Fix standard wing model lift drag calculations

[Jaeyoung-Lim]

Problem Description There were a few issues with the standard wing model. As a result, the pipeline was not able to estimate the liftdrag coefficients correctly.

This PR fixes the problem by addressing the underlying issues. Bug fixes

• There was a bug in the calculations, where the wrong calculation was done for the lift coefficients (cl_0 and cl_alpha was swapped). This has been fixed.
• The matrix calculation for cl_alpha was being swapped with cl_0

Improvements

• For fixed wing vehicles, we have almost little to no data in wing stall. However, the pipeline was trying to fit coefficients that are only effective in the stall region. (e.g. c_d_wing_xz_stall_min, "c_d_wing_xz_stall_90_deg, c_l_wing_xz_stall ). This resulted in basically "free" coefficients and was making the pipeline fit very strange curves outside the stall region.
• The current implementation of stall region aerodynamics were modeled as a linear force(fixed force proportional to the dynamic pressure), which is far from reality. If we are interested in modeling the behavior in this state space, we need to be more thorough on how to model the aerodynamics in this region. From the literature, it has been shown that airfoil geometry does not play an important role in stall. Therefore it the behavior of the wing is close to a flat plate. Reference:
  • Jategaonkar, Ravindra V. Flight vehicle system identification: a time domain methodology. American Institute of Aeronautics and Astronautics, 2006.
  • Cory, Rick, and Russ Tedrake. "Experiments in fixed-wing UAV perching." AIAA Guidance, Navigation and Control Conference and Exhibit. 2008.
  • Khan, Waqas. Dynamics modeling of agile fixed-wing unmanned aerial vehicles. McGill University (Canada), 2016.

Proposed Solution This PR reduces the estimated coefficients to lift and drag coefficients that are not in the stall region. While we can incorporate the flat plate model, I would like to push this out when getting the VTOL working, since this is not relevant for fixed wings.

Key changes include

• Removed stall aerodynamics related coefficients

Note that the coefficients of interest here are only for force estimation. Since the force estimation for aerodynamic effects were not working, this has been a blocker to move towards implementing aerodynamic moments.

This does not fix the standard wing model completely, since the perdictions are still not working correctly. However, creating the PR since I consider this as an improvement from the previous state

Testing

• Before PR

  coefficients:
  I_xx- I_yy: 0.0
  I_yy-I_zz: -0.007598505025841941
  I_zz-I_xx: 0.0
  c_d_wing_xz_lin: -5.519116340083283
  c_d_wing_xz_offset: -30.678184660898772
  c_d_wing_xz_quad: 1094.992324663788
  c_d_wing_xz_stall_90_deg: 97.80517579451308
  c_d_wing_xz_stall_min: -36.964144689594065
  c_l_wing_xz_lin: -6.43623980733897
  c_l_wing_xz_offset: 55.87508669765694
  c_l_wing_xz_stall: 4.217490468185637
  control_surface_0_c_d_delta: -41.57608570018073
  control_surface_0_c_l_delta: 28596.49127881699
  control_surface_1_c_d_delta: -41.55163703181258
  control_surface_1_c_l_delta: 28596.530728132144
  control_surface_2_c_d_delta: 0.02765507537996825
  control_surface_2_c_l_delta: 0.09187865783428958
  control_surface_3_c_d_delta: 0.008699739528148207
  control_surface_3_c_l_delta: 0.0011637003146216418
  control_surface_4_c_d_delta: -0.06355351363863997
  control_surface_4_c_l_delta: -0.005418664745054574
  intercept: 0.0
  puller_c_m_drag_z_lin: 0.00043925827905426113
  puller_c_m_drag_z_quad: 0.0003148634803411044
  puller_c_m_leaver_lin: 0.0
  puller_c_m_leaver_quad: 0.0
  puller_c_m_rolling: 0.006214136923116151
  puller_rot_drag_lin: 0.4950549977119333
  puller_rot_thrust_lin: 0.38161297501371066
  puller_rot_thrust_quad: 8.313833244491573
  metrics:
  R2: 0.9530785777023228

• After PR

coefficients:
  I_xx- I_yy: 0.0
  I_yy-I_zz: -0.007598505025841847
  I_zz-I_xx: 0.0
  c_d_wing_xz_lin: 136.19504547317766
  c_d_wing_xz_offset: 4.846470542724653
  c_d_wing_xz_quad: 2269.2579642974474
  c_l_wing_xz_lin: 9.139676641227844
  c_l_wing_xz_offset: 0.7868849978538761
  control_surface_0_c_d_delta: -25.5763438282221
  control_surface_0_c_l_delta: -342.74350667969543
  control_surface_1_c_d_delta: -25.569258043357184
  control_surface_1_c_l_delta: -342.7080217883057
  control_surface_2_c_d_delta: 0.007165974450208239
  control_surface_2_c_l_delta: 0.07865064519179457
  control_surface_3_c_d_delta: 0.009912942301746809
  control_surface_3_c_l_delta: 0.005275387243893323
  control_surface_4_c_d_delta: -0.05425386269446991
  control_surface_4_c_l_delta: 0.18933110710260334
  intercept: 0.0
  puller_c_m_drag_z_lin: 0.00043925827905427035
  puller_c_m_drag_z_quad: 0.00031486348034107965
  puller_c_m_leaver_lin: 0.0
  puller_c_m_leaver_quad: 0.0
  puller_c_m_rolling: 0.0062141369231162565
  puller_rot_drag_lin: 1.0736153262086319
  puller_rot_thrust_lin: 0.3461121304577288
  puller_rot_thrust_quad: 8.660280818444463
metrics:
  R2: 0.9300612408325579

Note that the estimation is quite sensitive to the flight log, since PX4 has a very small band in the angle of attack which the vehicle enteres during flight for fixedwing vehicles. With a better log:

Additional Context

• The prediction results are still not good, and this is something that still needs to be fixed.
• Fixes https://github.com/ethz-asl/data-driven-dynamics/issues/137