xy plane was set to coincide with the dorsal surface of the pronotum. (4) The locust coordinate

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1 Sulementary text Coordinate systems and kinematic analysis. Four coordinate systems were defined in order to analyse data obtained from the video (Fig. S): () the video coordinate system was attached to the juming latform and the marker ositions digitized from the videos are exressed in this system. () The ground coordinate system was attached to the locust's hind-leg contact oints with the juming latform. The ˆx and ŷ axes of this frame were established by a line connecting the hind-leg contact oints and the ẑ axis was set erendicular to the juming latform (Fig S), its origin was set midway between the two contact oints. Defining these two coordinate systems enabled us to differentiate between jums in which the locust had rotated its whole body, including the hind-leg contact oints, from jums in which the body was rotated while the hind-leg contact oints were ket stable (the latter was the common case in escae jums). () The ronotum coordinate system was attached to the locust body. The origin of this frame was set midway between the two markers at the base of the ronotum. The xy lane was set to coincide with the dorsal surface of the ronotum. (4) The locust coordinate system was similar in orientation to the ronotum system but its origin was translated to midway between the TC joints. Establishing the origin and the axes of this frame in this manner simlified calculations and is common ractice in robot modelling, where reference frame origins are set at joints, and axes are collinear with rotation axes. The jum trajectory is exressed as the translation and rotation of the locust system with resect to the ground system. Translation is described in sherical coordinates (Fig S) and rotations are described using the intrinsic yaw-itch-roll (YPR) rotation sequence convention. After marker coordinates were obtained from the videos for each jum, the jum trajectory was reconstructed. The axes vectors of the ground coordinate system were comuted: G G yˆ = ;z ˆ = eˆ ; xˆ = yˆ zˆ l r g g g g g Gl Gr 4 5 Where: G l and G r are the left and right hind legs' ground contact oints resectively. The ronotum system's origin, axes were comuted: m O m m O m m x y x y ( ) ˆ ˆ ˆ ˆ ˆ = + ; = ; = ;z = m m O m Where: m, m and m are the three markers drawn on the locust's ronotum. Because the locust and the ronotum systems have the same orientation, their axes were in the same directions and their direction cosine matrices (DCM) with resect to the ground system

2 were equal. In each frame the instantaneous DCM (matrix R ) was calculated (Diebel, 006) and then used for transforming vectors from the ground to the locust system and the yaw, itch and roll angles were also calculated through it. The digitized osition of the TC joint was used to calculate the vector from the origin of the ronotum system to that of the locust system: a = TC O ; a = R a ; g left l g Assuming that the locust body is symmetrical with resect to a vertical lane coinciding with its longitudinal axis, the vector second comonent of a l. b l connecting O to O l was constructed by eliminating the a l was indeendently calculated in four different video frames and averaged to reduce error. The instantaneous osition of the locust system could be found and described in sherical coordinates: T y x z x y O = O R b; α = atan ( O, O ); β = atan ( O, O + O ); r = O l l l l l l l l Calculation of velocities was conducted by numerically differentiating the time varying osition and Euler angles. To find the kinematics as exerienced by the locust, the Euler angle time derivative were transformed to rotational velocities about the ground system axis, and then multilied by the DCM to rotate to the locust system: ψ cos( θ)cos( φ) θsin( φ) ωg = ψ cos( θ)sin( φ) + θcos( φ) ; ωl = R ωg φ ψ sin( θ) References Diebel J Reresenting attitude: Euler angles, unit quaternions, and rotation vectors. Matrix 58:56. 50

3 Fig. S. Definition of coordinate systems for kinematic analysis. The ositions of markers m, m, m obtained from video analysis are exressed in the video coordinate system ( xv, yv, z v). The ronotum system ( x, y, z ) is set according to the marker ositions. The ground system ( xg, yg, z g) is set according to the contact oints of the hind legs with the ground ( G, G ). The locust system ( x, y, z ) is arallel to the ronotum system and l r l l l ositioned between the TC joints ( TC, TC ). During the jum, the locust osition is the left right difference between the origins of the locust and ground systems exressed in sherical coordinates ( αβ,, r). 6

4 Fig. S. Time-course of two jums from the beginning of the aiming manoeuvres till takeoff. Each jum is reresented by two grahs: the uer grah describes the osition of the locust and the bottom grah describes the locust's orientation. Two vertical dashed lines mark imortant events during the jum: The left line marks the moment when the hind legs start exerting thrust on the body. This moment was measured by noting the first frame in which the hind legs started to extend in each jum video. The right line marks the moment when the hind legs' thrust force 4

5 ends. This moment was measured by noting the frame in which the hind legs lost contact with the ground in each jum video. An image of the locust and the six coordinates describing its location and orientation are resented in figure S.C for. A. First jum- The aiming manoeuvres begin about 0 milliseconds before the thrust force begins. During this hase the locust's osition changes only by changing the α angle between aroximately 4 degrees at the beginning of the aiming manoeuver to aroximately 0 degrees when the thrust starts. Meanwhile, during the same hase the locust changes its orientation: The itch angle (θ ) almost does not change; The yaw angle (ϕ ) changes from aroximately 9 degrees to the right to 0 degrees. The roll angle (ψ ) changes from aroximately degrees to the left to 0 degrees to the left. Notice that the average velocity in which the roll was changed is aroximately 400 degrees er second. In the second hase, the thrust hase, which takes lace from the beginning of the thrust alication till takeoff, the main change in the locust's osition is its roagation, which can be seen in the rise of r at aroximately 0mm till takeoff. During this hase also the orientation of the locust changes: The itch and yaw angles (θ and ψ, resectively) continue changing in the same velocity till about 0 milliseconds before takeoff, when threir velocity starts to reduce. The roll (ψ ) on the other hand, changes direction and develos a higher velocity than in the revious hase. The change in roll in this hase is robably the result of torques roduced by the thrust force. B. Additional jum time-course. C. Locust model with coordinate notations Fig. S. Comarison of rotational velocity at take-off between real and simulated jums: A. Yaw velocity. B. Pitch velocity. C. Roll velocity. Please note that the x and y axes are not in the same scale. 5

6 Fig. S4. The timing of flight initiation as a function of itch velocity measured 5 msec before take-off. The lines denote linear regression (Analysis of variance of linear model, F-test). 05 6