Combining Optimization, Machine Learning, and Model Structure to Improve the Robustness and Agility of Modern Bipedal Machines

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Bipedal robots are being built to aid in search and rescue, provide last mile delivery of packages, and to assist people in their homes. Lower-limb exoskeletons are being designed to help patients recover the ability to walk after strokes or even severe injuries resulting in paralysis. While the feedback control algorithms required to allow a bipedal robot to walk and a patient to safely operate a lower-limb exoskeleton are not identical, they share enough common elements that pursing their investigation in tandem is insightful and important. This project combines recent advances in the ability to quickly compute energy optimal solutions of bipedal dynamical systems with the mathematics of machine learning and geometric control theory to achieve unprecedented performance and safety in bipedal walking. The proposed research will greatly expand the class of robots for which feedback controllers can be designed with provable stability and it will significantly enhance the safety than can be achieved with exoskeletons that allow a paraplegic to walk without the use of crutches. One of the many technical challenges to be overcome in this research is the complexity of the mathematical models that describe the movement these legged machines. For example, printing out the symbolic model for the exoskeleton studied here would take thousands of pages. If a human ever opened the files to examine them, they would be incomprehensible. Yet, the PI and his students provide concrete means for designing feedback controllers for these machines and say deep things about how the closed-loop system will behave. This is the beauty of feedback control theory when it is married with modern computational tools. In addition, each year, the PI and his students share the excitement of engineering by giving tours of his robotics lab to hundreds of students, from grade school through high school, sharing the excitement and personal fulfillment of careers in STEM fields. Presidents of major universities and management teams of corporations visit his lab for the pure pleasure of seeing a robot doing something amazing and yet at the same time, almost ordinary: walking roughly like a human. The PI works with the media to share with the general public the excitement of cutting-edge engineering research and how it benefits society. The project seeks major advances in the theoretical conception and practical synthesis of feedback controllers for bipedal robots and lower-limb exoskeletons. The theory will be carefully tested on a Cassie-series bipedal robot and an exoskeleton. The theoretical thrust of the proposal 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. The research seeks to 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). The special structure of mechanical models of bipedal robots is used 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 will also be addressed.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.