 Teaching Philosophy
 Although the beauty of control theories attracts many engineers, the inherent limitations of control theories are unavoidable in practice. Most of the control theories assume that a plant is given and seek a solution to obtain the desired performance by suggesting an appropriate control algorithm. EXO Lab’s research issues are all based on a fundamental question that the application of control theories should start from the beginning of mechanical design. Namely, the mechanical system should be designed considering the controllability and observability of the plant, such that the system has the minimal limitations in the controller design. Also, the controller design process should suggest both control parameters and mechanical design parameters for obtaining the most effective and energyefficient control performance. Therefore, students of EXO Lab learn both the mechanical design and control theories in an integrated way. This education philosophy may be different from typical educations in the field of Mechatronics or Robotics in a viewpoint that it deals with the interdisciplinary crossapplication of the mechanical design and control theories.
 Prof. Kyoungchul Kong, the director of EXO Lab, gives the following lectures.
 Graduate Courses
 Linear System Control (ME561)
 This lecture introduces general concepts for control of a class of linear systems. The “linear” system does not only mean an ideal system described by equations of motions, but also includes an actual mechanical system, the dominant dynamic behavior of which can be assumed to be linear. In order to deal with linear systems, this lecture first introduces linear system theory for understanding and modeling of linear systems. Linear control theory including state space descriptions, controllability/observability, transfer functions, timedomain analysis and stability are then introduced. The realworld systems, however, always show uncertainties in the dynamic characteristics, and thus this lecture also introduces robust control theory, such as small gain theorem and Hinfinity optimal control, for dealing with systems with uncertain dynamics. In this course, various numerical and mathematical methods will be introduced to design control algorithms.
 Digital System Control (ME562)
 This course is a comprehensive introduction to control system synthesis in which the digital computer plays a major role. The course covers elements of realtime computer architecture; inputoutput interfaces and data converters; analysis and synthesis of sampleddata control systems using classical and modern (statespace) methods; analysis of tradeoffs in control algorithms for computation speed and quantization effects. In addition to the fundamental theory in digital system control, this course introduces advanced control techniques such as discretetime linear quadratic control, adaptive control, parameter adaptation, repetitive control, learning control, and so on. Homework includes computer simulations where students can experience practical digital servo interfacing and implementation problems with timing, noise, and other practical issues.
 Undergraduate Courses
 Modeling and Control of Engineering System (ME361)
 The content of this lecture is to learn the principles, methods and techniques of modeling and controlling of engineering systems such as mechanical, electrical/electromechanical systems in theory and experimental aspects. This course focuses on proportional, integral, and derivative (PID) controllers and rootlocus techniques to design such controllers.
 Automatic Control (ME460)
 To promote the understanding of control fundamentals; to advance the theories, experiments, and applications of automatic control; to bridge new ideas of the future.
 Mechatronics
 In this lecture, mandatory knowledge for designing mechatronic systems are introduced, and an Arduino board is provided to every student for individual handson experience. The examples given to the students include the use of a motor driver and other fundamental electric components, the construction of a motor control system, the implementation of signal processing algorithms, and so on. The final term project is to develop a wheeled inverted pendulum from scratch, and students are evaluated mainly by the experimental results of their own system.
 Mechanical Systems Analysis
 This lecture introduces mathematical methods used in Mechanical Engineering, in particular linear algebra. This course reviews linear algebra covered in Engineering Mathematics, e.g., matrix arithmetic and determinants, vector spaces, eigenvalues and eigenvectors, linear transformations, homogeneous ordinary differential equations, and Fourier series.
 Linear Vibrations
 This is a typical linear vibrations course, which covers fundamentals in mechanics (e.g., linear system theory, Newtonian mechanics, Lagrangian mechanics, and state space realization), frequency and Laplace domain analyses of mechanical vibration systems, free and forced vibrations of lumped mass systems, and vibrations of distributed parameter systems.
 Academic Background
 EXO Lab is based on academic fundamentals of Dynamic Systems and Control, and students are mostly interested in and inspired from various control theories, in particular linear system theories and robust control theories with applications of robotic systems. The knowledge in the control theories provides students with a solid foundation for robotics research. As the major applications of the laboratory are robotic systems interacting with humans, where the control performance is evaluated not only by typical metrics in the control theory (e.g., tracking performance, robust stability, etc.) but also by clinical verification, as well as the qualitative judgement of human subjects, research topics of EXO Lab have focused on the practicality and implementability of control methods. Consequently, students and laboratory members could obtain extensive knowhow and expertise on application of the control theories. Prof. Kyoungchul Kong, the director of EXO Lab, emphasizes that understanding practical examples and connecting the control theories with appropriate applications are the best way to educate the next generation engineers and researchers in the field of Robotics, Dynamic Systems and Control.
