Wrapping up "Flexible Robotics"

I had the pleasure of teaching a new class called "Flexible Robotics" while on sabbatical at Bilkent University in Ankara, Turkey this Fall. The class was a 13 person, senior-level elective course that covered some of the same concepts as my graduate-level "Foldable Robotics" class that I have taught at ASU since 2016, but introduced about 75% new material, based on the needs of undergraduates in their senior year.

This course could not have been possible without the help and support of Onur Ozcan, who helped me get the course on the books in the first 24 hours I was in the country. The idea is that he will take on teaching responsibilities for this course at Bilkent in future years. His advice and guidance on getting the course set up in a different system than I am used to was critical. Thanks Onur!

What is Flexbile Robotics?

Flexible Robotics is a microcosm of some of the robotics research I do, and teaches a somewhat simplified version of the engineering approaches we use in my lab to design robots. It focuses on how to design robotic systems that are ultimately limited by the physics of the parts and materials they are constructed with. To find good designs, we have to know all about soft and flexible materials, motors and how they work, how to model non-ideal components using both first-principles and more realistic representations, and then the best practices for prototyping and validating the performance of our designs.

Flexible Robotics is also a class taught on a budget. I am of the belief that anyone should have access to robotics concepts, and so I have designed this course to use off-the shelf parts and materials that almost anyone can obtain. I teach using open-source software tools such as Python, so that anyone can run the code we use on any platform. And I teach experiment design and data collection using more accessible approaches that I believe serve as a proxy for the modern robotics lab. Not all undergraduates have access to high-speed motion capture systems, but everyone has a cell-phone. Not every department has a universal testing machine sitting in the student lab, but anyone can make a (relatively) standardized weight. When we focus on the concepts of how to create good experiments, and the tradeoffs between approaches, the ultimate resolution of the tool matters less.

Here's a summary of the high-level concepts baked into the course:

• I taught with a palette of low-cost parts and tools that are easily obtainable but didn't sacrifice or simplify the associated engineering challenges.
• I provided interactive coding experiences built into class time using Jupyter Notebook and Python.
• I reinforced the kinematics content students should already have had (3D vector operations, rotation matrices, and quaternions), but from a different perspective.
• I added MuJoCo for teaching many concepts in the second half of the course in order to simplify and streamline the number of different tools students had to pick up.
• The course focused on how flexible and compliant materials impact the modeling and design process, and which representations of compliance work best for modeling.
• I used the concepts of biomechanics, specifically terrestrial locomotion, as a way to focus design goals, observe and measure behavior, and talk about performance.

Course Highlights

Below is a list of the things I focused on when developing this course.

MuJoCo

Team 3's horse-inspired design

For the first time, I taught using MuJoCo as a design, modeling, and validation tool instead of my own Python dynamics package that I have previously taught with. I liked this shift because it made students more aware of the current challenges in simulation using a popular and powerful tool that is easier to learn than my own package. MuJoCo has much more thorough documentation, with more examples from the community, so I was not always "on call" supporting my own code. It also permitted the class to explore the role that contact and friction play at a deeper level than I had been able to take a class before. On the flip side, the tradeoffs of contact, friction, and "soft solvers" is complex and required more discussion than I gave it, without a satisfying or straightforward "answer" for how to apply it correctly.

Mechanisms and Kinematics

In contrast to the graduate class I teach, the senior-level Flexible Robotics spends more time reinforcing fundamental concepts in vectors, kinematics, and transformations, but uses the framework of flexible, foldable, and compliant systems to teach from a different perspective. For example, we defined spherical parallel mechanisms using quaternions instead of rotation matrices or DH parameters, and used the fundamental properties of vectors to define closed-loop constraint equations that we then solved numerically. Other approaches are often important in foldable systems, where kinematics are often defined from flat-foldable sheets of material rather than from rigid serial chains, and require efficient representations for faster solutions.

