Physical Design and Feedback Control of Hybrid Mechanical Systems

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The aim of this award is to develop computationally tractable methods for designing and controlling systems that experience impact. Impacts introduce discontinuities into the equations of motion, making traditional techniques in control theory difficult to employ. However, if a system can specify its configuration during impact a form of feedback control may be utilized. The work will use a combination of variational analysis for mechanical systems, shape optimization, and control theory to synthesize embedded controllers for a class of impacting systems with guarantees on stability, optimality, and computational complexity. The work will start with a simple example of a two-legged robot walking on terrain; later examples will include numerical models of high degree-of-freedom robots walking on uneven terrain and a biomechanical model of a human hand interacting with objects. Deliverables include mathematical proofs of algorithm properties, a software implementation of the feedback synthesis techniques in a variety of documented examples, articles describing the techniques, and training for students in control engineering and biomedical engineering.Impacts are present in applications ranging from robotic locomotion and grasping to manufacturing and even human prosthetics. Computer control of these systems depends on incorporating impacts into algorithms that stabilize motion. If successful, the proposed techniques will make practical regulation of many impacting systems as straightforward as regulation of non-impacting systems. Moreover, the techniques will provide an improved understanding of the role that contact plays in human neuromuscular control. The project will leverage international collaboration through NSF Office of International Science and Engineering (OISE) Global Venture Fund (GVF) co-funding to develop long-term collaboration with researchers in Germany. Software developed as part of this work will be incorporated into an ongoing clinical study of hand rehabilitation at the Rehabilitation Institute of Chicago and will be freely available to the public. In addition to enabling important technologies, the work will be highlighted in a museum, and student will participate in outreach with an urban high school in Chicago.