mirror of
https://gitee.com/mirrors_PX4/PX4-Autopilot.git
synced 2026-04-14 10:07:39 +08:00
299 lines
7.8 KiB
C++
299 lines
7.8 KiB
C++
/****************************************************************************
|
|
*
|
|
* Copyright (c) 2017-2022 PX4 Development Team. All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
*
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in
|
|
* the documentation and/or other materials provided with the
|
|
* distribution.
|
|
* 3. Neither the name PX4 nor the names of its contributors may be
|
|
* used to endorse or promote products derived from this software
|
|
* without specific prior written permission.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
|
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
|
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
|
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
|
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
|
|
* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
|
|
* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
|
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
|
* POSSIBILITY OF SUCH DAMAGE.
|
|
*
|
|
****************************************************************************/
|
|
|
|
/**
|
|
* @file Functions.hpp
|
|
*
|
|
* collection of rather simple mathematical functions that get used over and over again
|
|
*/
|
|
|
|
#pragma once
|
|
|
|
#include "Limits.hpp"
|
|
|
|
#include <px4_platform_common/defines.h>
|
|
#include <matrix/matrix/math.hpp>
|
|
|
|
namespace math
|
|
{
|
|
|
|
// Type-safe signum function with zero treated as positive
|
|
template<typename T>
|
|
int signNoZero(T val)
|
|
{
|
|
return (T(0) <= val) - (val < T(0));
|
|
}
|
|
|
|
/**
|
|
* Sign function based on a boolean
|
|
*
|
|
* @param[in] positive Truth value to take the sign from
|
|
* @return 1 if positive is true, -1 if positive is false
|
|
*/
|
|
inline int signFromBool(bool positive)
|
|
{
|
|
return positive ? 1 : -1;
|
|
}
|
|
|
|
template<typename T>
|
|
T sq(T val)
|
|
{
|
|
return val * val;
|
|
}
|
|
|
|
/*
|
|
* So called exponential curve function implementation.
|
|
* It is essentially a linear combination between a linear and a cubic function.
|
|
* @param value [-1,1] input value to function
|
|
* @param e [0,1] function parameter to set ratio between linear and cubic shape
|
|
* 0 - pure linear function
|
|
* 1 - pure cubic function
|
|
* @return result of function output
|
|
*/
|
|
template<typename T>
|
|
const T expo(const T &value, const T &e)
|
|
{
|
|
T x = constrain(value, (T) - 1, (T) 1);
|
|
T ec = constrain(e, (T) 0, (T) 1);
|
|
return (1 - ec) * x + ec * x * x * x;
|
|
}
|
|
|
|
/*
|
|
* So called SuperExpo function implementation.
|
|
* It is a 1/(1-x) function to further shape the rc input curve intuitively.
|
|
* I enhanced it compared to other implementations to keep the scale between [-1,1].
|
|
* @param value [-1,1] input value to function
|
|
* @param e [0,1] function parameter to set ratio between linear and cubic shape (see expo)
|
|
* @param g [0,1) function parameter to set SuperExpo shape
|
|
* 0 - pure expo function
|
|
* 0.99 - very strong bent curve, stays zero until maximum stick input
|
|
* @return result of function output
|
|
*/
|
|
template<typename T>
|
|
const T superexpo(const T &value, const T &e, const T &g)
|
|
{
|
|
T x = constrain(value, (T) - 1, (T) 1);
|
|
T gc = constrain(g, (T) 0, (T) 0.99);
|
|
return expo(x, e) * (1 - gc) / (1 - fabsf(x) * gc);
|
|
}
|
|
|
|
/*
|
|
* Deadzone function being linear and continuous outside of the deadzone
|
|
* 1 ------
|
|
* /
|
|
* --
|
|
* /
|
|
* -1 ------
|
|
* -1 -dz +dz 1
|
|
* @param value [-1,1] input value to function
|
|
* @param dz [0,1) ratio between deazone and complete span
|
|
* 0 - no deadzone, linear -1 to 1
|
|
* 0.5 - deadzone is half of the span [-0.5,0.5]
|
|
* 0.99 - almost entire span is deadzone
|
|
*/
|
|
template<typename T>
|
|
const T deadzone(const T &value, const T &dz)