Compliant Materials

It has been difficult introducing compliant material systems, even in the graduate level course I teach, without getting into some complex topics and not feeling like there is enough time to do the topic justice. In this course, we focused on a few basic concepts of compliant material systems, while leaving others just to discussion:

Comparison of 2-element pseudo-rigid-body model and 100-element representation

• Lumped-parameter models for series and parallel springs and dampers: refreshing students on this concept permits them to think critically about the impact of making beams longer or shorter, wider or narrower. It is a useful mental tool, though for cantilever beams under high deformation, simple linear expressions are not the best approximation. These limitations are discussed.
• Nonlinear FEA in Solidworks: We run through an example of running a nonlinear FEA simulation in Solidworks for a beam under high deformation. We discuss the tradeoffs associated with nonlinear FEA and simulation time.
• Pseudo-rigid-body models for cantilever beams: The pseudo-rigid-body-model is a useful tool for engineered shapes in which deformation can be represented more simply (as bending) than for completely soft systems, where FEA is more appropriate. We compare the behavior of high-deformation cantilever beams modeled with 1,2, 10, 100 joints using MuJoCo and discuss how the optimizer and our error metric impact the parameter fitting process; students then see how the behavior matches against the real-world in a homework assignment, finding the stiffness and damping joint parameters for a selected material they will use in their project. The benefit of this approach is that it is completely compatible with our selected dynamics engine. The drawback is that you have have some existing knowledge or correctly assume the primary modes of deformation in order to select the right system model.

What we don't get into. We have to leave other topics to just a discussion; I hope to expand on these topics with more offline content.

• Nonlinear material models. It would be nice to have a concrete example of where nonlinear stress/strain models help us estimate behavior.
• First-principles derivations: We don't get into the theory of continuum mechanics, nor do we derive the elliptic curve equations that beams adopt under high deformation. It would be nice to have time to justify our use of lumped parameter models.
• Finite Element Theory: This would be the most useful topic for a general-purpose soft robotics course, and would go well in this class as well. Learning a new tool and integrating it with the dynamics of MuJoCo would be difficult. Perhaps a different simulator would be needed in order to implement this effectively in Flexible Robotics. I am open to suggestions!

System Identification and Design Optimization

Servo-fitting example written up previously

I believe that in general, students need more experience collecting, analyzing, and working with real-world data within the engineering curriculum. I increased my focus on the use of optimization tools for the purposes of model fitting, parameter identification, and design optimization. In Flexible Robotics, students collected their own real-world data and fit the behavior they observed to the models they developed, primarily using cell-phones for video capture to enable optical motion-tracking. We used this approach to walk through a full characterization of an RC servo in class, the parameters of which the students could use in their models. Outside of class, students created their own experiments for measuring the stiffness and damping behaviour of compliant materials serving as the links and joints of their systems, measuring the mass and inertia of their links, and capturing the friction of the surfaces they tested their robots on. I primarily taught using the scipy.optimize package, which has a number of fundamental optimization algorithms available in the scipy.optimize.minimize() function.

Research Integration

I was lucky enough to join Onur's lab meetings and help contribute to some ongoing research with his students. Two of Onur's students presented their research to the class. I believe it was valuable for students to see how graduate researchers are using the same tools and approaches to solving research problems "in real life" from someone other than the professor. We talked through their current design challenge, some of their design and optimization goals, and they discussed the details of their modeling choices.

Parts and Materials

We settled on a list of parts readily available in Turkey. The cost per student was ~$15. Students who wanted to keep their parts at the end of the semester sourced them themselves; otherwise we loaned sets of parts to students who needed them. Most students

In terms of materials, the Bilkent bookstore was a good source for acetate sheets, which served as a good flexible material that is cheap and easy to work with. Various kinds of cardboard and posterboard were also available to create rigid elements.

Course Projects

There were two course projects. The first project focused on the kinematics and force/torque analysis of a proposed rigid subsystem like a leg, while the second project added compliant material considerations, experiment design and data collection, dynamic modeling, and design optimization at a system level. Teams of ~4 students contributed their individual kit of parts, so were capable of creating quite complex robots.

I insisted during the second project in meeting with each team to help them focus and trim down the scope of their project. The timing of this meeting was critical, and I saw dramatic improvements in simulation quality and experimental results. The project writeups actually seemed more complete because teams were able to more thorougly explore fewer goals.