mirror of https://github.com/ArduPilot/ardupilot
58 lines
2.2 KiB
C++
58 lines
2.2 KiB
C++
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/* SpeedToFly class by Samuel Tabor, 2021.
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Calculates the optimal speed to fly given drag polar, expected climb rate in next thermal and
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horizontal and vertical air movement between thermals.
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*/
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#include "SpeedToFly.h"
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void SpeedToFly::update(float Wx, float Wz, float Wexp, float CLmin, float CLmax)
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{
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// The solution to the speed-to-fly problem does not have a closed form solution. A Newton
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// method with some additional checks will converge to an acceptable level within 3-4 iterations.
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// However, to keep the computation constant per function call we just do a single iteration using
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// the previous approximation as a starting point.
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// This gives good accuracy as the inputs don't change rapidly. It would also be possible to store
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// the inputs and converge the solution over 3-4 function calls, but this real-time iteration
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// approach gives better accuracy in tests as well as simpler code.
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Wz *= -1.0f; // Sink defined positive.
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float sqrtfk = sqrtf(_polarParams.K);
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float minSink = (sqrtfk/sqrtf(CLmax)*(_polarParams.CD0 + _polarParams.B*CLmax*CLmax))/CLmax;
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if (!is_positive(minSink+Wz+Wexp)) {
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// Special case. If lift is greater than min sink speed, fly at min sink
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// speed.
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_CL_estimate = CLmax;
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return;
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}
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float CD0 = _polarParams.CD0;
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float B = _polarParams.B;
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float Wxp = Wx/sqrtfk;
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float WZ = (Wz + Wexp)/sqrtfk;
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// Guess starting location.
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float CL = _CL_estimate>0 ? _CL_estimate : 0.5f*(CLmax+CLmin);
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float t0 = powf(CL,1.5f);
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float t1 = CD0 + B*CL*CL + t0*WZ;
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float t2 = 1.5f*sqrtf(CL)*WZ + 2.0f*B*CL;
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float Jd = (1.5f*sqrtf(CL)*Wxp + 1.0f)/t1 - (t2*(CL + t0*Wxp))/(t1*t1);
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float Jdd = 2.0f*t2*t2*(CL + t0*Wxp)/powf(t1,3) - (2.0f*t2*(1.5f*sqrtf(CL)*Wxp + 1.0f))/(t1*t1) - ((2.0f*B + 0.75f*WZ/sqrtf(CL))*(CL + t0*Wxp))/(t1*t1) + 0.75f*Wxp/(sqrtf(CL)*t1);
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// Check we're heading to a maximum, not a minimum!!
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if (is_positive(Jdd)) {
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// Alternate mode, go uphill.
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CL = CL + 0.1 * (Jd>0.0f ? 1.0f : -1.0f);
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} else {
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// Newton should work.
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CL = CL - Jd/Jdd;
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}
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_CL_estimate = CL;
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_CL_estimate = constrain_float(_CL_estimate, CLmin, CLmax);
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}
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