Research Areas of Professor J.W. Grizzle

Current

1. Bipedal Robot Locomotion. Getting a machine to walk and run with the agility of a human being is an intellectually exciting and fun project. That is motivation enough to work on bipedal robotic locomotion! Here other reasons:
   • It is estimated that 70% of the earth's landmass is inaccessible to wheeled or tracked vehicles. This has stimulated interest in the design of robots that use legs as a means of locomotion. With legs, robots can step over obstacles or use sparse footholds (as in ladders). The research we are conducting under National Science Foundation (NSF) support is enhancing the ability to design robots that walk and run on two legs, under a feedback control system that provides dynamic balance, yielding a much more human-like motion than the plodding gaits achieved in most existing robots. The work is addressing both theoretical and experimental aspects of bipedal locomotion; see also our YouTube Channel: DynamicLegLocomotion.
   • Research on bipedal robotic locomotion has many medical spinoffs. Researchers at the University of Michigan and elsewhere are studying the design of lower-limb rehabilitation robotics for patients who have suffered partial spinal lesions or strokes (such patients have difficulties in standing posture, drop-foot, and locomotion, among others). Bimanual self-assist has been clinically shown to demonstrate greater improvements in range of motion and functional recovery than traditional therapy alone. Research is being done to generalize self-assist to lower limb rehabilitation with upper limb assistance.
   • Researchers hope to build rescue robots that could move around effectively in environments designed for humans, such as buildings, where manholes, ladders, and walkways are present.
   • The anthropomorphic nature of bipedal machines makes them a wonderful vehicle for motivating very challenging problems in engineering, without having to assume familiarity with advanced mathematics or physics. In this context, the concepts of dynamics, stability, sensing, actuation and feedback control become interesting and understandable to a broad audience. We use the intrinsic attraction of bipedal robots as a forum to demonstrate to students and to the lay public the excitement of a carer in engineering.
   • Bipedal robots are complex, hybrid systems. Their hybrid nature arises from the unilateral constraints at ground contact that vary throughout a gait and impulse-like forces at leg touchdown. Many interesting walking and running gaits correspond to periodic solutions of these complex hybrid systems. The associated feedback control algorithms that realize and stabilize these motions must be hybrid as well. Research on bipedal locomotion thus contributes very concretely to the development of feedback control theory for general hybrid systems. A major benefit of our approach is that we evaluate the capability of the theory to tolerate model imperfections. This is accomplished through experiments on MARLO and MABEL. The successful operation of these innovative machines requires equally innovative feedback control theory that works in concert with the natural dynamics of the system to achieve stability and robustness of the implemented behaviors.
   My true passion is the nonlinear control theory underlying bipedal locomotion. I am committed to confirming the theory with experiments.

2. Nonlinear Control. My primary research area used to be the theory of nonlinear control systems. My work now has a more applied focus emphasizing the modeling and control of automotive powertrain systems and bipedal robots. The models encountered in these subjects are more often than not nonlinear, and hence nonlinear control plays a big role in arriving at solutions to these problems. The big difference with my previous work is that now the questions I pose are based in practical engineering systems. Before, I could modify my hypotheses to arrive at a beautiful theorem, whereas now, reality is what it is, and I am challenged to discover the right control method for the problem at hand.

3. CPS: Frontier: Collaborative Research: Correct-by-Design Control Software Synthesis for Highly Dynamic Systems with Aaron Ames (TAMU), Hartmut Geyer (CMU), Huei Peng (Michigan), and Paulo Tabuada (UCLA). With special collaboration and support by Necmiye Ozay (Michigan). This project addresses highly dynamic Cyber-Physical Systems (CPSs) understood as systems where a computing delay of a few milliseconds or an incorrectly computed response to a disturbance can lead to catastrophic consequences. Such is the case of cars losing traction when cornering at high speed, unmanned air vehicles performing critical maneuvers such as landing, or disaster and rescue response bipedal robots rushing through the rubble to collect information or save human lives. The preceding examples currently share a common element: the design of their control software is made possible by extensive experience, laborious testing and fine tuning of parameters, and yet, the resulting closed-loop system has no formal guarantees of meeting specifications. The vision of this project is to provide a methodology that allows for complex and dynamic CPSs to meet real-world requirements in an efficient and robust way through the formal synthesis of control software. This proposal will develop a formal framework for correct-by-construction control software synthesis for highly dynamic CPSs with broad applications to automotive safety systems, prostheses, exoskeletons, aerospace systems, manufacturing, and legged robotics.

