What is it about?

The theoretical thrust of the paper aims to mitigate obstructions imposed by high-dimensional bipedal models (dimension 30 or more), without resorting to simplified pendulum models that are all too common in the robotics literature. We work directly with the full model of the robot, making it possible to generate motions that exploit its full capabilities while respecting actuator limitations, ground contact forces, and terrain variability. The process begins with trajectory optimization to design an open-loop periodic walking motion of the high-dimensional model and then adding to this solution, a carefully selected set of additional open-loop trajectories of the model that steer toward the nominal motion. Supervised Machine Learning is used to extract from the open-loop ``behavior'' (i.e., the collection of input and state trajectories) a low-dimensional state-variable realization (i.e., a low-dimensional manifold and associated vector field). We then use the special structure of mechanical models of bipedal robots to embed the low-dimensional model in the original model in such a manner that it is both invariant and locally exponentially attractive and show that this locally exponentially stabilizes the desired walking motion in the full state space of the robot. Transitions among periodic orbits can also be addressed.

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Why is it important?

Models of bipedal robots and exoskeletons are complex. Unilateral and other constraints exist on the forces and moments at the ground-foot interface of a walking robot. Thus, the natural way to describe bipedal locomotion is in the form of a hybrid system, that is, a system that displays both continuous and discrete behavior. The robot itself is classically modeled as a tree structure composed of rigid links, revolute or prismatic joints, actuators with inertia, gearing, and springs, with 20 states being a very small model. Forty and more are very common. This paper allows a control designer to use this complex model information directly in the design of a controller that creates exponentially stable gaits.


The main ideas for this work came from Dennis when he was a Ph.D. student. He got the ideas working on an Atrias-series robot and then brought them to me to show what he could do with machine learning and optimization. He had to do it this way because he knew that I did not believe that machine learning had a serious role to play in feedback control design. I was super impressed with what he had accomplished and wanted to understand how it worked. It took Dennis and me an entire summer---a frustrating period of going back and forth---before I could teach him enough mathematics for him to write down the "magic fomula". That joint process of discovery was one of the most rewarding experiences of my academic career.

Jessy Grizzle
University of Michigan

Read the Original

This page is a summary of: Combining trajectory optimization, supervised machine learning, and model structure for mitigating the curse of dimensionality in the control of bipedal robots, The International Journal of Robotics Research, July 2019, SAGE Publications,
DOI: 10.1177/0278364919859425.
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