 Three Different Applications in Human Assistive Robotics
 In order to explain the motivation and originality of our research outcomes, it is necessary to first explain three different human assistive technologies, which are distinguished by the target users, as follows.
 1. Assistive Technology for the Human Power Augmentation
 The first generation of human assistive robots were designed mainly for the normal subjected to physically demanding tasks, such as labors and soldiers. The purpose of the assistive technology for the normal was human power augmentation. In this case, the control and design of an assistive robot could take an advantage of the robust and intelligent control ability of the human motor system. Therefore, the research goal was to learn and follow the human motion characteristics, and the major research issues were how to recognize the human intention, how to synchronize the human and robot motions, how to increase the actuation power and efficiency, and so on.
 2. Assistive Technology for the Complete Paraplegics
 After the first generation of assistive robotics, many researchers have sought a new application to prove the functionality of assistive robots. Complete paraplegic patients were appropriate target users for such a purpose, because they definitely need physical assistance due to the complete lost of muscular strength. In this case, as the human motor system is not functional, the human motion could be dominated by the control system of the robot. Therefore, the control of an assistive robot for the complete paraplegic patients is relatively simple compared to ones for the normal; the robot is controlled to have the maximal impedance for the robot joint to follow the predefined trajectories. This is a typical feedback control problem, i.e., trajectory tracking with disturbance rejection. The precision in control performance is not a big issue, because the complete paraplegic patients do not feel any resistance from the robot due to the absence of a voluntary motion. The recognition of the human intention becomes simple as well; a joystick or a button is effective enough for the patients to make a command. It may be a challenging research issue to guarantee the gait stability; however, such a critical issue has been avoided by utilizing crutches.
 3. Assistive Technology for People with Partial Impairments
 Another important user group for assistive robots is people with partial impairments, who barely move with poor gait stability due to the weakened muscular strength. Such users include patients with neuromuscular diseases (e.g., muscular dystrophy, GuillainBarre syndrome, etc.), rehabilitation patients after the stroke or spinal cord injury, and even geriatric patients (i.e., elderly people) with muscular weakness. The design of an assistive robot for incomplete paraplegic patients demands unique requirements, such as the minimal mechanical impedance and high backdrivability, as well as the high power density. Mechanical parts must be ergonomically designed such that humans can use the devices for a long period of time without discomfort. The motor control function of the incomplete paraplegic patients is not as robust as that of the normal, and thus the overall human body system becomes vulnerable to disturbances (i.e., external forces, inclinations, etc.) or model variations (i.e., loads, etc.). It is, however, still active unlike the complete paraplegic patients, and thus the robot must not generate any unexpected resistance to the voluntary motions of incomplete paraplegic patients for their minimal discomfort. Therefore, both the design and control of assistive robots for incomplete paraplegic patients are very challenging.
 Design of Transparent Actuation Systems for Recovering Natural Dynamics
 To develop a transparent actuator system, We have investigated a cabledriven actuation system, a directdriven highpower actuator, and an actuator module with a flexible transmission mechanism. The cabledriven actuation system was to remove the weight of the actuator from the distal body segments and to make the wearable part soft. The directdriven actuator was to obtain large assistive forces with the minimal mechanical impedance by eliminating gears. In practice, the actuator module with a flexible transmission mechanism (i.e., a series elastic actuator (SEA)) was the most promising for assistive robots for incomplete paraplegic patients. The flexible transmission (i.e., a spring) isolated the actuator dynamics from the human body dynamics, which enabled the precise and robust control of the assistive force transferred through the flexible transmission. The mechanical design parameters, such as the spring constant, were obtained from optimal control theories (e.g., linear quadratic control or H∞ control) by modeling the interaction force of the transmission as a feedback control law. The gears were designed such that the effective inertias were evenly distributed in a twomass system representation, which was to maximize the openloop frequency bandwidth. The overall actuation system was able to precisely generate the desired torque without any friction, which enabled realization of the natural dynamics of the overall robot system.
