Discovery of Dynamic Mechanical Structures through Modeling and Analysis of Closed Chains using Homotopy-Based Optimization

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This project promotes the progress of science and advances national prosperity and welfare, by accelerating innovation in legged robotics. The usage and capability of legged robots has increased over the past years with applications in industrial/construction settings and, more recently, to triage patients at healthcare sites. Robotic limbs can be composed to incorporate closed chain structures with potentially transformative benefits on their speed, force, and stiffness capabilities. However, these benefits have so far not been fully realized due to the computational complexity involved with the modeling and analysis of the motions of closed chain structures. This grant supports foundational research to propose, develop, and demonstrate a new class of optimization techniques that are equipped to deal with these complexities. The new techniques will incorporate homotopy root finding routines with the aim of solving systems many orders of magnitude larger than the current state-of-the-art. This research involves blending the engineering of legged robots with new mathematical techniques. This multi-disciplinary approach will positively impact engineering education with a unique interdisciplinary educational experience and will help broaden participation of underrepresented groups. The modeling of robotic limbs composed of closed chain mechanisms is hindered by degeneracies that occur when exploring variations in their defining kinematic parameters. These degeneracies include workspace break-downs, locked configurations, zero link lengths, and changes in mobility. Their existence thwarts efforts to analyze patterns of kinematic parameters that lead to useful dynamic behaviors. To overcome these challenges, techniques in optimization are used to discover useful mechanisms. In particular, this project will develop new optimization techniques that leverage the algorithms of numerical homotopy continuation. The resulting techniques aim to gather nearly complete sets of minima in an efficient and coordinated manner to provide both a global minimum, as well as a survey of useful structures provided by exploring kinematic parameter variations. The research team plans to develop the optimization algorithms and apply them to relevant robot limb problems. The modeling and analysis techniques will be verified through simulation, prototyping, and testing.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.