|
|
{
|
|
T x = constrain(value, (T) - 1, (T) 1);
|
|
T dzc = constrain(dz, (T) 0, (T) 0.99);
|
|
// Rescale the input such that we get a piecewise linear function that will be continuous with applied deadzone
|
|
T out = (x - matrix::sign(x) * dzc) / (1 - dzc);
|
|
// apply the deadzone (values zero around the middle)
|
|
return out * (fabsf(x) > dzc);
|
|
}
|
|
|
|
template<typename T>
|
|
const T expo_deadzone(const T &value, const T &e, const T &dz)
|
|
{
|
|
return expo(deadzone(value, dz), e);
|
|
}
|
|
|
|
|
|
/*
|
|
* Constant, linear, constant function with the two corner points as parameters
|
|
* y_high -------
|
|
* /
|
|
* /
|
|
* /
|
|
* y_low -------
|
|
* x_low x_high
|
|
*/
|
|
template<typename T>
|
|
const T interpolate(const T &value, const T &x_low, const T &x_high, const T &y_low, const T &y_high)
|
|
{
|
|
if (value <= x_low) {
|
|
return y_low;
|
|
|
|
} else if (value > x_high) {
|
|
return y_high;
|
|
|
|
} else {
|
|
/* linear function between the two points */
|
|
T a = (y_high - y_low) / (x_high - x_low);
|
|
T b = y_low - a * x_low;
|
|
return a * value + b;
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Constant, piecewise linear, constant function with 1/N size intervalls and N corner points as parameters
|
|
* y[N-1] -------
|
|
* /
|
|
* /
|
|
* y[1] /
|
|
* /
|
|
* /
|
|
* /
|
|
* y[0] -------
|
|
* 0 1/(N-1) 2/(N-1) ... 1
|
|
*/
|
|
template<typename T, size_t N>
|
|
const T interpolateN(const T &value, const T(&y)[N])
|
|
{
|
|
size_t index = constrain((int)(value * (N - 1)), 0, (int)(N - 2));
|
|
return interpolate(value, (T)index / (T)(N - 1), (T)(index + 1) / (T)(N - 1), y[index], y[index + 1]);
|
|
}
|
|
|
|
/*
|
|
* Constant, piecewise linear, constant function with N corner points as parameters
|
|
* y[N-1] -------
|
|
* /
|
|
* /
|
|
* y[1] /
|
|
* /
|
|
* /
|
|
* /
|
|
* y[0] -------
|
|
* x[0] x[1] ... x[N-1]
|
|
* Note: x[N] corner coordinates have to be sorted in ascending order
|
|
*/
|
|
template<typename T, size_t N>
|
|
const T interpolateNXY(const T &value, const T(&x)[N], const T(&y)[N])
|
|
{
|
|
size_t index = 0;
|
|
|
|
while ((value > x[index + 1]) && (index < (N - 2))) {
|
|
index++;
|
|
}
|
|
|
|
return interpolate(value, x[index], x[index + 1], y[index], y[index + 1]);
|
|
}
|
|
|
|
/*
|
|
* Squareroot, linear function with fixed corner point at intersection (1,1)
|
|
* /
|
|
* linear /
|
|
* /
|
|
* 1 /
|
|
* /
|
|
* sqrt |
|
|
* |
|
|
* 0 -------
|
|
* 0 1
|
|
*/
|
|
template<typename T>
|
|
const T sqrt_linear(const T &value)
|
|
{
|
|
if (value < static_cast<T>(0)) {
|
|
return static_cast<T>(0);
|
|
|
|
} else if (value < static_cast<T>(1)) {
|
|
return sqrtf(value);
|
|
|
|
} else {
|
|
return value;
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Linear interpolation between 2 points a, and b.
|
|
* s=0 return a
|
|
* s=1 returns b
|
|
* Any value for s is valid.
|
|
*/
|
|
template<typename T>
|
|
const T lerp(const T &a, const T &b, const T &s)
|
|
{
|
|
return (static_cast<T>(1) - s) * a + s * b;
|
|
}
|
|
|
|
template<typename T>
|
|
constexpr T negate(T value)
|
|
{
|
|
static_assert(sizeof(T) > 2, "implement for T");
|
|
return -value;
|
|
}
|
|
|
|
template<>
|
|
constexpr int16_t negate<int16_t>(int16_t value)
|
|
{
|
|
if (value == INT16_MAX) {
|
|
return INT16_MIN;
|
|
|
|
} else if (value == INT16_MIN) {
|
|
return INT16_MAX;
|
|
}
|
|
|
|
return -value;
|
|
}
|
|
|
|
/*
|
|
* This function calculates the Hamming weight, i.e. counts the number of bits that are set
|
|
* in a given integer.
|
|
*/
|
|
|
|
template<typename T>
|
|
int countSetBits(T n)
|
|
{
|
|
int count = 0;
|
|
|
|
while (n) {
|
|
count += n & 1;
|
|
n >>= 1;
|
|
}
|
|
|
|
return count;
|
|
}
|
|
|
|
inline bool isFinite(const float &value)
|
|
{
|
|
return PX4_ISFINITE(value);
|
|
}
|
|
|
|
inline bool isFinite(const matrix::Vector3f &value)
|
|
{
|
|
return value.isAllFinite();
|
|
}
|
|
|
|
} /* namespace math */
|