Propelling and perturbing appendages together facilitate strenuous ground self-righting
- Department of Mechanical Engineering, Johns Hopkins University, United States
Figures
Figure 1 with 2 supplements
Strenuous, leg-assisted, winged ground self-righting of discoid cockroach.
(A) Representative snapshots of animal successfully self-righting by pitch (blue) and roll (red) modes after multiple failed attempts (black arrow). See Figure 1—video 1 for a typical trial, in …
Figure 1—video 1
Strenuous leg-assisted, winged self-righting with multiple failed attempts.
A discoid cockroach makes multiple failed attempts to pitch over the head by opening and pushing its wings against the ground and eventually rolls to self-right.
Figure 1—video 2
A discoid cockroach using wing opening and leg flailing together during strenuous winged self-righting.
A discoid cockroach opening and pushing its wings against ground and flailing its legs to self-right from a metastable state. Blue and red curves show trajectories of left and right hind leg tips. …
Figure 2 with 2 supplements
Animal leg modification and robotic physical model.
(A) Discoid cockroach with modified hind legs with stainless steel spheres attached. (B) Robotic physical model in metastable state with a triangular base of support (dashed triangle), formed by …
Figure 2—figure supplement 1
Robot wing and leg actuation and body orientation measurement.
(A) Schematic of leg-assisted, winged self-righting robot from front and side views with geometric dimensions. Front view illustrates wing rolling and leg oscillation and side view illustrates wing …
Figure 2—video 1
Wing and leg actuation of robotic physical model.
Wings can both pitch and roll relative to body. Leg oscillation emulates leg flailing of animal (inset).
Figure 3 with 4 supplements
Animal’s kinetic energy and self-righting probability.
Comparison of (A) average pitch and roll kinetic energy and (B) self-righting probability between intact animals and animals with modified hind legs. Error bars show ± s.d. Asterisk indicates a …
Figure 3—figure supplement 1
Animal kinetic energy calculation.
(A) Representative snapshot of body and appendage with definition of markers tracked. (B) Multi-body model of animal for calculating pitch and roll kinetic energy. Red and blue arrows show velocity …
Figure 3—figure supplement 2
Comparison of average percentage of time spent on winged and legged self-righting attempts between animals with intact and modified legs.
Error bars show ± s.d. n.s. indicates no significant difference. Winged: p = 0.19, F1,269 = 1.71; legged: p = 0.78, F1,269 = 0.07 mixed-effects ANOVA. Sample size: N = 30 animals, n = 150 trials for …
Figure 3—figure supplement 3
Correlation between animal’s body and leg motion.
(A–C) Pair-wise normalized cross-correlations between left hind leg tip height, right hind leg tip height, and abdomen tip height, as a function of lag between each pair of variables. (D–F) …
Figure 3—video 1
Leg flailing kinetic energy facilitates winged self-righting of animal.
Representative trials of strenuous leg-assisted, winged self-righting with and without hind leg modification (played three times).
Figure 4 with 1 supplement
Robot’s kinetic energy and self-righting performance.
(A, B) Average pitch and roll kinetic energy during self-righting as a function of leg oscillation amplitude θleg at different wing opening amplitudes θwing. (C, D) Self-righting probability and …
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Figure 4—source data 1
Statistical test results for Figure 4A–D.
- https://cdn.elifesciences.org/articles/60233/elife-60233-fig4-data1-v2.xlsx
Figure 4—video 1
Wing opening and leg flailing together facilitate winged self-righting of robot.
Left: Representative videos from top and front views. Top right: Commanded (solid) and measured (dashed) motor angles as a function of time. Blue and red curves are for wing and leg motors, …
Figure 5 with 4 supplements
Robot’s self-righting motion and potential energy landscape.
(A) Snapshots of reconstructed robot upside-down (i), in metastable state (ii), self-righting by pitch (iii) and roll (iii’) modes, and upright afterward (iv, iv’). (B) Snapshots of potential energy …
Figure 5—figure supplement 1
Animal’s potential energy landscape.
Snapshots of potential energy landscape at different wing opening angles. Black curve is representative trajectories of failed attempts and dashed blue and red curves are for successful attempt by …
Figure 5—video 1
Robot potential energy landscape modeling.
Top left: Illustrative robot body motion for self-righting via pitch and roll modes. Top right: Evolution of potential energy landscape as wings open, with robot state (dot) and state trajectory. …
Figure 5—video 2
Robot state trajectory on potential energy landscape.
Top left: Representative trial. Bottom left: Reconstructed 3D motion. Right: Potential energy landscape with robot state (dot) and state trajectory. Video first shows a failed trial without leg …
Figure 5—video 3
Bifurcation diagram for animal’s potential energy landscape.
