My ORCID Number is 0000-0001-7586-0142. My Google Scholar page is here.

Bipedal Robots: From January 1999 to April 2024, my graduate students and I spearheaded pioneering research that fundamentally transformed feedback control of agile bipedal locomotion. Prior to our efforts, the consensus was that the complexity of models in bipedal robotics made analytical approaches impratical. We discovered that a technique from geometric nonlinear control—specifically, Zero Dynamics—could be applied to these complex hybrid dynamical models with great efficiency. This breakthrough not only enabled us to thoroughly analyze but also to radically enhance the design of feedback algorithms for bipedal robots. By turning traditional methods from nonlinear control on their head and merging them with numerical optimization, we established a robust design methodology now known as Hybrid Zero Dynamics (HZD). This approach has redefined standards in the field, seamlessly integrating theoretical frameworks with practical engineering applications, demonstrated by my team and others on a wide variety of bipedal robots. Our work has significantly advanced the theoretical foundations of the field and has catalyzed innovations in robotic mobility and autonomy.

There was a BEFORE BIPED’s phase: I got my start in resarch as an undergraduate at Oklahoma State University in 1977, when Prof. Robert Mulholland recruited me as a research assitant for his work on Modeling the Global Carbon Cycle, a precursor to Climate Modeling. R. J. Mulholland and J. W. Grizzle, ``Modeling Perturbations of the Global Carbon Cycle,” Reprint, Proc. of the International Conference on Cybernetics and Society, pp. 690-694, 1979. And yes, it’s always been about fossil fuels. Beginning in 1980 at UT Austin, studying under Prof. Steven Marcus, my primary research area became the theory of nonlinear control systems. The work I did on control methods steeped in differential geometry laid the foundations for my later work in bipedal robotics. While I always maintained a strong interest in this subject and felt a sense of community with that body of researchers, my research activities significantly broadened over time. From 1986 to 2010, I worked with my dear friend and colleague, Jeffrey Cook, on various aspects of modeling and control of automotive powertrain systems and control; we turned the automotive area into a respecable academic discipline. From 2007 to 2012, I collaborated with Prof. Huei Pengon Hybrid Electric Vehciles (HEVs). From 1991-2001, I applied systems and control techniques to improve the operation of plasma-based microelectronics manufacturing equipment. From 2014 through 2018, I worked with an esteemed group of researchers on correct-by-construction control methods, with the primary application area being Advanced Driver Assist Systems.