Add lookup table calibration documentation

Author: sfe-SparkFro

Firmware/Lookup_Table_Calibration/3D_Printables/stepper_disc_mount.stl

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+
+# Number of CSV files to load
+num_files = 8;
+
+# Load CSV files
+for i = 1:num_files
+  var_uncalib_x(:,:,i) = csvread(["xcal_" char(i+48) ".csv"]);
+  var_uncalib_y(:,:,i) = csvread(["ycal_" char(i+48) ".csv"]);
+endfor
+
+# Meshgrid for true x/y velocities
+xy_max = 120;
+dxy = 1;
+num_points = xy_max*2+1;
+tx = ty = linspace (-xy_max, xy_max, num_points);
+[xx_true, yy_true] = meshgrid (tx, ty);
+
+# Plot scales
+xy_ticks = -xy_max:10:xy_max;
+z_limits = [0.8, 1.2];
+z_ticks = 0.8:0.01:1.2;
+c_limits_uncal_var = [.9, 1.0];
+c_limits_scalar_var = [1.0, 1.1];
+c_limits_cal_var = [.98, 1.02];
+
+# Clip out of bounds data points
+var_uncalib_x(var_uncalib_x < 0.8) = 0.8;
+var_uncalib_y(var_uncalib_y < 0.8) = 0.8;
+var_uncalib_x(var_uncalib_x > 1.2) = 1.2;
+var_uncalib_y(var_uncalib_y > 1.2) = 1.2;
+
+# Compute average variation of uncalibrated sensors
+var_uncalib_avg_x = mean(var_uncalib_x, 3);
+var_uncalib_avg_y = mean(var_uncalib_y, 3);
+
+% Plot average X-axis variation
+figure 1;
+clf;
+mesh(xx_true, yy_true, var_uncalib_avg_x);
+xlim([-xy_max, xy_max])
+ylim([-xy_max, xy_max])
+xticks(xy_ticks)
+yticks(xy_ticks)
+zticks(z_ticks)
+zlim(z_limits)
+caxis(c_limits_uncal_var)
+title("Average X-Axis Variation")
+xlabel("True X Velocity (IPS)")
+ylabel("True Y Velocity (IPS)")
+zlabel("Resolution Variation (Measured Velocity / True Velocity)")
+
+% Plot average Y-axis variation
+figure 2;
+clf;
+mesh(xx_true, yy_true, var_uncalib_avg_y);
+xlim([-xy_max, xy_max])
+ylim([-xy_max, xy_max])
+xticks(xy_ticks)
+yticks(xy_ticks)
+zticks(z_ticks)
+zlim(z_limits)
+caxis(c_limits_uncal_var)
+title("Average Y-Axis Variation")
+xlabel("True X Velocity (IPS)")
+ylabel("True Y Velocity (IPS)")
+zlabel("Resolution Variation (Measured Velocity / True Velocity)")
+
+# Compute scalars versus measured velocity
+for i = 1:num_points
+  for j = 1:num_points
+    xx_meas(i,j) = var_uncalib_avg_x(i,j) * xx_true(i,j);
+    yy_meas(i,j) = var_uncalib_avg_y(i,j) * yy_true(i,j);
+
+    scalar_uncalib_avg_x(i,j) = 1 / var_uncalib_avg_x(i,j);
+    scalar_uncalib_avg_y(i,j) = 1 / var_uncalib_avg_y(i,j);
+  end
+end
+
+# Plot average X-axis scalars
+figure 3;
+clf;
+mesh(xx_meas, yy_meas, scalar_uncalib_avg_x);
+xlim([-xy_max, xy_max])
+ylim([-xy_max, xy_max])
+xticks(xy_ticks)
+yticks(xy_ticks)
+zticks(z_ticks)
+zlim(z_limits)
+caxis(c_limits_scalar_var)
+title("Average X-Axis Scalars")
+xlabel("Measured X Velocity (IPS)")
+ylabel("Measured Y Velocity (IPS)")
+zlabel("Resolution Scalars (True Velocity / Measured Velocity)")
+
+# Plot average Y-axis scalars
+figure 4;
+clf;
+mesh(xx_meas, yy_meas, scalar_uncalib_avg_y);
+xlim([-xy_max, xy_max])
+ylim([-xy_max, xy_max])
+xticks(xy_ticks)
+yticks(xy_ticks)
+zticks(z_ticks)
+zlim(z_limits)
+caxis(c_limits_scalar_var)
+title("Average Y-Axis Scalars")
+xlabel("Measured X Velocity (IPS)")
+ylabel("Measured Y Velocity (IPS)")
+zlabel("Resolution Scalars (True Velocity / Measured Velocity)")
+
+# Re-mesh scalars
+scalar_uncalib_avg_x_remesh = griddata(xx_meas, yy_meas, scalar_uncalib_avg_x, xx_true, yy_true);
+scalar_uncalib_avg_y_remesh = griddata(xx_meas, yy_meas, scalar_uncalib_avg_y, xx_true, yy_true);
+
+# Plot average X-axis scalars
+figure 5;
+clf;
