ardupilot/Tools/ArdupilotMegaPlanner/HIL/Utils.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ArdupilotMega.HIL
{
    public class Utils
    {
        public const double rad2deg = (180 / System.Math.PI);
        public const double deg2rad = (1.0 / rad2deg);
        public const double ft2m = (1.0 / 3.2808399);
        public const double kts2fps = 1.68780986;

        public static double sin(double val)
        {
            return System.Math.Sin(val);
        }
        public static double cos(double val)
        {
            return System.Math.Cos(val);
        }
        public static double asin(double val)
        {
            return System.Math.Asin(val);
        }
        public static double atan2(double val, double val2)
        {
            return System.Math.Atan2(val, val2);
        }
        public static double radians(double val)
        {
            return val * deg2rad;
        }
        public static double degrees(double val)
        {
            return val * rad2deg;
        }
        public static double sqrt(double val)
        {
            return System.Math.Sqrt(val);
        }

        public static int[] range(int no)
        {
            int[] range = new int[no];
            for (int a = 0; a < no; a++)
            {
                range[a] = a;
            }
            return range;
        }

        public static double fabs(double val)
        {
            return System.Math.Abs(val);
        }

        public static double tan(double val)
        {
            return System.Math.Tan(val);
        }


        public static Tuple<double, double, double> EarthRatesToBodyRates(double roll, double pitch, double yaw,
                                 double rollRate, double pitchRate, double yawRate)
        {
            //convert the angular velocities from earth frame to
            //body frame. Thanks to James Goppert for the formula

            //all inputs and outputs are in degrees

            //returns a tuple, (p,q,r)


            var phi = radians(roll);
            var theta = radians(pitch);
            var phiDot = radians(rollRate);
            var thetaDot = radians(pitchRate);
            var psiDot = radians(yawRate);

            var p = phiDot - psiDot * sin(theta);
            var q = cos(phi) * thetaDot + sin(phi) * psiDot * cos(theta);
            var r = cos(phi) * psiDot * cos(theta) - sin(phi) * thetaDot;

            return new Tuple<double, double, double>(degrees(p), degrees(q), degrees(r));
        }

        public static Tuple<double, double, double> EarthRatesToBodyRatesRyan(double roll, double pitch, double yaw,
                         double x, double y, double z)
        {
            // thanks to ryan beall

            var phi = radians(roll);
            var theta = radians(pitch);
            var psi = radians((360 - yaw) * 1.0);
            var Po = radians(x);
            var Qo = radians(y);
            var Ro = radians(-z);

            var P = Po * cos(psi) * cos(theta) - Ro * sin(theta) + Qo * cos(theta) * sin(psi);

            var Q = Qo * (cos(phi) * cos(psi) + sin(phi) * sin(psi) * sin(theta)) - Po * (cos(phi) * sin(psi) - cos(psi) * sin(phi) * sin(theta)) + Ro * cos(theta) * sin(phi);

            var R = Po * (sin(phi) * sin(psi) + cos(phi) * cos(psi) * sin(theta)) - Qo * (cos(psi) * sin(phi) - cos(phi) * sin(psi) * sin(theta)) + Ro * cos(phi) * cos(theta);


            //            P = 0;
            //Q = 0;
            //R = 0;


            return new Tuple<double, double, double>(degrees(P), degrees(Q), degrees(R));
        }

        public static Tuple<double, double, double> EarthRatesToBodyRatesMine(double roll, double pitch, double yaw,
                 double rollRate, double pitchRate, double yawRate)
        {
            // thanks to ryan beall

            var phi = radians(roll);
            var theta = radians(pitch);
            var psi = radians(yaw);
            var Po = radians(pitchRate);
            var Ro = radians(yawRate);
            var Qo = radians(rollRate);

            var Q = Po * cos(psi) + Qo * sin(psi);

            var P = Po * sin(psi) + Qo * cos(psi); ;

            var R = Ro;

            return new Tuple<double, double, double>(degrees(P), degrees(Q), degrees(R));


            /*
            double Cr, Cp, Cz;
            double Sr, Sp, Sz;

            var phi = radians(roll);
            var theta = radians(pitch);
            var psi = radians(yaw);
            var Po = radians(rollRate);
            var Ro = radians(pitchRate);
            var Qo = radians(yawRate);

            Cr = Math.Cos((phi));
            Cp = Math.Cos((theta));
            Cz = Math.Cos((psi));
            Sr = Math.Sin((phi));
            Sp = Math.Sin((theta));
            Sz = Math.Sin((psi));

