mc_pos_control: moved responsibility of the x,y stick deadzone to a mathematical function

to prevent a setpoint step when moving the stick over the border of the deadzone
and to enable very small inputs even from a control stick that needs a big deadzone

src/lib/mathlib/math/Expo.hpp

@@ -35,7 +35,7 @@
  * @file Expo.hpp
  *
  * So called exponential curve function implementation.
- * It's essentially a linear combination between a linear and a cubic function.
+ * It is essentially a linear combination between a linear and a cubic function.
  */
 
 #pragma once
@@ -46,6 +46,11 @@
 namespace math
 {
 
+// Type-safe signum function
+template<typename T> int sign(T val) {
+	return (T(0) < val) - (val < T(0));
+}
+
 template<typename _Tp>
 inline const _Tp expo(const _Tp &value, const _Tp &e)
 {
@@ -53,4 +58,21 @@ inline const _Tp expo(const _Tp &value, const _Tp &e)
 	return (1-e)*x + e*x*x*x;
 }
 
+template<typename _Tp>
+inline const _Tp deadzone(const _Tp &value, const _Tp &dz)
+{
+	_Tp x = constrain(value ,(_Tp)-1, (_Tp)1);
+	// Rescale the input such that we get a piecewise linear function that will be continuous with applied deadzone
+	_Tp out = (x-sign(x)*dz)/(1-dz);
+	// apply the deadzone (values zero around the middle)
+	return out * (fabsf(x) > dz);
+}
+
+template<typename _Tp>
+inline const _Tp expo_deadzone(const _Tp &value, const _Tp &e, const _Tp &dz)
+{
+	_Tp x = constrain(value ,(_Tp)-1, (_Tp)1);
+	return expo(deadzone(x, dz),e);
+}
+
 }