI);
}
// Run LPF to reject a lot of noise
run_LPF(accel, gyro);
// add in accelerometer
float a_sqrd_norm = _accel_LPF.x*_accel_LPF.x + _accel_LPF.y*_accel_LPF.y + _accel_LPF.z*_accel_LPF.z;
if (use_acc && a_sqrd_norm < 1.15f*1.15f*9.80665f*9.80665f && a_sqrd_norm > 0.85f*0.85f*9.80665f*9.80665f)
{
// Get error estimated by accelerometer measurement
vector_t a = vector_normalize(_accel_LPF);
// Get the quaternion from accelerometer (low-frequency measure q)
// (Not in either paper)
quaternion_t q_acc_inv = quaternion_inverse(quat_from_two_vectors(a, g));
// Get the error quaternion between observer and low-freq q
// Below Eq. 45 Mahoney Paper
q_tilde = quaternion_multiply(q_acc_inv, q_hat);
// Correction Term of Eq. 47a and 47b Mahoney Paper
// w_acc = 2*s_tilde*v_tilde
w_acc.x = -2.0f*q_tilde.w*q_tilde.x;
w_acc.y = -2.0f*q_tilde.w*q_tilde.y;
w_acc.z = 0.0f; // Don't correct z, because it's unobservable from the accelerometer
// integrate biases from accelerometer feedback
// (eq 47b Mahoney Paper, using correction term w_acc found above)
b.x -= ki*w_acc.x*dt;
b.y -= ki*w_acc.y*dt;
b.z = 0.0; // Don't integrate z bias, because it's unobservable
}
else
{
w_acc.x = 0.0f;
w_acc.y = 0.0f;
w_acc.z = 0.0f;
}
// Pull out Gyro measurements
if (quad_int)
{
// Quadratic Integration (Eq. 14 Casey Paper)
// this integration step adds 12 us on the STM32F10x chips
wbar = vector_add(vector_add(scalar_multiply(-1.0f/12.0f,w2), scalar_multiply(8.0f/12.0f,w1)),
scalar_multiply(5.0f/12.0f,_gyro_LPF));
w2 = w1;
w1 = _gyro_LPF;
}
else
{
wbar = _gyro_LPF;
}
// Build the composite omega vector for kinematic propagation
// This the stuff inside the p function in eq. 47a - Mahoney Paper
wfinal = vector_add(vector_sub(wbar, b), scalar_multiply(kp, w_acc));
// Propagate Dynamics (only if we've moved)
float sqrd_norm_w = sqrd_norm(wfinal);
if (sqrd_norm_w > 0.0f)
{
float p = wfinal.x;
float q = wfinal.y;
float r = wfinal.z;
if (mat_exp)
{
// Matrix Exponential Approximation (From Attitude Representation and Kinematic
// Propagation for Low-Cost UAVs by Robert T. Casey)
// (Eq. 12 Casey Paper)
// This adds 90 us on STM32F10x chips
float norm_w = sqrtf(sqrd_norm_w);
quaternion_t qhat_np1;
float t1 = cosf((norm_w*dt)/2.0f);
float t2 = 1.0f/norm_w * sinf((norm_w*dt)/2.0f);
qhat_np1.w = t1*q_hat.w + t2*( - p*q_hat.x - q*q_hat.y - r*q_hat.z);
qhat_np1.x = t1*q_hat.x + t2*(p*q_hat.w + r*q_hat.y - q*q_hat.z);
qhat_np1.y = t1*q_hat.y + t2*(q*q_hat.w - r*q_hat.x + p*q_hat.z);
qhat_np1.z = t1*q_hat.z + t2*(r*q_hat.w + q*q_hat.x - p*q_hat.y);
q_hat = quaternion_normalize(qhat_np1);
}
else
{
// Euler Integration
// (Eq. 47a Mahoney Paper), but this is pretty straight-forward
quaternion_t qdot = {0.5f * ( - p*q_hat.x - q*q_hat.y - r*q_hat.z),
0.5f * ( p*q_hat.w + r*q_hat.y - q*q_hat.z),
0.5f * ( q*q_hat.w - r*q_hat.x + p*q_hat.z),
0.5f * ( r*q_hat.w + q*q_hat.x - p*q_hat.y)
};
q_hat.w += qdot.w*dt;
q_hat.x += qdot.x*dt;
q_hat.y += qdot.y*dt;
q_hat.z += qdot.z*dt;
q_hat = quaternion_normalize(q_hat);
}
}
// Save attitude estimate
_current_state.q = q_hat;
// Extract Euler Angles for controller
euler_from_quat(_current_state.q, &_current_state.euler.x, &_current_state.euler.y, &_current_state.euler.z);
// Save off adjust gyro measurements with estimated biases for control
_current_state.omega = vector_sub(_gyro_LPF, b);
}