 To design an effective assistive mechanism, we investigated various mechanical components that can effectively support the body weight without disturbing the voluntary motions. In order to maximize the energy efficiency of locomotion, the human musculoskeletal system has been evolved to be actuated by both active (i.e., voluntarily contractile) muscles and passive elements (e.g., the ligament and the tendon), where the main role of the passive elements is absorbing and releasing energy exerted from the environment. Inspired by this principle, we have devised and utilized a controllable pneumatic cylinder in parallel with the transparent actuators at the robot joints. The controllable pneumatic cylinder behaves as a gas spring when the valve is closed, while it has a small friction when the valve is open. Therefore, the valve was controlled such that it supports the body weight by its compressibility during the stance phase and that it imposes the minimal resistance during the swing phase. The gas spring constant was determined based on optimal control theories by modeling the interaction force of the pneumatic cylinder as a linear state feedback control law. The use of the pneumatic cylinder effectively removed the bias in the control signal generated in practice, which implies that the burden of the actuation system was lowered.
 Design of Sensor Systems for Observing Dynamic States and Monitoring Health Conditions
 For accurate observation of the dynamic state of the human body, we have focused on the accurate measurement of ground reaction forces (GRF). Theoretically, the dynamic state of the human body system can be observed if the motion of each body segment and the external forces are known. When the human wears an assistive robot, it is possible to measure the body motions using the sensors of the robot. However, the GRF, which is the most significant external force in the human body system, was difficult to accurately measure in practice. Addressing these practical issues, we proposed a simple yet effective GRF sensing method based on airbladders and airpressure sensors. Aerodynamics in the airbladders was analyzed in the Laplace domain, and the obtained transfer function was utilized as a filtering algorithm for rejecting the hysteresis in the sensor signals. For this purpose, the zerophaseerrortracking control (ZPETC) method was utilized to guarantee the stability of the filtering process. Based on the accurate GRF measurement, the whole body dynamics could be analyzed accurately.
 The GRF measurement was further processed to obtain the likelihoods of gait phases and to quantitatively analyze the abnormality of a gait. The proposed GRF sensors were integrated into a shoe, called Smart Shoe, and it was clinically verified that the Smart Shoe was an effective means for selfrehabilitation of particular patients, such as poliomyelitis patients, even without an assistive robot.
 In addition to the GRF measurement, the observation of human muscular activities plays an important role in human assistive robotics. Electromyography (EMG) was one of the most common and intuitive methods used for detecting the muscular activities. The EMG, however, was in general too sensitive to environmental disturbances, such as electrical noise, electromagnetic signals, humidity, and so on. Therefore, we proposed a new method that detects the muscular activities by measuring the change of the airpressure in an airbladder contacting the muscles. Since the change of the airpressure could be more robustly and accurately measured by airpressue sensors installed inside the clothes, the proposed sensing method was a promising solution that can replace the EMG sensors in healthcare mechatronic systems.
 Control Applications in Healthcare Mechatronic Systems
 The control of human assistive robots for incomplete paraplegic patients is challenging, because (1) the human body dynamics is uncertain and timevarying, (2) the human motor control function is active but feeble, (3) the nonlinearity in an actuation system is to be completely rejected, and (4) the control algorithm should be implemented in a mobile control system. In these aspects, a disturbance observer (DOB) has played an important role in our research. The DOB is a simple but effective control method; it consists only of two components, an inverse of a nominal plant model and a filter, called the Q filter. It rejects exogenous disturbances and cancels modeling discrepancies by feeding an estimated disturbance back into the system. Realization of the ideal performance of the DOB in human assistive robot systems, however, was challenging, and thus we have investigated on the DOB from the theory to the implementation.
 In order to clarify the motivation and originality of our research outcomes on the DOB, it is important to first explain our fundamental question on the DOB, as follows.
 A Fundamental Question on the DOB
 We started questioning from the fundamental of the DOB; what is the inverse of the plant model in the discretetime domain? When a plant is controlled by a digital computer, a discretized plant model is obtained by the zeroorderholder (ZOH) equivalent, which includes the dynamics of digitaltoanalog and analogtodigital converters. Although the ZOH equivalent is an accurate interpretation of a relationship from the control input to the output, however, it is not necessarily appropriate for estimating the exogenous disturbance, because the ZOH dynamics is not involved in the relationship from the disturbance to the output. Does the use of the inverse of a plant model discretized by the ZOH equivalent cause any problem? Yes, it does. The ZOH dynamics introduces a zero if the relative order of the plant model is greater than one. The zero introduced by the ZOH is close to −1, and thus the inverse of the plant model possesses a high frequency oscillation mode. This problem has been often avoided by applying the DOB in the velocity loop, because the discretized plant model does not have such a high frequency oscillation mode when the relative order of the original plant model is less than or equal to one. Such an alternative solution is available only if the plant model has a second order. When the relative order is higher than one, or when the DOB is to be applied in the position loop, the cutoff frequency of the Q filter has been greatly lowered to neutralize the high frequency oscillation mode, which deteriorates the DOB performance. This is not an clever way to solve the problem; the solution must be sought from the “design” of an appropriate model inverse.