Top left: Potential energy landscape over body pitch-roll space and its equilibrium points along body roll = 0° (blue dots) and body pitch = 0° (red dots). Top right: Body pitch of equilibrium …
Figure 6 with 2 supplements
Robot state trajectories on potential energy landscape.
(A) θwing = 60°. (B) θwing = 72°. (C) θwing = 83°. Columns i and ii show successful (white) and failed (black) self-righting attempts, respectively. n is the number of successful or failed attempts …
Figure 6—figure supplement 1
Robot’s stereotyped body motion during self-righting.
State trajectories in body pitch, body roll, and center of mass height space. (A) θwing = 60°. (B) θwing = 72°. (C) θwing = 83°. Columns i and ii show successful and failed self-righting attempts, …
Figure 6—video 1
Robot state trajectory ensemble on potential energy landscape.
Evolution of potential energy landscape and robot state trajectories during self-righting attempts. White and black curves show trajectories for successful and failed self-righting attempts, …
Figure 7 with 3 supplements
Robot’s potential energy barriers for self-righting via pitch and roll modes.
(A) Potential energy during self-righting via pitch mode as a function of body pitch and wing opening angle. (B) Potential energy during self-righting via roll mode as a function of body roll and …
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Figure 7—source data 1
Statistical test results for Figure 7—figure supplements 2 and 3.
n = 134 attempts.
- https://cdn.elifesciences.org/articles/60233/elife-60233-fig7-data1-v2.xlsx
Figure 7—figure supplement 1
Animal’s potential energy barriers for self-righting via pitch and roll modes.
(A) Potential energy of self-righting via pitch mode as a function body pitch and wing opening amplitude. (B) Potential energy of self-righting via roll mode as a function of body roll and wing …
Figure 7—figure supplement 2
Comparison between robot’s roll kinetic energy and roll potential energy barrier.
(A) Roll kinetic energy, (B) roll potential energy barrier, and (C) roll kinetic energy minus potential energy barrier along roll direction over time for a representative successful and failed …
Figure 7—figure supplement 3
Comparison between robot’s pitch kinetic energy and pitch potential energy barrier.
(A) Kinetic energy, (B) potential energy barrier, and (C) kinetic energy minus potential energy barrier as a function of time for a representative successful (i) and failed (ii) attempt. Between two …
Figure 8 with 1 supplement
Dependence of potential energy landscape on ground geometry.
(A) Grounds of different geometry. (i) Flat ground. (ii, iii) Uneven ground with small (ii) and large (iii) asperities compared to animal/robot size. (B) Potential energy landscapes for …
Figure 8—video 1
Potential energy landscape changes with ground geometry.
Potential energy landscape evolves as wing opening angle increases. Definitions follow Figure 8.
Author response image 1
Potential energy landscape for an extended body pitch-roll space.
Landscape shown for a wing opening angle of 51.2°. Black square shows the range of landscape used in the paper for analysis. Panels show the statically stable equilibrium configurations of the …
Tables
Table 1
Mass distribution of the robot.
| Component | Mass (g) |
|---|---|
| Head | 13.4 |
| Leg rod | 4.3 |
| Leg added mass | 51.5 |
| Leg motor | 28.6 |
| Two wings | 57.4 |
| Two wing pitch motors | 56.0 |
| Two wing roll motors | 48.8 |
| Total | 260.0 |
Table 2
Comparison between animal and robot.
| Parameter | Animal | Robot | Ratio | |
|---|---|---|---|---|
| Body length 2a (mm) | 53 | 260 | 4.9 | |
| Body width 2b (mm) | 23 | 220 | 9.6 | |
| Body thickness 2c (mm) | 8 | 43 | 5.4 | |
| Mass attached to leg (g) | 0.14 | 51.5 | 368 | |
| Total mass m* (g) | 2.84 | 260 | 90 | |
| Density ρ (×10−3 g mm−3) | 0.88 | 2.05 | 2.3 | |
| Expected length scale factor (m/ρ)1/3 | 1.47 | 5.06 | 3.4 | |
| Expected potential energy scale factor m4/3/ρ1/3 | 4.28 | 1306 | 305 | |
| Maximum pitch potential energy barrier (mJ) | 0.58 | 282 | 486 | |
| Maximum roll potential energy barrier (mJ) | 0.19 | 244 | 1284 | |
| Froude number for leg flailing Fr | Intact legs | 0.37 | 0.78 | 2.1 |
| Modified legs | 1.27 | 0.61 | ||
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*Includes mass attached to the legs.