   Past

4. Diabetes Treatment in the ICU. I am working with a diabetologist/endocrinologist to improve the regulation of blood glucose (BG) levels in patients in the intensive care setting, especially those who are there postoperatively. The intense management of diabetes mellitus (DM, or diabetes for short) in the outpatient arena has been a priority for several years, but BG management in the hospital has only recently moved to the forefront. Clinically translating the physiological basis of the side-effects of acute hyperglycemia has only lately occurred, and has shifted the paradigm. Several randomized controlled trials have established the link between glycemic control and improved morbidity and mortality in hospitalized patients, especially in Intensive Care (ICU) settings. Elevated BG levels are found in ICU patients with and without a known history of diabetes. Since known diabetes is a co-morbid condition in 30-40 % of hospitalized patients, addition of stress-induced hyperglycemia (SIH) to the picture is increasing BG management in an ICU to an epidemic proportion. Hospitals around the country and the world now recognize BG as a modifiable risk factor. The goals of the project are
   1. Perform an extensive control analysis of the University of Michigan insulin infusion protocol in closed-loop with a validated dynamic model of the class of patients seen in the ICU. We will study its nominal response and its response to a wide range of model parameter variations. From this, we will predict the fraction of patients the protocol will maintain within a given goal range.
   2. Perform a similar analysis for protocols from other hospitals.
   3. On the basis of the model building and closed-loop control analysis performed above, we will propose improvements to the University of Michigan's protocol.
   This was a new area for me; it is currently on hold. Several other control specialists work in this area, including Frank Doyle, Roman Hovorka, Clyde Martin, and Dale Seborg.
5. Hybrid Electric Vehicles are vehicles with two or more power sources, such as an internal combustion engine, a battery, and an electric motor. When an HEV is certified for emissions and fuel economy, its power management system must be charge sustaining over the drive cycle, meaning that the battery state of charge (SOC) must be at least as high at the end of the test as it was at the beginning of the test. During the test cycle, the power management system is free to vary the battery SOC so as to minimize a weighted combination of fuel consumption and exhaust emissions. Our work has shown that shortest path stochastic dynamic programming (SP-SDP) offers a more natural formulation of the optimal control problem associated with the design of the power management system because it allows deviations of battery SOC from a desired setpoint to be penalized only at key-off. This method has been illustrated on a parallel hybrid electric truck model that had previously been analyzed using infinite-horizon stochastic dynamic programming with discounted future cost. Both formulations of the optimization problem yield a time-invariant causal state-feedback controller that can be directly implemented on the vehicle. The advantages of the shortest path formulation include that a single tuning parameter is needed to tradeoff fuel economy and emissions versus battery SOC deviation, as compared to two parameters in the discounted, infinite-horizon case, and for the same level of complexity as a discounted future-cost controller, the shortest-path controller demonstrates better fuel and emission minimization while also achieving better SOC control when the vehicle is turned off.

6. Modeling and Control of Automotive Powertrain Systems. I have been working in this area since 1986, when I was a faculty research scientist at the Scientific Research Laboratory of Ford Motor Company. The overall goal in this project has been to develop, adapt and apply system theoretic notions to the problem of reducing emissions in automobile engines while meeting performance and drivability requirements. The need to satisfy Federal regulations is driving the development of advanced engine technology to meet the ever-increasing demands for lower emissions. These engines are fundamentally described by nonlinear, hybrid (mixed continuous and discrete time) mathematical models, and require sophisticated control systems for their proper functioning. I have partnered with engineers at Ford to construct and validate engine and exhaust system models, and for evaluating modern, model-based feedback design concepts. This is a unique university-industry cooperative research arrangement for developing and applying advanced system theory and control methods to problems important to society.
7. Rehabilitation Robotics. Assisting the human body in the recovery of locomotor ability requires a multidisciplinary perspective. Our research team involved five faculty members, one each from Kinesiology (Ferris), Mechanical Engineering (Gillepsie), and Neurology (Aldridge), and two from Electrical Engineering and Computer Science (Koditschek and Grizzle).
8. Microelectronics Manufacturing. [My current activity in this area is extremely minimal.] This was a very multidisciplinary project! It involved a team of faculty from control systems, solid state physics and electromagnetics working to reduce variability and increase precision in standard semiconductor manufacturing processes. Our work encompassed both sensor development and algorithm development for real-time process control. Our primary research vehicle was the etch of 0.1 micron gate structure, on a Lam 9400.