2.2.3 Design: figures of merit, robustness

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Robotics: Mobility

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University of Pennsylvania

Robotics: Mobility

422 ratings

Course 3 of 6 in the Specialization Robotics

How can robots use their motors and sensors to move around in an unstructured environment? You will understand how to design robot bodies and behaviors that recruit limbs and more general appendages to apply physical forces that confer reliable mobility in a complex and dynamic world. We develop an approach to composing simple dynamical abstractions that partially automate the generation of complicated sensorimotor programs. Specific topics that will be covered include: mobility in animals and robots, kinematics and dynamics of legged machines, and design of dynamical behavior via energy landscapes.

From the lesson

Behavioral (Templates) & Physical (Bodies)

We’ll start with behavioral components that take the form of what we call “templates:” very simple mechanisms whose motions are fundamental to the more complex limbed strategies employed by animal and robot locomotors. We’ll focus on the “compass gait” (the motion of a two spoked rimless wheel) and the spring loaded inverted pendulum – the abbreviated versions of legged walkers and legged runners, respectively.We’ll then shift over to look at the physical components of mobility. We’ll start with the notion of physical scaling laws and then review useful materials properties and their associated figures of merit. We’ll end with a brief but crucial look at the science and technology of actuators – the all important sources of the driving forces and torques in our robots. Link to bibliography: https://www.coursera.org/learn/robotics-mobility/resources/pqYOc

2.2.1 Metrics and Scaling: mass, length, strength3:45

2.2.2 Materials, manufacturing, and assembly5:17

2.2.3 Design: figures of merit, robustness3:35

Meet the Instructors

Daniel E. Koditschek
Professor of Electrical and Systems Engineering
School of Engineering and Applied Science

In this section, we consider basic material properties relevant to design.

Material properties of interest, such as strength and stiffness are typically

mass normalized and specific strength and specific stiffness computed.

In this figure, we see a log log plot of youngs modulus or

stiffness plotted against density.

In the top right, we see that there are many metals

at the very favorable high stiffness at the price of significant density.

Moving down in stiffness, we see many ceramics that seem favorable, but

are typically very brittle.

Moving down in stiffness a little bit more,

we see composite materials, which will be of interest later in this section.

We now revisit the implications of posture on stress in a simplified bone model.

In this figure,

we see how changes in posture influence loading in bones in a simplified model.

For a more upright posture, there is nearly pure compressive loading.

This results in a uniform stress distribution,

which in our example does not exceed the ultimate strength of the material.

In the more sprawled animal, we see a combination of compression and bending.

The principle of superposition let's us simply add the stress profiles to see

the resulting profile on the right.

This resulting profile has peak stress above the ultimate strength

of the material.

And so in this case, the bone in the sprawled animal would break.

As mentioned, all materials up to this point have been isotropic.

Which means when loaded in different conditions, they respond the same way.

We now consider anisotropic materials such as composites,

which have very different responses depending on loading conditions.

In this video, we see an example of an anisotropic material that

has a grain similar to something like wood.

When the material is loaded in the direction of the grain,

it is very compliant.

When it is rotated 90 degrees, however and loaded against the grain,

it becomes very rigid.

In this video,

we see the implications of combining two of these samples in different ways.

When the two samples are combines with that the grains are parallel, once again,

the combined samples are very compliant when loaded in the direction of the grain.

When the samples are combined, so that the grains are perpendicular.

We now have a more isotropic material, which is stiff in both directions.

In this image, we see the robot XRL that has two different kind of composites.

These composites are layered differently to achieve different material properties.

In both cases,

we would like the ultimate strength of the material to be as high as possible.

In the shell, however, we prioritize stiffness.

And in the legs, we prioritize compliance.

Now, we consider anisotropic materials at various scales.

These are known as hierarchical structures.

In this figure,

we see hierarchical structures found in nature, such as bone and bamboo.

These are both examples of using hierarchical features

to change the property of the overall material as distinct

from the material properties of the constituents.

In this figure,

we see the use of hierarchical compliance in the sticky bot robot, which is able

to keep the toes of the machine a fixed to a surface, even on irregular terrain.

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