Extended Data Fig. 7: Simulation of free flight maneuvers using the state-space system and Model Predictive Control.

a, Schematic of the state-space system and MPC loop, including system matrix (A), control matrix (B), the state vector (x), temporal derivative (\(\dot{x}\)) left and right steering muscle activity (u_L, u_R), initial state (x_init) and goal state (x_goal). b, Forward flight simulation with wingtip traces in red and blue. c, Wing motion during forward flight simulation plotted in stationary body frame. d, Backward flight simulation. e, Wing motion during backward flight simulation plotted in stationary body frame. f, Left and right steering muscle activity during the forward flight manoeuvre. g, State vector during forward flight manoeuvre. h, Steering muscle activity for the backward flight manoeuvre. i, State vector for the backward flight maneuver. j, CNN-predicted left (red) and right (blue) wing kinematics for the forward flight manoeuvre. Note that because this is a bilaterally symmetric flight manoeuvre, the model generates left and right wing kinematics that are identical. The left wing kinematics are displayed underneath the right kinematics,and thus cannot be seen. A baseline wingbeat is shown to emphasize the relative changes in wing motion. k, CNN-predicted wing motion for the backward flight manoeuvre.