Tail- assisted pitch control in lizards, robots and dinosaursBruce Carmany and Michael Wiegand

March 8th, 2013

Hypothesis Perturbed animals

manipulate angular momentum using their tails.

Specifically, the Agama lizard controls their swing using their tails in a measured manner to redirect angular momentum from their bodies to their tails, stabilizing body attitude in the sagittal plane.

Figure 1: Agama lizard (Agama agama)

Hypothesis

Maintenance of body pitch before landing was spent entirely in the air, where only aerodynamic forces acted on the animal.

Other dinosaurs such as the Deinonychus had similar abilities to that of a leopard, and prove its hunting techniques.

Goals

Run the experiment and development models for the Agama lizard, the velociraptor and a robot simulator.

The robot lizard will have an active tail that utilizes a sensory feedback system.

Compare results against rigid and tailless body rotation.Figure 2: Leaping velociraptor

Goals

Through use of morphometrics, find a dynamic model that accurately measures the agama lizards moment of inertia (MOI) about their center of mass (COM) and see if this is related to extinct animals such as the velociraptor.

In simpler terms, develop a standard state-space model that accurately summarizes flight of a tail-bearing animal.

X=f(x)+g(x)u

Goals

Advance our understanding of appendage evolution.

Be able to provide biological inspiration for next generation search-and-rescue robots.

Figure 3: Search-and-rescue robot

Background

Only animals (with tails) with certain dimensions are able to stabilize themselves in flight (weights are proportional to the cube of their lengths).

The strengths of their bones and muscles are proportional only to cross-sectional areas, with their lengths squared (Horses are the largest known animal to exhibit this phenomenon).

Perturbation magnitude is defined as the angle through which an individual’s body would rotate without its tail, given the observed angular momentum and trial duration.

Methods: Agama Collect six wild-caught Red-Headed Agama

lizards (Agama agama). The lizards average mass were 66.96 g with an average snout-vent length of 12.75 cm.

Lizards were kept in a controlled environment similar to their indigenous one (25⁰C, 27% humidity), and a day/night cycle was simulated for the duration of the experiment.

The lizards were also fed their standard diet of water and crickets.

Methods: Agama Using a specially

constructed track (150cm x 30cm x 40cm), lizards ran down the track and leaped off a vault onto a 22cm high wall.

At the top of the wall was an enclosed plastic shelter, to which the lizards ran due to an escape response.

Figure 4: Vault apparatus

Methods: Agama

At the beginning of each trial, the escape response was initiated by brushing the lizards tail.

The animal then accelerated into a run, made an initial jump onto the vault, and then a final jump to the wall.

When the lizards initial speed was high, a period of bipedial running occurred before the vault, and the vault was used as a launch platform for at least one hind foot.

Contact with the vault was critical to the jump, if no contact with the vault occurred the jump was often unsuccessful and not used in final calculations.

Methods: Agama To create a variable,

perturbations were added to increase or decrease traction on the vault (the most critical transition area of the jump).

Glossy card stock (less traction) or 60-grit sandpaper (more traction) were used as the perturbation variables.

Typographical correction fluid was used to place photo-sensitive markers on the head, torso, and tail for kinematic analysis.

Figure 5: Sandpaper

Figure 6: Glossy cardstock

Methods: Robot Design a model using an

inertial appendage to stabilize aerial maneuvers. A small radio controlled toy was used.

The gear train of the toy was modified so one motor drove the front wheels.

The other motor drove a single pin joint attached to a makeshift tail approximately twice as long as the toy.

Figure 7: Altered robot

Methods: Robot The factory ‘guts’ of the toy were removed and

replaced with: a microcontroller, a single axis microelectricalmechanical systems gyroscope, and a motor controller.

This system enables a test of simple feedback controllers to use a ‘tail’ to stabilize body pitch during flight (during nose-up/nose-down perturbation).

Orientation of the model was found by integration of the angular rate signal readings taken from the gyroscope.

To record flight, a high speed (1000 frames per second) camera was used.

Methods: Velociraptor To determine tail stabilization performance of an

extinct animal, properties from a 2-dimensional rendering were used.

The tail was represented digitally as a truncated cone in dorsal and sagittal reconstructions.

The density of the velociraptor’s tissues was 1000 kgm-3, with a tail tissue density of 1500 kgm-3 to account for the excess bone.

The velociraptor during the jump was modeled in two configurations, one with the limbs extended and one in which the limbs were retracted.

http://www.youtube.com/watch?v=eXdjNqw2oVI

Overall Results The dynamic model

revealed that bodies with a swinging tail experienced less rotation (angular momentum) than those with a rigid tail, passively compliant tail or no tail at all.

Leaping lizards demonstrate inertial control of body attitude, and can lead to improvements in technology.

Figure 8: Three models used

Figure 9: Sensitivity of body rotation to a perturbation in a lizard and robot

Figure 10: Pitch stabilization using a tail in a lizard and robot

Collected Data

Cases where the lizard struck the vault while climbing onto it were omitted.

34 leaps were taken from sandpaper, 43 leaps were taken from the smooth substrate.

High-speed video captured it at 500 frames/second.

Lizards rested between 10-15 between trials, and 90 minutes after every 10 trials.

Kinematics were extracted from the video and analyzed using MATLAB to determine models.

Results: Robot

PD-feedback-controlled robot experienced 72% less rotation after a perturbation than it would have with a rigid tail, 85% less rotation than if it had a passive tail and 91% less rotation that if it had no tail at all.

The synthetic tail contained 31% more angular momentum than if it were rotating rigidly with the body, and the body contained 40% less.

Confirmed the hypothesis that the PD feedback controller regulated body angle by redirecting angular momentum from the body to the tail.

Results: Agama lizard Lizards were compared to the robot and three

different models (tailless, rigid-tailed animal and compliant-tailed). The addition of a tail to the tailless model reduced sensitivity to rotation by 36-58%.

The Agama lizards were significantly less sensitive to perturbations than any model (i.e. rigid, passive or no) 48% less than rigid tails during the aerial phase

66% less than had they had a compliant tail

78% less than if they had no tail at all

Results: Agama lizard

Figure to the left represents the state-space model derived from the experiment.

The state-space model used data from both the robot and lizard trials.

A total of 77 trials were used (at least 8 from each lizard).

Figure 11: State-space model

Results: Velociraptor

Using the conservative morphometric reconstruction model (and a hypothetical specimen being of 20kg, 1.5m tall biped with a tail effectiveness of 1.23), the muscular model could have outperformed any Agama lizard.

The proximal tail base could bend up to 90⁰, this would allow the velociraptor to sustain perturbation that would rotate that of a tailless animal by more than 110⁰.

Criticisms The study on used six Red-headed Agama lizards.

The study was useful in trying to compute a model for current artificial intelligence, but it seemed like a stretch when trying to model an extinct animal.

The robot was launching off a completely different apparatus so that made data comparisons difficult (ski-jump ramp).

If allotted, measure three-dimensions of movement and not just two. It was noted that most of the time these lizards are jumping between off-angled cracks in walls.

Use more than two different take-off surfaces.

Questions?