Research Interests and Projects

Design and Implementation of Robotic Devices for Rehabilitation

Stroke, experienced by over 500,000 patients in the U.S. each year, is the leading cause of long-term disability in adults. The most effective post-stroke treatment for impaired patients is physical rehabilitation. Even though rehabilitation robots promise a great value by reducing the work load of physical therapists and providing assist modes that are not feasible otherwise, there does not exist a consensus on how to actually implement robotic assistance. This project proposes to team up with a group of physicians and occupational therapists, and to design and build several robotic devices to provide patients with tools to improve their quality of life. Moreover, the project includes human subject experiments on stroke patients to test efficacy of different robotic assist modes during rehabilitation. Results of this research have strong implications to design of robot assisted rehabilitation schemes and will benefit numerous stroke survivors.

Modeling of Human Motor Control and Learning

The neural mechanisms for acquisition of sophisticated motor behavior in humans are very complex. There exists strong evidence in literature that human nervous system may be adaptively tuning internal models of the controlled system dynamics during motor learning. This project investigates existence and formation of internal models during sensorimotor learning by conducting human subject experiments on an underactuated dynamic task with various haptic assistance modes. Studying the aftereffects revealed by the experimental data, the aim of the project is to verify efficacy of several techniques as models of internal model adaptation. Results of this study will enable novel shared control paradigms that improve the rate of internal model adaptation through use of haptic aid. Contributing to basic understanding of human senorimotor behavior, this study has numerous implications in rehabilitation and manual skill training.

Modeling, Simulation, Control and Estimation of Switching (Hybrid) Dynamical Systems

An important set of open problems in the field of hybrid dynamical systems is the development of stable state and parameter estimation algorithms. Hybrid estimation is significantly more challenging than its continuous counterpart due to the inherent nonlinearities introduced by the mode changes. This project aims to develope a family of hybrid model reference adaptive parameter estimators to remedy the limited applicability of existing methods. Unlike traditional approaches, these estimators operate directly on systems with changing contact conditions. Capturing the information contained within the mode changes, these hybrid estimators can identify parameters that are not identifiable with their continuous counterparts. The proposed estimation algorithms are based on the utilization of hybrid trajectory sensitivities to perform updates on a multiple-mode adaptive estimator architecture. Enhancing the properties of the existing methods, these estimators contribute to the filed of hybrid systems and will have an impact on various applications including biped robotic walking and automatic generation of the mechanical impedance of virtual objects.

Haptic Rendering of Parametric Surfaces

Existing collision detection algorithms lack stability guarantees and have limited extensibility. We have contributed a novel closest point algorithm that possesses provable global convergence and greater extensibility than the previously available methods. This new algorithm is simpler to implement and is robust against disturbances. Furthermore, since the analytic limits of performance are available for the algorithm, it can be easily tuned for optimal computational efficiency without sacrificing stability. To develop such an algorithm, weI formulated the problem as a hybrid dynamical system that incorporates dependence on rigid body motion, surface shape, and surface boundary interconnectedness. Then we solved this optimization problem using a switching feedback controller derived from a common control Lyapunov function. Supervisory control (switching) is required to render the surface patch invariant resulting in global stability. Besides its impact in computer simulations, the potential uses of the new algorithms include CAD/CAM and robot path planning.

Addressing Current Challanges in Bilateral Control

Arguably the destabilizing effect of time delays remains the most important difficulty facing teleoperation technology. In this project, we are interested in employing system identification techniques to construct local models of the remote environment such that when used with predictive algorithms the instability induced by time delays can be remedied. I plan to utilize adaptive estimators for automatic generation of the impedances that describe a given remote environment and aim to synthesize nonlinear controllers that ensure stability and high-fidelity. In addition to greatly improving teleoperator performances, this research will significantly influence exploration with mobile robots and control of mechatronic devices through the internet.

Applying Controls Theory to a Class of Computational Geometry Problems

Existing algorithms to solve many practical problems in computational geometry, such as calculating Voronoi diagrams, tracing the intersection curves of interpenetrated geometries, and locating the visible regions of non-convex objects are computationally demanding since they are derived from extensive iterative searches. Moreover, lacking stability proofs or large basins of attraction, most of these traditional algorithms are very sensitive to numerical disturbances. In this project, we propose to design fast and robust algorithms based on control theoretic tools. We intend to model the geometric problems as differential problems and to design feedback stabilized integration algorithms taking advantage of the relative simplicity of my models. Essentially, this project represents a generalization of our previous work in minimum distance algorithms to a larger class of geometrical problems. Just as an initialization point can be stabilized at the closest point solution, multiple initialization points spread over an object can be stabilized at a set of distinct points, for example, defining the Voronoi diagram. Efficient and reliable solutions to these problems have direct and immediate relevance to applications in computer graphics, mobile robotics and simulation.