 Solutions to the Fundamental Question and Applications of the DOB
 As the plant model discretized by the ZOH equivalent is not necessarily an accurate model from the disturbance input to the output, we released the condition of the model inverse in the DOB and designed a new filter that properly describes the relationship from the output to the disturbance input. One of the most promising solutions was to adjust the model parameters by a numerical optimization method (i.e., nonlinear programming), such that the frequency responses of the filter and the model inverse are matched while the robust stability of the DOBloop is guaranteed in the discretetime domain. For this purpose, we defined the maximum allowable displacement of the DOBloop poles as a measure of stability robustness. By this method, we could obtain a filter that enables the implementation of a DOB with a Q filter with a high cutoff frequency. The theoretical stability robustness of the DOB loop, which is analyzed by the small gain theorem in the continuoustime domain, could also be maintained in the discretetime domain and even in experiments. In human assistive systems, however, there was another practical limitation in the design of a Q filter due to the large and drastic variation of the model parameters. The dynamic characteristics of the human body significantly change according to the impedance change by the cocontraction of muscles, the ground contact, the rigidity of the muscles, and so on. Moreover, even if the control parameters were welltuned for a user, they were not necessarily appropriate for another user. Therefore, we proposed an adaptive disturbance observer (ADOB), where a parameter adaptation algorithm (PAA) is applied to the plant model used in the DOB loop. This method, however, could not be stabilized, because there existed an interference between the PAA and the DOB. In order to avoid the instability problem of the ADOB, we applied the PAA to adapt the model parameters from the output to the input, i.e., the inverse of the plant model. Namely, the proposed ADOB was to recursively minimize an error between the actual input and the estimated input, while the typical PAA minimizes an error between the actual output and the estimated output. Based on the similarity between the proposed ADOB and typical PAA, the stability of the ADOB could be proved by hyperstability theory. The cutoff frequency of the Q filter could be increased up to the half of the Nyquist frequency, and the performance of the ADOB in experiments was impressive. Although the ADOB was effective for the control of systems with different model parameters, such as robots worn by different users, but it was not effective for drastically changing model parameters. This issue was critical, because the model parameters change drastically according to the gait phases (i.e., ground contact condition). To address this issue, we introduced a hybrid system model into the ADOB, such that the model could be switched according to the gait phases. The gait phases were detected by the Smart Shoe. The ADOB with a hybrid system model could recursively find the parameters of two different models alternately according to the gait phases. Based on this method, the transparency and the control performance of actuation systems could be maintained regardless of the users and the ground contact conditions.
 Control Applications for Assisting Humans
 The DOB was utilized to robustly and precisely control the actuation systems, and thus a higherlevel control method was still necessary to determine the required assistive force/torque in realtime. To develop such a higherlevel control method for incomplete paraplegic patients, we first analyzed the characteristics of the human motor control system, which consists of the muscles, the spinal cord, the cerebrum, and the motor/sensory neurons. Modeling the human motor control system as a feedback control loop, we applied a loopshaping method to recover the sensitivity of the human body system. The neuromuscular weakness was treated as a lowered loop gain, and a fictitious filter was introduced to restore the loop gain. Robust control methods, such as the H∞ loop shaping method, were applied for the loop shaping. Then a feedback controller of the assistive robot was designed to realize the effect of the fictitious filter. Consequently, the human wear5 ing an assistive robot could feel as if the dynamic sensitivity of his/her body was changed by the fictitious filter. In this approach, neither the recognition of the human intention nor the predetermined joint trajectory was necessary, which is a major difference compared with conventional control methods in assistive robotics. In addition, we also utilized a springloadedinvertedpendulum (SLIP) model for the control of an assistive robot. The SLIP model has been studied mainly for analyzing running motions, but we discovered that it is also a good strategy to assist the walking motions of incomplete paraplegic patients. The SLIP model was particularly effective for generating the desired assistive torques during the stance phase in a gait. Since our assistive robots are equipped with controllable pneumatic cylinders, the virtual spring effect by the SLIP model could be realized by both the controlled compressibility of the cylinder and the actuation force of the transparent actuation module.