+mesh(xx_true, yy_true, scalar_uncalib_avg_x_remesh);
+xlim([-xy_max, xy_max])
+ylim([-xy_max, xy_max])
+xticks(xy_ticks)
+yticks(xy_ticks)
+zticks(z_ticks)
+zlim(z_limits)
+caxis(c_limits_scalar_var)
+title("Average X-Axis Scalars")
+xlabel("Measured X Velocity (IPS)")
+ylabel("Measured Y Velocity (IPS)")
+zlabel("Resolution Scalars (True Velocity / Measured Velocity)")
+
+# Plot average Y-axis scalars
+figure 6;
+clf;
+mesh(xx_true, yy_true, scalar_uncalib_avg_y_remesh);
+xlim([-xy_max, xy_max])
+ylim([-xy_max, xy_max])
+xticks(xy_ticks)
+yticks(xy_ticks)
+zticks(z_ticks)
+zlim(z_limits)
+caxis(c_limits_scalar_var)
+title("Average Y-Axis Scalars")
+xlabel("Measured X Velocity (IPS)")
+ylabel("Measured Y Velocity (IPS)")
+zlabel("Resolution Scalars (True Velocity / Measured Velocity)")
+
+# Sparse grid for lookup table, values chosen by hand
+#lut_indices = [-100 -90 -80 -70 -65 -57 -50 -45 -40 -33 -27 -21 -15 -10 -7 -2 2 7 10 15 21 27 33 40 45 50 57 65 70 80 90 100];
+lut_indices = [-100 -93 -88 -83 -78 -73 -68 -64 -59 -55 -50 -45 -41 -37 -33 -28 -26 -21 -17 -15 -12 -10 -7 -5 -3 0 3 5 7 10 12 15 17 21 26 28 33 37 41 45 50 55 59 64 68 73 78 83 88 93 100];
+[xx_lut, yy_lut] = meshgrid (lut_indices, lut_indices);
+
+# Compute lookup table values
+#lut_scalars_x = griddata(xx_meas, yy_meas, scalar_uncalib_avg_x, xx_lut, yy_lut);
+#lut_scalars_y = griddata(xx_meas, yy_meas, scalar_uncalib_avg_y, xx_lut, yy_lut);
+lut_scalars_x = griddata(xx_true, yy_true, scalar_uncalib_avg_x_remesh, xx_lut, yy_lut);
+lut_scalars_y = griddata(xx_true, yy_true, scalar_uncalib_avg_y_remesh, xx_lut, yy_lut);
+
+# Overlap lookup table on scalar plots
+figure 5;
+hold on;
+mesh(xx_lut, yy_lut, lut_scalars_x)
+figure 6;
+hold on;
+mesh(xx_lut, yy_lut, lut_scalars_y)
+
+# Compute expected variation after implementing lookup table
+var_calib_avg_x = var_uncalib_avg_x .* interp2(xx_lut, yy_lut, lut_scalars_x, xx_true, yy_true);
+var_calib_avg_y = var_uncalib_avg_y .* interp2(xx_lut, yy_lut, lut_scalars_y, xx_true, yy_true);
+
+% Plot average X-axis variation after implementing lookup table
+figure 7;
+clf;
+mesh(xx_true, yy_true, var_calib_avg_x);
+xlim([-xy_max, xy_max])
+ylim([-xy_max, xy_max])
+xticks(xy_ticks)
+yticks(xy_ticks)
+zticks(z_ticks)
+zlim(z_limits)
+caxis(c_limits_cal_var)
+title("Average X-Axis Variation")
+xlabel("True X Velocity (IPS)")
+ylabel("True Y Velocity (IPS)")
+zlabel("Resolution Variation (Measured Velocity / True Velocity)")
+
+% Plot average Y-axis variation after implementing lookup table
+figure 8;
+clf;
+mesh(xx_true, yy_true, var_calib_avg_y);
+xlim([-xy_max, xy_max])
+ylim([-xy_max, xy_max])
+xticks(xy_ticks)
+yticks(xy_ticks)
+zticks(z_ticks)
+zlim(z_limits)
+caxis(c_limits_cal_var)
+title("Average Y-Axis Variation")
+xlabel("True X Velocity (IPS)")
+ylabel("True Y Velocity (IPS)")
+zlabel("Resolution Variation (Measured Velocity / True Velocity)")
+
+# Compute integer lookup table values. These are in increments of 0.2% per LSB
+# to minimize flash size
+lut_scalers_x_int = round((lut_scalars_x - 1) / .002);
+lut_scalers_y_int = round((lut_scalars_y - 1) / .002);
+
+lut_scalers_x_int(lut_scalers_x_int > 127) = 127;
+lut_scalers_x_int(lut_scalers_x_int < -128) = -128;
+lut_scalers_y_int(lut_scalers_y_int > 127) = 127;
+lut_scalers_y_int(lut_scalers_y_int < -128) = -128;
+
+# Save lookup table to CSV files
+csvwrite("lut_x.csv", lut_scalers_x_int)
+csvwrite("lut_y.csv", lut_scalers_y_int)
+