            // http://planning.cs.uiuc.edu/node102.html
            //        Z    Y     X
            // roll  -Sp, CpSr, CpCr
            // pitch SzCp, SzSpSr+CzCr, SzSpCr-CpCr
            // yaw   CzCp, CzSpSr-SzCr, CzSpCr+SzSr
            
            var P = -(Qo * Sp) + Po * Cp * Sr + Ro * Cp * Cr;

            var Q = Qo * (Sz * Cp) + Po * (Sz * Sp * Sr + Cz * Cr) + Ro * (Sz * Sp * Cr - Cp * Cr);

            var R = Qo * (Cz * Cp) + Po * (Cz * Sp * Sr - Sz * Cr) + Ro * (Cz * Sp * Cr + Sz * Sr);
            
            return new Tuple<double, double, double>(degrees(P), degrees(Q), degrees(R));
             * */
        }

        public static Tuple<double, double, double> OGLtoBCBF(double phi, double theta, double psi, double x, double y, double z)
        {
            double x_NED, y_NED, z_NED;
            double Cr, Cp, Cy;
            double Sr, Sp, Sy;

            //Accelerations in X-Plane are expressed in the local OpenGL reference frame, for whatever reason. 
            //This coordinate system is defined as follows (taken from the X-Plane SDK Wiki):

            //	The origin 0,0,0 is on the surface of the earth at sea level at some "reference point".
            //	The +X axis points east from the reference point.
            //	The +Z axis points south from the reference point.
            //	The +Y axis points straight up away from the center of the earth at the reference point.

            // First we shall convert from this East Up South frame, to a more conventional NED (North East Down) frame.
            x_NED = (x) * -1.0;
            y_NED = (y) * 1.0;
            z_NED = (z) * -1.0;

            // Next calculate cos & sin of angles for use in the transformation matrix.
            // r, p & y subscripts stand for roll pitch and yaw.

            Cr = Math.Cos((phi));
            Cp = Math.Cos((theta));
            Cy = Math.Cos((psi));
            Sr = Math.Sin((phi));
            Sp = Math.Sin((theta));
            Sy = Math.Sin((psi));

            // Next we need to rotate our accelerations from the NED reference frame, into the body fixed reference frame

            // THANKS TO GEORGE M SIOURIS WHOSE "MISSILE GUIDANCE AND CONTROL SYSTEMS" BOOK SEEMS TO BE THE ONLY EASY TO FIND REFERENCE THAT
            // ACTUALLY GETS THE NED TO BODY FRAME ROTATION MATRIX CORRECT!!

            // CpCy, CpSy, -Sp					| local_ax
            // SrSpCy-CrSy, SrSpSy+CrCy, SrCp	| local_ay
            // CrSpCy+SrSy, CrSpSy-SrCy, CrCp	| local_az

            x = (x_NED * Cp * Cy) + (y_NED * Cp * Sy) - (z_NED * Sp);
            y = (x_NED * ((Sr * Sp * Cy) - (Cr * Sy))) + (y_NED * ((Sr * Sp * Sy) + (Cr * Cy))) + (z_NED * Sr * Cp);
            z = (x_NED * ((Cr * Sp * Cy) + (Sr * Sy))) + (y_NED * ((Cr * Sp * Sy) - (Sr * Cy))) + (z_NED * Cr * Cp);

            return new Tuple<double, double, double>((x), (y), (z));
        }


        /// <summary>
        /// From http://code.google.com/p/gentlenav/source/browse/trunk/Tools/XP_UDB_HILSIM/utility.cpp
        /// Converts from xplanes to fixed body ref
        /// </summary>
        /// <param name="x"></param>
        /// <param name="y"></param>
        /// <param name="z"></param>
        /// <param name="alpha"></param>
        /// <param name="beta"></param>
        public static void FLIGHTtoBCBF(ref float x, ref float y, ref float z, float alpha, float beta)
        {
            float Ca = (float)Math.Cos(alpha);
             float Cb = (float)Math.Cos(beta);
             float Sa = (float)Math.Sin(alpha);
             float Sb = (float)Math.Sin(beta);

             float X_plane = (x * Ca * Cb) - (z * Sa * Cb) - (y * Sb);
             float Y_plane = (z * Sa * Sb) - (x * Ca * Sb) - (y * Cb);
             float Z_plane = (x * Sa) + (z * Ca);

             x = X_plane;
            y = Y_plane;
            z = Z_plane;
        }

        public static Vector3 BodyRatesToEarthRates(Matrix3 dcm, Vector3 gyro)
        {
            //'''convert the angular velocities from body frame to
            //earth frame.

            //all inputs and outputs are in radians/s

            //returns a earth rate vector
            //'''

            var p = gyro.x;
            var q = gyro.y;
            var r = gyro.z;

            double phi = 0;
            double theta = 0;
            double psi = 0;

            dcm.to_euler(ref phi, ref theta, ref psi);

            var phiDot = p + tan(theta) * (q * sin(phi) + r * cos(phi));
            var thetaDot = q * cos(phi) - r * sin(phi);
            if (fabs(cos(theta)) < 1.0e-20)
                theta += 1.0e-10;
            var psiDot = (q * sin(phi) + r * cos(phi)) / cos(theta);

            return new Vector3((phiDot), (thetaDot), (psiDot));
        }
    }
}